Subgroups — C₂×#22623800 #33994337

Order 18688.

8622 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623800	C₂	1	32	yes	maximal, direct product factor
2	C₂×#17989320	C₂	1	2	yes	maximal, complemented
3	C₂×#17989319	C₂	1	2	yes	maximal, complemented
4	C₂×#17989256	C₂	1	2	yes	maximal, complemented
5	C₂×#17989255	C₂	1	2	yes	maximal, complemented
6	C₂×#17989234	C₂	1	2	yes	maximal, complemented
7	C₂×#17989232	C₂	1	2	yes	maximal, complemented
8	C₂×#17989230	C₂	1	2	yes	maximal, complemented
9	C₂×#17989225	C₂	1	2	yes	maximal, complemented
10	C₂×#17989190	C₂	1	2	yes	maximal, complemented
11	C₂×#17989188	C₂	1	2	yes	maximal, complemented
12	C₂×#17989153	C₂	1	2	yes	maximal, complemented
13	C₂×#17989142	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#17989138	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#17989137	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#17989135	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#127×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#17989059	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×#11924028	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#532×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂²×#11924029	C₂²	1	2	yes	complemented
22	C₂²×#11924028	C₂²	1	1	yes	characteristic
23	C₂²×#11924028	C₂²	1	2	yes	complemented
24	C₂²×#11924027	C₂²	1	2	yes	complemented
25	C₂²×D₄×D₇₃	C₂²	1	2	yes	—
26	C₂²×D₄×D₇₃	C₂²	1	2	yes	—
27	C₂²×D₄×D₇₃	C₂²	1	2	yes	—
28	#17989320	C₂²	1	32	yes	complemented
29	#17989319	C₂²	1	32	yes	complemented
30	#17989256	C₂²	1	32	yes	complemented
31	#17989255	C₂²	1	32	yes	complemented
32	#17989234	C₂²	1	32	yes	complemented
33	#17989232	C₂²	1	32	yes	complemented
34	#17989230	C₂²	1	32	yes	complemented
35	#17989225	C₂²	1	32	yes	complemented
36	#17989190	C₂²	1	32	yes	complemented
37	#17989188	C₂²	1	32	yes	complemented
38	#17989153	C₂²	1	32	yes	complemented
39	#17989142	C₂²	1	16	yes	complemented
40	#17989138	C₂²	1	16	yes	complemented
41	#17989137	C₂²	1	16	yes	complemented
42	#17989135	C₂²	1	16	yes	complemented
43	C₂×#14556591	C₂²	1	1	yes	characteristic, complemented
44	C₂×#14556588	C₂²	1	1	yes	characteristic
45	C₂×#14556587	C₂²	1	2	yes	—
46	C₂×#14556587	C₂²	1	2	yes	—
47	C₂×#14556587	C₂²	1	2	yes	—
48	C₂×#14556587	C₂²	1	4	yes	complemented
49	#127×D₇₃	C₂²	1	16	yes	complemented
50	C₂×#14556582	C₂²	1	2	yes	complemented
51	C₂×#14556580	C₂²	1	2	yes	complemented
52	C₂×#14556579	C₂²	1	2	yes	complemented
53	C₂×#14556578	C₂²	1	2	yes	complemented
54	C₂×#14556577	C₂²	1	4	yes	complemented
55	C₂×#14556575	C₂²	1	4	yes	complemented
56	C₂×#14556574	C₂²	1	4	yes	complemented
57	C₂×#14556573	C₂²	1	4	yes	complemented
58	C₂×#14556573	C₂²	1	4	yes	complemented
59	C₂×#14556571	C₂²	1	2	yes	—
60	C₂×#14556567	C₂²	1	2	yes	—
61	C₂×#14556566	C₂²	1	2	yes	complemented
62	C₂×#14556566	C₂²	1	2	yes	complemented
63	C₂×#14556565	C₂²	1	2	yes	complemented
64	C₂×#14556565	C₂²	1	4	yes	complemented
65	C₂×#14556565	C₂²	1	2	yes	complemented
66	C₂×#14556564	C₂²	1	4	yes	complemented
67	C₂×#14556563	C₂²	1	4	yes	complemented
68	C₂×#14556562	C₂²	1	2	yes	complemented
69	C₂×#14556562	C₂²	1	4	yes	complemented
70	C₂×#14556562	C₂²	1	2	yes	complemented
71	C₂×#14556561	C₂²	1	4	yes	—
72	C₂×#14556559	C₂²	1	4	yes	—
73	#17989059	C₂²	1	32	yes	complemented
74	C₄×#11924028	C₂²	1	16	yes	complemented
75	C₂×Q₈×Dic₇₃	C₂²	1	2	yes	complemented
76	C₂×C₄×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
77	C₂×C₄×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
78	C₂×#14556556	C₂²	1	2	yes	complemented
79	C₂×C₄×D₂₉₂	C₂²	1	1	yes	characteristic
80	C₂×C₄×D₂₉₂	C₂²	1	1	yes	characteristic
81	C₂×C₄×D₂₉₂	C₂²	1	2	yes	complemented
82	C₂×C₄×D₂₉₂	C₂²	1	2	yes	complemented
83	C₂×D₄×Dic₇₃	C₂²	1	2	yes	complemented
84	C₂×D₄×Dic₇₃	C₂²	1	2	yes	complemented
85	C₂×#14556553	C₂²	1	2	yes	complemented
86	C₂×#14556553	C₂²	1	2	yes	complemented
87	C₂×C₄×C₂²⋊D₇₃	C₂²	1	1	yes	characteristic
88	C₂×C₄×C₂²⋊D₇₃	C₂²	1	1	yes	characteristic
89	C₂×C₄×C₂²⋊D₇₃	C₂²	1	4	yes	complemented
90	C₂×C₄×C₂²⋊D₇₃	C₂²	1	1	yes	characteristic, complemented
91	C₂×C₄×C₂²⋊D₇₃	C₂²	1	1	yes	characteristic, complemented
92	C₂×#14556551	C₂²	1	4	yes	complemented
93	C₂×#14556550	C₂²	1	1	yes	characteristic, complemented
94	C₂×#14556549	C₂²	1	2	yes	—
95	C₂×#14556548	C₂²	1	1	yes	characteristic
96	C₂×#14556548	C₂²	1	1	yes	characteristic, complemented
97	C₂²×#11924005	C₂²	1	4	yes	—
98	C₂×C₂²⋊C₄×D₇₃	C₂²	1	4	yes	—
99	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
100	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic, complemented
101	C₂²×#41×C₇₃	C₂²	1	2	yes	complemented
102	#532×C₇₃	C₂²	1	16	yes	complemented
103	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
104	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
105	C₂×#124×C₇₃	C₂²	1	2	yes	complemented
106	C₂×#121×C₇₃	C₂²	1	2	yes	complemented
107	C₂×#121×C₇₃	C₂²	1	2	yes	complemented
108	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	complemented
109	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	complemented
110	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic, complemented
111	C₂⁴×D₇₃	C₂³	1	4	yes	—
112	C₂×#11924029	—	4	8	no	—
113	C₂×#11924029	C₂³	1	16	yes	complemented
114	C₂×#11924028	—	2	8	no	—
115	C₂×#11924028	—	4	8	no	—
116	C₂×#11924028	C₂³	1	8	yes	—
117	C₂×#11924028	C₂³	1	16	yes	complemented
118	C₂×#11924027	—	4	8	no	—
119	C₂×#11924027	C₂³	1	16	yes	complemented
120	C₂²×Dic₁₄₆	C₂³	1	2	yes	—
121	C₂²×Dic₁₄₆	C₂³	1	1	yes	characteristic
122	C₂²×D₂₉₂	C₂³	1	2	yes	—
123	C₂²×D₂₉₂	C₂³	1	2	yes	—
124	C₂²×D₂₉₂	C₂³	1	2	yes	—
125	C₂²×D₂₉₂	C₂³	1	1	yes	characteristic
126	C₂²×D₂₉₂	C₂³	1	4	yes	—
127	C₂²×C₂²⋊D₇₃	C₂³	1	4	yes	—
128	C₂²×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
129	C₂²×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
130	C₂²×C₂²⋊D₇₃	C₂³	1	4	yes	—
131	C₂²×C₂²⋊D₇₃	C₂³	1	4	yes	—
132	C₂²×C₂²⋊D₇₃	C₂³	1	4	yes	—
133	C₂²×C₂²⋊D₇₃	C₂³	1	4	yes	—
134	C₂×D₄×D₇₃	—	2	16	no	—
135	C₂×D₄×D₇₃	—	4	8	no	—
136	C₂×D₄×D₇₃	—	4	8	no	—
137	C₂×D₄×D₇₃	C₂³	1	16	yes	—
138	C₂×D₄×D₇₃	C₂³	1	16	yes	—
139	C₂×D₄×D₇₃	C₂³	1	16	yes	—
140	C₂³×Dic₇₃	C₂³	1	4	yes	—
141	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
142	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
143	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
144	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
145	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
146	C₂²×C₄×D₇₃	C₂³	1	4	yes	—
147	C₂²×C₄×D₇₃	C₂³	1	4	yes	—
148	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
149	#14556591	C₂³	1	8	yes	complemented
150	#14556588	C₂³	1	8	yes	—
151	#14556587	C₂³	1	16	yes	—
152	#14556587	C₂³	1	16	yes	—
153	#14556587	C₂³	1	16	yes	—
154	#14556587	C₂³	1	32	yes	complemented
155	#14556582	C₂³	1	16	yes	complemented
156	#14556580	C₂³	1	16	yes	complemented
157	#14556579	C₂³	1	16	yes	complemented
158	#14556578	C₂³	1	16	yes	complemented
159	#14556577	C₂³	1	32	yes	complemented
160	#14556575	C₂³	1	32	yes	complemented
161	#14556574	C₂³	1	32	yes	complemented
162	#14556573	C₂³	1	32	yes	complemented
163	#14556573	C₂³	1	32	yes	complemented
164	#14556571	C₂³	1	16	yes	—
165	#14556567	C₂³	1	16	yes	—
166	#14556566	C₂³	1	16	yes	complemented
167	#14556566	C₂³	1	16	yes	complemented
168	#14556565	C₂³	1	16	yes	complemented
169	#14556565	C₂³	1	16	yes	complemented
170	#14556565	C₂³	1	32	yes	complemented
171	#14556564	C₂³	1	32	yes	complemented
172	#14556563	C₂³	1	32	yes	complemented
173	#14556562	C₂³	1	16	yes	complemented
174	#14556562	C₂³	1	16	yes	complemented
175	#14556562	C₂³	1	32	yes	complemented
176	#14556561	C₂³	1	32	yes	—
177	#14556559	C₂³	1	32	yes	—
178	Q₈×Dic₇₃	C₂³	1	16	yes	complemented
179	C₄×Dic₁₄₆	C₂³	1	8	yes	complemented
180	C₄×Dic₁₄₆	C₂³	1	8	yes	complemented
181	#14556556	C₂³	1	16	yes	complemented
182	C₄×D₂₉₂	C₂³	1	8	yes	—
183	C₄×D₂₉₂	C₂³	1	8	yes	—
184	C₄×D₂₉₂	C₂³	1	16	yes	complemented
185	C₄×D₂₉₂	C₂³	1	16	yes	complemented
186	D₄×Dic₇₃	C₂³	1	16	yes	complemented
187	D₄×Dic₇₃	C₂³	1	16	yes	complemented
188	#14556553	C₂³	1	16	yes	complemented
189	#14556553	C₂³	1	16	yes	complemented
190	C₄×C₂²⋊D₇₃	C₂³	1	8	yes	—
191	C₄×C₂²⋊D₇₃	C₂³	1	8	yes	—
192	C₄×C₂²⋊D₇₃	C₂³	1	8	yes	complemented
193	C₄×C₂²⋊D₇₃	C₂³	1	8	yes	complemented
194	C₄×C₂²⋊D₇₃	C₂³	1	32	yes	complemented
195	#14556551	C₂³	1	32	yes	complemented
196	#14556550	C₂³	1	8	yes	complemented
197	#14556549	C₂³	1	16	yes	—
198	#14556548	C₂³	1	8	yes	—
199	#14556548	C₂³	1	8	yes	complemented
200	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
201	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
202	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
204	C₂×C₄⋊Dic₇₃	C₂³	1	4	yes	—
205	C₂×#11924007	C₂³	1	1	yes	characteristic
206	C₂×#11924007	C₂³	1	1	yes	characteristic
207	C₂×#11924007	C₂³	1	1	yes	characteristic
208	C₂×#11924007	C₂³	1	1	yes	characteristic
209	C₂×#11924007	C₂³	1	4	yes	—
210	C₂×C₂²⋊Dic₇₃	C₂³	1	4	yes	—
211	C₂×C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊Dic₇₃	C₂³	1	4	yes	—
214	C₂×#11924005	C₂³	1	32	yes	—
215	C₂×#11924005	C₂³	1	1	yes	characteristic
216	C₂×#11924005	C₂³	1	4	yes	—
217	C₂×#11924005	C₂³	1	1	yes	characteristic
218	C₂×#11924005	C₂³	1	4	yes	—
219	C₂×#11924005	C₂³	1	4	yes	—
220	C₂×#11924005	C₂³	1	1	yes	characteristic
221	C₂×#11924005	C₂³	1	1	yes	characteristic
222	C₂×#11924005	C₂³	1	4	yes	—
223	C₂×#11924005	C₂³	1	4	yes	—
224	C₂²⋊C₄×D₇₃	C₂³	1	32	yes	—
225	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
226	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
227	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
228	C₂×C₄×Dic₇₃	C₂³	1	4	yes	—
229	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
230	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
231	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
232	C₄²×D₇₃	C₂³	1	8	yes	—
233	C₄²×D₇₃	C₂³	1	8	yes	complemented
234	C₂×#41×C₇₃	—	4	8	no	—
235	C₂×#41×C₇₃	C₂³	1	16	yes	complemented
236	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
237	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
238	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
239	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
240	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
241	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
242	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
243	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
244	C₂³×C₄×C₇₃	C₂³	1	4	yes	—
245	C₄⋊Q₈×C₇₃	C₂³	1	8	yes	complemented
246	#127×C₇₃	C₂³	1	8	yes	—
247	#124×C₇₃	C₂³	1	16	yes	complemented
248	#121×C₇₃	C₂³	1	16	yes	complemented
249	#121×C₇₃	C₂³	1	16	yes	complemented
250	C₄×D₄×C₇₃	C₂³	1	16	yes	complemented
251	C₄×D₄×C₇₃	C₂³	1	16	yes	complemented
252	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
253	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
254	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
255	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
256	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
257	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
258	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
259	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
260	C₂×C₄²×C₇₃	C₂³	1	8	yes	complemented
261	C₂³×D₇₃	—	2	16	no	—
262	C₂³×D₇₃	—	4	8	no	—
263	C₂³×D₇₃	—	4	8	no	—
264	C₂³×D₇₃	C₂⁴	1	4	yes	—
265	C₂³×D₇₃	C₂⁴	1	1	yes	characteristic
266	C₂³×D₇₃	C₂⁴	1	1	yes	characteristic
267	C₂³×D₇₃	C₂⁴	1	16	yes	—
268	#11924029	—	4	32	no	—
269	#11924028	—	2	32	no	—
270	#11924028	—	4	32	no	—
271	#11924027	—	4	32	no	—
272	C₂×Dic₁₄₆	—	2	8	no	—
273	C₂×Dic₁₄₆	—	2	4	no	—
274	C₂×Dic₁₄₆	C₂⁴	1	8	yes	—
275	C₂×Dic₁₄₆	C₂⁴	1	4	yes	—
276	C₂×D₂₉₂	—	2	4	no	—
277	C₂×D₂₉₂	—	2	8	no	—
278	C₂×D₂₉₂	—	2	8	no	—
279	C₂×D₂₉₂	—	2	8	no	—
280	C₂×D₂₉₂	—	4	8	no	—
281	C₂×D₂₉₂	C₂⁴	1	8	yes	—
282	C₂×D₂₉₂	C₂⁴	1	8	yes	—
283	C₂×D₂₉₂	C₂⁴	1	4	yes	—
284	C₂×D₂₉₂	C₂⁴	1	8	yes	—
285	C₂×D₂₉₂	C₂⁴	1	16	yes	—
286	C₂×C₂²⋊D₇₃	—	2	4	no	—
287	C₂×C₂²⋊D₇₃	—	2	16	no	—
288	C₂×C₂²⋊D₇₃	—	2	4	no	—
289	C₂×C₂²⋊D₇₃	—	4	8	no	—
290	C₂×C₂²⋊D₇₃	—	4	8	no	—
291	C₂×C₂²⋊D₇₃	—	4	8	no	—
292	C₂×C₂²⋊D₇₃	—	4	8	no	—
293	C₂×C₂²⋊D₇₃	C₂⁴	1	16	yes	—
294	C₂×C₂²⋊D₇₃	C₂⁴	1	4	yes	—
295	C₂×C₂²⋊D₇₃	C₂⁴	1	4	yes	—
296	C₂×C₂²⋊D₇₃	C₂⁴	1	16	yes	—
297	C₂×C₂²⋊D₇₃	C₂⁴	1	16	yes	—
298	C₂×C₂²⋊D₇₃	C₂⁴	1	16	yes	—
299	C₂×C₂²⋊D₇₃	C₂⁴	1	16	yes	—
300	D₄×D₇₃	—	2	64	no	—
301	D₄×D₇₃	—	4	32	no	—
302	D₄×D₇₃	—	4	32	no	—
303	C₂²×Dic₇₃	—	4	8	no	—
304	C₂²×Dic₇₃	C₂⁴	1	1	yes	characteristic
305	C₂²×Dic₇₃	C₂⁴	1	1	yes	characteristic
306	C₂²×Dic₇₃	C₂⁴	1	1	yes	characteristic
307	C₂²×Dic₇₃	C₂⁴	1	1	yes	characteristic
308	C₂²×Dic₇₃	C₂⁴	1	1	yes	characteristic
309	C₂²×Dic₇₃	C₂⁴	1	4	yes	—
310	C₂²×Dic₇₃	C₂⁴	1	16	yes	—
311	C₂²×Dic₇₃	C₂⁴	1	1	yes	characteristic
312	C₂×C₄×D₇₃	—	2	4	no	—
313	C₂×C₄×D₇₃	—	2	4	no	—
314	C₂×C₄×D₇₃	—	2	4	no	—
315	C₂×C₄×D₇₃	—	2	4	no	—
316	C₂×C₄×D₇₃	—	2	4	no	—
317	C₂×C₄×D₇₃	—	4	8	no	—
318	C₂×C₄×D₇₃	—	4	8	no	—
319	C₂×C₄×D₇₃	#41	1	8	yes	complemented
320	C₂×C₄×D₇₃	C₂⁴	1	4	yes	—
321	C₂×C₄×D₇₃	C₂⁴	1	4	yes	—
322	C₂×C₄×D₇₃	C₂⁴	1	4	yes	—
323	C₂×C₄×D₇₃	C₂⁴	1	4	yes	—
324	C₂×C₄×D₇₃	C₂⁴	1	4	yes	—
325	C₂×C₄×D₇₃	C₂⁴	1	16	yes	—
326	C₂×C₄×D₇₃	C₂⁴	1	16	yes	—
327	C₂×C₄×D₇₃	C₂⁴	1	4	yes	—
328	C₄⋊Dic₇₃	C₂⁴	1	8	yes	—
329	C₄⋊Dic₇₃	C₂⁴	1	4	yes	—
330	C₄⋊Dic₇₃	C₂⁴	1	4	yes	—
331	C₄⋊Dic₇₃	C₂⁴	1	8	yes	—
332	C₄⋊Dic₇₃	C₂⁴	1	16	yes	—
333	#11924007	C₂⁴	1	4	yes	—
334	#11924007	C₂⁴	1	4	yes	—
335	#11924007	C₂⁴	1	4	yes	—
336	#11924007	C₂⁴	1	4	yes	—
337	#11924007	C₂⁴	1	16	yes	—
338	C₂²⋊Dic₇₃	C₂⁴	1	16	yes	—
339	C₂²⋊Dic₇₃	C₂⁴	1	4	yes	—
340	C₂²⋊Dic₇₃	C₂⁴	1	4	yes	—
341	C₂²⋊Dic₇₃	C₂⁴	1	16	yes	—
342	#11924005	C₂⁴	1	4	yes	—
343	#11924005	C₂⁴	1	16	yes	—
344	#11924005	C₂⁴	1	4	yes	—
345	#11924005	C₂⁴	1	16	yes	—
346	#11924005	C₂⁴	1	16	yes	—
347	#11924005	C₂⁴	1	4	yes	—
348	#11924005	C₂⁴	1	4	yes	—
349	#11924005	C₂⁴	1	16	yes	—
350	#11924005	C₂⁴	1	16	yes	—
351	C₄×Dic₇₃	C₂⁴	1	4	yes	—
352	C₄×Dic₇₃	C₂⁴	1	4	yes	—
353	C₄×Dic₇₃	C₂⁴	1	4	yes	—
354	C₄×Dic₇₃	C₂⁴	1	4	yes	—
355	C₄×Dic₇₃	C₂⁴	1	4	yes	—
356	C₄×Dic₇₃	C₂⁴	1	4	yes	—
357	C₄×Dic₇₃	C₂⁴	1	16	yes	—
358	C₂⁴×C₇₃	C₂⁴	1	4	yes	—
359	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
360	#41×C₇₃	—	4	32	no	—
361	C₂×Q₈×C₇₃	—	2	8	no	—
362	C₂×Q₈×C₇₃	C₂⁴	1	8	yes	—
363	C₂×D₄×C₇₃	—	2	8	no	—
364	C₂×D₄×C₇₃	—	2	8	no	—
365	C₂×D₄×C₇₃	—	2	8	no	—
366	C₂×D₄×C₇₃	—	4	8	no	—
367	C₂×D₄×C₇₃	C₂⁴	1	8	yes	—
368	C₂×D₄×C₇₃	C₂⁴	1	8	yes	—
369	C₂×D₄×C₇₃	C₂⁴	1	8	yes	—
370	C₂×D₄×C₇₃	C₂⁴	1	16	yes	—
371	C₂²×C₄×C₇₃	—	2	4	no	—
372	C₂²×C₄×C₇₃	—	2	4	no	—
373	C₂²×C₄×C₇₃	—	2	4	no	—
374	C₂²×C₄×C₇₃	—	4	8	no	—
375	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
378	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
379	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
380	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
381	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
382	C₂²×C₄×C₇₃	C₂⁴	1	16	yes	—
383	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
384	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
386	C₄⋊C₄×C₇₃	C₂⁴	1	8	yes	—
387	C₄⋊C₄×C₇₃	C₂⁴	1	8	yes	—
388	C₂²⋊C₄×C₇₃	C₂⁴	1	16	yes	—
389	C₂²⋊C₄×C₇₃	C₂⁴	1	16	yes	—
390	C₄²×C₇₃	C₂⁴	1	4	yes	—
391	C₄²×C₇₃	C₂⁴	1	4	yes	—
392	C₄²×C₇₃	C₂⁴	1	4	yes	—
393	C₄²×C₇₃	C₂⁴	1	4	yes	—
394	C₂³×C₇₃	—	2	2	no	—
395	C₂³×C₇₃	—	2	8	no	—
396	C₂³×C₇₃	—	2	2	no	—
397	C₂³×C₇₃	—	2	2	no	—
398	C₂³×C₇₃	—	2	8	no	—
399	C₂³×C₇₃	—	2	8	no	—
400	C₂³×C₇₃	C₂⁵	1	8	yes	—
401	C₂³×C₇₃	C₂⁵	1	2	yes	—
402	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
403	C₂²×D₇₃	—	2	2	no	—
404	C₂²×D₇₃	—	2	2	no	—
405	C₂²×D₇₃	—	2	2	no	—
406	C₂²×D₇₃	—	2	8	no	—
407	C₂²×D₇₃	—	2	2	no	—
408	C₂²×D₇₃	—	2	2	no	—
409	C₂²×D₇₃	—	2	8	no	—
410	C₂²×D₇₃	—	2	8	no	—
411	C₂²×D₇₃	—	2	32	no	—
412	C₂²×D₇₃	—	4	16	no	—
413	C₂²×D₇₃	—	4	16	no	—
414	C₂²×D₇₃	—	8	32	no	—
415	C₂²×D₇₃	C₂×#41	1	4	yes	—
416	C₂²×D₇₃	C₂⁵	1	8	yes	—
417	C₂²×D₇₃	C₂⁵	1	2	yes	—
418	C₂²×D₇₃	C₂⁵	1	2	yes	—
419	Q₈×C₇₃	—	2	16	no	—
420	D₄×C₇₃	—	2	16	no	—
421	D₄×C₇₃	—	2	16	no	—
422	D₄×C₇₃	—	2	16	no	—
423	D₄×C₇₃	—	4	16	no	—
424	C₂×C₄×C₇₃	—	2	2	no	—
425	C₂×C₄×C₇₃	—	2	2	no	—
426	C₂×C₄×C₇₃	—	2	2	no	—
427	C₂×C₄×C₇₃	—	2	8	no	—
428	C₂×C₄×C₇₃	—	2	8	no	—
429	C₂×C₄×C₇₃	—	2	8	no	—
430	C₂×C₄×C₇₃	—	2	8	no	—
431	C₂×C₄×C₇₃	—	4	16	no	—
432	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
433	C₂×C₄×C₇₃	H(5,𝔽₂)	1	4	yes	—
434	C₂×C₄×C₇₃	H(5,𝔽₂)	1	4	yes	—
435	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
436	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
437	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
438	C₂×C₄×C₇₃	C₂⁵	1	8	yes	—
439	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
440	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
441	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
442	C₂²⋊D₇₃	—	2	8	no	—
443	C₂²⋊D₇₃	—	2	32	no	—
444	C₂²⋊D₇₃	—	2	8	no	—
445	C₂²⋊D₇₃	—	4	16	no	—
446	C₂²⋊D₇₃	—	4	16	no	—
447	C₂²⋊D₇₃	—	4	16	no	—
448	C₂²⋊D₇₃	—	4	16	no	—
449	C₂×Dic₇₃	—	2	2	no	—
450	C₂×Dic₇₃	—	2	2	no	—
451	C₂×Dic₇₃	—	2	2	no	—
452	C₂×Dic₇₃	—	2	2	no	—
453	C₂×Dic₇₃	—	2	2	no	—
454	C₂×Dic₇₃	—	2	8	no	—
455	C₂×Dic₇₃	—	4	16	no	—
456	C₂×Dic₇₃	C₂×#41	1	4	yes	—
457	C₂×Dic₇₃	C₂⁵	1	2	yes	—
458	C₂×Dic₇₃	C₂⁵	1	2	yes	—
459	C₂×Dic₇₃	C₂⁵	1	2	yes	—
460	C₂×Dic₇₃	C₂⁵	1	2	yes	—
461	C₂×Dic₇₃	C₂⁵	1	2	yes	—
462	C₂×Dic₇₃	C₂⁵	1	8	yes	—
463	C₂×Dic₇₃	C₂⁵	1	2	yes	—
464	D₂₉₂	—	2	8	no	—
465	D₂₉₂	—	2	16	no	—
466	D₂₉₂	—	2	16	no	—
467	D₂₉₂	—	2	16	no	—
468	D₂₉₂	—	4	16	no	—
469	C₄×D₇₃	—	2	8	no	—
470	C₄×D₇₃	—	2	8	no	—
471	C₄×D₇₃	—	2	8	no	—
472	C₄×D₇₃	—	2	8	no	—
473	C₄×D₇₃	—	2	8	no	—
474	C₄×D₇₃	—	4	16	no	—
475	C₄×D₇₃	—	4	16	no	—
476	C₄×D₇₃	C₂×#41	1	16	yes	complemented
477	Dic₁₄₆	—	2	16	no	—
478	Dic₁₄₆	—	2	8	no	—
479	C₂²×C₇₃	—	2	2	no	—
480	C₂²×C₇₃	—	2	8	no	—
481	C₂²×C₇₃	—	2	8	no	—
482	C₂²×C₇₃	—	2	2	no	—
483	C₂²×C₇₃	—	2	8	no	—
484	C₂²×C₇₃	—	2	2	no	—
485	C₂²×C₇₃	—	4	16	no	—
486	C₂²×C₇₃	—	4	4	no	—
487	C₂²×C₇₃	C₂²×#41	1	2	yes	—
488	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	2	yes	—
489	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	2	yes	—
490	C₂²×C₇₃	C₂⁶	1	1	yes	characteristic
491	C₂×D₇₃	—	2	2	no	—
492	C₂×D₇₃	—	2	2	no	—
493	C₂×D₇₃	—	2	8	no	—
494	C₂×D₇₃	—	2	2	no	—
495	C₂×D₇₃	—	2	8	no	—
496	C₂×D₇₃	—	2	2	no	—
497	C₂×D₇₃	—	2	2	no	—
498	C₂×D₇₃	—	2	8	no	—
499	C₂×D₇₃	—	2	8	no	—
500	C₂×D₇₃	—	4	4	no	—
501	C₂×D₇₃	—	4	16	no	—
502	C₂×D₇₃	—	8	32	no	—
503	C₂×D₇₃	C₂²×#41	1	4	yes	—
504	C₄×C₇₃	—	2	2	no	—
505	C₄×C₇₃	—	2	2	no	—
506	C₄×C₇₃	—	2	8	no	—
507	C₄×C₇₃	—	2	2	no	—
508	C₄×C₇₃	C₂²×#41	1	4	yes	—
509	C₄×C₇₃	C₂×H(5,𝔽₂)	1	4	yes	—
510	C₄×C₇₃	C₂×H(5,𝔽₂)	1	4	yes	—
511	Dic₇₃	—	2	2	no	—
512	Dic₇₃	—	2	8	no	—
513	Dic₇₃	—	2	2	no	—
514	Dic₇₃	—	2	2	no	—
515	Dic₇₃	—	2	2	no	—
516	Dic₇₃	—	2	2	no	—
517	Dic₇₃	C₂²×#41	1	4	yes	—
518	C₂×#3508	—	73	1	no	maximal, Sylow
519	C₂×C₇₃	—	4	8	no	—
520	C₂×C₇₃	—	4	2	no	—
521	C₂×C₇₃	#3508	1	4	yes	complemented
522	C₂×C₇₃	C₂³×#41	1	1	yes	characteristic
523	C₂×C₇₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
524	C₂×C₇₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
525	D₇₃	—	2	4	no	—
526	D₇₃	—	4	2	no	—
527	D₇₃	—	4	8	no	—
528	#3508	—	73	32	no	—
529	C₂×#559	—	73	2	no	—
530	C₂×#559	—	73	2	no	—
531	C₂×#550	—	73	2	no	—
532	C₂×#550	—	73	2	no	—
533	C₂×#546	—	73	2	no	—
534	C₂×#546	—	73	2	no	—
535	C₂×#546	—	73	2	no	—
536	C₂×#546	—	73	2	no	—
537	C₂×#540	—	73	2	no	—
538	C₂×#540	—	73	2	no	—
539	C₂×#535	—	73	2	no	—
540	C₂×#533	—	73	1	no	—
541	C₂×#532	—	73	1	no	—
542	C₂×#532	—	73	1	no	—
543	C₂×#532	—	73	1	no	—
544	C₂×#532	D₇₃	1	1	yes	characteristic, complemented
545	C₂²×#127	—	73	1	no	—
546	C₂×#518	—	73	2	no	—
547	C₂×C₄×#41	—	73	1	no	—
548	C₇₃	C₂×#3508	1	1	yes	characteristic, complemented, Sylow
549	C₂²×#41	—	73	2	no	—
550	C₂²×#41	—	73	2	no	—
551	C₂²×#41	—	73	2	no	—
552	C₂²×#41	—	73	1	no	—
553	C₂²×#41	C₂×D₇₃	1	2	yes	complemented
554	C₂³×D₄	—	73	2	no	—
555	C₂³×D₄	—	73	2	no	—
556	C₂³×D₄	—	73	2	no	—
557	#559	—	73	32	no	—
558	#559	—	73	32	no	—
559	#550	—	73	32	no	—
560	#550	—	73	32	no	—
561	#546	—	73	32	no	—
562	#546	—	73	32	no	—
563	#546	—	73	32	no	—
564	#546	—	73	32	no	—
565	#540	—	73	32	no	—
566	#540	—	73	32	no	—
567	#535	—	73	32	no	—
568	#533	—	73	16	no	—
569	#532	—	73	16	no	—
570	#532	—	73	16	no	—
571	#532	—	73	16	no	—
572	#532	C₂×D₇₃	1	16	yes	complemented
573	C₂×C₄⋊Q₈	—	73	1	no	—
574	C₂×C₄⋊Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
575	C₂×#127	—	73	2	no	—
576	C₂×#127	—	73	2	no	—
577	C₂×#127	—	73	2	no	—
578	C₂×#127	—	73	4	no	—
579	C₂×#127	—	73	16	no	—
580	C₂×#127	—	73	1	no	—
581	C₂×#127	C₂×D₇₃	1	1	yes	characteristic
582	C₂×#125	—	73	2	no	—
583	C₂×#124	—	73	2	no	—
584	C₂×#124	—	73	2	no	—
585	C₂×#124	—	73	4	no	—
586	C₂×#124	—	73	2	no	—
587	C₂×#124	C₂×D₇₃	1	2	yes	complemented
588	C₂×#123	—	73	4	no	—
589	C₂×#123	—	73	4	no	—
590	C₂×#123	—	73	4	no	—
591	C₂×#123	—	73	4	no	—
592	C₂×C₂²⋊Q₈	—	73	2	no	—
593	C₂×C₂²⋊Q₈	—	73	2	no	—
594	C₂×#121	—	73	2	no	—
595	C₂×#121	—	73	2	no	—
596	C₂×#121	—	73	4	no	—
597	C₂×#121	—	73	4	no	—
598	C₂×#121	—	73	2	no	—
599	C₂×#121	—	73	2	no	—
600	C₂×#121	—	73	4	no	—
601	C₂×#121	—	73	2	no	—
602	C₂×#121	—	73	2	no	—
603	C₂×#121	—	73	4	no	—
604	C₂×#121	C₂×D₇₃	1	2	yes	complemented
605	C₂×#121	C₂×D₇₃	1	2	yes	complemented
606	C₂×#120	—	73	4	no	—
607	C₂×#120	—	73	4	no	—
608	#518	—	73	32	no	—
609	C₄×#41	—	73	16	no	—
610	C₂×C₄×Q₈	—	73	2	no	—
611	C₂×C₄×Q₈	—	73	2	no	—
612	C₂×C₄×Q₈	—	73	1	no	—
613	C₂×C₄×Q₈	—	73	1	no	—
614	C₂×C₄×D₄	—	73	2	no	—
615	C₂×C₄×D₄	—	73	2	no	—
616	C₂×C₄×D₄	—	73	1	no	—
617	C₂×C₄×D₄	—	73	1	no	—
618	C₂×C₄×D₄	—	73	1	no	—
619	C₂×C₄×D₄	—	73	1	no	—
620	C₂×C₄×D₄	—	73	4	no	—
621	C₂×C₄×D₄	—	73	2	no	—
622	C₂×C₄×D₄	—	73	2	no	—
623	C₂×C₄×D₄	—	73	4	no	—
624	C₂×C₄×D₄	—	73	1	no	—
625	C₂×C₄×D₄	—	73	1	no	—
626	C₂×C₄×D₄	—	73	2	no	—
627	C₂×C₄×D₄	—	73	2	no	—
628	C₂×C₄×D₄	C₂×D₇₃	1	2	yes	complemented
629	C₂×C₄×D₄	C₂×D₇₃	1	2	yes	complemented
630	C₂×#117	—	73	1	no	—
631	C₂×#117	—	73	2	no	—
632	C₂×#117	—	73	1	no	—
633	C₂×#117	—	73	1	no	—
634	C₂²×C₂²⋊C₄	—	73	4	no	—
635	C₂²×C₂²⋊C₄	—	73	4	no	—
636	C₂²×C₄²	—	73	1	no	—
637	C₂²×C₄²	—	73	1	no	—
638	C₂²×C₄²	C₂×D₇₃	1	1	yes	characteristic, complemented
639	C₂⁵	—	73	4	no	—
640	C₂×#41	—	4	8	no	—
641	C₂×#41	—	292	8	no	—
642	C₂×#41	—	292	8	no	—
643	C₂×#41	—	292	8	no	—
644	C₂×#41	—	73	16	no	—
645	C₂×#41	—	73	16	no	—
646	C₂×#41	—	73	16	no	—
647	C₂×#41	—	73	8	no	—
648	C₂×#41	—	146	8	no	—
649	C₂×#41	C₂²×D₇₃	1	16	yes	complemented
650	C₂²×Q₈	—	73	1	no	—
651	C₂²×Q₈	—	73	2	no	—
652	C₂²×Q₈	C₂²×D₇₃	1	2	yes	—
653	C₂²×D₄	—	292	8	no	—
654	C₂²×D₄	—	292	8	no	—
655	C₂²×D₄	—	73	4	no	—
656	C₂²×D₄	—	73	4	no	—
657	C₂²×D₄	—	73	4	no	—
658	C₂²×D₄	—	73	4	no	—
659	C₂²×D₄	—	73	16	no	—
660	C₂²×D₄	—	73	16	no	—
661	C₂²×D₄	—	73	1	no	—
662	C₂²×D₄	—	73	4	no	—
663	C₂²×D₄	—	73	1	no	—
664	C₂²×D₄	—	73	16	no	—
665	C₂²×D₄	—	73	4	no	—
666	C₂²×D₄	—	73	1	no	—
667	C₂²×D₄	—	73	2	no	—
668	C₂²×D₄	—	73	2	no	—
669	C₂²×D₄	—	73	2	no	—
670	C₂²×D₄	—	146	16	no	—
671	C₂²×D₄	C₂²×D₇₃	1	2	yes	—
672	C₂²×D₄	C₂²×D₇₃	1	2	yes	—
673	C₂²×D₄	C₂²×D₇₃	1	2	yes	—
674	C₂²×D₄	C₂²×D₇₃	1	4	yes	—
675	C₂³×C₄	—	73	4	no	—
676	C₂³×C₄	—	73	4	no	—
677	C₂³×C₄	—	73	4	no	—
678	C₂³×C₄	—	73	1	no	—
679	C₂³×C₄	—	73	1	no	—
680	C₂³×C₄	—	73	1	no	—
681	C₂³×C₄	—	73	1	no	—
682	C₂³×C₄	—	73	1	no	—
683	C₂³×C₄	—	73	1	no	—
684	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
685	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
686	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
687	C₂³×C₄	C₂²×D₇₃	1	4	yes	—
688	C₄⋊Q₈	—	73	8	no	—
689	C₄⋊Q₈	C₂²×D₇₃	1	8	yes	complemented
690	#127	—	73	16	no	—
691	#127	—	73	16	no	—
692	#127	—	73	16	no	—
693	#127	—	73	32	no	—
694	#127	—	73	8	no	—
695	#127	C₂²×D₇₃	1	8	yes	—
696	#125	—	73	16	no	—
697	#124	—	73	16	no	—
698	#124	—	73	16	no	—
699	#124	—	73	32	no	—
700	#124	—	73	16	no	—
701	#124	C₂²×D₇₃	1	16	yes	complemented
702	#123	—	73	32	no	—
703	#123	—	73	32	no	—
704	#123	—	73	32	no	—
705	#123	—	73	32	no	—
706	C₂²⋊Q₈	—	73	16	no	—
707	C₂²⋊Q₈	—	73	16	no	—
708	#121	—	73	16	no	—
709	#121	—	73	16	no	—
710	#121	—	73	32	no	—
711	#121	—	73	32	no	—
712	#121	—	73	16	no	—
713	#121	—	73	16	no	—
714	#121	—	73	32	no	—
715	#121	—	73	16	no	—
716	#121	—	73	16	no	—
717	#121	—	73	32	no	—
718	#121	C₂²×D₇₃	1	16	yes	complemented
719	#121	C₂²×D₇₃	1	16	yes	complemented
720	#120	—	73	32	no	—
721	#120	—	73	32	no	—
722	C₄×Q₈	—	73	16	no	—
723	C₄×Q₈	—	73	16	no	—
724	C₄×Q₈	—	73	8	no	—
725	C₄×Q₈	—	73	8	no	—
726	C₄×D₄	—	73	16	no	—
727	C₄×D₄	—	73	16	no	—
728	C₄×D₄	—	73	8	no	—
729	C₄×D₄	—	73	8	no	—
730	C₄×D₄	—	73	8	no	—
731	C₄×D₄	—	73	8	no	—
732	C₄×D₄	—	73	32	no	—
733	C₄×D₄	—	73	16	no	—
734	C₄×D₄	—	73	16	no	—
735	C₄×D₄	—	73	32	no	—
736	C₄×D₄	—	73	8	no	—
737	C₄×D₄	—	73	8	no	—
738	C₄×D₄	—	73	16	no	—
739	C₄×D₄	—	73	16	no	—
740	C₄×D₄	C₂²×D₇₃	1	16	yes	complemented
741	C₄×D₄	C₂²×D₇₃	1	16	yes	complemented
742	#117	—	73	8	no	—
743	#117	—	73	16	no	—
744	#117	—	73	8	no	—
745	#117	—	73	8	no	—
746	C₂×C₄⋊C₄	—	73	1	no	—
747	C₂×C₄⋊C₄	—	73	1	no	—
748	C₂×C₄⋊C₄	—	73	2	no	—
749	C₂×C₄⋊C₄	—	73	1	no	—
750	C₂×C₄⋊C₄	—	73	1	no	—
751	C₂×C₄⋊C₄	—	73	1	no	—
752	C₂×C₄⋊C₄	—	73	1	no	—
753	C₂×C₄⋊C₄	—	73	2	no	—
754	C₂×C₄⋊C₄	—	73	4	no	—
755	C₂×C₄⋊C₄	—	73	4	no	—
756	C₂×C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
757	C₂×C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
758	C₂×C₂²⋊C₄	—	73	4	no	—
759	C₂×C₂²⋊C₄	—	73	1	no	—
760	C₂×C₂²⋊C₄	—	73	1	no	—
761	C₂×C₂²⋊C₄	—	73	4	no	—
762	C₂×C₂²⋊C₄	—	73	1	no	—
763	C₂×C₂²⋊C₄	—	73	1	no	—
764	C₂×C₂²⋊C₄	—	73	4	no	—
765	C₂×C₂²⋊C₄	—	73	4	no	—
766	C₂×C₂²⋊C₄	—	73	4	no	—
767	C₂×C₂²⋊C₄	—	73	32	no	—
768	C₂×C₂²⋊C₄	—	73	1	no	—
769	C₂×C₂²⋊C₄	—	73	1	no	—
770	C₂×C₂²⋊C₄	—	73	4	no	—
771	C₂×C₂²⋊C₄	—	73	4	no	—
772	C₂×C₂²⋊C₄	—	73	32	no	—
773	C₂×C₂²⋊C₄	C₂²×D₇₃	1	4	yes	—
774	C₂×C₂²⋊C₄	C₂²×D₇₃	1	4	yes	—
775	C₂×C₄²	—	73	1	no	—
776	C₂×C₄²	—	73	1	no	—
777	C₂×C₄²	—	73	4	no	—
778	C₂×C₄²	—	73	1	no	—
779	C₂×C₄²	—	73	1	no	—
780	C₂×C₄²	—	73	1	no	—
781	C₂×C₄²	—	73	1	no	—
782	C₂×C₄²	—	73	8	no	—
783	C₂×C₄²	—	73	8	no	—
784	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
785	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
786	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
787	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
788	C₂×C₄²	C₂²×D₇₃	1	8	yes	complemented
789	C₂⁴	—	292	8	no	—
790	C₂⁴	—	292	8	no	—
791	C₂⁴	—	73	16	no	—
792	C₂⁴	—	73	1	no	—
793	C₂⁴	—	73	4	no	—
794	C₂⁴	—	73	1	no	—
795	C₂⁴	—	146	16	no	—
796	C₂⁴	C₂³×D₇₃	1	4	yes	—
797	C₂⁴	C₂³×D₇₃	1	1	yes	characteristic
798	#41	—	4	32	no	—
799	#41	—	292	32	no	—
800	#41	—	292	32	no	—
801	#41	—	292	32	no	—
802	#41	—	146	32	no	—
803	C₂×Q₈	—	2	8	no	—
804	C₂×Q₈	—	73	4	no	—
805	C₂×Q₈	—	73	8	no	—
806	C₂×Q₈	—	146	4	no	—
807	C₂×Q₈	—	146	8	no	—
808	C₂×Q₈	C₂³×D₇₃	1	8	yes	—
809	C₂×D₄	—	2	8	no	—
810	C₂×D₄	—	2	8	no	—
811	C₂×D₄	—	2	8	no	—
812	C₂×D₄	—	4	8	no	—
813	C₂×D₄	—	292	8	no	—
814	C₂×D₄	—	292	32	no	—
815	C₂×D₄	—	292	32	no	—
816	C₂×D₄	—	292	8	no	—
817	C₂×D₄	—	292	8	no	—
818	C₂×D₄	—	292	8	no	—
819	C₂×D₄	—	292	8	no	—
820	C₂×D₄	—	73	16	no	—
821	C₂×D₄	—	73	16	no	—
822	C₂×D₄	—	73	16	no	—
823	C₂×D₄	—	73	16	no	—
824	C₂×D₄	—	73	4	no	—
825	C₂×D₄	—	73	16	no	—
826	C₂×D₄	—	73	4	no	—
827	C₂×D₄	—	73	16	no	—
828	C₂×D₄	—	73	4	no	—
829	C₂×D₄	—	73	8	no	—
830	C₂×D₄	—	73	8	no	—
831	C₂×D₄	—	73	8	no	—
832	C₂×D₄	—	146	4	no	—
833	C₂×D₄	—	146	64	no	—
834	C₂×D₄	—	146	16	no	—
835	C₂×D₄	—	146	4	no	—
836	C₂×D₄	—	146	4	no	—
837	C₂×D₄	—	146	8	no	—
838	C₂×D₄	—	146	8	no	—
839	C₂×D₄	—	146	8	no	—
840	C₂×D₄	C₂³×D₇₃	1	8	yes	—
841	C₂×D₄	C₂³×D₇₃	1	8	yes	—
842	C₂×D₄	C₂³×D₇₃	1	8	yes	—
843	C₂×D₄	C₂³×D₇₃	1	16	yes	—
844	C₂²×C₄	—	2	4	no	—
845	C₂²×C₄	—	2	4	no	—
846	C₂²×C₄	—	2	4	no	—
847	C₂²×C₄	—	4	8	no	—
848	C₂²×C₄	—	292	8	no	—
849	C₂²×C₄	—	292	8	no	—
850	C₂²×C₄	—	292	8	no	—
851	C₂²×C₄	—	73	16	no	—
852	C₂²×C₄	—	73	16	no	—
853	C₂²×C₄	—	73	16	no	—
854	C₂²×C₄	—	73	1	no	—
855	C₂²×C₄	—	73	8	no	—
856	C₂²×C₄	—	73	4	no	—
857	C₂²×C₄	—	73	1	no	—
858	C₂²×C₄	—	73	1	no	—
859	C₂²×C₄	—	73	1	no	—
860	C₂²×C₄	—	73	1	no	—
861	C₂²×C₄	—	73	1	no	—
862	C₂²×C₄	—	73	4	no	—
863	C₂²×C₄	—	73	4	no	—
864	C₂²×C₄	—	73	4	no	—
865	C₂²×C₄	—	73	4	no	—
866	C₂²×C₄	—	73	4	no	—
867	C₂²×C₄	—	73	4	no	—
868	C₂²×C₄	—	146	4	no	—
869	C₂²×C₄	—	146	4	no	—
870	C₂²×C₄	—	146	4	no	—
871	C₂²×C₄	—	146	4	no	—
872	C₂²×C₄	—	146	4	no	—
873	C₂²×C₄	C₂³×D₇₃	1	4	yes	—
874	C₂²×C₄	C₂³×D₇₃	1	4	yes	—
875	C₂²×C₄	C₂³×D₇₃	1	4	yes	—
876	C₂²×C₄	C₂³×D₇₃	1	4	yes	—
877	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
878	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
879	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
880	C₂²×C₄	C₂³×D₇₃	1	16	yes	—
881	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
882	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
883	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
884	C₄⋊C₄	—	73	4	no	—
885	C₄⋊C₄	—	73	4	no	—
886	C₄⋊C₄	—	73	4	no	—
887	C₄⋊C₄	—	73	4	no	—
888	C₄⋊C₄	—	73	16	no	—
889	C₄⋊C₄	—	73	8	no	—
890	C₄⋊C₄	—	73	4	no	—
891	C₄⋊C₄	—	73	4	no	—
892	C₄⋊C₄	—	73	8	no	—
893	C₄⋊C₄	—	73	16	no	—
894	C₄⋊C₄	C₂³×D₇₃	1	8	yes	—
895	C₄⋊C₄	C₂³×D₇₃	1	8	yes	—
896	C₂²⋊C₄	—	73	16	no	—
897	C₂²⋊C₄	—	73	4	no	—
898	C₂²⋊C₄	—	73	4	no	—
899	C₂²⋊C₄	—	73	16	no	—
900	C₂²⋊C₄	—	73	4	no	—
901	C₂²⋊C₄	—	73	4	no	—
902	C₂²⋊C₄	—	73	16	no	—
903	C₂²⋊C₄	—	73	16	no	—
904	C₂²⋊C₄	—	73	16	no	—
905	C₂²⋊C₄	—	73	4	no	—
906	C₂²⋊C₄	—	73	4	no	—
907	C₂²⋊C₄	—	73	16	no	—
908	C₂²⋊C₄	—	73	16	no	—
909	C₂²⋊C₄	C₂³×D₇₃	1	16	yes	—
910	C₂²⋊C₄	C₂³×D₇₃	1	16	yes	—
911	C₄²	—	73	4	no	—
912	C₄²	—	73	4	no	—
913	C₄²	—	73	4	no	—
914	C₄²	—	73	4	no	—
915	C₄²	—	73	4	no	—
916	C₄²	—	73	4	no	—
917	C₄²	—	73	16	no	—
918	C₄²	C₂³×D₇₃	1	4	yes	—
919	C₄²	C₂³×D₇₃	1	4	yes	—
920	C₄²	C₂³×D₇₃	1	4	yes	—
921	C₄²	C₂³×D₇₃	1	4	yes	—
922	C₂³	—	2	2	no	—
923	C₂³	—	2	8	no	—
924	C₂³	—	2	2	no	—
925	C₂³	—	2	8	no	—
926	C₂³	—	2	2	no	—
927	C₂³	—	2	8	no	—
928	C₂³	—	292	16	no	—
929	C₂³	—	292	16	no	—
930	C₂³	—	584	32	no	—
931	C₂³	—	73	4	no	—
932	C₂³	—	73	2	no	—
933	C₂³	—	73	8	no	—
934	C₂³	—	73	2	no	—
935	C₂³	—	146	32	no	—
936	C₂³	—	146	2	no	—
937	C₂³	—	146	8	no	—
938	C₂³	—	146	8	no	—
939	C₂³	—	146	2	no	—
940	C₂³	—	146	8	no	—
941	C₂³	—	146	2	no	—
942	C₂³	—	146	2	no	—
943	C₂³	—	146	2	no	—
944	C₂³	C₂⁴×D₇₃	1	8	yes	—
945	C₂³	C₂⁴×D₇₃	1	2	yes	—
946	C₂³	C₂⁴×D₇₃	1	1	yes	characteristic
947	Q₈	—	2	16	no	—
948	Q₈	—	146	8	no	—
949	Q₈	—	146	16	no	—
950	D₄	—	2	16	no	—
951	D₄	—	2	16	no	—
952	D₄	—	2	16	no	—
953	D₄	—	4	16	no	—
954	D₄	—	292	16	no	—
955	D₄	—	292	16	no	—
956	D₄	—	292	16	no	—
957	D₄	—	292	16	no	—
958	D₄	—	292	16	no	—
959	D₄	—	146	8	no	—
960	D₄	—	146	32	no	—
961	D₄	—	146	8	no	—
962	D₄	—	146	8	no	—
963	D₄	—	146	16	no	—
964	D₄	—	146	16	no	—
965	D₄	—	146	16	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	8	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	8	no	—
971	C₂×C₄	—	2	8	no	—
972	C₂×C₄	—	2	8	no	—
973	C₂×C₄	—	4	16	no	—
974	C₂×C₄	—	292	16	no	—
975	C₂×C₄	—	292	16	no	—
976	C₂×C₄	—	292	16	no	—
977	C₂×C₄	—	73	4	no	—
978	C₂×C₄	—	73	2	no	—
979	C₂×C₄	—	73	16	no	—
980	C₂×C₄	—	73	2	no	—
981	C₂×C₄	—	73	2	no	—
982	C₂×C₄	—	73	2	no	—
983	C₂×C₄	—	73	2	no	—
984	C₂×C₄	—	73	2	no	—
985	C₂×C₄	—	73	8	no	—
986	C₂×C₄	—	146	2	no	—
987	C₂×C₄	—	146	2	no	—
988	C₂×C₄	—	146	2	no	—
989	C₂×C₄	—	146	2	no	—
990	C₂×C₄	—	146	8	no	—
991	C₂×C₄	—	146	2	no	—
992	C₂×C₄	—	146	8	no	—
993	C₂×C₄	—	146	8	no	—
994	C₂×C₄	—	146	8	no	—
995	C₂×C₄	—	146	8	no	—
996	C₂×C₄	—	146	8	no	—
997	C₂×C₄	#41×D₇₃	1	4	yes	—
998	C₂×C₄	#14556636	1	4	yes	—
999	C₂×C₄	#14556637	1	4	yes	—
1000	C₂×C₄	C₂⁴×D₇₃	1	8	yes	—
1001	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
1002	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
1003	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
1004	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
1005	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
1006	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
1007	C₂²	—	2	2	no	—
1008	C₂²	—	2	8	no	—
1009	C₂²	—	2	2	no	—
1010	C₂²	—	2	8	no	—
1011	C₂²	—	2	2	no	—
1012	C₂²	—	2	8	no	—
1013	C₂²	—	4	16	no	—
1014	C₂²	—	4	4	no	—
1015	C₂²	—	292	16	no	—
1016	C₂²	—	292	4	no	—
1017	C₂²	—	584	32	no	—
1018	C₂²	—	73	4	no	—
1019	C₂²	—	146	2	no	—
1020	C₂²	—	146	8	no	—
1021	C₂²	—	146	8	no	—
1022	C₂²	—	146	2	no	—
1023	C₂²	—	146	8	no	—
1024	C₂²	—	146	2	no	—
1025	C₂²	—	146	8	no	—
1026	C₂²	—	146	2	no	—
1027	C₂²	—	146	2	no	—
1028	C₂²	C₂×#41×D₇₃	1	2	yes	—
1029	C₂²	C₂×#14556636	1	2	yes	—
1030	C₂²	C₂×#14556637	1	2	yes	—
1031	C₂²	C₂⁵×D₇₃	1	1	yes	characteristic
1032	C₄	—	2	2	no	—
1033	C₄	—	2	2	no	—
1034	C₄	—	2	8	no	—
1035	C₄	—	2	2	no	—
1036	C₄	—	73	4	no	—
1037	C₄	—	146	2	no	—
1038	C₄	—	146	2	no	—
1039	C₄	—	146	2	no	—
1040	C₄	—	146	2	no	—
1041	C₄	—	146	8	no	—
1042	C₄	—	146	2	no	—
1043	C₄	C₂×#41×D₇₃	1	4	yes	—
1044	C₄	C₂×#14556636	1	4	yes	—
1045	C₄	C₂×#14556637	1	4	yes	—
1046	C₂	—	4	8	no	—
1047	C₂	—	4	2	no	—
1048	C₂	—	292	8	no	—
1049	C₂	—	292	2	no	—
1050	C₂	—	146	4	no	—
1051	C₂	#22623800	1	4	yes	direct product factor
1052	C₂	C₂²×#41×D₇₃	1	1	yes	characteristic
1053	C₂	C₂²×#14556636	1	1	yes	characteristic
1054	C₂	C₂²×#14556637	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₇₃
commutator, cosocle	C₂²×C₇₃	C₂⁶
Frattini	C₂²	C₂⁵×D₇₃
Fitting	C₂×#532×C₇₃	C₂
socle	C₂³×C₇₃	C₂⁵
hypercenter	C₂×#532	D₇₃
hypocenter	C₇₃	C₂×#3508
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. #22623800	C₂	direct (N × H)
2. C₂×#17989320	C₂	semidirect
3. C₂×#17989319	C₂	semidirect
4. C₂×#17989256	C₂	semidirect
5. C₂×#17989255	C₂	semidirect
6. C₂×#17989234	C₂	semidirect
7. C₂×#17989232	C₂	semidirect
8. C₂×#17989230	C₂	semidirect
9. C₂×#17989225	C₂	semidirect
10. C₂×#17989190	C₂	semidirect
11. C₂×#17989188	C₂	semidirect
12. C₂×#17989153	C₂	semidirect
13. C₂×#17989142	C₂	semidirect
14. C₂×#17989138	C₂	semidirect
15. C₂×#17989137	C₂	semidirect
16. C₂×#17989135	C₂	semidirect
17. C₂×#127×D₇₃	C₂	semidirect
18. C₂×#17989059	C₂	semidirect
19. C₂×C₄×#11924028	C₂	semidirect
20. C₂×#532×C₇₃	C₂	semidirect
21. C₂²×#11924029	C₂²	semidirect
23. C₂²×#11924028	C₂²	semidirect
24. C₂²×#11924027	C₂²	semidirect
28. #17989320	C₂²	semidirect
29. #17989319	C₂²	semidirect
30. #17989256	C₂²	semidirect
31. #17989255	C₂²	semidirect
32. #17989234	C₂²	semidirect
33. #17989232	C₂²	semidirect
34. #17989230	C₂²	semidirect
35. #17989225	C₂²	semidirect
36. #17989190	C₂²	semidirect
37. #17989188	C₂²	semidirect
38. #17989153	C₂²	semidirect
39. #17989142	C₂²	semidirect
40. #17989138	C₂²	semidirect
41. #17989137	C₂²	semidirect
42. #17989135	C₂²	semidirect
43. C₂×#14556591	C₂²	semidirect
48. C₂×#14556587	C₂²	semidirect
49. #127×D₇₃	C₂²	semidirect
50. C₂×#14556582	C₂²	semidirect
51. C₂×#14556580	C₂²	semidirect
52. C₂×#14556579	C₂²	semidirect
53. C₂×#14556578	C₂²	semidirect
54. C₂×#14556577	C₂²	semidirect
55. C₂×#14556575	C₂²	semidirect
56. C₂×#14556574	C₂²	semidirect
57. C₂×#14556573	C₂²	semidirect
58. C₂×#14556573	C₂²	semidirect
61. C₂×#14556566	C₂²	semidirect
62. C₂×#14556566	C₂²	semidirect
63. C₂×#14556565	C₂²	semidirect
64. C₂×#14556565	C₂²	semidirect
65. C₂×#14556565	C₂²	semidirect
66. C₂×#14556564	C₂²	semidirect
67. C₂×#14556563	C₂²	semidirect
68. C₂×#14556562	C₂²	semidirect
69. C₂×#14556562	C₂²	semidirect
70. C₂×#14556562	C₂²	semidirect
73. #17989059	C₂²	semidirect
74. C₄×#11924028	C₂²	semidirect
75. C₂×Q₈×Dic₇₃	C₂²	semidirect
76. C₂×C₄×Dic₁₄₆	C₂²	semidirect
77. C₂×C₄×Dic₁₄₆	C₂²	semidirect
78. C₂×#14556556	C₂²	semidirect
81. C₂×C₄×D₂₉₂	C₂²	semidirect
82. C₂×C₄×D₂₉₂	C₂²	semidirect
83. C₂×D₄×Dic₇₃	C₂²	semidirect
84. C₂×D₄×Dic₇₃	C₂²	semidirect
85. C₂×#14556553	C₂²	semidirect
86. C₂×#14556553	C₂²	semidirect
89. C₂×C₄×C₂²⋊D₇₃	C₂²	semidirect
90. C₂×C₄×C₂²⋊D₇₃	C₂²	semidirect
91. C₂×C₄×C₂²⋊D₇₃	C₂²	semidirect
92. C₂×#14556551	C₂²	semidirect
93. C₂×#14556550	C₂²	semidirect
96. C₂×#14556548	C₂²	semidirect
100. C₂×C₄²×D₇₃	C₂²	semidirect
101. C₂²×#41×C₇₃	C₂²	semidirect
102. #532×C₇₃	C₂²	semidirect
103. C₂×C₄⋊Q₈×C₇₃	C₂²	semidirect
105. C₂×#124×C₇₃	C₂²	semidirect
106. C₂×#121×C₇₃	C₂²	semidirect
107. C₂×#121×C₇₃	C₂²	semidirect
108. C₂×C₄×D₄×C₇₃	C₂²	semidirect
109. C₂×C₄×D₄×C₇₃	C₂²	semidirect
110. C₂²×C₄²×C₇₃	C₂²	semidirect
113. C₂×#11924029	C₂³	semidirect
117. C₂×#11924028	C₂³	semidirect
119. C₂×#11924027	C₂³	semidirect
149. #14556591	C₂³	semidirect
154. #14556587	C₂³	semidirect
155. #14556582	C₂³	semidirect
156. #14556580	C₂³	semidirect
157. #14556579	C₂³	semidirect
158. #14556578	C₂³	semidirect
159. #14556577	C₂³	semidirect
160. #14556575	C₂³	semidirect
161. #14556574	C₂³	semidirect
162. #14556573	C₂³	semidirect
163. #14556573	C₂³	semidirect
166. #14556566	C₂³	semidirect
167. #14556566	C₂³	semidirect
168. #14556565	C₂³	semidirect
169. #14556565	C₂³	semidirect
170. #14556565	C₂³	semidirect
171. #14556564	C₂³	semidirect
172. #14556563	C₂³	semidirect
173. #14556562	C₂³	semidirect
174. #14556562	C₂³	semidirect
175. #14556562	C₂³	semidirect
178. Q₈×Dic₇₃	C₂³	semidirect
179. C₄×Dic₁₄₆	C₂³	semidirect
180. C₄×Dic₁₄₆	C₂³	semidirect
181. #14556556	C₂³	semidirect
184. C₄×D₂₉₂	C₂³	semidirect
185. C₄×D₂₉₂	C₂³	semidirect
186. D₄×Dic₇₃	C₂³	semidirect
187. D₄×Dic₇₃	C₂³	semidirect
188. #14556553	C₂³	semidirect
189. #14556553	C₂³	semidirect
192. C₄×C₂²⋊D₇₃	C₂³	semidirect
193. C₄×C₂²⋊D₇₃	C₂³	semidirect
194. C₄×C₂²⋊D₇₃	C₂³	semidirect
195. #14556551	C₂³	semidirect
196. #14556550	C₂³	semidirect
199. #14556548	C₂³	semidirect
233. C₄²×D₇₃	C₂³	semidirect
235. C₂×#41×C₇₃	C₂³	semidirect
245. C₄⋊Q₈×C₇₃	C₂³	semidirect
247. #124×C₇₃	C₂³	semidirect
248. #121×C₇₃	C₂³	semidirect
249. #121×C₇₃	C₂³	semidirect
250. C₄×D₄×C₇₃	C₂³	semidirect
251. C₄×D₄×C₇₃	C₂³	semidirect
260. C₂×C₄²×C₇₃	C₂³	semidirect
319. C₂×C₄×D₇₃	#41	semidirect
476. C₄×D₇₃	C₂×#41	semidirect
521. C₂×C₇₃	#3508	semidirect
544. C₂×#532	D₇₃	semidirect
548. C₇₃	C₂×#3508	semidirect
553. C₂²×#41	C₂×D₇₃	semidirect
572. #532	C₂×D₇₃	semidirect
574. C₂×C₄⋊Q₈	C₂×D₇₃	semidirect
587. C₂×#124	C₂×D₇₃	semidirect
604. C₂×#121	C₂×D₇₃	semidirect
605. C₂×#121	C₂×D₇₃	semidirect
628. C₂×C₄×D₄	C₂×D₇₃	semidirect
629. C₂×C₄×D₄	C₂×D₇₃	semidirect
638. C₂²×C₄²	C₂×D₇₃	semidirect
649. C₂×#41	C₂²×D₇₃	semidirect
689. C₄⋊Q₈	C₂²×D₇₃	semidirect
701. #124	C₂²×D₇₃	semidirect
718. #121	C₂²×D₇₃	semidirect
719. #121	C₂²×D₇₃	semidirect
740. C₄×D₄	C₂²×D₇₃	semidirect
741. C₄×D₄	C₂²×D₇₃	semidirect
788. C₂×C₄²	C₂²×D₇₃	semidirect
1051. C₂	#22623800	direct (N × H)

Maximal subgroups

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

subgroup	index
#22623800	2
C₂×#17989320	2
C₂×#17989319	2
C₂×#17989256	2
C₂×#17989255	2
C₂×#17989234	2
C₂×#17989232	2
C₂×#17989230	2
C₂×#17989225	2
C₂×#17989190	2
C₂×#17989188	2
C₂×#17989153	2
C₂×#17989142	2
C₂×#17989138	2
C₂×#17989137	2
C₂×#17989135	2
C₂×#127×D₇₃	2
C₂×#17989059	2
C₂×C₄×#11924028	2
C₂×#532×C₇₃	2
C₂×#3508	73

Subgroups — C2×#22623800 #33994337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22623800 #33994337