Subgroups — C₂×#22623542 #33993071

Order 18688.

8722 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623542	C₂	1	32	yes	maximal, direct product factor
2	C₂×#17989322	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#17989298	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#17989290	C₂	1	2	yes	maximal, complemented
5	C₂×#17989285	C₂	1	2	yes	maximal, complemented
6	C₂×#17989264	C₂	1	4	yes	maximal, complemented
7	C₂×#17989232	C₂	1	2	yes	maximal, complemented
8	C₂×#17989228	C₂	1	2	yes	maximal, complemented
9	C₂×D₄×D₂₉₂	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#17989138	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#17989123	C₂	1	2	yes	maximal, complemented
12	C₂×#17989122	C₂	1	2	yes	maximal, complemented
13	C₂×#17989100	C₂	1	4	yes	maximal, complemented
14	C₂×C₄×#11924029	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×#11924027	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#14556553	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×D₄×D₇₃	C₂	1	2	yes	maximal, complemented
18	C₂×#554×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#11924029	C₂²	1	1	yes	characteristic
20	C₂²×#11924029	C₂²	1	2	yes	complemented
21	C₂²×#11924027	C₂²	1	1	yes	characteristic
22	C₂³×D₂₉₂	C₂²	1	2	yes	—
23	C₂²×D₄×D₇₃	C₂²	1	2	yes	—
24	C₂³×C₄×D₇₃	C₂²	1	4	yes	complemented
25	#17989322	C₂²	1	16	yes	complemented
26	#17989298	C₂²	1	16	yes	complemented
27	#17989290	C₂²	1	32	yes	complemented
28	#17989285	C₂²	1	32	yes	complemented
29	#17989264	C₂²	1	64	yes	complemented
30	#17989232	C₂²	1	32	yes	complemented
31	#17989228	C₂²	1	32	yes	complemented
32	D₄×D₂₉₂	C₂²	1	16	yes	complemented
33	#17989138	C₂²	1	16	yes	complemented
34	C₂×#14556588	C₂²	1	1	yes	characteristic
35	#17989123	C₂²	1	32	yes	complemented
36	#17989122	C₂²	1	32	yes	complemented
37	C₂×#14556586	C₂²	1	4	yes	complemented
38	C₂×#14556586	C₂²	1	4	yes	complemented
39	C₂×#14556582	C₂²	1	2	yes	complemented
40	C₂×#14556580	C₂²	1	2	yes	complemented
41	C₂×#14556580	C₂²	1	2	yes	complemented
42	C₂×#14556579	C₂²	1	2	yes	complemented
43	#17989100	C₂²	1	64	yes	complemented
44	C₂×#14556576	C₂²	1	4	yes	complemented
45	C₂×#14556576	C₂²	1	4	yes	complemented
46	C₂×#14556576	C₂²	1	4	yes	complemented
47	C₂×#14556575	C₂²	1	4	yes	complemented
48	C₂×#14556571	C₂²	1	2	yes	complemented
49	C₂×#14556567	C₂²	1	4	yes	complemented
50	C₂×#14556566	C₂²	1	2	yes	—
51	C₂×#14556566	C₂²	1	4	yes	complemented
52	C₂×#14556566	C₂²	1	2	yes	complemented
53	C₂×#14556566	C₂²	1	2	yes	complemented
54	C₂×#14556565	C₂²	1	2	yes	—
55	C₂×#14556565	C₂²	1	4	yes	complemented
56	C₂×#14556561	C₂²	1	4	yes	—
57	C₂×#14556561	C₂²	1	4	yes	complemented
58	C₄×#11924029	C₂²	1	16	yes	complemented
59	C₄×#11924027	C₂²	1	16	yes	complemented
60	C₂×Q₈×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₄×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
62	C₂×#14556556	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₄×D₂₉₂	C₂²	1	1	yes	characteristic
64	C₂×C₄×D₂₉₂	C₂²	1	2	yes	complemented
65	C₂×C₄×D₂₉₂	C₂²	1	2	yes	complemented
66	C₂×D₄×Dic₇₃	C₂²	1	1	yes	characteristic
67	C₂×#14556553	C₂²	1	1	yes	characteristic
68	C₂×#14556553	C₂²	1	2	yes	—
69	C₂×#14556553	C₂²	1	2	yes	complemented
70	C₂×#14556553	C₂²	1	2	yes	complemented
71	C₂×#14556553	C₂²	1	4	yes	complemented
72	C₂×#14556553	C₂²	1	4	yes	complemented
73	C₂×#14556553	C₂²	1	2	yes	complemented
74	C₂×#14556553	C₂²	1	2	yes	complemented
75	C₂×#14556553	C₂²	1	32	yes	complemented
76	C₂×C₄×C₂²⋊D₇₃	C₂²	1	4	yes	complemented
77	C₂×C₄×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
78	C₂×#14556551	C₂²	1	4	yes	complemented
79	C₂×#14556551	C₂²	1	2	yes	complemented
80	C₄×D₄×D₇₃	C₂²	1	32	yes	complemented
81	C₂×#14556549	C₂²	1	1	yes	characteristic, complemented
82	C₂×#14556549	C₂²	1	2	yes	complemented
83	C₂×#14556549	C₂²	1	1	yes	characteristic, complemented
84	C₂×#14556549	C₂²	1	4	yes	complemented
85	C₂×#14556547	C₂²	1	2	yes	complemented
86	C₂×C₄⋊C₄×D₇₃	C₂²	1	2	yes	complemented
87	C₂²×#11924005	C₂²	1	4	yes	complemented
88	C₂×C₂²⋊C₄×D₇₃	C₂²	1	4	yes	complemented
89	C₂²×C₄×Dic₇₃	C₂²	1	2	yes	complemented
90	C₂×C₄²×D₇₃	C₂²	1	2	yes	complemented
91	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic, complemented
92	#554×C₇₃	C₂²	1	16	yes	complemented
93	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
94	C₂×#125×C₇₃	C₂²	1	2	yes	complemented
95	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	complemented
96	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	4	yes	complemented
97	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
98	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
99	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
100	C₂²×C₄⋊C₄×C₇₃	C₂²	1	2	yes	complemented
101	C₂⁴×D₇₃	C₂³	1	4	yes	—
102	C₂×#11924029	—	2	8	no	—
103	C₂×#11924029	—	4	8	no	—
104	C₂×#11924029	C₂³	1	8	yes	—
105	C₂×#11924029	C₂³	1	16	yes	complemented
106	C₂×#11924027	—	2	8	no	—
107	C₂×#11924027	C₂³	1	8	yes	—
108	C₂²×Dic₁₄₆	C₂³	1	1	yes	characteristic
109	C₂²×D₂₉₂	—	2	16	no	—
110	C₂²×D₂₉₂	C₂³	1	2	yes	—
111	C₂²×D₂₉₂	C₂³	1	2	yes	—
112	C₂²×D₂₉₂	C₂³	1	16	yes	—
113	C₂²×D₂₉₂	C₂³	1	4	yes	—
114	C₂²×D₂₉₂	C₂³	1	2	yes	—
115	C₂²×D₂₉₂	C₂³	1	2	yes	—
116	C₂²×D₂₉₂	C₂³	1	4	yes	—
117	C₂²×D₂₉₂	C₂³	1	1	yes	characteristic
118	C₂²×C₂²⋊D₇₃	C₂³	1	4	yes	—
119	C₂²×C₂²⋊D₇₃	C₂³	1	2	yes	—
120	C₂×D₄×D₇₃	—	2	16	no	—
121	C₂×D₄×D₇₃	C₂³	1	16	yes	—
122	C₂³×Dic₇₃	C₂³	1	2	yes	—
123	C₂³×Dic₇₃	C₂³	1	2	yes	—
124	C₂²×C₄×D₇₃	—	4	16	no	—
125	C₂²×C₄×D₇₃	C₂³	1	2	yes	—
126	C₂²×C₄×D₇₃	C₂³	1	4	yes	—
127	C₂²×C₄×D₇₃	C₂³	1	2	yes	—
128	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
129	C₂²×C₄×D₇₃	C₂³	1	2	yes	—
130	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
131	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
132	C₂²×C₄×D₇₃	C₂³	1	4	yes	—
133	C₂²×C₄×D₇₃	C₂³	1	4	yes	—
134	C₂²×C₄×D₇₃	C₂³	1	32	yes	complemented
135	#14556588	C₂³	1	8	yes	—
136	#14556586	C₂³	1	32	yes	complemented
137	#14556586	C₂³	1	32	yes	complemented
138	#14556582	C₂³	1	16	yes	complemented
139	#14556580	C₂³	1	16	yes	complemented
140	#14556580	C₂³	1	16	yes	complemented
141	#14556579	C₂³	1	16	yes	complemented
142	#14556576	C₂³	1	32	yes	complemented
143	#14556576	C₂³	1	32	yes	complemented
144	#14556576	C₂³	1	32	yes	complemented
145	#14556575	C₂³	1	32	yes	complemented
146	#14556571	C₂³	1	16	yes	complemented
147	#14556567	C₂³	1	32	yes	complemented
148	#14556566	C₂³	1	16	yes	—
149	#14556566	C₂³	1	16	yes	complemented
150	#14556566	C₂³	1	16	yes	complemented
151	#14556566	C₂³	1	32	yes	complemented
152	#14556565	C₂³	1	16	yes	—
153	#14556565	C₂³	1	32	yes	complemented
154	#14556561	C₂³	1	32	yes	—
155	#14556561	C₂³	1	32	yes	complemented
156	Q₈×Dic₇₃	C₂³	1	8	yes	complemented
157	C₄×Dic₁₄₆	C₂³	1	8	yes	complemented
158	#14556556	C₂³	1	8	yes	complemented
159	C₄×D₂₉₂	C₂³	1	8	yes	—
160	C₄×D₂₉₂	C₂³	1	16	yes	complemented
161	C₄×D₂₉₂	C₂³	1	16	yes	complemented
162	D₄×Dic₇₃	C₂³	1	8	yes	—
163	#14556553	C₂³	1	16	yes	—
164	#14556553	C₂³	1	8	yes	—
165	#14556553	C₂³	1	16	yes	complemented
166	#14556553	C₂³	1	32	yes	complemented
167	#14556553	C₂³	1	16	yes	complemented
168	#14556553	C₂³	1	32	yes	complemented
169	#14556553	C₂³	1	16	yes	complemented
170	#14556553	C₂³	1	16	yes	complemented
171	C₄×C₂²⋊D₇₃	C₂³	1	16	yes	complemented
172	C₄×C₂²⋊D₇₃	C₂³	1	32	yes	complemented
173	#14556551	C₂³	1	32	yes	complemented
174	#14556551	C₂³	1	16	yes	complemented
175	#14556549	C₂³	1	32	yes	complemented
176	#14556549	C₂³	1	16	yes	complemented
177	#14556549	C₂³	1	8	yes	complemented
178	#14556549	C₂³	1	8	yes	complemented
179	#14556547	C₂³	1	16	yes	complemented
180	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
183	C₂×C₄⋊Dic₇₃	C₂³	1	4	yes	—
184	C₂×#11924007	C₂³	1	4	yes	—
185	C₂×#11924007	C₂³	1	2	yes	—
186	C₂×#11924007	C₂³	1	2	yes	—
187	C₄⋊C₄×D₇₃	C₂³	1	16	yes	complemented
188	C₂×C₂²⋊Dic₇₃	C₂³	1	2	yes	—
189	C₂×#11924005	C₂³	1	4	yes	—
190	C₂×#11924005	C₂³	1	4	yes	—
191	C₂×#11924005	C₂³	1	2	yes	—
192	C₂×#11924005	C₂³	1	4	yes	—
193	C₂×#11924005	C₂³	1	4	yes	—
194	C₂×#11924005	C₂³	1	4	yes	—
195	C₂×#11924005	C₂³	1	2	yes	—
196	C₂×#11924005	C₂³	1	2	yes	—
197	C₂×#11924005	C₂³	1	2	yes	—
198	C₂×#11924005	C₂³	1	4	yes	—
199	C₂×#11924005	C₂³	1	4	yes	—
200	C₂×#11924005	C₂³	1	32	yes	complemented
201	C₂²⋊C₄×D₇₃	C₂³	1	32	yes	complemented
202	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
203	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
204	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
205	C₂×C₄×Dic₇₃	C₂³	1	2	yes	—
206	C₂×C₄×Dic₇₃	C₂³	1	2	yes	—
207	C₂×C₄×Dic₇₃	C₂³	1	2	yes	—
208	C₂×C₄×Dic₇₃	C₂³	1	2	yes	—
209	C₂×C₄×Dic₇₃	C₂³	1	2	yes	—
210	C₂×C₄×Dic₇₃	C₂³	1	16	yes	complemented
211	C₄²×D₇₃	C₂³	1	16	yes	complemented
212	C₄²×D₇₃	C₂³	1	8	yes	complemented
213	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
214	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
215	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
216	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
217	C₂³×C₄×C₇₃	C₂³	1	4	yes	—
218	C₄⋊Q₈×C₇₃	C₂³	1	8	yes	complemented
219	#125×C₇₃	C₂³	1	16	yes	complemented
220	C₂²⋊Q₈×C₇₃	C₂³	1	16	yes	complemented
221	C₂²⋊Q₈×C₇₃	C₂³	1	32	yes	complemented
222	C₄×Q₈×C₇₃	C₂³	1	8	yes	complemented
223	C₄×D₄×C₇₃	C₂³	1	8	yes	—
224	C₄×D₄×C₇₃	C₂³	1	16	yes	—
225	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
227	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
228	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
230	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
231	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
232	C₂×C₄⋊C₄×C₇₃	C₂³	1	16	yes	complemented
233	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
234	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
235	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
237	C₂³×D₇₃	—	2	16	no	—
238	C₂³×D₇₃	—	2	16	no	—
239	C₂³×D₇₃	—	4	8	no	—
240	C₂³×D₇₃	C₂⁴	1	4	yes	—
241	C₂³×D₇₃	C₂⁴	1	1	yes	characteristic
242	C₂³×D₇₃	C₂⁴	1	16	yes	—
243	C₂³×D₇₃	C₂⁴	1	2	yes	—
244	#11924029	—	2	32	no	—
245	#11924029	—	4	32	no	—
246	#11924027	—	2	32	no	—
247	C₂×Dic₁₄₆	—	2	4	no	—
248	C₂×Dic₁₄₆	C₂⁴	1	4	yes	—
249	C₂×D₂₉₂	—	2	16	no	—
250	C₂×D₂₉₂	—	2	8	no	—
251	C₂×D₂₉₂	—	2	8	no	—
252	C₂×D₂₉₂	—	2	8	no	—
253	C₂×D₂₉₂	—	2	64	no	—
254	C₂×D₂₉₂	—	4	8	no	—
255	C₂×D₂₉₂	—	4	4	no	—
256	C₂×D₂₉₂	#41	1	8	yes	complemented
257	C₂×D₂₉₂	C₂⁴	1	16	yes	—
258	C₂×D₂₉₂	C₂⁴	1	8	yes	—
259	C₂×D₂₉₂	C₂⁴	1	8	yes	—
260	C₂×D₂₉₂	C₂⁴	1	8	yes	—
261	C₂×D₂₉₂	C₂⁴	1	8	yes	—
262	C₂×D₂₉₂	C₂⁴	1	16	yes	—
263	C₂×D₂₉₂	C₂⁴	1	4	yes	—
264	C₂×C₂²⋊D₇₃	—	2	16	no	—
265	C₂×C₂²⋊D₇₃	—	2	8	no	—
266	C₂×C₂²⋊D₇₃	C₂⁴	1	16	yes	—
267	C₂×C₂²⋊D₇₃	C₂⁴	1	8	yes	—
268	D₄×D₇₃	—	2	64	no	—
269	C₂²×Dic₇₃	—	2	8	no	—
270	C₂²×Dic₇₃	—	2	8	no	—
271	C₂²×Dic₇₃	C₂⁴	1	1	yes	characteristic
272	C₂²×Dic₇₃	C₂⁴	1	1	yes	characteristic
273	C₂²×Dic₇₃	C₂⁴	1	2	yes	—
274	C₂²×Dic₇₃	C₂⁴	1	2	yes	—
275	C₂²×Dic₇₃	C₂⁴	1	2	yes	—
276	C₂²×Dic₇₃	C₂⁴	1	8	yes	—
277	C₂²×Dic₇₃	C₂⁴	1	8	yes	—
278	C₂²×Dic₇₃	C₂⁴	1	1	yes	characteristic
279	C₂×C₄×D₇₃	—	2	8	no	—
280	C₂×C₄×D₇₃	—	2	8	no	—
281	C₂×C₄×D₇₃	—	2	4	no	—
282	C₂×C₄×D₇₃	—	2	4	no	—
283	C₂×C₄×D₇₃	—	2	8	no	—
284	C₂×C₄×D₇₃	—	2	16	no	—
285	C₂×C₄×D₇₃	—	2	4	no	—
286	C₂×C₄×D₇₃	—	4	64	no	—
287	C₂×C₄×D₇₃	—	4	8	no	—
288	C₂×C₄×D₇₃	—	4	8	no	—
289	C₂×C₄×D₇₃	C₂⁴	1	8	yes	—
290	C₂×C₄×D₇₃	C₂⁴	1	8	yes	—
291	C₂×C₄×D₇₃	C₂⁴	1	4	yes	—
292	C₂×C₄×D₇₃	C₂⁴	1	4	yes	—
293	C₂×C₄×D₇₃	C₂⁴	1	4	yes	—
294	C₂×C₄×D₇₃	C₂⁴	1	8	yes	—
295	C₂×C₄×D₇₃	C₂⁴	1	16	yes	—
296	C₂×C₄×D₇₃	C₂⁴	1	16	yes	—
297	C₂×C₄×D₇₃	C₂⁴	1	16	yes	—
298	C₄⋊Dic₇₃	C₂⁴	1	4	yes	—
299	C₄⋊Dic₇₃	C₂⁴	1	4	yes	—
300	C₄⋊Dic₇₃	C₂⁴	1	8	yes	—
301	C₄⋊Dic₇₃	C₂⁴	1	16	yes	—
302	#11924007	C₂⁴	1	16	yes	—
303	#11924007	C₂⁴	1	8	yes	—
304	#11924007	C₂⁴	1	8	yes	—
305	C₂²⋊Dic₇₃	C₂⁴	1	8	yes	—
306	#11924005	C₂⁴	1	16	yes	—
307	#11924005	C₂⁴	1	16	yes	—
308	#11924005	C₂⁴	1	8	yes	—
309	#11924005	C₂⁴	1	16	yes	—
310	#11924005	C₂⁴	1	16	yes	—
311	#11924005	C₂⁴	1	16	yes	—
312	#11924005	C₂⁴	1	8	yes	—
313	#11924005	C₂⁴	1	8	yes	—
314	#11924005	C₂⁴	1	8	yes	—
315	#11924005	C₂⁴	1	16	yes	—
316	#11924005	C₂⁴	1	16	yes	—
317	C₄×Dic₇₃	C₂⁴	1	4	yes	—
318	C₄×Dic₇₃	C₂⁴	1	4	yes	—
319	C₄×Dic₇₃	C₂⁴	1	4	yes	—
320	C₄×Dic₇₃	C₂⁴	1	8	yes	—
321	C₄×Dic₇₃	C₂⁴	1	8	yes	—
322	C₄×Dic₇₃	C₂⁴	1	8	yes	—
323	C₄×Dic₇₃	C₂⁴	1	8	yes	—
324	C₄×Dic₇₃	C₂⁴	1	8	yes	—
325	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
326	C₂×Q₈×C₇₃	—	2	4	no	—
327	C₂×Q₈×C₇₃	—	4	4	no	—
328	C₂×Q₈×C₇₃	C₂⁴	1	4	yes	—
329	C₂×Q₈×C₇₃	C₂⁴	1	8	yes	—
330	C₂×D₄×C₇₃	#41	1	8	yes	complemented
331	C₂×D₄×C₇₃	C₂⁴	1	4	yes	—
332	C₂²×C₄×C₇₃	—	2	8	no	—
333	C₂²×C₄×C₇₃	—	4	8	no	—
334	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
335	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
337	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
338	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
339	C₂²×C₄×C₇₃	C₂⁴	1	8	yes	—
340	C₂²×C₄×C₇₃	C₂⁴	1	16	yes	—
341	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
343	C₄⋊C₄×C₇₃	C₂⁴	1	4	yes	—
344	C₄⋊C₄×C₇₃	C₂⁴	1	16	yes	—
345	C₄⋊C₄×C₇₃	C₂⁴	1	8	yes	—
346	C₄⋊C₄×C₇₃	C₂⁴	1	4	yes	—
347	C₄⋊C₄×C₇₃	C₂⁴	1	8	yes	—
348	C₄⋊C₄×C₇₃	C₂⁴	1	8	yes	—
349	C₄⋊C₄×C₇₃	C₂⁴	1	16	yes	—
350	C₂²⋊C₄×C₇₃	C₂⁴	1	16	yes	—
351	C₂²⋊C₄×C₇₃	C₂⁴	1	8	yes	—
352	C₄²×C₇₃	C₂⁴	1	8	yes	—
353	C₄²×C₇₃	C₂⁴	1	4	yes	—
354	C₂³×C₇₃	—	2	4	no	—
355	C₂³×C₇₃	—	2	4	no	—
356	C₂³×C₇₃	C₂×#41	1	8	yes	—
357	C₂³×C₇₃	C₂⁵	1	4	yes	—
358	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
359	C₂²×D₇₃	—	2	4	no	—
360	C₂²×D₇₃	—	2	4	no	—
361	C₂²×D₇₃	—	2	2	no	—
362	C₂²×D₇₃	—	2	2	no	—
363	C₂²×D₇₃	—	2	32	no	—
364	C₂²×D₇₃	—	2	8	no	—
365	C₂²×D₇₃	—	2	8	no	—
366	C₂²×D₇₃	—	2	8	no	—
367	C₂²×D₇₃	—	2	2	no	—
368	C₂²×D₇₃	—	2	32	no	—
369	C₂²×D₇₃	—	4	16	no	—
370	C₂²×D₇₃	—	4	64	no	—
371	C₂²×D₇₃	C₂×#41	1	8	yes	—
372	C₂²×D₇₃	C₂⁵	1	8	yes	—
373	C₂²×D₇₃	C₂⁵	1	2	yes	—
374	C₂²×D₇₃	C₂⁵	1	4	yes	—
375	Q₈×C₇₃	—	2	8	no	—
376	Q₈×C₇₃	—	4	8	no	—
377	D₄×C₇₃	C₂×#41	1	16	yes	complemented
378	C₂×C₄×C₇₃	—	2	4	no	—
379	C₂×C₄×C₇₃	—	2	4	no	—
380	C₂×C₄×C₇₃	—	2	4	no	—
381	C₂×C₄×C₇₃	—	2	8	no	—
382	C₂×C₄×C₇₃	—	2	2	no	—
383	C₂×C₄×C₇₃	—	2	16	no	—
384	C₂×C₄×C₇₃	—	4	16	no	—
385	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
386	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
387	C₂×C₄×C₇₃	C₂⁵	1	4	yes	—
388	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
389	C₂×C₄×C₇₃	C₂⁵	1	4	yes	—
390	C₂×C₄×C₇₃	C₂⁵	1	4	yes	—
391	C₂×C₄×C₇₃	C₂⁵	1	8	yes	—
392	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
393	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
394	C₂²⋊D₇₃	—	2	32	no	—
395	C₂²⋊D₇₃	—	2	16	no	—
396	C₂×Dic₇₃	—	2	2	no	—
397	C₂×Dic₇₃	—	2	2	no	—
398	C₂×Dic₇₃	—	2	4	no	—
399	C₂×Dic₇₃	—	2	4	no	—
400	C₂×Dic₇₃	—	2	16	no	—
401	C₂×Dic₇₃	—	2	4	no	—
402	C₂×Dic₇₃	—	2	16	no	—
403	C₂×Dic₇₃	H(5,𝔽₂)	1	4	yes	—
404	C₂×Dic₇₃	C₂⁵	1	2	yes	—
405	C₂×Dic₇₃	C₂⁵	1	2	yes	—
406	C₂×Dic₇₃	C₂⁵	1	4	yes	—
407	C₂×Dic₇₃	C₂⁵	1	4	yes	—
408	C₂×Dic₇₃	C₂⁵	1	4	yes	—
409	C₂×Dic₇₃	C₂⁵	1	2	yes	—
410	D₂₉₂	—	2	32	no	—
411	D₂₉₂	—	2	16	no	—
412	D₂₉₂	—	2	16	no	—
413	D₂₉₂	—	2	16	no	—
414	D₂₉₂	—	4	16	no	—
415	D₂₉₂	—	4	8	no	—
416	D₂₉₂	C₂×#41	1	16	yes	complemented
417	C₄×D₇₃	—	2	16	no	—
418	C₄×D₇₃	—	2	16	no	—
419	C₄×D₇₃	—	2	8	no	—
420	C₄×D₇₃	—	2	8	no	—
421	C₄×D₇₃	—	2	16	no	—
422	C₄×D₇₃	—	2	32	no	—
423	C₄×D₇₃	—	2	8	no	—
424	C₄×D₇₃	—	4	16	no	—
425	C₄×D₇₃	—	4	16	no	—
426	Dic₁₄₆	—	2	8	no	—
427	C₂²×C₇₃	—	2	4	no	—
428	C₂²×C₇₃	—	2	4	no	—
429	C₂²×C₇₃	—	2	16	no	—
430	C₂²×C₇₃	C₂²×#41	1	2	yes	—
431	C₂²×C₇₃	C₂²×#41	1	8	yes	—
432	C₂²×C₇₃	C₂²×#41	1	2	yes	—
433	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	2	yes	—
434	C₂²×C₇₃	C₂⁶	1	1	yes	characteristic
435	C₂×D₇₃	—	2	4	no	—
436	C₂×D₇₃	—	2	4	no	—
437	C₂×D₇₃	—	2	16	no	—
438	C₂×D₇₃	—	2	2	no	—
439	C₂×D₇₃	—	2	2	no	—
440	C₂×D₇₃	—	2	8	no	—
441	C₂×D₇₃	—	2	8	no	—
442	C₂×D₇₃	—	2	8	no	—
443	C₂×D₇₃	—	2	2	no	—
444	C₂×D₇₃	—	4	64	no	—
445	C₂×D₇₃	—	4	4	no	—
446	C₂×D₇₃	—	4	16	no	—
447	C₂×D₇₃	C₂²×#41	1	8	yes	—
448	C₄×C₇₃	—	2	4	no	—
449	C₄×C₇₃	—	2	4	no	—
450	C₄×C₇₃	—	2	4	no	—
451	C₄×C₇₃	—	2	8	no	—
452	C₄×C₇₃	—	2	2	no	—
453	C₄×C₇₃	C₂²×#41	1	4	yes	—
454	C₄×C₇₃	C₂²×#41	1	4	yes	—
455	Dic₇₃	—	2	4	no	—
456	Dic₇₃	—	2	2	no	—
457	Dic₇₃	—	2	2	no	—
458	Dic₇₃	—	2	4	no	—
459	Dic₇₃	—	2	4	no	—
460	Dic₇₃	C₂×H(5,𝔽₂)	1	4	yes	—
461	C₂×#3481	—	73	1	no	maximal, Sylow
462	C₂×C₇₃	—	2	8	no	—
463	C₂×C₇₃	#3481	1	4	yes	complemented
464	C₂×C₇₃	C₂³×#41	1	1	yes	characteristic
465	C₂×C₇₃	C₂³×#41	1	1	yes	characteristic
466	C₂×C₇₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
467	D₇₃	—	2	8	no	—
468	D₇₃	—	4	2	no	—
469	D₇₃	—	4	8	no	—
470	#3481	—	73	32	no	—
471	C₂×#559	—	73	1	no	—
472	C₂×#554	—	73	1	no	—
473	C₂×#554	D₇₃	1	1	yes	characteristic, complemented
474	C₂×#553	—	73	2	no	—
475	C₂×#553	—	73	2	no	—
476	C₂×#551	—	73	4	no	—
477	C₂×#546	—	73	2	no	—
478	C₂×#546	—	73	2	no	—
479	C₂×D₄²	—	73	1	no	—
480	C₂×#532	—	73	1	no	—
481	C₂×#529	—	73	2	no	—
482	C₂×#529	—	73	2	no	—
483	C₂×#525	—	73	4	no	—
484	C₂×C₄×#41	—	73	1	no	—
485	C₂×C₄×#41	—	73	1	no	—
486	C₂²×C₄×D₄	—	73	2	no	—
487	C₂²×C₄×D₄	—	73	2	no	—
488	C₇₃	C₂×#3481	1	1	yes	characteristic, complemented, Sylow
489	C₂²×#41	—	73	2	no	—
490	C₂²×#41	—	73	1	no	—
491	C₂²×#41	—	73	1	no	—
492	C₂³×D₄	—	73	2	no	—
493	C₂³×D₄	—	73	2	no	—
494	C₂⁴×C₄	—	73	4	no	—
495	#559	—	73	16	no	—
496	#554	—	73	16	no	—
497	#554	C₂×D₇₃	1	16	yes	complemented
498	#553	—	73	32	no	—
499	#553	—	73	32	no	—
500	#551	—	73	64	no	—
501	#546	—	73	32	no	—
502	#546	—	73	32	no	—
503	D₄²	—	73	16	no	—
504	#532	—	73	16	no	—
505	C₂×C₄⋊Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
506	C₂×#127	—	73	1	no	—
507	#529	—	73	32	no	—
508	#529	—	73	32	no	—
509	C₂×#126	—	73	4	no	—
510	C₂×#126	—	73	4	no	—
511	C₂×#125	—	73	2	no	—
512	C₂×#125	C₂×D₇₃	1	2	yes	complemented
513	C₂×#124	—	73	2	no	—
514	C₂×#124	—	73	2	no	—
515	C₂×#124	—	73	2	no	—
516	#525	—	73	64	no	—
517	C₂×#123	—	73	4	no	—
518	C₂×#123	—	73	4	no	—
519	C₂×#123	—	73	4	no	—
520	C₂×#123	—	73	4	no	—
521	C₂×C₂²⋊Q₈	—	73	4	no	—
522	C₂×C₂²⋊Q₈	—	73	2	no	—
523	C₂×C₂²⋊Q₈	C₂×D₇₃	1	4	yes	complemented
524	C₂×C₂²⋊Q₈	C₂×D₇₃	1	2	yes	complemented
525	C₂×#121	—	73	4	no	—
526	C₂×#121	—	73	2	no	—
527	C₂×#121	—	73	4	no	—
528	C₂×#121	—	73	2	no	—
529	C₂×#121	—	73	2	no	—
530	C₂×#121	—	73	2	no	—
531	C₂×#120	—	73	4	no	—
532	C₂×#120	—	73	4	no	—
533	C₄×#41	—	73	16	no	—
534	C₄×#41	—	73	16	no	—
535	C₂×C₄×Q₈	—	73	1	no	—
536	C₂×C₄×Q₈	—	73	1	no	—
537	C₂×C₄×Q₈	—	73	1	no	—
538	C₂×C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
539	C₂×C₄×D₄	—	73	1	no	—
540	C₂×C₄×D₄	—	73	4	no	—
541	C₂×C₄×D₄	—	73	2	no	—
542	C₂×C₄×D₄	—	73	32	no	—
543	C₂×C₄×D₄	—	73	1	no	—
544	C₂×C₄×D₄	—	73	4	no	—
545	C₂×C₄×D₄	—	73	2	no	—
546	C₂×C₄×D₄	—	73	2	no	—
547	C₂×C₄×D₄	—	73	2	no	—
548	C₂×C₄×D₄	—	73	4	no	—
549	C₂×C₄×D₄	—	73	2	no	—
550	C₂×C₄×D₄	—	73	2	no	—
551	C₂×C₄×D₄	—	73	32	no	—
552	C₂×C₄×D₄	—	73	4	no	—
553	C₂×C₄×D₄	—	73	2	no	—
554	C₂×C₄×D₄	—	73	2	no	—
555	C₂×C₄×D₄	—	73	1	no	—
556	C₂×C₄×D₄	—	73	2	no	—
557	C₂×C₄×D₄	C₂×D₇₃	1	2	yes	—
558	C₂×C₄×D₄	C₂×D₇₃	1	1	yes	characteristic
559	C₂×#117	—	73	2	no	—
560	C₂×#117	—	73	1	no	—
561	C₂×#117	—	73	1	no	—
562	C₂×#117	—	73	4	no	—
563	C₂×#117	—	73	2	no	—
564	C₂²×C₄⋊C₄	—	73	2	no	—
565	C₂²×C₄⋊C₄	C₂×D₇₃	1	2	yes	complemented
566	C₂²×C₂²⋊C₄	—	73	4	no	—
567	C₂²×C₂²⋊C₄	—	73	4	no	—
568	C₂²×C₄²	—	73	2	no	—
569	C₂²×C₄²	—	73	2	no	—
570	C₂²×C₄²	—	73	1	no	—
571	C₂⁵	—	73	4	no	—
572	C₂×#41	—	292	8	no	—
573	C₂×#41	—	73	16	no	—
574	C₂×#41	—	73	8	no	—
575	C₂×#41	—	73	8	no	—
576	C₂×#41	—	146	8	no	—
577	C₂×#41	—	146	8	no	—
578	C₂²×Q₈	—	73	1	no	—
579	C₂²×Q₈	C₂²×D₇₃	1	1	yes	characteristic
580	C₂²×Q₈	C₂²×D₇₃	1	2	yes	—
581	C₂²×D₄	—	73	2	no	—
582	C₂²×D₄	—	73	4	no	—
583	C₂²×D₄	—	73	16	no	—
584	C₂²×D₄	—	73	2	no	—
585	C₂²×D₄	—	73	4	no	—
586	C₂²×D₄	—	73	1	no	—
587	C₂²×D₄	—	73	2	no	—
588	C₂²×D₄	—	73	4	no	—
589	C₂²×D₄	—	73	2	no	—
590	C₂²×D₄	—	73	2	no	—
591	C₂²×D₄	—	73	16	no	—
592	C₂²×D₄	—	146	16	no	—
593	C₂²×D₄	—	146	16	no	—
594	C₂²×D₄	C₂²×D₇₃	1	1	yes	characteristic
595	C₂³×C₄	—	292	16	no	—
596	C₂³×C₄	—	73	4	no	—
597	C₂³×C₄	—	73	4	no	—
598	C₂³×C₄	—	73	32	no	—
599	C₂³×C₄	—	73	2	no	—
600	C₂³×C₄	—	73	2	no	—
601	C₂³×C₄	—	73	2	no	—
602	C₂³×C₄	—	73	2	no	—
603	C₂³×C₄	—	73	4	no	—
604	C₂³×C₄	—	73	1	no	—
605	C₂³×C₄	—	73	1	no	—
606	C₂³×C₄	—	73	2	no	—
607	C₂³×C₄	—	73	1	no	—
608	C₂³×C₄	C₂²×D₇₃	1	2	yes	—
609	C₂³×C₄	C₂²×D₇₃	1	4	yes	—
610	C₄⋊Q₈	C₂²×D₇₃	1	8	yes	complemented
611	#127	—	73	8	no	—
612	#126	—	73	32	no	—
613	#126	—	73	32	no	—
614	#125	—	73	16	no	—
615	#125	C₂²×D₇₃	1	16	yes	complemented
616	#124	—	73	16	no	—
617	#124	—	73	16	no	—
618	#124	—	73	16	no	—
619	#123	—	73	32	no	—
620	#123	—	73	32	no	—
621	#123	—	73	32	no	—
622	#123	—	73	32	no	—
623	C₂²⋊Q₈	—	73	32	no	—
624	C₂²⋊Q₈	—	73	16	no	—
625	C₂²⋊Q₈	C₂²×D₇₃	1	32	yes	complemented
626	C₂²⋊Q₈	C₂²×D₇₃	1	16	yes	complemented
627	#121	—	73	32	no	—
628	#121	—	73	16	no	—
629	#121	—	73	32	no	—
630	#121	—	73	16	no	—
631	#121	—	73	16	no	—
632	#121	—	73	16	no	—
633	#120	—	73	32	no	—
634	#120	—	73	32	no	—
635	C₄×Q₈	—	73	8	no	—
636	C₄×Q₈	—	73	8	no	—
637	C₄×Q₈	—	73	8	no	—
638	C₄×Q₈	C₂²×D₇₃	1	8	yes	complemented
639	C₄×D₄	—	73	8	no	—
640	C₄×D₄	—	73	32	no	—
641	C₄×D₄	—	73	16	no	—
642	C₄×D₄	—	73	8	no	—
643	C₄×D₄	—	73	32	no	—
644	C₄×D₄	—	73	16	no	—
645	C₄×D₄	—	73	16	no	—
646	C₄×D₄	—	73	16	no	—
647	C₄×D₄	—	73	32	no	—
648	C₄×D₄	—	73	16	no	—
649	C₄×D₄	—	73	16	no	—
650	C₄×D₄	—	73	32	no	—
651	C₄×D₄	—	73	16	no	—
652	C₄×D₄	—	73	16	no	—
653	C₄×D₄	—	73	8	no	—
654	C₄×D₄	—	73	16	no	—
655	C₄×D₄	C₂²×D₇₃	1	16	yes	—
656	C₄×D₄	C₂²×D₇₃	1	8	yes	—
657	#117	—	73	16	no	—
658	#117	—	73	8	no	—
659	#117	—	73	8	no	—
660	#117	—	73	32	no	—
661	#117	—	73	16	no	—
662	C₂×C₄⋊C₄	—	73	1	no	—
663	C₂×C₄⋊C₄	—	73	4	no	—
664	C₂×C₄⋊C₄	—	73	1	no	—
665	C₂×C₄⋊C₄	—	73	2	no	—
666	C₂×C₄⋊C₄	—	73	2	no	—
667	C₂×C₄⋊C₄	—	73	2	no	—
668	C₂×C₄⋊C₄	—	73	4	no	—
669	C₂×C₄⋊C₄	—	73	16	no	—
670	C₂×C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
671	C₂×C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
672	C₂×C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
673	C₂×C₄⋊C₄	C₂²×D₇₃	1	4	yes	—
674	C₂×C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
675	C₂×C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
676	C₂×C₄⋊C₄	C₂²×D₇₃	1	4	yes	—
677	C₂×C₄⋊C₄	C₂²×D₇₃	1	16	yes	complemented
678	C₂×C₂²⋊C₄	—	73	2	no	—
679	C₂×C₂²⋊C₄	—	73	2	no	—
680	C₂×C₂²⋊C₄	—	73	4	no	—
681	C₂×C₂²⋊C₄	—	73	4	no	—
682	C₂×C₂²⋊C₄	—	73	4	no	—
683	C₂×C₂²⋊C₄	—	73	4	no	—
684	C₂×C₂²⋊C₄	—	73	4	no	—
685	C₂×C₂²⋊C₄	—	73	32	no	—
686	C₂×C₂²⋊C₄	—	73	2	no	—
687	C₂×C₂²⋊C₄	—	73	2	no	—
688	C₂×C₂²⋊C₄	—	73	2	no	—
689	C₂×C₂²⋊C₄	—	73	4	no	—
690	C₂×C₂²⋊C₄	—	73	4	no	—
691	C₂×C₂²⋊C₄	—	73	32	no	—
692	C₂×C₂²⋊C₄	C₂²×D₇₃	1	4	yes	—
693	C₂×C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
694	C₂×C₄²	—	73	1	no	—
695	C₂×C₄²	—	73	2	no	—
696	C₂×C₄²	—	73	2	no	—
697	C₂×C₄²	—	73	2	no	—
698	C₂×C₄²	—	73	2	no	—
699	C₂×C₄²	—	73	2	no	—
700	C₂×C₄²	—	73	1	no	—
701	C₂×C₄²	—	73	1	no	—
702	C₂×C₄²	—	73	16	no	—
703	C₂×C₄²	—	73	16	no	—
704	C₂×C₄²	—	73	8	no	—
705	C₂×C₄²	C₂²×D₇₃	1	2	yes	—
706	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
707	C₂⁴	—	292	8	no	—
708	C₂⁴	—	73	16	no	—
709	C₂⁴	—	73	2	no	—
710	C₂⁴	—	73	4	no	—
711	C₂⁴	—	73	1	no	—
712	C₂⁴	—	146	16	no	—
713	C₂⁴	—	146	16	no	—
714	C₂⁴	C₂³×D₇₃	1	2	yes	—
715	#41	—	292	32	no	—
716	#41	—	146	32	no	—
717	#41	—	146	32	no	—
718	C₂×Q₈	—	2	4	no	—
719	C₂×Q₈	—	4	4	no	—
720	C₂×Q₈	—	73	4	no	—
721	C₂×Q₈	—	146	4	no	—
722	C₂×Q₈	C₂³×D₇₃	1	4	yes	—
723	C₂×Q₈	C₂³×D₇₃	1	8	yes	—
724	C₂×D₄	—	292	8	no	—
725	C₂×D₄	—	292	4	no	—
726	C₂×D₄	—	73	8	no	—
727	C₂×D₄	—	73	16	no	—
728	C₂×D₄	—	73	8	no	—
729	C₂×D₄	—	73	8	no	—
730	C₂×D₄	—	73	16	no	—
731	C₂×D₄	—	73	4	no	—
732	C₂×D₄	—	73	8	no	—
733	C₂×D₄	—	73	16	no	—
734	C₂×D₄	—	73	8	no	—
735	C₂×D₄	—	73	8	no	—
736	C₂×D₄	—	146	64	no	—
737	C₂×D₄	—	146	16	no	—
738	C₂×D₄	—	146	8	no	—
739	C₂×D₄	—	146	16	no	—
740	C₂×D₄	—	146	8	no	—
741	C₂×D₄	—	146	64	no	—
742	C₂×D₄	—	146	8	no	—
743	C₂×D₄	—	146	8	no	—
744	C₂×D₄	#11924029	1	8	yes	complemented
745	C₂×D₄	C₂³×D₇₃	1	4	yes	—
746	C₂²×C₄	—	2	8	no	—
747	C₂²×C₄	—	4	8	no	—
748	C₂²×C₄	—	292	8	no	—
749	C₂²×C₄	—	292	8	no	—
750	C₂²×C₄	—	292	64	no	—
751	C₂²×C₄	—	73	16	no	—
752	C₂²×C₄	—	73	16	no	—
753	C₂²×C₄	—	73	1	no	—
754	C₂²×C₄	—	73	8	no	—
755	C₂²×C₄	—	73	8	no	—
756	C₂²×C₄	—	73	1	no	—
757	C₂²×C₄	—	73	1	no	—
758	C₂²×C₄	—	73	2	no	—
759	C₂²×C₄	—	73	2	no	—
760	C₂²×C₄	—	73	2	no	—
761	C₂²×C₄	—	73	8	no	—
762	C₂²×C₄	—	73	8	no	—
763	C₂²×C₄	—	73	4	no	—
764	C₂²×C₄	—	73	4	no	—
765	C₂²×C₄	—	73	8	no	—
766	C₂²×C₄	—	73	4	no	—
767	C₂²×C₄	—	73	16	no	—
768	C₂²×C₄	—	146	8	no	—
769	C₂²×C₄	—	146	16	no	—
770	C₂²×C₄	—	146	4	no	—
771	C₂²×C₄	—	146	8	no	—
772	C₂²×C₄	—	146	8	no	—
773	C₂²×C₄	—	146	8	no	—
774	C₂²×C₄	—	146	4	no	—
775	C₂²×C₄	—	146	8	no	—
776	C₂²×C₄	—	146	4	no	—
777	C₂²×C₄	C₂³×D₇₃	1	8	yes	—
778	C₂²×C₄	C₂³×D₇₃	1	2	yes	—
779	C₂²×C₄	C₂³×D₇₃	1	2	yes	—
780	C₂²×C₄	C₂³×D₇₃	1	2	yes	—
781	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
782	C₂²×C₄	C₂³×D₇₃	1	4	yes	—
783	C₂²×C₄	C₂³×D₇₃	1	16	yes	—
784	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
785	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
786	C₄⋊C₄	—	73	16	no	—
787	C₄⋊C₄	—	73	8	no	—
788	C₄⋊C₄	—	73	8	no	—
789	C₄⋊C₄	—	73	4	no	—
790	C₄⋊C₄	—	73	4	no	—
791	C₄⋊C₄	—	73	8	no	—
792	C₄⋊C₄	—	73	16	no	—
793	C₄⋊C₄	C₂³×D₇₃	1	8	yes	—
794	C₄⋊C₄	C₂³×D₇₃	1	4	yes	—
795	C₄⋊C₄	C₂³×D₇₃	1	8	yes	—
796	C₄⋊C₄	C₂³×D₇₃	1	16	yes	—
797	C₄⋊C₄	C₂³×D₇₃	1	8	yes	—
798	C₄⋊C₄	C₂³×D₇₃	1	4	yes	—
799	C₄⋊C₄	C₂³×D₇₃	1	16	yes	—
800	C₂²⋊C₄	—	73	8	no	—
801	C₂²⋊C₄	—	73	8	no	—
802	C₂²⋊C₄	—	73	16	no	—
803	C₂²⋊C₄	—	73	16	no	—
804	C₂²⋊C₄	—	73	16	no	—
805	C₂²⋊C₄	—	73	16	no	—
806	C₂²⋊C₄	—	73	16	no	—
807	C₂²⋊C₄	—	73	8	no	—
808	C₂²⋊C₄	—	73	8	no	—
809	C₂²⋊C₄	—	73	8	no	—
810	C₂²⋊C₄	—	73	16	no	—
811	C₂²⋊C₄	—	73	16	no	—
812	C₂²⋊C₄	C₂³×D₇₃	1	16	yes	—
813	C₂²⋊C₄	C₂³×D₇₃	1	8	yes	—
814	C₄²	—	73	4	no	—
815	C₄²	—	73	4	no	—
816	C₄²	—	73	4	no	—
817	C₄²	—	73	8	no	—
818	C₄²	—	73	8	no	—
819	C₄²	—	73	8	no	—
820	C₄²	—	73	8	no	—
821	C₄²	—	73	8	no	—
822	C₄²	C₂³×D₇₃	1	8	yes	—
823	C₄²	C₂³×D₇₃	1	4	yes	—
824	C₂³	—	2	4	no	—
825	C₂³	—	2	4	no	—
826	C₂³	—	292	64	no	—
827	C₂³	—	292	16	no	—
828	C₂³	—	73	8	no	—
829	C₂³	—	73	4	no	—
830	C₂³	—	73	8	no	—
831	C₂³	—	73	2	no	—
832	C₂³	—	146	32	no	—
833	C₂³	—	146	2	no	—
834	C₂³	—	146	8	no	—
835	C₂³	—	146	2	no	—
836	C₂³	—	146	32	no	—
837	C₂³	—	146	8	no	—
838	C₂³	—	146	8	no	—
839	C₂³	—	146	2	no	—
840	C₂³	—	146	4	no	—
841	C₂³	—	146	4	no	—
842	C₂³	C₂×#11924029	1	8	yes	—
843	C₂³	C₂⁴×D₇₃	1	4	yes	—
844	C₂³	C₂⁴×D₇₃	1	1	yes	characteristic
845	Q₈	—	2	8	no	—
846	Q₈	—	4	8	no	—
847	Q₈	—	146	8	no	—
848	D₄	—	292	16	no	—
849	D₄	—	292	8	no	—
850	D₄	—	73	16	no	—
851	D₄	—	146	32	no	—
852	D₄	—	146	16	no	—
853	D₄	—	146	32	no	—
854	D₄	—	146	16	no	—
855	D₄	—	146	16	no	—
856	D₄	—	146	16	no	—
857	D₄	C₂×#11924029	1	16	yes	complemented
858	C₂×C₄	—	2	4	no	—
859	C₂×C₄	—	2	4	no	—
860	C₂×C₄	—	2	4	no	—
861	C₂×C₄	—	2	8	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	16	no	—
864	C₂×C₄	—	4	16	no	—
865	C₂×C₄	—	292	16	no	—
866	C₂×C₄	—	292	16	no	—
867	C₂×C₄	—	73	4	no	—
868	C₂×C₄	—	73	2	no	—
869	C₂×C₄	—	73	2	no	—
870	C₂×C₄	—	73	2	no	—
871	C₂×C₄	—	73	4	no	—
872	C₂×C₄	—	73	4	no	—
873	C₂×C₄	—	73	4	no	—
874	C₂×C₄	—	146	16	no	—
875	C₂×C₄	—	146	32	no	—
876	C₂×C₄	—	146	8	no	—
877	C₂×C₄	—	146	16	no	—
878	C₂×C₄	—	146	16	no	—
879	C₂×C₄	—	146	2	no	—
880	C₂×C₄	—	146	2	no	—
881	C₂×C₄	—	146	4	no	—
882	C₂×C₄	—	146	4	no	—
883	C₂×C₄	—	146	16	no	—
884	C₂×C₄	—	146	4	no	—
885	C₂×C₄	—	146	8	no	—
886	C₂×C₄	—	146	16	no	—
887	C₂×C₄	—	146	8	no	—
888	C₂×C₄	#41×D₇₃	1	4	yes	—
889	C₂×C₄	C₂×#11924029	1	4	yes	—
890	C₂×C₄	C₂⁴×D₇₃	1	4	yes	—
891	C₂×C₄	C₂⁴×D₇₃	1	4	yes	—
892	C₂×C₄	C₂⁴×D₇₃	1	4	yes	—
893	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
894	C₂×C₄	C₂⁴×D₇₃	1	8	yes	—
895	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
896	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
897	C₂²	—	2	16	no	—
898	C₂²	—	2	4	no	—
899	C₂²	—	2	4	no	—
900	C₂²	—	292	64	no	—
901	C₂²	—	292	16	no	—
902	C₂²	—	292	4	no	—
903	C₂²	—	73	8	no	—
904	C₂²	—	146	2	no	—
905	C₂²	—	146	8	no	—
906	C₂²	—	146	2	no	—
907	C₂²	—	146	8	no	—
908	C₂²	—	146	8	no	—
909	C₂²	—	146	2	no	—
910	C₂²	—	146	16	no	—
911	C₂²	—	146	4	no	—
912	C₂²	—	146	4	no	—
913	C₂²	C₂×#41×D₇₃	1	2	yes	—
914	C₂²	C₂²×#11924029	1	8	yes	—
915	C₂²	C₂²×#11924029	1	2	yes	—
916	C₂²	H(5,𝔽₂)×D₇₃	1	2	yes	—
917	C₂²	C₂⁵×D₇₃	1	1	yes	characteristic
918	C₄	—	2	4	no	—
919	C₄	—	2	4	no	—
920	C₄	—	2	4	no	—
921	C₄	—	2	8	no	—
922	C₄	—	2	2	no	—
923	C₄	—	73	4	no	—
924	C₄	—	146	2	no	—
925	C₄	—	146	2	no	—
926	C₄	—	146	4	no	—
927	C₄	—	146	4	no	—
928	C₄	—	146	4	no	—
929	C₄	C₂×#41×D₇₃	1	4	yes	—
930	C₄	C₂²×#11924029	1	4	yes	—
931	C₂	—	2	8	no	—
932	C₂	—	292	8	no	—
933	C₂	—	292	2	no	—
934	C₂	—	146	8	no	—
935	C₂	#22623542	1	4	yes	direct product factor
936	C₂	C₂²×#41×D₇₃	1	1	yes	characteristic
937	C₂	C₂³×#11924029	1	1	yes	characteristic
938	C₂	C₂×H(5,𝔽₂)×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₇₃
commutator, cosocle	C₂²×C₇₃	C₂⁶
Frattini	C₂²	C₂⁵×D₇₃
Fitting	C₂×#554×C₇₃	C₂
socle	C₂³×C₇₃	C₂⁵
hypercenter	C₂×#554	D₇₃
hypocenter	C₇₃	C₂×#3481
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×#554

Complements

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

N	H ≅ G/N	type
1. #22623542	C₂	direct (N × H)
2. C₂×#17989322	C₂	semidirect
3. C₂×#17989298	C₂	semidirect
4. C₂×#17989290	C₂	semidirect
5. C₂×#17989285	C₂	semidirect
6. C₂×#17989264	C₂	semidirect
7. C₂×#17989232	C₂	semidirect
8. C₂×#17989228	C₂	semidirect
9. C₂×D₄×D₂₉₂	C₂	semidirect
10. C₂×#17989138	C₂	semidirect
11. C₂×#17989123	C₂	semidirect
12. C₂×#17989122	C₂	semidirect
13. C₂×#17989100	C₂	semidirect
14. C₂×C₄×#11924029	C₂	semidirect
15. C₂×C₄×#11924027	C₂	semidirect
16. C₂²×#14556553	C₂	semidirect
17. C₂×C₄×D₄×D₇₃	C₂	semidirect
18. C₂×#554×C₇₃	C₂	semidirect
20. C₂²×#11924029	C₂²	semidirect
24. C₂³×C₄×D₇₃	C₂²	semidirect
25. #17989322	C₂²	semidirect
26. #17989298	C₂²	semidirect
27. #17989290	C₂²	semidirect
28. #17989285	C₂²	semidirect
29. #17989264	C₂²	semidirect
30. #17989232	C₂²	semidirect
31. #17989228	C₂²	semidirect
32. D₄×D₂₉₂	C₂²	semidirect
33. #17989138	C₂²	semidirect
35. #17989123	C₂²	semidirect
36. #17989122	C₂²	semidirect
37. C₂×#14556586	C₂²	semidirect
38. C₂×#14556586	C₂²	semidirect
39. C₂×#14556582	C₂²	semidirect
40. C₂×#14556580	C₂²	semidirect
41. C₂×#14556580	C₂²	semidirect
42. C₂×#14556579	C₂²	semidirect
43. #17989100	C₂²	semidirect
44. C₂×#14556576	C₂²	semidirect
45. C₂×#14556576	C₂²	semidirect
46. C₂×#14556576	C₂²	semidirect
47. C₂×#14556575	C₂²	semidirect
48. C₂×#14556571	C₂²	semidirect
49. C₂×#14556567	C₂²	semidirect
51. C₂×#14556566	C₂²	semidirect
52. C₂×#14556566	C₂²	semidirect
53. C₂×#14556566	C₂²	semidirect
55. C₂×#14556565	C₂²	semidirect
57. C₂×#14556561	C₂²	semidirect
58. C₄×#11924029	C₂²	semidirect
59. C₄×#11924027	C₂²	semidirect
60. C₂×Q₈×Dic₇₃	C₂²	semidirect
61. C₂×C₄×Dic₁₄₆	C₂²	semidirect
62. C₂×#14556556	C₂²	semidirect
64. C₂×C₄×D₂₉₂	C₂²	semidirect
65. C₂×C₄×D₂₉₂	C₂²	semidirect
69. C₂×#14556553	C₂²	semidirect
70. C₂×#14556553	C₂²	semidirect
71. C₂×#14556553	C₂²	semidirect
72. C₂×#14556553	C₂²	semidirect
73. C₂×#14556553	C₂²	semidirect
74. C₂×#14556553	C₂²	semidirect
75. C₂×#14556553	C₂²	semidirect
76. C₂×C₄×C₂²⋊D₇₃	C₂²	semidirect
77. C₂×C₄×C₂²⋊D₇₃	C₂²	semidirect
78. C₂×#14556551	C₂²	semidirect
79. C₂×#14556551	C₂²	semidirect
80. C₄×D₄×D₇₃	C₂²	semidirect
81. C₂×#14556549	C₂²	semidirect
82. C₂×#14556549	C₂²	semidirect
83. C₂×#14556549	C₂²	semidirect
84. C₂×#14556549	C₂²	semidirect
85. C₂×#14556547	C₂²	semidirect
86. C₂×C₄⋊C₄×D₇₃	C₂²	semidirect
87. C₂²×#11924005	C₂²	semidirect
88. C₂×C₂²⋊C₄×D₇₃	C₂²	semidirect
89. C₂²×C₄×Dic₇₃	C₂²	semidirect
90. C₂×C₄²×D₇₃	C₂²	semidirect
91. C₂×C₄²×D₇₃	C₂²	semidirect
92. #554×C₇₃	C₂²	semidirect
93. C₂×C₄⋊Q₈×C₇₃	C₂²	semidirect
94. C₂×#125×C₇₃	C₂²	semidirect
95. C₂×C₂²⋊Q₈×C₇₃	C₂²	semidirect
96. C₂×C₂²⋊Q₈×C₇₃	C₂²	semidirect
97. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
100. C₂²×C₄⋊C₄×C₇₃	C₂²	semidirect
105. C₂×#11924029	C₂³	semidirect
134. C₂²×C₄×D₇₃	C₂³	semidirect
136. #14556586	C₂³	semidirect
137. #14556586	C₂³	semidirect
138. #14556582	C₂³	semidirect
139. #14556580	C₂³	semidirect
140. #14556580	C₂³	semidirect
141. #14556579	C₂³	semidirect
142. #14556576	C₂³	semidirect
143. #14556576	C₂³	semidirect
144. #14556576	C₂³	semidirect
145. #14556575	C₂³	semidirect
146. #14556571	C₂³	semidirect
147. #14556567	C₂³	semidirect
149. #14556566	C₂³	semidirect
150. #14556566	C₂³	semidirect
151. #14556566	C₂³	semidirect
153. #14556565	C₂³	semidirect
155. #14556561	C₂³	semidirect
156. Q₈×Dic₇₃	C₂³	semidirect
157. C₄×Dic₁₄₆	C₂³	semidirect
158. #14556556	C₂³	semidirect
160. C₄×D₂₉₂	C₂³	semidirect
161. C₄×D₂₉₂	C₂³	semidirect
165. #14556553	C₂³	semidirect
166. #14556553	C₂³	semidirect
167. #14556553	C₂³	semidirect
168. #14556553	C₂³	semidirect
169. #14556553	C₂³	semidirect
170. #14556553	C₂³	semidirect
171. C₄×C₂²⋊D₇₃	C₂³	semidirect
172. C₄×C₂²⋊D₇₃	C₂³	semidirect
173. #14556551	C₂³	semidirect
174. #14556551	C₂³	semidirect
175. #14556549	C₂³	semidirect
176. #14556549	C₂³	semidirect
177. #14556549	C₂³	semidirect
178. #14556549	C₂³	semidirect
179. #14556547	C₂³	semidirect
187. C₄⋊C₄×D₇₃	C₂³	semidirect
200. C₂×#11924005	C₂³	semidirect
201. C₂²⋊C₄×D₇₃	C₂³	semidirect
210. C₂×C₄×Dic₇₃	C₂³	semidirect
211. C₄²×D₇₃	C₂³	semidirect
212. C₄²×D₇₃	C₂³	semidirect
218. C₄⋊Q₈×C₇₃	C₂³	semidirect
219. #125×C₇₃	C₂³	semidirect
220. C₂²⋊Q₈×C₇₃	C₂³	semidirect
221. C₂²⋊Q₈×C₇₃	C₂³	semidirect
222. C₄×Q₈×C₇₃	C₂³	semidirect
232. C₂×C₄⋊C₄×C₇₃	C₂³	semidirect
256. C₂×D₂₉₂	#41	semidirect
330. C₂×D₄×C₇₃	#41	semidirect
377. D₄×C₇₃	C₂×#41	semidirect
416. D₂₉₂	C₂×#41	semidirect
463. C₂×C₇₃	#3481	semidirect
473. C₂×#554	D₇₃	semidirect
488. C₇₃	C₂×#3481	semidirect
497. #554	C₂×D₇₃	semidirect
505. C₂×C₄⋊Q₈	C₂×D₇₃	semidirect
512. C₂×#125	C₂×D₇₃	semidirect
523. C₂×C₂²⋊Q₈	C₂×D₇₃	semidirect
524. C₂×C₂²⋊Q₈	C₂×D₇₃	semidirect
538. C₂×C₄×Q₈	C₂×D₇₃	semidirect
565. C₂²×C₄⋊C₄	C₂×D₇₃	semidirect
610. C₄⋊Q₈	C₂²×D₇₃	semidirect
615. #125	C₂²×D₇₃	semidirect
625. C₂²⋊Q₈	C₂²×D₇₃	semidirect
626. C₂²⋊Q₈	C₂²×D₇₃	semidirect
638. C₄×Q₈	C₂²×D₇₃	semidirect
677. C₂×C₄⋊C₄	C₂²×D₇₃	semidirect
744. C₂×D₄	#11924029	semidirect
857. D₄	C₂×#11924029	semidirect
935. C₂	#22623542	direct (N × H)

Maximal subgroups

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

subgroup	index
#22623542	2
C₂×#17989322	2
C₂×#17989298	2
C₂×#17989290	2
C₂×#17989285	2
C₂×#17989264	2
C₂×#17989232	2
C₂×#17989228	2
C₂×D₄×D₂₉₂	2
C₂×#17989138	2
C₂×#17989123	2
C₂×#17989122	2
C₂×#17989100	2
C₂×C₄×#11924029	2
C₂×C₄×#11924027	2
C₂²×#14556553	2
C₂×C₄×D₄×D₇₃	2
C₂×#554×C₇₃	2
C₂×#3481	73

Subgroups — C2×#22623542 #33993071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22623542 #33993071