Subgroups — C₂×#22623890 #33994078

Order 18688.

8006 conjugacy classes of subgroups.

The subgroup lattice has 1356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623890	C₂	1	32	yes	maximal, direct product factor
2	C₂×#17989319	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#17989308	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#17989303	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#17989301	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#17989265	C₂	1	2	yes	maximal, complemented
7	C₂×#17989264	C₂	1	2	yes	maximal, complemented
8	C₂×#17989252	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#17989247	C₂	1	2	yes	maximal, complemented
10	C₂×#17989230	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#17989229	C₂	1	2	yes	maximal, complemented
12	C₂×#17989228	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#17989221	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#17989209	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#17989176	C₂	1	2	yes	maximal, complemented
16	C₂×#17989171	C₂	1	2	yes	maximal, complemented
17	C₂×#17989134	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#17989120	C₂	1	2	yes	maximal, complemented
19	C₂×#17989115	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#124×D₇₃	C₂	1	2	yes	maximal, complemented
21	C₂×#17989061	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#17989059	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×#11924029	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#542×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂²×#11924029	C₂²	1	1	yes	characteristic
26	C₂²×#11924028	C₂²	1	2	yes	complemented
27	C₂²×Q₈×D₇₃	C₂²	1	2	yes	complemented
28	C₂³×D₂₉₂	C₂²	1	1	yes	characteristic
29	C₂²×D₄×D₇₃	C₂²	1	1	yes	characteristic
30	C₂²×D₄×D₇₃	C₂²	1	2	yes	—
31	#17989319	C₂²	1	16	yes	complemented
32	#17989308	C₂²	1	16	yes	complemented
33	#17989303	C₂²	1	16	yes	complemented
34	#17989301	C₂²	1	16	yes	complemented
35	#17989265	C₂²	1	32	yes	complemented
36	#17989264	C₂²	1	32	yes	complemented
37	#17989252	C₂²	1	16	yes	complemented
38	#17989247	C₂²	1	32	yes	complemented
39	#17989230	C₂²	1	16	yes	complemented
40	#17989229	C₂²	1	32	yes	complemented
41	#17989228	C₂²	1	16	yes	complemented
42	#17989221	C₂²	1	16	yes	complemented
43	#17989209	C₂²	1	16	yes	complemented
44	#17989176	C₂²	1	32	yes	complemented
45	#17989171	C₂²	1	32	yes	complemented
46	#17989134	C₂²	1	16	yes	complemented
47	C₂×#14556590	C₂²	1	1	yes	characteristic, complemented
48	C₂×#14556590	C₂²	1	1	yes	characteristic, complemented
49	C₂×#14556587	C₂²	1	1	yes	characteristic
50	#17989120	C₂²	1	32	yes	complemented
51	#17989115	C₂²	1	16	yes	complemented
52	C₂×#14556586	C₂²	1	2	yes	complemented
53	C₂×#14556586	C₂²	1	1	yes	characteristic, complemented
54	C₂×#14556585	C₂²	1	2	yes	complemented
55	C₂×#14556584	C₂²	1	2	yes	complemented
56	C₂×#14556584	C₂²	1	1	yes	characteristic, complemented
57	C₂×#14556581	C₂²	1	1	yes	characteristic, complemented
58	C₂×#14556580	C₂²	1	1	yes	characteristic, complemented
59	C₂×#14556580	C₂²	1	2	yes	complemented
60	C₂×#14556580	C₂²	1	2	yes	complemented
61	C₂×#14556579	C₂²	1	2	yes	complemented
62	C₂×#14556578	C₂²	1	2	yes	complemented
63	C₂×#14556577	C₂²	1	2	yes	—
64	C₂×#14556577	C₂²	1	1	yes	characteristic
65	C₂×#14556577	C₂²	1	2	yes	complemented
66	C₂×#14556577	C₂²	1	2	yes	complemented
67	C₂×#14556577	C₂²	1	2	yes	complemented
68	#124×D₇₃	C₂²	1	32	yes	complemented
69	C₂×#14556576	C₂²	1	1	yes	characteristic, complemented
70	C₂×#14556576	C₂²	1	2	yes	complemented
71	C₂×#14556576	C₂²	1	2	yes	complemented
72	C₂×#14556575	C₂²	1	2	yes	complemented
73	C₂×#14556573	C₂²	1	2	yes	complemented
74	C₂×#14556573	C₂²	1	1	yes	characteristic, complemented
75	C₂×#14556573	C₂²	1	2	yes	complemented
76	C₂×#14556569	C₂²	1	2	yes	complemented
77	C₂×#14556569	C₂²	1	2	yes	complemented
78	C₂×#14556569	C₂²	1	2	yes	complemented
79	C₂×#14556569	C₂²	1	1	yes	characteristic, complemented
80	C₂×#14556567	C₂²	1	2	yes	complemented
81	C₂×#14556567	C₂²	1	1	yes	characteristic, complemented
82	C₂×#14556566	C₂²	1	1	yes	characteristic
83	C₂×#14556566	C₂²	1	2	yes	complemented
84	C₂×#14556566	C₂²	1	2	yes	complemented
85	C₂×#14556566	C₂²	1	1	yes	characteristic, complemented
86	C₂×#14556564	C₂²	1	2	yes	—
87	C₂×#14556564	C₂²	1	1	yes	characteristic
88	C₂×#14556564	C₂²	1	2	yes	complemented
89	C₂×#14556564	C₂²	1	2	yes	complemented
90	C₂×#14556563	C₂²	1	2	yes	complemented
91	C₂×#14556562	C₂²	1	1	yes	characteristic, complemented
92	C₂×#14556561	C₂²	1	2	yes	—
93	C₂×#14556561	C₂²	1	2	yes	complemented
94	C₂×#14556561	C₂²	1	2	yes	complemented
95	C₂×#14556559	C₂²	1	2	yes	—
96	#17989061	C₂²	1	16	yes	complemented
97	#17989059	C₂²	1	16	yes	complemented
98	C₄×#11924029	C₂²	1	16	yes	complemented
99	C₂×Q₈×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
100	C₂×C₄×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
101	C₂×#14556556	C₂²	1	2	yes	complemented
102	C₂×C₄×D₂₉₂	C₂²	1	1	yes	characteristic
103	C₂×C₄×D₂₉₂	C₂²	1	1	yes	characteristic
104	C₂×C₄×D₂₉₂	C₂²	1	1	yes	characteristic, complemented
105	C₂×C₄×D₂₉₂	C₂²	1	2	yes	complemented
106	C₂×C₄×D₂₉₂	C₂²	1	1	yes	characteristic, complemented
107	C₂×C₄×D₂₉₂	C₂²	1	1	yes	characteristic, complemented
108	C₂×D₄×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
109	C₂×#14556553	C₂²	1	1	yes	characteristic
110	C₂×#14556553	C₂²	1	1	yes	characteristic
111	C₂×#14556553	C₂²	1	2	yes	complemented
112	C₂×#14556553	C₂²	1	2	yes	complemented
113	C₂×#14556553	C₂²	1	2	yes	complemented
114	C₂×C₄×C₂²⋊D₇₃	C₂²	1	1	yes	characteristic
115	C₂×C₄×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
116	C₂×C₄×C₂²⋊D₇₃	C₂²	1	1	yes	characteristic, complemented
117	C₂×C₄×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
118	C₂×#14556551	C₂²	1	2	yes	complemented
119	C₂×#14556551	C₂²	1	2	yes	complemented
120	C₂×#14556550	C₂²	1	1	yes	characteristic, complemented
121	C₂×#14556549	C₂²	1	2	yes	complemented
122	C₂×#14556549	C₂²	1	1	yes	characteristic, complemented
123	C₂×#14556549	C₂²	1	1	yes	characteristic, complemented
124	C₂×#14556549	C₂²	1	2	yes	complemented
125	C₂×#14556548	C₂²	1	1	yes	characteristic, complemented
126	C₂×#14556547	C₂²	1	2	yes	complemented
127	C₂²×#11924005	C₂²	1	2	yes	complemented
128	C₂×C₂²⋊C₄×D₇₃	C₂²	1	2	yes	complemented
129	C₂×C₂²⋊C₄×D₇₃	C₂²	1	2	yes	complemented
130	C₂×C₂²⋊C₄×D₇₃	C₂²	1	2	yes	complemented
131	C₂×C₂²⋊C₄×D₇₃	C₂²	1	2	yes	complemented
132	C₂×C₂²⋊C₄×D₇₃	C₂²	1	2	yes	complemented
133	C₂×C₄²×D₇₃	C₂²	1	2	yes	complemented
134	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic, complemented
135	#542×C₇₃	C₂²	1	16	yes	complemented
136	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
137	C₂×#126×C₇₃	C₂²	1	2	yes	complemented
138	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic, complemented
139	C₂×#124×C₇₃	C₂²	1	2	yes	complemented
140	C₂×#123×C₇₃	C₂²	1	2	yes	complemented
141	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
142	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	complemented
143	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
144	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
145	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
146	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic, complemented
147	C₂⁴×D₇₃	C₂³	1	2	yes	—
148	C₂⁴×D₇₃	C₂³	1	2	yes	—
149	C₂×#11924029	—	2	8	no	—
150	C₂×#11924029	C₂³	1	8	yes	—
151	C₂×#11924028	—	4	8	no	—
152	C₂×#11924028	C₂³	1	16	yes	complemented
153	C₂²×Dic₁₄₆	C₂³	1	2	yes	—
154	C₂²×Dic₁₄₆	C₂³	1	1	yes	characteristic
155	C₂²×Dic₁₄₆	C₂³	1	2	yes	—
156	C₂×Q₈×D₇₃	—	4	8	no	—
157	C₂×Q₈×D₇₃	C₂³	1	16	yes	complemented
158	C₂²×D₂₉₂	—	2	8	no	—
159	C₂²×D₂₉₂	C₂³	1	1	yes	characteristic
160	C₂²×D₂₉₂	C₂³	1	8	yes	—
161	C₂²×D₂₉₂	C₂³	1	2	yes	—
162	C₂²×D₂₉₂	C₂³	1	2	yes	—
163	C₂²×D₂₉₂	C₂³	1	2	yes	—
164	C₂²×D₂₉₂	C₂³	1	2	yes	—
165	C₂²×D₂₉₂	C₂³	1	1	yes	characteristic
166	C₂²×D₂₉₂	C₂³	1	1	yes	characteristic
167	C₂²×C₂²⋊D₇₃	C₂³	1	2	yes	—
168	C₂²×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
169	C₂²×C₂²⋊D₇₃	C₂³	1	2	yes	—
170	C₂²×C₂²⋊D₇₃	C₂³	1	2	yes	—
171	C₂²×C₂²⋊D₇₃	C₂³	1	2	yes	—
172	C₂²×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
173	C₂×D₄×D₇₃	—	2	8	no	—
174	C₂×D₄×D₇₃	—	4	8	no	—
175	C₂×D₄×D₇₃	C₂³	1	8	yes	—
176	C₂×D₄×D₇₃	C₂³	1	16	yes	—
177	C₂³×Dic₇₃	C₂³	1	2	yes	—
178	C₂²×C₄×D₇₃	C₂³	1	2	yes	—
179	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
180	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
181	C₂²×C₄×D₇₃	C₂³	1	2	yes	—
182	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
183	C₂²×C₄×D₇₃	C₂³	1	2	yes	—
184	C₂²×C₄×D₇₃	C₂³	1	2	yes	—
185	C₂²×C₄×D₇₃	C₂³	1	2	yes	—
186	C₂²×C₄×D₇₃	C₂³	1	2	yes	—
187	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
188	C₂²×C₄×D₇₃	C₂³	1	2	yes	—
189	#14556590	C₂³	1	8	yes	complemented
190	#14556590	C₂³	1	8	yes	complemented
191	#14556587	C₂³	1	8	yes	—
192	#14556586	C₂³	1	16	yes	complemented
193	#14556586	C₂³	1	8	yes	complemented
194	#14556585	C₂³	1	16	yes	complemented
195	#14556584	C₂³	1	16	yes	complemented
196	#14556584	C₂³	1	8	yes	complemented
197	#14556581	C₂³	1	8	yes	complemented
198	#14556580	C₂³	1	16	yes	complemented
199	#14556580	C₂³	1	8	yes	complemented
200	#14556580	C₂³	1	16	yes	complemented
201	#14556579	C₂³	1	16	yes	complemented
202	#14556578	C₂³	1	16	yes	complemented
203	#14556577	C₂³	1	16	yes	—
204	#14556577	C₂³	1	8	yes	—
205	#14556577	C₂³	1	16	yes	complemented
206	#14556577	C₂³	1	16	yes	complemented
207	#14556577	C₂³	1	16	yes	complemented
208	#14556576	C₂³	1	16	yes	complemented
209	#14556576	C₂³	1	8	yes	complemented
210	#14556576	C₂³	1	16	yes	complemented
211	#14556575	C₂³	1	16	yes	complemented
212	#14556573	C₂³	1	16	yes	complemented
213	#14556573	C₂³	1	8	yes	complemented
214	#14556573	C₂³	1	16	yes	complemented
215	#14556569	C₂³	1	16	yes	complemented
216	#14556569	C₂³	1	16	yes	complemented
217	#14556569	C₂³	1	16	yes	complemented
218	#14556569	C₂³	1	8	yes	complemented
219	#14556567	C₂³	1	16	yes	complemented
220	#14556567	C₂³	1	8	yes	complemented
221	#14556566	C₂³	1	8	yes	—
222	#14556566	C₂³	1	8	yes	complemented
223	#14556566	C₂³	1	16	yes	complemented
224	#14556566	C₂³	1	16	yes	complemented
225	#14556564	C₂³	1	16	yes	—
226	#14556564	C₂³	1	8	yes	—
227	#14556564	C₂³	1	16	yes	complemented
228	#14556564	C₂³	1	16	yes	complemented
229	#14556563	C₂³	1	16	yes	complemented
230	#14556562	C₂³	1	8	yes	complemented
231	#14556561	C₂³	1	16	yes	—
232	#14556561	C₂³	1	16	yes	complemented
233	#14556561	C₂³	1	16	yes	complemented
234	#14556559	C₂³	1	16	yes	—
235	Q₈×Dic₇₃	C₂³	1	8	yes	complemented
236	C₄×Dic₁₄₆	C₂³	1	8	yes	complemented
237	#14556556	C₂³	1	16	yes	complemented
238	C₄×D₂₉₂	C₂³	1	8	yes	—
239	C₄×D₂₉₂	C₂³	1	8	yes	—
240	C₄×D₂₉₂	C₂³	1	8	yes	complemented
241	C₄×D₂₉₂	C₂³	1	16	yes	complemented
242	C₄×D₂₉₂	C₂³	1	8	yes	complemented
243	C₄×D₂₉₂	C₂³	1	8	yes	complemented
244	D₄×Dic₇₃	C₂³	1	8	yes	complemented
245	#14556553	C₂³	1	8	yes	—
246	#14556553	C₂³	1	8	yes	—
247	#14556553	C₂³	1	16	yes	complemented
248	#14556553	C₂³	1	16	yes	complemented
249	#14556553	C₂³	1	16	yes	complemented
250	C₄×C₂²⋊D₇₃	C₂³	1	8	yes	—
251	C₄×C₂²⋊D₇₃	C₂³	1	16	yes	complemented
252	C₄×C₂²⋊D₇₃	C₂³	1	8	yes	complemented
253	C₄×C₂²⋊D₇₃	C₂³	1	16	yes	complemented
254	#14556551	C₂³	1	16	yes	complemented
255	#14556551	C₂³	1	16	yes	complemented
256	#14556550	C₂³	1	8	yes	complemented
257	#14556549	C₂³	1	16	yes	complemented
258	#14556549	C₂³	1	16	yes	complemented
259	#14556549	C₂³	1	8	yes	complemented
260	#14556549	C₂³	1	8	yes	complemented
261	#14556548	C₂³	1	8	yes	complemented
262	#14556547	C₂³	1	16	yes	complemented
263	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
267	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
268	C₂×#11924007	C₂³	1	2	yes	—
269	C₂×#11924007	C₂³	1	2	yes	—
270	C₂×#11924007	C₂³	1	1	yes	characteristic
271	C₂×#11924007	C₂³	1	1	yes	characteristic
272	C₂×#11924007	C₂³	1	1	yes	characteristic
273	C₂×#11924007	C₂³	1	1	yes	characteristic
274	C₂×#11924007	C₂³	1	1	yes	characteristic
275	C₂×#11924007	C₂³	1	2	yes	—
276	C₂×#11924007	C₂³	1	1	yes	characteristic
277	C₂×C₂²⋊Dic₇₃	C₂³	1	2	yes	—
278	C₂×C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
279	C₂×C₂²⋊Dic₇₃	C₂³	1	2	yes	—
280	C₂×C₂²⋊Dic₇₃	C₂³	1	2	yes	—
281	C₂×C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
282	C₂×#11924005	C₂³	1	1	yes	characteristic
283	C₂×#11924005	C₂³	1	1	yes	characteristic
284	C₂×#11924005	C₂³	1	2	yes	—
285	C₂×#11924005	C₂³	1	2	yes	—
286	C₂×#11924005	C₂³	1	2	yes	—
287	C₂×#11924005	C₂³	1	2	yes	—
288	C₂×#11924005	C₂³	1	2	yes	—
289	C₂×#11924005	C₂³	1	2	yes	—
290	C₂×#11924005	C₂³	1	2	yes	—
291	C₂×#11924005	C₂³	1	2	yes	—
292	C₂×#11924005	C₂³	1	1	yes	characteristic
293	C₂×#11924005	C₂³	1	2	yes	—
294	C₂×#11924005	C₂³	1	2	yes	—
295	C₂×#11924005	C₂³	1	2	yes	—
296	C₂×#11924005	C₂³	1	2	yes	—
297	C₂×#11924005	C₂³	1	2	yes	—
298	C₂×#11924005	C₂³	1	1	yes	characteristic
299	C₂×#11924005	C₂³	1	1	yes	characteristic
300	C₂×#11924005	C₂³	1	1	yes	characteristic
301	C₂×#11924005	C₂³	1	16	yes	complemented
302	C₂²⋊C₄×D₇₃	C₂³	1	16	yes	complemented
303	C₂²⋊C₄×D₇₃	C₂³	1	16	yes	complemented
304	C₂²⋊C₄×D₇₃	C₂³	1	16	yes	complemented
305	C₂²⋊C₄×D₇₃	C₂³	1	16	yes	complemented
306	C₂²⋊C₄×D₇₃	C₂³	1	16	yes	complemented
307	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
308	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
309	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
310	C₂×C₄×Dic₇₃	C₂³	1	2	yes	—
311	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
312	C₂×C₄×Dic₇₃	C₂³	1	2	yes	—
313	C₂×C₄×Dic₇₃	C₂³	1	2	yes	—
314	C₂×C₄×Dic₇₃	C₂³	1	2	yes	—
315	C₄²×D₇₃	C₂³	1	16	yes	complemented
316	C₄²×D₇₃	C₂³	1	8	yes	complemented
317	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
318	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
319	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
320	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
321	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
322	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
323	C₄⋊Q₈×C₇₃	C₂³	1	8	yes	complemented
324	#126×C₇₃	C₂³	1	16	yes	complemented
325	#124×C₇₃	C₂³	1	16	yes	complemented
326	#124×C₇₃	C₂³	1	8	yes	complemented
327	#123×C₇₃	C₂³	1	16	yes	complemented
328	C₂²⋊Q₈×C₇₃	C₂³	1	8	yes	complemented
329	C₂²⋊Q₈×C₇₃	C₂³	1	16	yes	complemented
330	#121×C₇₃	C₂³	1	8	yes	—
331	C₄×Q₈×C₇₃	C₂³	1	8	yes	complemented
332	C₄×D₄×C₇₃	C₂³	1	8	yes	complemented
333	#117×C₇₃	C₂³	1	8	yes	complemented
334	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
335	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
336	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
337	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
338	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
339	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
340	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
341	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
342	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
343	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
344	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
345	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
346	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
347	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
348	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
349	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
350	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
351	C₂³×D₇₃	—	2	8	no	—
352	C₂³×D₇₃	—	2	8	no	—
353	C₂³×D₇₃	—	4	4	no	—
354	C₂³×D₇₃	—	4	4	no	—
355	C₂³×D₇₃	—	4	4	no	—
356	C₂³×D₇₃	—	4	4	no	—
357	C₂³×D₇₃	C₂⁴	1	1	yes	characteristic
358	C₂³×D₇₃	C₂⁴	1	2	yes	—
359	C₂³×D₇₃	C₂⁴	1	1	yes	characteristic
360	C₂³×D₇₃	C₂⁴	1	2	yes	—
361	C₂³×D₇₃	C₂⁴	1	8	yes	—
362	C₂³×D₇₃	C₂⁴	1	8	yes	—
363	#11924029	—	2	32	no	—
364	#11924028	—	4	32	no	—
365	C₂×Dic₁₄₆	—	2	4	no	—
366	C₂×Dic₁₄₆	—	2	8	no	—
367	C₂×Dic₁₄₆	—	4	4	no	—
368	C₂×Dic₁₄₆	C₂⁴	1	8	yes	—
369	C₂×Dic₁₄₆	C₂⁴	1	4	yes	—
370	C₂×Dic₁₄₆	C₂⁴	1	8	yes	—
371	Q₈×D₇₃	—	4	32	no	—
372	C₂×D₂₉₂	—	2	8	no	—
373	C₂×D₂₉₂	—	2	8	no	—
374	C₂×D₂₉₂	—	2	4	no	—
375	C₂×D₂₉₂	—	2	32	no	—
376	C₂×D₂₉₂	—	4	4	no	—
377	C₂×D₂₉₂	—	4	2	no	—
378	C₂×D₂₉₂	—	4	4	no	—
379	C₂×D₂₉₂	#41	1	8	yes	complemented
380	C₂×D₂₉₂	C₂⁴	1	8	yes	—
381	C₂×D₂₉₂	C₂⁴	1	8	yes	—
382	C₂×D₂₉₂	C₂⁴	1	4	yes	—
383	C₂×D₂₉₂	C₂⁴	1	4	yes	—
384	C₂×D₂₉₂	C₂⁴	1	8	yes	—
385	C₂×D₂₉₂	C₂⁴	1	8	yes	—
386	C₂×D₂₉₂	C₂⁴	1	4	yes	—
387	C₂×C₂²⋊D₇₃	—	2	8	no	—
388	C₂×C₂²⋊D₇₃	—	2	4	no	—
389	C₂×C₂²⋊D₇₃	—	2	8	no	—
390	C₂×C₂²⋊D₇₃	—	4	4	no	—
391	C₂×C₂²⋊D₇₃	—	4	2	no	—
392	C₂×C₂²⋊D₇₃	—	4	4	no	—
393	C₂×C₂²⋊D₇₃	C₂⁴	1	8	yes	—
394	C₂×C₂²⋊D₇₃	C₂⁴	1	8	yes	—
395	C₂×C₂²⋊D₇₃	C₂⁴	1	4	yes	—
396	C₂×C₂²⋊D₇₃	C₂⁴	1	8	yes	—
397	C₂×C₂²⋊D₇₃	C₂⁴	1	4	yes	—
398	C₂×C₂²⋊D₇₃	C₂⁴	1	8	yes	—
399	D₄×D₇₃	—	2	32	no	—
400	D₄×D₇₃	—	4	32	no	—
401	C₂²×Dic₇₃	—	4	4	no	—
402	C₂²×Dic₇₃	C₂⁴	1	2	yes	—
403	C₂²×Dic₇₃	C₂⁴	1	1	yes	characteristic
404	C₂²×Dic₇₃	C₂⁴	1	1	yes	characteristic
405	C₂²×Dic₇₃	C₂⁴	1	1	yes	characteristic
406	C₂²×Dic₇₃	C₂⁴	1	1	yes	characteristic
407	C₂²×Dic₇₃	C₂⁴	1	1	yes	characteristic
408	C₂²×Dic₇₃	C₂⁴	1	2	yes	—
409	C₂²×Dic₇₃	C₂⁴	1	8	yes	—
410	C₂²×Dic₇₃	C₂⁴	1	1	yes	characteristic
411	C₂×C₄×D₇₃	—	2	8	no	—
412	C₂×C₄×D₇₃	—	2	4	no	—
413	C₂×C₄×D₇₃	—	2	4	no	—
414	C₂×C₄×D₇₃	—	2	8	no	—
415	C₂×C₄×D₇₃	—	2	4	no	—
416	C₂×C₄×D₇₃	—	4	4	no	—
417	C₂×C₄×D₇₃	—	4	4	no	—
418	C₂×C₄×D₇₃	—	4	2	no	—
419	C₂×C₄×D₇₃	—	4	4	no	—
420	C₂×C₄×D₇₃	—	4	4	no	—
421	C₂×C₄×D₇₃	—	4	4	no	—
422	C₂×C₄×D₇₃	C₂⁴	1	8	yes	—
423	C₂×C₄×D₇₃	C₂⁴	1	4	yes	—
424	C₂×C₄×D₇₃	C₂⁴	1	8	yes	—
425	C₂×C₄×D₇₃	C₂⁴	1	4	yes	—
426	C₂×C₄×D₇₃	C₂⁴	1	4	yes	—
427	C₂×C₄×D₇₃	C₂⁴	1	8	yes	—
428	C₂×C₄×D₇₃	C₂⁴	1	4	yes	—
429	C₂×C₄×D₇₃	C₂⁴	1	8	yes	—
430	C₂×C₄×D₇₃	C₂⁴	1	8	yes	—
431	C₂×C₄×D₇₃	C₂⁴	1	8	yes	—
432	C₂×C₄×D₇₃	C₂⁴	1	8	yes	—
433	C₄⋊Dic₇₃	C₂⁴	1	4	yes	—
434	C₄⋊Dic₇₃	C₂⁴	1	4	yes	—
435	C₄⋊Dic₇₃	C₂⁴	1	8	yes	—
436	C₄⋊Dic₇₃	C₂⁴	1	4	yes	—
437	C₄⋊Dic₇₃	C₂⁴	1	4	yes	—
438	#11924007	C₂⁴	1	4	yes	—
439	#11924007	C₂⁴	1	8	yes	—
440	#11924007	C₂⁴	1	4	yes	—
441	#11924007	C₂⁴	1	4	yes	—
442	#11924007	C₂⁴	1	4	yes	—
443	#11924007	C₂⁴	1	4	yes	—
444	#11924007	C₂⁴	1	8	yes	—
445	#11924007	C₂⁴	1	8	yes	—
446	#11924007	C₂⁴	1	4	yes	—
447	C₂²⋊Dic₇₃	C₂⁴	1	8	yes	—
448	C₂²⋊Dic₇₃	C₂⁴	1	4	yes	—
449	C₂²⋊Dic₇₃	C₂⁴	1	8	yes	—
450	C₂²⋊Dic₇₃	C₂⁴	1	8	yes	—
451	C₂²⋊Dic₇₃	C₂⁴	1	4	yes	—
452	#11924005	C₂⁴	1	4	yes	—
453	#11924005	C₂⁴	1	4	yes	—
454	#11924005	C₂⁴	1	8	yes	—
455	#11924005	C₂⁴	1	8	yes	—
456	#11924005	C₂⁴	1	8	yes	—
457	#11924005	C₂⁴	1	8	yes	—
458	#11924005	C₂⁴	1	8	yes	—
459	#11924005	C₂⁴	1	8	yes	—
460	#11924005	C₂⁴	1	8	yes	—
461	#11924005	C₂⁴	1	8	yes	—
462	#11924005	C₂⁴	1	4	yes	—
463	#11924005	C₂⁴	1	8	yes	—
464	#11924005	C₂⁴	1	8	yes	—
465	#11924005	C₂⁴	1	8	yes	—
466	#11924005	C₂⁴	1	8	yes	—
467	#11924005	C₂⁴	1	8	yes	—
468	#11924005	C₂⁴	1	4	yes	—
469	#11924005	C₂⁴	1	4	yes	—
470	#11924005	C₂⁴	1	4	yes	—
471	C₄×Dic₇₃	C₂⁴	1	4	yes	—
472	C₄×Dic₇₃	C₂⁴	1	8	yes	—
473	C₄×Dic₇₃	C₂⁴	1	4	yes	—
474	C₄×Dic₇₃	C₂⁴	1	8	yes	—
475	C₄×Dic₇₃	C₂⁴	1	4	yes	—
476	C₄×Dic₇₃	C₂⁴	1	8	yes	—
477	C₄×Dic₇₃	C₂⁴	1	4	yes	—
478	C₄×Dic₇₃	C₂⁴	1	8	yes	—
479	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
480	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
481	C₂×Q₈×C₇₃	—	2	4	no	—
482	C₂×Q₈×C₇₃	—	4	4	no	—
483	C₂×Q₈×C₇₃	C₂⁴	1	4	yes	—
484	C₂×Q₈×C₇₃	C₂⁴	1	8	yes	—
485	C₂×D₄×C₇₃	—	2	4	no	—
486	C₂×D₄×C₇₃	—	4	4	no	—
487	C₂×D₄×C₇₃	C₂⁴	1	4	yes	—
488	C₂×D₄×C₇₃	C₂⁴	1	8	yes	—
489	C₂²×C₄×C₇₃	—	2	4	no	—
490	C₂²×C₄×C₇₃	—	4	4	no	—
491	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
492	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
493	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
494	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
495	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
496	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
497	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
498	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
499	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
500	C₂²×C₄×C₇₃	C₂⁴	1	8	yes	—
501	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
502	C₄⋊C₄×C₇₃	C₂⁴	1	4	yes	—
503	C₄⋊C₄×C₇₃	C₂⁴	1	4	yes	—
504	C₄⋊C₄×C₇₃	C₂⁴	1	4	yes	—
505	C₄⋊C₄×C₇₃	C₂⁴	1	4	yes	—
506	C₄⋊C₄×C₇₃	C₂⁴	1	8	yes	—
507	C₄⋊C₄×C₇₃	C₂⁴	1	8	yes	—
508	C₄⋊C₄×C₇₃	C₂⁴	1	8	yes	—
509	C₂²⋊C₄×C₇₃	C₂⁴	1	4	yes	—
510	C₂²⋊C₄×C₇₃	C₂⁴	1	4	yes	—
511	C₂²⋊C₄×C₇₃	C₂⁴	1	8	yes	—
512	C₂²⋊C₄×C₇₃	C₂⁴	1	8	yes	—
513	C₂²⋊C₄×C₇₃	C₂⁴	1	8	yes	—
514	C₂²⋊C₄×C₇₃	C₂⁴	1	8	yes	—
515	C₂²⋊C₄×C₇₃	C₂⁴	1	8	yes	—
516	C₄²×C₇₃	C₂⁴	1	4	yes	—
517	C₄²×C₇₃	C₂⁴	1	4	yes	—
518	C₄²×C₇₃	C₂⁴	1	8	yes	—
519	C₂³×C₇₃	—	2	2	no	—
520	C₂³×C₇₃	—	2	4	no	—
521	C₂³×C₇₃	—	2	4	no	—
522	C₂³×C₇₃	—	2	2	no	—
523	C₂³×C₇₃	—	2	4	no	—
524	C₂³×C₇₃	—	2	2	no	—
525	C₂³×C₇₃	C₂⁵	1	2	yes	—
526	C₂³×C₇₃	C₂⁵	1	4	yes	—
527	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
528	C₂²×D₇₃	—	2	4	no	—
529	C₂²×D₇₃	—	2	4	no	—
530	C₂²×D₇₃	—	2	2	no	—
531	C₂²×D₇₃	—	2	2	no	—
532	C₂²×D₇₃	—	2	4	no	—
533	C₂²×D₇₃	—	2	2	no	—
534	C₂²×D₇₃	—	2	4	no	—
535	C₂²×D₇₃	—	2	2	no	—
536	C₂²×D₇₃	—	2	2	no	—
537	C₂²×D₇₃	—	2	4	no	—
538	C₂²×D₇₃	—	2	2	no	—
539	C₂²×D₇₃	—	2	16	no	—
540	C₂²×D₇₃	—	2	16	no	—
541	C₂²×D₇₃	—	4	8	no	—
542	C₂²×D₇₃	—	4	8	no	—
543	C₂²×D₇₃	—	4	8	no	—
544	C₂²×D₇₃	—	4	8	no	—
545	C₂²×D₇₃	—	8	16	no	—
546	C₂²×D₇₃	—	8	16	no	—
547	C₂²×D₇₃	C₂×#41	1	8	yes	—
548	C₂²×D₇₃	C₂⁵	1	2	yes	—
549	C₂²×D₇₃	C₂⁵	1	4	yes	—
550	C₂²×D₇₃	C₂⁵	1	2	yes	—
551	C₂²×D₇₃	C₂⁵	1	4	yes	—
552	Q₈×C₇₃	—	2	8	no	—
553	Q₈×C₇₃	—	4	8	no	—
554	D₄×C₇₃	—	2	8	no	—
555	D₄×C₇₃	—	4	8	no	—
556	C₂×C₄×C₇₃	—	2	2	no	—
557	C₂×C₄×C₇₃	—	2	4	no	—
558	C₂×C₄×C₇₃	—	2	2	no	—
559	C₂×C₄×C₇₃	—	2	4	no	—
560	C₂×C₄×C₇₃	—	2	4	no	—
561	C₂×C₄×C₇₃	—	2	2	no	—
562	C₂×C₄×C₇₃	—	2	2	no	—
563	C₂×C₄×C₇₃	—	2	2	no	—
564	C₂×C₄×C₇₃	—	2	8	no	—
565	C₂×C₄×C₇₃	—	4	8	no	—
566	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
567	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
568	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
569	C₂×C₄×C₇₃	C₂⁵	1	4	yes	—
570	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
571	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
572	C₂×C₄×C₇₃	C₂⁵	1	4	yes	—
573	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
574	C₂×C₄×C₇₃	C₂⁵	1	4	yes	—
575	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
576	C₂²⋊D₇₃	—	2	16	no	—
577	C₂²⋊D₇₃	—	2	8	no	—
578	C₂²⋊D₇₃	—	2	16	no	—
579	C₂²⋊D₇₃	—	4	8	no	—
580	C₂²⋊D₇₃	—	4	4	no	—
581	C₂²⋊D₇₃	—	4	8	no	—
582	C₂×Dic₇₃	—	2	2	no	—
583	C₂×Dic₇₃	—	2	2	no	—
584	C₂×Dic₇₃	—	2	4	no	—
585	C₂×Dic₇₃	—	2	2	no	—
586	C₂×Dic₇₃	—	2	4	no	—
587	C₂×Dic₇₃	—	2	2	no	—
588	C₂×Dic₇₃	—	2	2	no	—
589	C₂×Dic₇₃	—	4	8	no	—
590	C₂×Dic₇₃	H(5,𝔽₂)	1	4	yes	—
591	C₂×Dic₇₃	C₂⁵	1	4	yes	—
592	C₂×Dic₇₃	C₂⁵	1	2	yes	—
593	C₂×Dic₇₃	C₂⁵	1	2	yes	—
594	C₂×Dic₇₃	C₂⁵	1	2	yes	—
595	C₂×Dic₇₃	C₂⁵	1	2	yes	—
596	C₂×Dic₇₃	C₂⁵	1	2	yes	—
597	C₂×Dic₇₃	C₂⁵	1	4	yes	—
598	C₂×Dic₇₃	C₂⁵	1	2	yes	—
599	D₂₉₂	—	2	16	no	—
600	D₂₉₂	—	2	16	no	—
601	D₂₉₂	—	2	8	no	—
602	D₂₉₂	—	4	8	no	—
603	D₂₉₂	—	4	4	no	—
604	D₂₉₂	—	4	8	no	—
605	D₂₉₂	C₂×#41	1	16	yes	complemented
606	C₄×D₇₃	—	2	16	no	—
607	C₄×D₇₃	—	2	8	no	—
608	C₄×D₇₃	—	2	8	no	—
609	C₄×D₇₃	—	2	16	no	—
610	C₄×D₇₃	—	2	8	no	—
611	C₄×D₇₃	—	4	8	no	—
612	C₄×D₇₃	—	4	8	no	—
613	C₄×D₇₃	—	4	4	no	—
614	C₄×D₇₃	—	4	8	no	—
615	C₄×D₇₃	—	4	8	no	—
616	C₄×D₇₃	—	4	8	no	—
617	Dic₁₄₆	—	2	8	no	—
618	Dic₁₄₆	—	2	16	no	—
619	Dic₁₄₆	—	4	8	no	—
620	C₂²×C₇₃	—	2	4	no	—
621	C₂²×C₇₃	—	2	2	no	—
622	C₂²×C₇₃	—	2	4	no	—
623	C₂²×C₇₃	—	2	2	no	—
624	C₂²×C₇₃	—	2	4	no	—
625	C₂²×C₇₃	—	2	2	no	—
626	C₂²×C₇₃	—	4	4	no	—
627	C₂²×C₇₃	—	4	8	no	—
628	C₂²×C₇₃	C₂²×#41	1	2	yes	—
629	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	2	yes	—
630	C₂²×C₇₃	#585	1	2	yes	—
631	C₂²×C₇₃	C₂⁶	1	1	yes	characteristic
632	C₂×D₇₃	—	2	4	no	—
633	C₂×D₇₃	—	2	4	no	—
634	C₂×D₇₃	—	2	16	no	—
635	C₂×D₇₃	—	2	2	no	—
636	C₂×D₇₃	—	2	2	no	—
637	C₂×D₇₃	—	2	4	no	—
638	C₂×D₇₃	—	2	2	no	—
639	C₂×D₇₃	—	2	4	no	—
640	C₂×D₇₃	—	2	2	no	—
641	C₂×D₇₃	—	2	2	no	—
642	C₂×D₇₃	—	2	4	no	—
643	C₂×D₇₃	—	2	2	no	—
644	C₂×D₇₃	—	4	4	no	—
645	C₂×D₇₃	—	4	8	no	—
646	C₂×D₇₃	—	4	4	no	—
647	C₂×D₇₃	—	8	16	no	—
648	C₂×D₇₃	—	8	16	no	—
649	C₂×D₇₃	C₂²×#41	1	8	yes	—
650	C₄×C₇₃	—	2	4	no	—
651	C₄×C₇₃	—	2	2	no	—
652	C₄×C₇₃	—	2	2	no	—
653	C₄×C₇₃	—	2	4	no	—
654	C₄×C₇₃	—	2	4	no	—
655	C₄×C₇₃	—	2	2	no	—
656	C₄×C₇₃	—	2	2	no	—
657	C₄×C₇₃	—	2	2	no	—
658	C₄×C₇₃	C₂²×#41	1	4	yes	—
659	Dic₇₃	—	2	2	no	—
660	Dic₇₃	—	2	2	no	—
661	Dic₇₃	—	2	2	no	—
662	Dic₇₃	—	2	4	no	—
663	Dic₇₃	—	2	4	no	—
664	Dic₇₃	—	2	2	no	—
665	Dic₇₃	—	2	2	no	—
666	Dic₇₃	C₂×H(5,𝔽₂)	1	4	yes	—
667	C₂×#3514	—	73	1	no	maximal, Sylow
668	C₂×C₇₃	—	4	2	no	—
669	C₂×C₇₃	—	4	4	no	—
670	C₂×C₇₃	#3514	1	4	yes	complemented
671	C₂×C₇₃	C₂³×#41	1	1	yes	characteristic
672	C₂×C₇₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
673	C₂×C₇₃	C₂×#585	1	1	yes	characteristic
674	D₇₃	—	2	8	no	—
675	D₇₃	—	4	2	no	—
676	D₇₃	—	4	4	no	—
677	D₇₃	—	4	2	no	—
678	#3514	—	73	32	no	—
679	C₂×#559	—	73	1	no	—
680	C₂×#556	—	73	1	no	—
681	C₂×#555	—	73	1	no	—
682	C₂×#555	—	73	1	no	—
683	C₂×#551	—	73	2	no	—
684	C₂×#551	—	73	2	no	—
685	C₂×D₄×Q₈	—	73	1	no	—
686	C₂×#548	—	73	2	no	—
687	C₂×#546	—	73	1	no	—
688	C₂×#546	—	73	2	no	—
689	C₂×#546	—	73	1	no	—
690	C₂×D₄²	—	73	1	no	—
691	C₂×#542	—	73	1	no	—
692	C₂×#542	D₇₃	1	1	yes	characteristic, complemented
693	C₂×#538	—	73	2	no	—
694	C₂×#538	—	73	2	no	—
695	C₂×#532	—	73	1	no	—
696	C₂×#529	—	73	2	no	—
697	C₂×#529	—	73	1	no	—
698	C₂²×#124	—	73	2	no	—
699	C₂×#518	—	73	1	no	—
700	C₂×#518	—	73	1	no	—
701	C₂×C₄×#41	—	73	1	no	—
702	C₇₃	C₂×#3514	1	1	yes	characteristic, complemented, Sylow
703	C₂²×#41	—	73	1	no	—
704	C₂²×#41	—	73	2	no	—
705	C₂³×Q₈	—	73	2	no	—
706	C₂³×D₄	—	73	2	no	—
707	C₂³×D₄	—	73	1	no	—
708	C₂³×D₄	—	73	1	no	—
709	#559	—	73	16	no	—
710	#556	—	73	16	no	—
711	#555	—	73	16	no	—
712	#555	—	73	16	no	—
713	#551	—	73	32	no	—
714	#551	—	73	32	no	—
715	D₄×Q₈	—	73	16	no	—
716	#548	—	73	32	no	—
717	#546	—	73	16	no	—
718	#546	—	73	32	no	—
719	#546	—	73	16	no	—
720	D₄²	—	73	16	no	—
721	#542	—	73	16	no	—
722	#542	C₂×D₇₃	1	16	yes	complemented
723	#538	—	73	32	no	—
724	#538	—	73	32	no	—
725	#532	—	73	16	no	—
726	C₂×C₄⋊Q₈	—	73	1	no	—
727	C₂×C₄⋊Q₈	—	73	1	no	—
728	C₂×C₄⋊Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
729	C₂×#127	—	73	1	no	—
730	#529	—	73	32	no	—
731	#529	—	73	16	no	—
732	C₂×#126	—	73	1	no	—
733	C₂×#126	—	73	2	no	—
734	C₂×#126	—	73	1	no	—
735	C₂×#126	—	73	2	no	—
736	C₂×#126	—	73	2	no	—
737	C₂×#126	C₂×D₇₃	1	2	yes	complemented
738	C₂×#125	—	73	1	no	—
739	C₂×#124	—	73	2	no	—
740	C₂×#124	—	73	2	no	—
741	C₂×#124	—	73	1	no	—
742	C₂×#124	—	73	2	no	—
743	C₂×#124	—	73	32	no	—
744	C₂×#124	—	73	1	no	—
745	C₂×#124	—	73	2	no	—
746	C₂×#124	—	73	2	no	—
747	C₂×#124	—	73	2	no	—
748	C₂×#124	—	73	2	no	—
749	C₂×#124	—	73	2	no	—
750	C₂×#124	C₂×D₇₃	1	2	yes	complemented
751	C₂×#124	C₂×D₇₃	1	1	yes	characteristic, complemented
752	C₂×#123	—	73	1	no	—
753	C₂×#123	—	73	2	no	—
754	C₂×#123	—	73	2	no	—
755	C₂×#123	—	73	1	no	—
756	C₂×#123	—	73	2	no	—
757	C₂×#123	—	73	2	no	—
758	C₂×#123	—	73	2	no	—
759	C₂×#123	C₂×D₇₃	1	2	yes	complemented
760	C₂×C₂²⋊Q₈	—	73	2	no	—
761	C₂×C₂²⋊Q₈	—	73	1	no	—
762	C₂×C₂²⋊Q₈	—	73	2	no	—
763	C₂×C₂²⋊Q₈	—	73	1	no	—
764	C₂×C₂²⋊Q₈	—	73	2	no	—
765	C₂×C₂²⋊Q₈	—	73	2	no	—
766	C₂×C₂²⋊Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
767	C₂×C₂²⋊Q₈	C₂×D₇₃	1	2	yes	complemented
768	C₂×#121	—	73	1	no	—
769	C₂×#121	—	73	2	no	—
770	C₂×#121	—	73	1	no	—
771	C₂×#121	—	73	2	no	—
772	C₂×#121	—	73	2	no	—
773	C₂×#121	—	73	1	no	—
774	C₂×#121	—	73	2	no	—
775	C₂×#121	—	73	1	no	—
776	C₂×#121	—	73	2	no	—
777	C₂×#121	—	73	2	no	—
778	C₂×#121	C₂×D₇₃	1	1	yes	characteristic
779	C₂×#120	—	73	2	no	—
780	C₂×#120	—	73	2	no	—
781	C₂×#120	—	73	2	no	—
782	C₂×#120	—	73	2	no	—
783	#518	—	73	16	no	—
784	#518	—	73	16	no	—
785	C₄×#41	—	73	16	no	—
786	C₂×C₄×Q₈	—	73	1	no	—
787	C₂×C₄×Q₈	—	73	2	no	—
788	C₂×C₄×Q₈	—	73	1	no	—
789	C₂×C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
790	C₂×C₄×D₄	—	73	1	no	—
791	C₂×C₄×D₄	—	73	2	no	—
792	C₂×C₄×D₄	—	73	1	no	—
793	C₂×C₄×D₄	—	73	1	no	—
794	C₂×C₄×D₄	—	73	2	no	—
795	C₂×C₄×D₄	—	73	1	no	—
796	C₂×C₄×D₄	—	73	2	no	—
797	C₂×C₄×D₄	—	73	2	no	—
798	C₂×C₄×D₄	—	73	1	no	—
799	C₂×C₄×D₄	—	73	2	no	—
800	C₂×C₄×D₄	—	73	2	no	—
801	C₂×C₄×D₄	—	73	2	no	—
802	C₂×C₄×D₄	—	73	1	no	—
803	C₂×C₄×D₄	—	73	2	no	—
804	C₂×C₄×D₄	—	73	1	no	—
805	C₂×C₄×D₄	—	73	1	no	—
806	C₂×C₄×D₄	—	73	1	no	—
807	C₂×C₄×D₄	—	73	1	no	—
808	C₂×C₄×D₄	C₂×D₇₃	1	1	yes	characteristic, complemented
809	C₂×#117	—	73	1	no	—
810	C₂×#117	—	73	2	no	—
811	C₂×#117	—	73	1	no	—
812	C₂×#117	—	73	1	no	—
813	C₂×#117	—	73	2	no	—
814	C₂×#117	—	73	2	no	—
815	C₂×#117	—	73	1	no	—
816	C₂×#117	C₂×D₇₃	1	1	yes	characteristic, complemented
817	C₂²×C₂²⋊C₄	—	73	2	no	—
818	C₂²×C₂²⋊C₄	—	73	2	no	—
819	C₂²×C₂²⋊C₄	—	73	2	no	—
820	C₂²×C₂²⋊C₄	—	73	2	no	—
821	C₂²×C₂²⋊C₄	—	73	2	no	—
822	C₂²×C₂²⋊C₄	—	73	2	no	—
823	C₂²×C₄²	—	73	2	no	—
824	C₂²×C₄²	—	73	1	no	—
825	C₂⁵	—	73	2	no	—
826	C₂⁵	—	73	2	no	—
827	C₂×#41	—	292	8	no	—
828	C₂×#41	—	73	8	no	—
829	C₂×#41	—	73	16	no	—
830	C₂×#41	—	146	8	no	—
831	C₂²×Q₈	—	292	8	no	—
832	C₂²×Q₈	—	73	16	no	—
833	C₂²×Q₈	—	73	2	no	—
834	C₂²×Q₈	—	73	1	no	—
835	C₂²×Q₈	—	73	2	no	—
836	C₂²×Q₈	C₂²×D₇₃	1	1	yes	characteristic
837	C₂²×Q₈	C₂²×D₇₃	1	2	yes	—
838	C₂²×D₄	—	292	8	no	—
839	C₂²×D₄	—	73	1	no	—
840	C₂²×D₄	—	73	2	no	—
841	C₂²×D₄	—	73	2	no	—
842	C₂²×D₄	—	73	16	no	—
843	C₂²×D₄	—	73	2	no	—
844	C₂²×D₄	—	73	1	no	—
845	C₂²×D₄	—	73	2	no	—
846	C₂²×D₄	—	73	8	no	—
847	C₂²×D₄	—	73	1	no	—
848	C₂²×D₄	—	73	2	no	—
849	C₂²×D₄	—	73	2	no	—
850	C₂²×D₄	—	73	1	no	—
851	C₂²×D₄	—	73	2	no	—
852	C₂²×D₄	—	73	2	no	—
853	C₂²×D₄	—	73	1	no	—
854	C₂²×D₄	—	73	8	no	—
855	C₂²×D₄	—	146	8	no	—
856	C₂²×D₄	—	146	8	no	—
857	C₂²×D₄	C₂²×D₇₃	1	1	yes	characteristic
858	C₂²×D₄	C₂²×D₇₃	1	2	yes	—
859	C₂³×C₄	—	73	2	no	—
860	C₂³×C₄	—	73	2	no	—
861	C₂³×C₄	—	73	2	no	—
862	C₂³×C₄	—	73	2	no	—
863	C₂³×C₄	—	73	2	no	—
864	C₂³×C₄	—	73	2	no	—
865	C₂³×C₄	—	73	1	no	—
866	C₂³×C₄	—	73	2	no	—
867	C₂³×C₄	—	73	1	no	—
868	C₂³×C₄	—	73	1	no	—
869	C₂³×C₄	—	73	2	no	—
870	C₂³×C₄	—	73	1	no	—
871	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
872	C₂³×C₄	C₂²×D₇₃	1	2	yes	—
873	C₄⋊Q₈	—	73	8	no	—
874	C₄⋊Q₈	—	73	8	no	—
875	C₄⋊Q₈	C₂²×D₇₃	1	8	yes	complemented
876	#127	—	73	8	no	—
877	#126	—	73	8	no	—
878	#126	—	73	16	no	—
879	#126	—	73	8	no	—
880	#126	—	73	16	no	—
881	#126	—	73	16	no	—
882	#126	C₂²×D₇₃	1	16	yes	complemented
883	#125	—	73	8	no	—
884	#124	—	73	16	no	—
885	#124	—	73	16	no	—
886	#124	—	73	8	no	—
887	#124	—	73	16	no	—
888	#124	—	73	8	no	—
889	#124	—	73	16	no	—
890	#124	—	73	16	no	—
891	#124	—	73	16	no	—
892	#124	—	73	16	no	—
893	#124	—	73	16	no	—
894	#124	C₂²×D₇₃	1	16	yes	complemented
895	#124	C₂²×D₇₃	1	8	yes	complemented
896	#123	—	73	8	no	—
897	#123	—	73	16	no	—
898	#123	—	73	16	no	—
899	#123	—	73	8	no	—
900	#123	—	73	16	no	—
901	#123	—	73	16	no	—
902	#123	—	73	16	no	—
903	#123	C₂²×D₇₃	1	16	yes	complemented
904	C₂²⋊Q₈	—	73	16	no	—
905	C₂²⋊Q₈	—	73	8	no	—
906	C₂²⋊Q₈	—	73	16	no	—
907	C₂²⋊Q₈	—	73	8	no	—
908	C₂²⋊Q₈	—	73	16	no	—
909	C₂²⋊Q₈	—	73	16	no	—
910	C₂²⋊Q₈	C₂²×D₇₃	1	8	yes	complemented
911	C₂²⋊Q₈	C₂²×D₇₃	1	16	yes	complemented
912	#121	—	73	8	no	—
913	#121	—	73	16	no	—
914	#121	—	73	8	no	—
915	#121	—	73	16	no	—
916	#121	—	73	16	no	—
917	#121	—	73	8	no	—
918	#121	—	73	16	no	—
919	#121	—	73	8	no	—
920	#121	—	73	16	no	—
921	#121	—	73	16	no	—
922	#121	C₂²×D₇₃	1	8	yes	—
923	#120	—	73	16	no	—
924	#120	—	73	16	no	—
925	#120	—	73	16	no	—
926	#120	—	73	16	no	—
927	C₄×Q₈	—	73	8	no	—
928	C₄×Q₈	—	73	16	no	—
929	C₄×Q₈	—	73	8	no	—
930	C₄×Q₈	C₂²×D₇₃	1	8	yes	complemented
931	C₄×D₄	—	73	8	no	—
932	C₄×D₄	—	73	16	no	—
933	C₄×D₄	—	73	8	no	—
934	C₄×D₄	—	73	8	no	—
935	C₄×D₄	—	73	16	no	—
936	C₄×D₄	—	73	8	no	—
937	C₄×D₄	—	73	16	no	—
938	C₄×D₄	—	73	16	no	—
939	C₄×D₄	—	73	8	no	—
940	C₄×D₄	—	73	16	no	—
941	C₄×D₄	—	73	16	no	—
942	C₄×D₄	—	73	16	no	—
943	C₄×D₄	—	73	8	no	—
944	C₄×D₄	—	73	16	no	—
945	C₄×D₄	—	73	8	no	—
946	C₄×D₄	—	73	8	no	—
947	C₄×D₄	—	73	8	no	—
948	C₄×D₄	—	73	8	no	—
949	C₄×D₄	C₂²×D₇₃	1	8	yes	complemented
950	#117	—	73	8	no	—
951	#117	—	73	16	no	—
952	#117	—	73	8	no	—
953	#117	—	73	8	no	—
954	#117	—	73	16	no	—
955	#117	—	73	16	no	—
956	#117	—	73	8	no	—
957	#117	C₂²×D₇₃	1	8	yes	complemented
958	C₂×C₄⋊C₄	—	73	1	no	—
959	C₂×C₄⋊C₄	—	73	1	no	—
960	C₂×C₄⋊C₄	—	73	1	no	—
961	C₂×C₄⋊C₄	—	73	1	no	—
962	C₂×C₄⋊C₄	—	73	1	no	—
963	C₂×C₄⋊C₄	—	73	1	no	—
964	C₂×C₄⋊C₄	—	73	2	no	—
965	C₂×C₄⋊C₄	—	73	2	no	—
966	C₂×C₄⋊C₄	—	73	1	no	—
967	C₂×C₄⋊C₄	—	73	1	no	—
968	C₂×C₄⋊C₄	—	73	2	no	—
969	C₂×C₄⋊C₄	—	73	2	no	—
970	C₂×C₄⋊C₄	—	73	1	no	—
971	C₂×C₄⋊C₄	—	73	1	no	—
972	C₂×C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
973	C₂×C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
974	C₂×C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
975	C₂×C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
976	C₂×C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
977	C₂×C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
978	C₂×C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
979	C₂×C₂²⋊C₄	—	73	2	no	—
980	C₂×C₂²⋊C₄	—	73	1	no	—
981	C₂×C₂²⋊C₄	—	73	2	no	—
982	C₂×C₂²⋊C₄	—	73	2	no	—
983	C₂×C₂²⋊C₄	—	73	1	no	—
984	C₂×C₂²⋊C₄	—	73	2	no	—
985	C₂×C₂²⋊C₄	—	73	1	no	—
986	C₂×C₂²⋊C₄	—	73	2	no	—
987	C₂×C₂²⋊C₄	—	73	1	no	—
988	C₂×C₂²⋊C₄	—	73	1	no	—
989	C₂×C₂²⋊C₄	—	73	2	no	—
990	C₂×C₂²⋊C₄	—	73	2	no	—
991	C₂×C₂²⋊C₄	—	73	2	no	—
992	C₂×C₂²⋊C₄	—	73	2	no	—
993	C₂×C₂²⋊C₄	—	73	2	no	—
994	C₂×C₂²⋊C₄	—	73	16	no	—
995	C₂×C₂²⋊C₄	—	73	2	no	—
996	C₂×C₂²⋊C₄	—	73	2	no	—
997	C₂×C₂²⋊C₄	—	73	2	no	—
998	C₂×C₂²⋊C₄	—	73	2	no	—
999	C₂×C₂²⋊C₄	—	73	2	no	—
1000	C₂×C₂²⋊C₄	—	73	1	no	—
1001	C₂×C₂²⋊C₄	—	73	2	no	—
1002	C₂×C₂²⋊C₄	—	73	1	no	—
1003	C₂×C₂²⋊C₄	—	73	1	no	—
1004	C₂×C₂²⋊C₄	—	73	16	no	—
1005	C₂×C₂²⋊C₄	—	73	16	no	—
1006	C₂×C₂²⋊C₄	—	73	16	no	—
1007	C₂×C₂²⋊C₄	—	73	16	no	—
1008	C₂×C₂²⋊C₄	—	73	16	no	—
1009	C₂×C₂²⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
1010	C₂×C₂²⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
1011	C₂×C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
1012	C₂×C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
1013	C₂×C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
1014	C₂×C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
1015	C₂×C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
1016	C₂×C₄²	—	73	2	no	—
1017	C₂×C₄²	—	73	2	no	—
1018	C₂×C₄²	—	73	2	no	—
1019	C₂×C₄²	—	73	1	no	—
1020	C₂×C₄²	—	73	1	no	—
1021	C₂×C₄²	—	73	2	no	—
1022	C₂×C₄²	—	73	1	no	—
1023	C₂×C₄²	—	73	1	no	—
1024	C₂×C₄²	—	73	16	no	—
1025	C₂×C₄²	—	73	8	no	—
1026	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
1027	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
1028	C₂×C₄²	C₂²×D₇₃	1	2	yes	—
1029	C₂⁴	—	292	4	no	—
1030	C₂⁴	—	292	4	no	—
1031	C₂⁴	—	292	4	no	—
1032	C₂⁴	—	292	4	no	—
1033	C₂⁴	—	73	8	no	—
1034	C₂⁴	—	73	8	no	—
1035	C₂⁴	—	73	2	no	—
1036	C₂⁴	—	73	1	no	—
1037	C₂⁴	—	73	2	no	—
1038	C₂⁴	—	73	1	no	—
1039	C₂⁴	—	146	8	no	—
1040	C₂⁴	—	146	8	no	—
1041	C₂⁴	C₂³×D₇₃	1	1	yes	characteristic
1042	C₂⁴	C₂³×D₇₃	1	2	yes	—
1043	#41	—	292	32	no	—
1044	#41	—	146	32	no	—
1045	C₂×Q₈	—	2	4	no	—
1046	C₂×Q₈	—	4	4	no	—
1047	C₂×Q₈	—	292	4	no	—
1048	C₂×Q₈	—	292	32	no	—
1049	C₂×Q₈	—	73	8	no	—
1050	C₂×Q₈	—	73	4	no	—
1051	C₂×Q₈	—	73	8	no	—
1052	C₂×Q₈	—	146	4	no	—
1053	C₂×Q₈	—	146	8	no	—
1054	C₂×Q₈	C₂³×D₇₃	1	4	yes	—
1055	C₂×Q₈	C₂³×D₇₃	1	8	yes	—
1056	C₂×D₄	—	2	4	no	—
1057	C₂×D₄	—	4	4	no	—
1058	C₂×D₄	—	292	4	no	—
1059	C₂×D₄	—	292	2	no	—
1060	C₂×D₄	—	292	4	no	—
1061	C₂×D₄	—	292	32	no	—
1062	C₂×D₄	—	292	2	no	—
1063	C₂×D₄	—	292	4	no	—
1064	C₂×D₄	—	292	4	no	—
1065	C₂×D₄	—	73	4	no	—
1066	C₂×D₄	—	73	8	no	—
1067	C₂×D₄	—	73	8	no	—
1068	C₂×D₄	—	73	8	no	—
1069	C₂×D₄	—	73	4	no	—
1070	C₂×D₄	—	73	8	no	—
1071	C₂×D₄	—	73	8	no	—
1072	C₂×D₄	—	73	4	no	—
1073	C₂×D₄	—	73	8	no	—
1074	C₂×D₄	—	73	8	no	—
1075	C₂×D₄	—	73	4	no	—
1076	C₂×D₄	—	73	8	no	—
1077	C₂×D₄	—	73	8	no	—
1078	C₂×D₄	—	73	4	no	—
1079	C₂×D₄	—	146	32	no	—
1080	C₂×D₄	—	146	8	no	—
1081	C₂×D₄	—	146	8	no	—
1082	C₂×D₄	—	146	4	no	—
1083	C₂×D₄	—	146	8	no	—
1084	C₂×D₄	—	146	32	no	—
1085	C₂×D₄	—	146	8	no	—
1086	C₂×D₄	—	146	4	no	—
1087	C₂×D₄	C₂³×D₇₃	1	4	yes	—
1088	C₂×D₄	C₂³×D₇₃	1	8	yes	—
1089	C₂²×C₄	—	2	4	no	—
1090	C₂²×C₄	—	4	4	no	—
1091	C₂²×C₄	—	292	4	no	—
1092	C₂²×C₄	—	292	2	no	—
1093	C₂²×C₄	—	292	4	no	—
1094	C₂²×C₄	—	292	4	no	—
1095	C₂²×C₄	—	292	4	no	—
1096	C₂²×C₄	—	292	4	no	—
1097	C₂²×C₄	—	292	4	no	—
1098	C₂²×C₄	—	73	8	no	—
1099	C₂²×C₄	—	73	8	no	—
1100	C₂²×C₄	—	73	4	no	—
1101	C₂²×C₄	—	73	8	no	—
1102	C₂²×C₄	—	73	8	no	—
1103	C₂²×C₄	—	73	8	no	—
1104	C₂²×C₄	—	73	8	no	—
1105	C₂²×C₄	—	73	1	no	—
1106	C₂²×C₄	—	73	1	no	—
1107	C₂²×C₄	—	73	2	no	—
1108	C₂²×C₄	—	73	1	no	—
1109	C₂²×C₄	—	73	1	no	—
1110	C₂²×C₄	—	73	1	no	—
1111	C₂²×C₄	—	73	1	no	—
1112	C₂²×C₄	—	73	2	no	—
1113	C₂²×C₄	—	73	8	no	—
1114	C₂²×C₄	—	73	4	no	—
1115	C₂²×C₄	—	73	8	no	—
1116	C₂²×C₄	—	73	4	no	—
1117	C₂²×C₄	—	73	4	no	—
1118	C₂²×C₄	—	146	8	no	—
1119	C₂²×C₄	—	146	4	no	—
1120	C₂²×C₄	—	146	8	no	—
1121	C₂²×C₄	—	146	4	no	—
1122	C₂²×C₄	—	146	4	no	—
1123	C₂²×C₄	C₂³×D₇₃	1	4	yes	—
1124	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
1125	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
1126	C₂²×C₄	C₂³×D₇₃	1	2	yes	—
1127	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
1128	C₂²×C₄	C₂³×D₇₃	1	2	yes	—
1129	C₂²×C₄	C₂³×D₇₃	1	2	yes	—
1130	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
1131	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
1132	C₂²×C₄	C₂³×D₇₃	1	8	yes	—
1133	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
1134	C₄⋊C₄	—	73	4	no	—
1135	C₄⋊C₄	—	73	4	no	—
1136	C₄⋊C₄	—	73	4	no	—
1137	C₄⋊C₄	—	73	8	no	—
1138	C₄⋊C₄	—	73	4	no	—
1139	C₄⋊C₄	—	73	4	no	—
1140	C₄⋊C₄	—	73	8	no	—
1141	C₄⋊C₄	—	73	8	no	—
1142	C₄⋊C₄	—	73	4	no	—
1143	C₄⋊C₄	—	73	4	no	—
1144	C₄⋊C₄	—	73	4	no	—
1145	C₄⋊C₄	—	73	4	no	—
1146	C₄⋊C₄	—	73	8	no	—
1147	C₄⋊C₄	—	73	4	no	—
1148	C₄⋊C₄	C₂³×D₇₃	1	4	yes	—
1149	C₄⋊C₄	C₂³×D₇₃	1	4	yes	—
1150	C₄⋊C₄	C₂³×D₇₃	1	8	yes	—
1151	C₄⋊C₄	C₂³×D₇₃	1	8	yes	—
1152	C₄⋊C₄	C₂³×D₇₃	1	4	yes	—
1153	C₄⋊C₄	C₂³×D₇₃	1	4	yes	—
1154	C₄⋊C₄	C₂³×D₇₃	1	8	yes	—
1155	C₂²⋊C₄	—	73	8	no	—
1156	C₂²⋊C₄	—	73	4	no	—
1157	C₂²⋊C₄	—	73	8	no	—
1158	C₂²⋊C₄	—	73	8	no	—
1159	C₂²⋊C₄	—	73	4	no	—
1160	C₂²⋊C₄	—	73	8	no	—
1161	C₂²⋊C₄	—	73	4	no	—
1162	C₂²⋊C₄	—	73	8	no	—
1163	C₂²⋊C₄	—	73	4	no	—
1164	C₂²⋊C₄	—	73	4	no	—
1165	C₂²⋊C₄	—	73	8	no	—
1166	C₂²⋊C₄	—	73	8	no	—
1167	C₂²⋊C₄	—	73	8	no	—
1168	C₂²⋊C₄	—	73	8	no	—
1169	C₂²⋊C₄	—	73	8	no	—
1170	C₂²⋊C₄	—	73	8	no	—
1171	C₂²⋊C₄	—	73	8	no	—
1172	C₂²⋊C₄	—	73	8	no	—
1173	C₂²⋊C₄	—	73	8	no	—
1174	C₂²⋊C₄	—	73	8	no	—
1175	C₂²⋊C₄	—	73	4	no	—
1176	C₂²⋊C₄	—	73	8	no	—
1177	C₂²⋊C₄	—	73	4	no	—
1178	C₂²⋊C₄	—	73	4	no	—
1179	C₂²⋊C₄	C₂³×D₇₃	1	4	yes	—
1180	C₂²⋊C₄	C₂³×D₇₃	1	4	yes	—
1181	C₂²⋊C₄	C₂³×D₇₃	1	8	yes	—
1182	C₂²⋊C₄	C₂³×D₇₃	1	8	yes	—
1183	C₂²⋊C₄	C₂³×D₇₃	1	8	yes	—
1184	C₂²⋊C₄	C₂³×D₇₃	1	8	yes	—
1185	C₂²⋊C₄	C₂³×D₇₃	1	8	yes	—
1186	C₄²	—	73	4	no	—
1187	C₄²	—	73	8	no	—
1188	C₄²	—	73	4	no	—
1189	C₄²	—	73	8	no	—
1190	C₄²	—	73	4	no	—
1191	C₄²	—	73	8	no	—
1192	C₄²	—	73	8	no	—
1193	C₄²	—	73	4	no	—
1194	C₄²	C₂³×D₇₃	1	4	yes	—
1195	C₄²	C₂³×D₇₃	1	8	yes	—
1196	C₄²	C₂³×D₇₃	1	4	yes	—
1197	C₂³	—	2	2	no	—
1198	C₂³	—	2	4	no	—
1199	C₂³	—	2	4	no	—
1200	C₂³	—	2	2	no	—
1201	C₂³	—	2	4	no	—
1202	C₂³	—	2	2	no	—
1203	C₂³	—	292	8	no	—
1204	C₂³	—	292	8	no	—
1205	C₂³	—	292	8	no	—
1206	C₂³	—	292	8	no	—
1207	C₂³	—	584	16	no	—
1208	C₂³	—	584	16	no	—
1209	C₂³	—	73	8	no	—
1210	C₂³	—	73	4	no	—
1211	C₂³	—	73	2	no	—
1212	C₂³	—	73	4	no	—
1213	C₂³	—	73	2	no	—
1214	C₂³	—	146	16	no	—
1215	C₂³	—	146	16	no	—
1216	C₂³	—	146	2	no	—
1217	C₂³	—	146	2	no	—
1218	C₂³	—	146	4	no	—
1219	C₂³	—	146	4	no	—
1220	C₂³	—	146	2	no	—
1221	C₂³	—	146	2	no	—
1222	C₂³	—	146	2	no	—
1223	C₂³	—	146	4	no	—
1224	C₂³	—	146	2	no	—
1225	C₂³	—	146	4	no	—
1226	C₂³	—	146	4	no	—
1227	C₂³	C₂⁴×D₇₃	1	2	yes	—
1228	C₂³	C₂⁴×D₇₃	1	4	yes	—
1229	C₂³	C₂⁴×D₇₃	1	1	yes	characteristic
1230	Q₈	—	2	8	no	—
1231	Q₈	—	4	8	no	—
1232	Q₈	—	292	8	no	—
1233	Q₈	—	146	8	no	—
1234	Q₈	—	146	16	no	—
1235	D₄	—	2	8	no	—
1236	D₄	—	4	8	no	—
1237	D₄	—	292	8	no	—
1238	D₄	—	292	8	no	—
1239	D₄	—	292	4	no	—
1240	D₄	—	292	8	no	—
1241	D₄	—	292	4	no	—
1242	D₄	—	292	8	no	—
1243	D₄	—	73	16	no	—
1244	D₄	—	146	16	no	—
1245	D₄	—	146	16	no	—
1246	D₄	—	146	8	no	—
1247	D₄	—	146	16	no	—
1248	D₄	—	146	16	no	—
1249	D₄	—	146	8	no	—
1250	C₂×C₄	—	2	2	no	—
1251	C₂×C₄	—	2	4	no	—
1252	C₂×C₄	—	2	2	no	—
1253	C₂×C₄	—	2	4	no	—
1254	C₂×C₄	—	2	2	no	—
1255	C₂×C₄	—	2	4	no	—
1256	C₂×C₄	—	2	2	no	—
1257	C₂×C₄	—	2	2	no	—
1258	C₂×C₄	—	2	8	no	—
1259	C₂×C₄	—	4	8	no	—
1260	C₂×C₄	—	292	8	no	—
1261	C₂×C₄	—	292	8	no	—
1262	C₂×C₄	—	292	8	no	—
1263	C₂×C₄	—	292	8	no	—
1264	C₂×C₄	—	292	4	no	—
1265	C₂×C₄	—	292	8	no	—
1266	C₂×C₄	—	292	8	no	—
1267	C₂×C₄	—	73	4	no	—
1268	C₂×C₄	—	73	2	no	—
1269	C₂×C₄	—	73	2	no	—
1270	C₂×C₄	—	73	4	no	—
1271	C₂×C₄	—	73	2	no	—
1272	C₂×C₄	—	73	2	no	—
1273	C₂×C₄	—	73	2	no	—
1274	C₂×C₄	—	73	2	no	—
1275	C₂×C₄	—	73	4	no	—
1276	C₂×C₄	—	146	16	no	—
1277	C₂×C₄	—	146	8	no	—
1278	C₂×C₄	—	146	16	no	—
1279	C₂×C₄	—	146	2	no	—
1280	C₂×C₄	—	146	2	no	—
1281	C₂×C₄	—	146	4	no	—
1282	C₂×C₄	—	146	2	no	—
1283	C₂×C₄	—	146	4	no	—
1284	C₂×C₄	—	146	2	no	—
1285	C₂×C₄	—	146	2	no	—
1286	C₂×C₄	—	146	8	no	—
1287	C₂×C₄	—	146	8	no	—
1288	C₂×C₄	#41×D₇₃	1	4	yes	—
1289	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
1290	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
1291	C₂×C₄	C₂⁴×D₇₃	1	4	yes	—
1292	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
1293	C₂×C₄	C₂⁴×D₇₃	1	4	yes	—
1294	C₂×C₄	C₂⁴×D₇₃	1	4	yes	—
1295	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
1296	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
1297	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
1298	C₂²	—	2	2	no	—
1299	C₂²	—	2	4	no	—
1300	C₂²	—	2	4	no	—
1301	C₂²	—	2	2	no	—
1302	C₂²	—	2	4	no	—
1303	C₂²	—	2	2	no	—
1304	C₂²	—	4	4	no	—
1305	C₂²	—	4	8	no	—
1306	C₂²	—	292	4	no	—
1307	C₂²	—	292	8	no	—
1308	C₂²	—	292	4	no	—
1309	C₂²	—	584	16	no	—
1310	C₂²	—	584	16	no	—
1311	C₂²	—	73	8	no	—
1312	C₂²	—	146	2	no	—
1313	C₂²	—	146	2	no	—
1314	C₂²	—	146	4	no	—
1315	C₂²	—	146	4	no	—
1316	C₂²	—	146	2	no	—
1317	C₂²	—	146	2	no	—
1318	C₂²	—	146	2	no	—
1319	C₂²	—	146	4	no	—
1320	C₂²	—	146	2	no	—
1321	C₂²	—	146	16	no	—
1322	C₂²	—	146	4	no	—
1323	C₂²	—	146	4	no	—
1324	C₂²	C₂×#41×D₇₃	1	2	yes	—
1325	C₂²	H(5,𝔽₂)×D₇₃	1	2	yes	—
1326	C₂²	#17989424	1	2	yes	—
1327	C₂²	C₂⁵×D₇₃	1	1	yes	characteristic
1328	C₄	—	2	2	no	—
1329	C₄	—	2	4	no	—
1330	C₄	—	2	2	no	—
1331	C₄	—	2	4	no	—
1332	C₄	—	2	2	no	—
1333	C₄	—	2	4	no	—
1334	C₄	—	2	2	no	—
1335	C₄	—	2	2	no	—
1336	C₄	—	73	4	no	—
1337	C₄	—	146	2	no	—
1338	C₄	—	146	2	no	—
1339	C₄	—	146	4	no	—
1340	C₄	—	146	2	no	—
1341	C₄	—	146	4	no	—
1342	C₄	—	146	2	no	—
1343	C₄	—	146	2	no	—
1344	C₄	C₂×#41×D₇₃	1	4	yes	—
1345	C₂	—	4	2	no	—
1346	C₂	—	4	4	no	—
1347	C₂	—	292	2	no	—
1348	C₂	—	292	4	no	—
1349	C₂	—	292	2	no	—
1350	C₂	—	146	8	no	—
1351	C₂	#22623890	1	4	yes	direct product factor
1352	C₂	C₂²×#41×D₇₃	1	1	yes	characteristic
1353	C₂	C₂×H(5,𝔽₂)×D₇₃	1	1	yes	characteristic
1354	C₂	C₂×#17989424	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₇₃
commutator, cosocle	C₂²×C₇₃	C₂⁶
Frattini	C₂²	C₂⁵×D₇₃
Fitting	C₂×#542×C₇₃	C₂
socle	C₂³×C₇₃	C₂⁵
hypercenter	C₂×#542	D₇₃
hypocenter	C₇₃	C₂×#3514
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×#542

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #22623890	C₂	direct (N × H)
2. C₂×#17989319	C₂	semidirect
3. C₂×#17989308	C₂	semidirect
4. C₂×#17989303	C₂	semidirect
5. C₂×#17989301	C₂	semidirect
6. C₂×#17989265	C₂	semidirect
7. C₂×#17989264	C₂	semidirect
8. C₂×#17989252	C₂	semidirect
9. C₂×#17989247	C₂	semidirect
10. C₂×#17989230	C₂	semidirect
11. C₂×#17989229	C₂	semidirect
12. C₂×#17989228	C₂	semidirect
13. C₂×#17989221	C₂	semidirect
14. C₂×#17989209	C₂	semidirect
15. C₂×#17989176	C₂	semidirect
16. C₂×#17989171	C₂	semidirect
17. C₂×#17989134	C₂	semidirect
18. C₂×#17989120	C₂	semidirect
19. C₂×#17989115	C₂	semidirect
20. C₂×#124×D₇₃	C₂	semidirect
21. C₂×#17989061	C₂	semidirect
22. C₂×#17989059	C₂	semidirect
23. C₂×C₄×#11924029	C₂	semidirect
24. C₂×#542×C₇₃	C₂	semidirect
26. C₂²×#11924028	C₂²	semidirect
27. C₂²×Q₈×D₇₃	C₂²	semidirect
31. #17989319	C₂²	semidirect
32. #17989308	C₂²	semidirect
33. #17989303	C₂²	semidirect
34. #17989301	C₂²	semidirect
35. #17989265	C₂²	semidirect
36. #17989264	C₂²	semidirect
37. #17989252	C₂²	semidirect
38. #17989247	C₂²	semidirect
39. #17989230	C₂²	semidirect
40. #17989229	C₂²	semidirect
41. #17989228	C₂²	semidirect
42. #17989221	C₂²	semidirect
43. #17989209	C₂²	semidirect
44. #17989176	C₂²	semidirect
45. #17989171	C₂²	semidirect
46. #17989134	C₂²	semidirect
47. C₂×#14556590	C₂²	semidirect
48. C₂×#14556590	C₂²	semidirect
50. #17989120	C₂²	semidirect
51. #17989115	C₂²	semidirect
52. C₂×#14556586	C₂²	semidirect
53. C₂×#14556586	C₂²	semidirect
54. C₂×#14556585	C₂²	semidirect
55. C₂×#14556584	C₂²	semidirect
56. C₂×#14556584	C₂²	semidirect
57. C₂×#14556581	C₂²	semidirect
58. C₂×#14556580	C₂²	semidirect
59. C₂×#14556580	C₂²	semidirect
60. C₂×#14556580	C₂²	semidirect
61. C₂×#14556579	C₂²	semidirect
62. C₂×#14556578	C₂²	semidirect
65. C₂×#14556577	C₂²	semidirect
66. C₂×#14556577	C₂²	semidirect
67. C₂×#14556577	C₂²	semidirect
68. #124×D₇₃	C₂²	semidirect
69. C₂×#14556576	C₂²	semidirect
70. C₂×#14556576	C₂²	semidirect
71. C₂×#14556576	C₂²	semidirect
72. C₂×#14556575	C₂²	semidirect
73. C₂×#14556573	C₂²	semidirect
74. C₂×#14556573	C₂²	semidirect
75. C₂×#14556573	C₂²	semidirect
76. C₂×#14556569	C₂²	semidirect
77. C₂×#14556569	C₂²	semidirect
78. C₂×#14556569	C₂²	semidirect
79. C₂×#14556569	C₂²	semidirect
80. C₂×#14556567	C₂²	semidirect
81. C₂×#14556567	C₂²	semidirect
83. C₂×#14556566	C₂²	semidirect
84. C₂×#14556566	C₂²	semidirect
85. C₂×#14556566	C₂²	semidirect
88. C₂×#14556564	C₂²	semidirect
89. C₂×#14556564	C₂²	semidirect
90. C₂×#14556563	C₂²	semidirect
91. C₂×#14556562	C₂²	semidirect
93. C₂×#14556561	C₂²	semidirect
94. C₂×#14556561	C₂²	semidirect
96. #17989061	C₂²	semidirect
97. #17989059	C₂²	semidirect
98. C₄×#11924029	C₂²	semidirect
99. C₂×Q₈×Dic₇₃	C₂²	semidirect
100. C₂×C₄×Dic₁₄₆	C₂²	semidirect
101. C₂×#14556556	C₂²	semidirect
104. C₂×C₄×D₂₉₂	C₂²	semidirect
105. C₂×C₄×D₂₉₂	C₂²	semidirect
106. C₂×C₄×D₂₉₂	C₂²	semidirect
107. C₂×C₄×D₂₉₂	C₂²	semidirect
108. C₂×D₄×Dic₇₃	C₂²	semidirect
111. C₂×#14556553	C₂²	semidirect
112. C₂×#14556553	C₂²	semidirect
113. C₂×#14556553	C₂²	semidirect
115. C₂×C₄×C₂²⋊D₇₃	C₂²	semidirect
116. C₂×C₄×C₂²⋊D₇₃	C₂²	semidirect
117. C₂×C₄×C₂²⋊D₇₃	C₂²	semidirect
118. C₂×#14556551	C₂²	semidirect
119. C₂×#14556551	C₂²	semidirect
120. C₂×#14556550	C₂²	semidirect
121. C₂×#14556549	C₂²	semidirect
122. C₂×#14556549	C₂²	semidirect
123. C₂×#14556549	C₂²	semidirect
124. C₂×#14556549	C₂²	semidirect
125. C₂×#14556548	C₂²	semidirect
126. C₂×#14556547	C₂²	semidirect
127. C₂²×#11924005	C₂²	semidirect
128. C₂×C₂²⋊C₄×D₇₃	C₂²	semidirect
129. C₂×C₂²⋊C₄×D₇₃	C₂²	semidirect
130. C₂×C₂²⋊C₄×D₇₃	C₂²	semidirect
131. C₂×C₂²⋊C₄×D₇₃	C₂²	semidirect
132. C₂×C₂²⋊C₄×D₇₃	C₂²	semidirect
133. C₂×C₄²×D₇₃	C₂²	semidirect
134. C₂×C₄²×D₇₃	C₂²	semidirect
135. #542×C₇₃	C₂²	semidirect
136. C₂×C₄⋊Q₈×C₇₃	C₂²	semidirect
137. C₂×#126×C₇₃	C₂²	semidirect
138. C₂×#124×C₇₃	C₂²	semidirect
139. C₂×#124×C₇₃	C₂²	semidirect
140. C₂×#123×C₇₃	C₂²	semidirect
141. C₂×C₂²⋊Q₈×C₇₃	C₂²	semidirect
142. C₂×C₂²⋊Q₈×C₇₃	C₂²	semidirect
144. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
145. C₂×C₄×D₄×C₇₃	C₂²	semidirect
146. C₂×#117×C₇₃	C₂²	semidirect
152. C₂×#11924028	C₂³	semidirect
157. C₂×Q₈×D₇₃	C₂³	semidirect
189. #14556590	C₂³	semidirect
190. #14556590	C₂³	semidirect
192. #14556586	C₂³	semidirect
193. #14556586	C₂³	semidirect
194. #14556585	C₂³	semidirect
195. #14556584	C₂³	semidirect
196. #14556584	C₂³	semidirect
197. #14556581	C₂³	semidirect
198. #14556580	C₂³	semidirect
199. #14556580	C₂³	semidirect
200. #14556580	C₂³	semidirect
201. #14556579	C₂³	semidirect
202. #14556578	C₂³	semidirect
205. #14556577	C₂³	semidirect
206. #14556577	C₂³	semidirect
207. #14556577	C₂³	semidirect
208. #14556576	C₂³	semidirect
209. #14556576	C₂³	semidirect
210. #14556576	C₂³	semidirect
211. #14556575	C₂³	semidirect
212. #14556573	C₂³	semidirect
213. #14556573	C₂³	semidirect
214. #14556573	C₂³	semidirect
215. #14556569	C₂³	semidirect
216. #14556569	C₂³	semidirect
217. #14556569	C₂³	semidirect
218. #14556569	C₂³	semidirect
219. #14556567	C₂³	semidirect
220. #14556567	C₂³	semidirect
222. #14556566	C₂³	semidirect
223. #14556566	C₂³	semidirect
224. #14556566	C₂³	semidirect
227. #14556564	C₂³	semidirect
228. #14556564	C₂³	semidirect
229. #14556563	C₂³	semidirect
230. #14556562	C₂³	semidirect
232. #14556561	C₂³	semidirect
233. #14556561	C₂³	semidirect
235. Q₈×Dic₇₃	C₂³	semidirect
236. C₄×Dic₁₄₆	C₂³	semidirect
237. #14556556	C₂³	semidirect
240. C₄×D₂₉₂	C₂³	semidirect
241. C₄×D₂₉₂	C₂³	semidirect
242. C₄×D₂₉₂	C₂³	semidirect
243. C₄×D₂₉₂	C₂³	semidirect
244. D₄×Dic₇₃	C₂³	semidirect
247. #14556553	C₂³	semidirect
248. #14556553	C₂³	semidirect
249. #14556553	C₂³	semidirect
251. C₄×C₂²⋊D₇₃	C₂³	semidirect
252. C₄×C₂²⋊D₇₃	C₂³	semidirect
253. C₄×C₂²⋊D₇₃	C₂³	semidirect
254. #14556551	C₂³	semidirect
255. #14556551	C₂³	semidirect
256. #14556550	C₂³	semidirect
257. #14556549	C₂³	semidirect
258. #14556549	C₂³	semidirect
259. #14556549	C₂³	semidirect
260. #14556549	C₂³	semidirect
261. #14556548	C₂³	semidirect
262. #14556547	C₂³	semidirect
301. C₂×#11924005	C₂³	semidirect
302. C₂²⋊C₄×D₇₃	C₂³	semidirect
303. C₂²⋊C₄×D₇₃	C₂³	semidirect
304. C₂²⋊C₄×D₇₃	C₂³	semidirect
305. C₂²⋊C₄×D₇₃	C₂³	semidirect
306. C₂²⋊C₄×D₇₃	C₂³	semidirect
315. C₄²×D₇₃	C₂³	semidirect
316. C₄²×D₇₃	C₂³	semidirect
323. C₄⋊Q₈×C₇₃	C₂³	semidirect
324. #126×C₇₃	C₂³	semidirect
325. #124×C₇₃	C₂³	semidirect
326. #124×C₇₃	C₂³	semidirect
327. #123×C₇₃	C₂³	semidirect
328. C₂²⋊Q₈×C₇₃	C₂³	semidirect
329. C₂²⋊Q₈×C₇₃	C₂³	semidirect
331. C₄×Q₈×C₇₃	C₂³	semidirect
332. C₄×D₄×C₇₃	C₂³	semidirect
333. #117×C₇₃	C₂³	semidirect
379. C₂×D₂₉₂	#41	semidirect
605. D₂₉₂	C₂×#41	semidirect
670. C₂×C₇₃	#3514	semidirect
692. C₂×#542	D₇₃	semidirect
702. C₇₃	C₂×#3514	semidirect
722. #542	C₂×D₇₃	semidirect
728. C₂×C₄⋊Q₈	C₂×D₇₃	semidirect
737. C₂×#126	C₂×D₇₃	semidirect
750. C₂×#124	C₂×D₇₃	semidirect
751. C₂×#124	C₂×D₇₃	semidirect
759. C₂×#123	C₂×D₇₃	semidirect
766. C₂×C₂²⋊Q₈	C₂×D₇₃	semidirect
767. C₂×C₂²⋊Q₈	C₂×D₇₃	semidirect
789. C₂×C₄×Q₈	C₂×D₇₃	semidirect
808. C₂×C₄×D₄	C₂×D₇₃	semidirect
816. C₂×#117	C₂×D₇₃	semidirect
875. C₄⋊Q₈	C₂²×D₇₃	semidirect
882. #126	C₂²×D₇₃	semidirect
894. #124	C₂²×D₇₃	semidirect
895. #124	C₂²×D₇₃	semidirect
903. #123	C₂²×D₇₃	semidirect
910. C₂²⋊Q₈	C₂²×D₇₃	semidirect
911. C₂²⋊Q₈	C₂²×D₇₃	semidirect
930. C₄×Q₈	C₂²×D₇₃	semidirect
949. C₄×D₄	C₂²×D₇₃	semidirect
957. #117	C₂²×D₇₃	semidirect
1351. C₂	#22623890	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#22623890	2
C₂×#17989319	2
C₂×#17989308	2
C₂×#17989303	2
C₂×#17989301	2
C₂×#17989265	2
C₂×#17989264	2
C₂×#17989252	2
C₂×#17989247	2
C₂×#17989230	2
C₂×#17989229	2
C₂×#17989228	2
C₂×#17989221	2
C₂×#17989209	2
C₂×#17989176	2
C₂×#17989171	2
C₂×#17989134	2
C₂×#17989120	2
C₂×#17989115	2
C₂×#124×D₇₃	2
C₂×#17989061	2
C₂×#17989059	2
C₂×C₄×#11924029	2
C₂×#542×C₇₃	2
C₂×#3514	73

Subgroups — C2×#22623890 #33994078

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22623890 #33994078