Subgroups — #35152957

Order 20224.

1914 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23776956	C₂	1	1	yes	maximal, characteristic
2	#23772419	C₂	1	1	yes	maximal, characteristic, complemented
3	#23772417	C₂	1	1	yes	maximal, characteristic, complemented
4	#23772405	C₂	1	1	yes	maximal, characteristic, complemented
5	#23772402	C₂	1	2	yes	maximal, complemented
6	#23772401	C₂	1	2	yes	maximal, complemented
7	#23772401	C₂	1	1	yes	maximal, characteristic, complemented
8	#23772382	C₂	1	2	yes	maximal, complemented
9	#23772381	C₂	1	2	yes	maximal, complemented
10	#23772378	C₂	1	1	yes	maximal, characteristic, complemented
11	#23772366	C₂	1	1	yes	maximal, characteristic, complemented
12	#23772365	C₂	1	1	yes	maximal, characteristic, complemented
13	#23772342	C₂	1	1	yes	maximal, characteristic, complemented
14	#23772331	C₂	1	1	yes	maximal, characteristic, complemented
15	D₄×#11929607	C₂	1	1	yes	maximal, characteristic, complemented
16	#23772120	C₂	1	2	yes	maximal, complemented
17	#23772098	C₂	1	2	yes	maximal, complemented
18	#436×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#23772067	C₂	1	1	yes	maximal, characteristic, complemented
20	#23772056	C₂	1	2	yes	maximal, complemented
21	C₄×#14579167	C₂	1	1	yes	maximal, characteristic, complemented
22	#23771816	C₂	1	2	yes	maximal, complemented
23	C₇₉×#2966	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14579167	C₂²	1	1	yes	characteristic
25	C₂×#14579167	C₂²	1	1	yes	characteristic
26	C₂²×#11929607	C₂²	1	2	yes	—
27	C₂×M₁₆×D₇₉	C₂²	1	2	yes	—
28	#19099282	C₄	1	1	yes	characteristic
29	#19099277	C₄	1	1	yes	characteristic
30	#19099269	C₄	1	1	yes	characteristic
31	#19099258	C₄	1	2	yes	—
32	#19099251	C₄	1	1	yes	characteristic
33	#19099249	C₄	1	2	yes	—
34	#19099247	C₄	1	1	yes	characteristic
35	#19099241	C₄	1	2	yes	—
36	#19099238	C₄	1	2	yes	—
37	#19099215	C₄	1	1	yes	characteristic
38	#19099210	C₄	1	1	yes	characteristic
39	#19099206	C₄	1	1	yes	characteristic
40	#19099117	C₂²	1	1	yes	characteristic
41	#19099095	C₂²	1	1	yes	characteristic
42	#19099095	C₂²	1	2	yes	—
43	#19099091	C₂²	1	2	yes	—
44	#19099072	C₂²	1	2	yes	—
45	C₄×#11929625	C₂²	1	1	yes	characteristic
46	C₄×#11929624	C₂²	1	1	yes	characteristic
47	C₄×#11929624	C₂²	1	1	yes	characteristic
48	C₄×D₄×D₇₉	C₂²	1	1	yes	characteristic
49	#117×D₇₉	C₂²	1	2	yes	—
50	#19098694	C₂²	1	1	yes	characteristic, complemented
51	#19098693	C₂²	1	1	yes	characteristic, complemented
52	#19098693	C₂²	1	1	yes	characteristic, complemented
53	#19098693	C₂²	1	2	yes	complemented
54	#19098692	C₂²	1	2	yes	complemented
55	#19098691	C₂²	1	2	yes	complemented
56	Q₈×C₇₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
57	#19098687	C₂²	1	1	yes	characteristic, complemented
58	#19098687	C₂²	1	1	yes	characteristic, complemented
59	#19098687	C₂²	1	2	yes	complemented
60	#19098642	C₂²	1	1	yes	characteristic
61	#19098642	C₂²	1	1	yes	characteristic
62	#19098642	C₂²	1	2	yes	complemented
63	#19098641	C₂²	1	1	yes	characteristic
64	#19098641	C₂²	1	2	yes	complemented
65	#19098640	C₂²	1	1	yes	characteristic
66	#19098640	C₂²	1	1	yes	characteristic
67	#19098640	C₂²	1	2	yes	complemented
68	#19098639	C₂²	1	2	yes	—
69	#19098638	C₂²	1	2	yes	—
70	#19098638	C₂²	1	2	yes	complemented
71	#19098638	C₂²	1	2	yes	complemented
72	#19098638	C₂²	1	2	yes	complemented
73	#19098636	C₂²	1	2	yes	complemented
74	#19098635	C₂²	1	2	yes	complemented
75	#19098634	C₂²	1	2	yes	—
76	#19098634	C₂²	1	2	yes	complemented
77	#19098634	C₂²	1	2	yes	complemented
78	#19098634	C₂²	1	2	yes	complemented
79	#19098633	C₂²	1	2	yes	complemented
80	#19098632	C₂²	1	2	yes	complemented
81	#19098631	C₂²	1	2	yes	—
82	D₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
83	(C₂²⋊D₇₉)⋊C₈	C₂²	1	2	yes	complemented
84	#19098625	C₂²	1	2	yes	complemented
85	#19098624	C₂²	1	2	yes	complemented
86	#19098621	C₂²	1	2	yes	complemented
87	#19098621	C₂²	1	2	yes	complemented
88	#19098621	C₂²	1	2	yes	complemented
89	#19098619	C₂²	1	2	yes	complemented
90	#19098619	C₂²	1	1	yes	characteristic, complemented
91	#19098618	C₂²	1	2	yes	complemented
92	#19098616	C₂²	1	1	yes	characteristic, complemented
93	#19098615	C₂²	1	2	yes	complemented
94	#19098615	C₂²	1	1	yes	characteristic, complemented
95	#19098614	C₂²	1	2	yes	complemented
96	#19098588	C₂²	1	2	yes	—
97	#19098588	C₂²	1	2	yes	—
98	#19098585	C₂²	1	1	yes	characteristic
99	C₄⋊C₈×D₇₉	C₂²	1	1	yes	characteristic
100	#19098528	C₂²	1	2	yes	—
101	#19098525	C₂²	1	2	yes	—
102	C₂²⋊C₈×D₇₉	C₂²	1	2	yes	—
103	#19098521	C₂²	1	2	yes	complemented
104	#19098520	C₂²	1	2	yes	—
105	#19098520	C₂²	1	2	yes	—
106	#19098519	C₂²	1	2	yes	complemented
107	#19098518	C₂²	1	2	yes	complemented
108	#19098518	C₂²	1	1	yes	characteristic, complemented
109	#19098518	C₂²	1	1	yes	characteristic, complemented
110	#19098517	C₂²	1	1	yes	characteristic
111	#19098517	C₂²	1	1	yes	characteristic
112	#19098517	C₂²	1	2	yes	—
113	#19098517	C₂²	1	1	yes	characteristic, complemented
114	#19098517	C₂²	1	1	yes	characteristic, complemented
115	C₄×#11929608	C₂²	1	1	yes	characteristic, complemented
116	#19098515	C₂²	1	2	yes	complemented
117	#19098515	C₂²	1	2	yes	complemented
118	C₄×#11929607	C₂²	1	1	yes	characteristic
119	C₄×#11929607	C₂²	1	2	yes	complemented
120	C₄×#11929607	C₂²	1	1	yes	characteristic, complemented
121	C₄×#11929607	C₂²	1	2	yes	complemented
122	C₄×C₈×D₇₉	C₂²	1	1	yes	characteristic
123	C₄×C₈×D₇₉	C₂²	1	1	yes	characteristic, complemented
124	#529×C₇₉	C₂²	1	1	yes	characteristic
125	#446×C₇₉	C₂²	1	1	yes	characteristic, complemented
126	C₈×Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
127	#436×C₇₉	C₂²	1	1	yes	characteristic
128	#435×C₇₉	C₂²	1	2	yes	complemented
129	C₈×D₄×C₇₉	C₂²	1	1	yes	characteristic
130	C₈×D₄×C₇₉	C₂²	1	2	yes	complemented
131	#433×C₇₉	C₂²	1	2	yes	complemented
132	#432×C₇₉	C₂²	1	1	yes	characteristic, complemented
133	#405×C₇₉	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
135	C₂×#11929625	C₂×C₄	1	1	yes	characteristic
136	C₂×#11929624	C₂×C₄	1	1	yes	characteristic
137	C₂×#11929624	C₂³	1	1	yes	characteristic
138	C₂×D₄×D₇₉	C₂×C₄	1	1	yes	characteristic
139	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
140	#14579167	—	2	4	no	—
141	#14579167	—	2	4	no	—
142	C₂×#11929608	C₂³	1	1	yes	characteristic
143	C₂×#11929608	C₂³	1	2	yes	—
144	C₂×#11929608	C₂³	1	1	yes	characteristic
145	C₂×#11929607	—	2	8	no	—
146	C₂×#11929607	C₂³	1	2	yes	—
147	C₂×#11929607	C₂³	1	2	yes	—
148	C₂×#11929607	C₂³	1	1	yes	characteristic
149	C₂×#11929607	C₂³	1	2	yes	—
150	C₂×#11929607	C₂³	1	2	yes	—
151	C₂×#11929607	C₂³	1	1	yes	characteristic
152	C₂×#11929607	C₂³	1	1	yes	characteristic
153	C₂×#11929607	C₂³	1	2	yes	—
154	C₂×#11929607	C₂³	1	1	yes	characteristic
155	M₁₆×D₇₉	—	2	8	no	—
156	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
157	C₂×C₈×D₇₉	C₂³	1	1	yes	characteristic
158	C₂×C₈×D₇₉	C₂³	1	1	yes	characteristic
159	C₂×C₈×D₇₉	C₂³	1	1	yes	characteristic
160	C₂×C₈×D₇₉	C₂³	1	2	yes	—
161	C₂×C₈×D₇₉	C₂³	1	1	yes	characteristic
162	#14579160	C₂×C₄	1	1	yes	characteristic
163	#14579159	C₂×C₄	1	1	yes	characteristic
164	#14579156	C₂×C₄	1	2	yes	—
165	#14579154	C₂×C₄	1	2	yes	—
166	#14579154	C₂×C₄	1	2	yes	—
167	#14579154	C₂×C₄	1	2	yes	—
168	#14579154	C₂×C₄	1	2	yes	—
169	#14579152	C₂×C₄	1	1	yes	characteristic
170	#14579152	C₂×C₄	1	2	yes	—
171	#14579151	C₂×C₄	1	2	yes	—
172	#14579151	C₂×C₄	1	2	yes	—
173	#14579148	C₂×C₄	1	1	yes	characteristic
174	#14579148	C₂×C₄	1	2	yes	—
175	#14579147	C₂×C₄	1	2	yes	—
176	#14579146	C₂×C₄	1	2	yes	—
177	#14579146	C₂×C₄	1	2	yes	—
178	#14579143	C₂×C₄	1	2	yes	—
179	#14579143	C₂×C₄	1	2	yes	—
180	#14579143	C₂×C₄	1	2	yes	—
181	#14579143	C₂×C₄	1	2	yes	—
182	#14579143	C₂×C₄	1	2	yes	—
183	#14579141	C₂×C₄	1	1	yes	characteristic
184	#14579141	C₂×C₄	1	1	yes	characteristic
185	#14579141	C₂×C₄	1	2	yes	—
186	#14579139	C₂×C₄	1	2	yes	—
187	#14579139	C₂×C₄	1	2	yes	—
188	#14579139	C₂×C₄	1	2	yes	—
189	#14579138	C₂×C₄	1	2	yes	—
190	#14579137	C₂×C₄	1	1	yes	characteristic
191	#14579134	C₂×C₄	1	2	yes	—
192	#14579134	C₂×C₄	1	2	yes	—
193	#14579133	C₂×C₄	1	2	yes	—
194	#14579132	C₂×C₄	1	1	yes	characteristic
195	#14579132	C₂×C₄	1	2	yes	—
196	#14579131	C₂×C₄	1	2	yes	—
197	#14579129	C₂×C₄	1	2	yes	—
198	Q₈×Dic₇₉	C₂×C₄	1	1	yes	characteristic
199	C₄×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
200	C₄×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
201	C₄×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
202	C₄×Dic₁₅₈	C₂³	1	1	yes	characteristic
203	C₄×Dic₁₅₈	C₂³	1	2	yes	—
204	C₄×D₃₁₆	C₂×C₄	1	1	yes	characteristic
205	C₄×D₃₁₆	C₂×C₄	1	1	yes	characteristic
206	C₄×D₃₁₆	C₂×C₄	1	1	yes	characteristic
207	C₄×D₃₁₆	C₂³	1	2	yes	—
208	C₄×D₃₁₆	C₂³	1	1	yes	characteristic
209	D₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
210	#14579123	C₂×C₄	1	1	yes	characteristic
211	#14579123	C₂×C₄	1	1	yes	characteristic
212	#14579123	C₂×C₄	1	2	yes	—
213	C₄×C₂²⋊D₇₉	C₂×C₄	1	1	yes	characteristic
214	C₄×C₂²⋊D₇₉	C₂×C₄	1	1	yes	characteristic
215	C₄×C₂²⋊D₇₉	C₂×C₄	1	1	yes	characteristic
216	C₄×C₂²⋊D₇₉	C₂×C₄	1	2	yes	—
217	C₄×C₂²⋊D₇₉	C₂×C₄	1	1	yes	characteristic
218	C₄×C₂²⋊D₇₉	C₂³	1	2	yes	—
219	C₄×C₂²⋊D₇₉	C₂³	1	2	yes	—
220	C₄×C₂²⋊D₇₉	C₂³	1	2	yes	—
221	(C₂²⋊D₇₉)⋊C₄	C₂×C₄	1	2	yes	—
222	#14579120	C₂×C₄	1	1	yes	characteristic
223	#14579120	C₂³	1	2	yes	—
224	#14579120	C₂³	1	1	yes	characteristic
225	#14579119	C₂×C₄	1	2	yes	—
226	#14579119	C₂×C₄	1	2	yes	—
227	#14579119	C₂×C₄	1	2	yes	—
228	#14579119	C₂×C₄	1	1	yes	characteristic
229	#14579118	C₂×C₄	1	2	yes	—
230	#14579118	C₂³	1	1	yes	characteristic
231	#14579118	C₂³	1	1	yes	characteristic
232	#14579118	C₂³	1	2	yes	—
233	#14579117	C₂×C₄	1	2	yes	—
234	#14579117	C₂×C₄	1	2	yes	—
235	C₄⋊C₄×D₇₉	C₂×C₄	1	2	yes	—
236	C₄⋊C₄×D₇₉	C₂×C₄	1	1	yes	characteristic
237	C₄⋊C₄×D₇₉	C₂×C₄	1	2	yes	—
238	C₂²⋊C₄×D₇₉	C₂×C₄	1	2	yes	—
239	C₂²⋊C₄×D₇₉	C₂×C₄	1	2	yes	—
240	C₂²⋊C₄×D₇₉	C₂×C₄	1	2	yes	—
241	C₄²×D₇₉	C₂³	1	2	yes	—
242	C₄²×D₇₉	C₂³	1	2	yes	—
243	C₄²×D₇₉	C₂³	1	1	yes	characteristic
244	C₄²×D₇₉	C₂³	1	1	yes	characteristic
245	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
246	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
247	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
248	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
249	Dic₇₉⋊C₈	C₂³	1	2	yes	—
250	Dic₇₉⋊C₈	C₂³	1	2	yes	—
251	Dic₇₉⋊C₈	C₂³	1	2	yes	—
252	Dic₇₉⋊C₈	C₂³	1	2	yes	—
253	Dic₇₉⋊C₈	C₂³	1	2	yes	—
254	Dic₇₉⋊C₈	C₂³	1	2	yes	—
255	C₂²⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
256	C₂²⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
257	C₂²⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
258	(C₂×D₇₉)⋊C₈	C₂³	1	2	yes	—
259	(C₂×D₇₉)⋊C₈	C₂³	1	2	yes	—
260	(C₂×D₇₉)⋊C₈	C₂³	1	2	yes	—
261	(C₂×D₇₉)⋊C₈	C₂³	1	2	yes	—
262	(C₂×D₇₉)⋊C₈	C₂³	1	2	yes	—
263	(C₂×D₇₉)⋊C₈	C₂³	1	2	yes	—
264	#14579072	C₂³	1	1	yes	characteristic
265	#14579072	C₂³	1	2	yes	—
266	#14579072	C₂³	1	1	yes	characteristic
267	#14579071	C₂³	1	1	yes	characteristic
268	#14579071	C₂³	1	2	yes	—
269	#14579071	C₂³	1	1	yes	characteristic
270	#14579071	C₂³	1	2	yes	—
271	#14579071	C₂³	1	1	yes	characteristic
272	#14579071	C₂³	1	1	yes	characteristic
273	#14579071	C₂³	1	2	yes	—
274	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
275	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
276	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
277	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
278	C₈×Dic₇₉	C₂³	1	2	yes	—
279	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
280	C₈×Dic₇₉	C₂³	1	2	yes	—
281	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
282	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
283	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
284	C₈×Dic₇₉	C₂³	1	2	yes	—
285	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
286	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
287	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
288	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
289	#126×C₇₉	C₂×C₄	1	2	yes	—
290	#125×C₇₉	C₂×C₄	1	1	yes	characteristic
291	#124×C₇₉	C₂×C₄	1	1	yes	characteristic
292	#123×C₇₉	C₂×C₄	1	2	yes	—
293	C₂²⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
294	#121×C₇₉	C₂×C₄	1	1	yes	characteristic
295	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
296	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
297	C₄×D₄×C₇₉	C₂³	1	2	yes	—
298	#117×C₇₉	C₂³	1	2	yes	—
299	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
300	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
301	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
302	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
303	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₇₉	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₇₉	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₇₉	C₂³	1	2	yes	—
307	#97×C₇₉	C₂³	1	2	yes	—
308	#97×C₇₉	C₂³	1	2	yes	—
309	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₇₉	C₂³	1	2	yes	—
312	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
314	C₂³×D₇₉	C₂²×C₄	1	2	yes	—
315	#11929625	—	4	2	no	—
316	#11929624	—	2	2	no	—
317	#11929624	—	2	2	no	—
318	#11929624	—	4	2	no	—
319	C₂×Dic₁₅₈	C₂²×C₄	1	1	yes	characteristic
320	C₂×Dic₁₅₈	C₂²×C₄	1	1	yes	characteristic
321	C₂×Dic₁₅₈	C₂²×C₄	1	2	yes	—
322	C₂×D₃₁₆	C₂²×C₄	1	1	yes	characteristic
323	C₂×D₃₁₆	C₂²×C₄	1	1	yes	characteristic
324	C₂×D₃₁₆	C₂²×C₄	1	2	yes	—
325	C₂×C₂²⋊D₇₉	C₂²×C₄	1	1	yes	characteristic
326	C₂×C₂²⋊D₇₉	C₂²×C₄	1	1	yes	characteristic
327	C₂×C₂²⋊D₇₉	C₂²×C₄	1	2	yes	—
328	C₂×C₂²⋊D₇₉	C₂²×C₄	1	2	yes	—
329	C₂×C₂²⋊D₇₉	C₂²×C₄	1	2	yes	—
330	D₄×D₇₉	—	4	2	no	—
331	C₂²×Dic₇₉	C₂²×C₄	1	2	yes	—
332	C₂×C₄×D₇₉	—	2	4	no	—
333	C₂×C₄×D₇₉	—	2	4	no	—
334	C₂×C₄×D₇₉	C₂²×C₄	1	1	yes	characteristic
335	C₂×C₄×D₇₉	C₂²×C₄	1	1	yes	characteristic
336	C₂×C₄×D₇₉	C₂²×C₄	1	2	yes	—
337	C₂×C₄×D₇₉	C₂²×C₄	1	2	yes	—
338	C₂×C₄×D₇₉	C₂²×C₄	1	2	yes	—
339	C₂×C₄×D₇₉	C₂²×C₄	1	2	yes	—
340	C₂×C₄×D₇₉	C₂²×C₄	1	1	yes	characteristic
341	C₂×C₄×D₇₉	C₂²×C₄	1	2	yes	—
342	C₂×C₄×D₇₉	C₂²×C₄	1	2	yes	—
343	C₂×C₄×D₇₉	C₂²×C₄	1	1	yes	characteristic
344	C₂×C₄×D₇₉	C₂⁴	1	1	yes	characteristic
345	C₂×C₄×D₇₉	C₂⁴	1	2	yes	—
346	C₂×C₄×D₇₉	C₂⁴	1	1	yes	characteristic
347	#11929608	—	2	4	no	—
348	#11929608	—	2	2	no	—
349	#11929608	—	2	2	no	—
350	#11929607	—	2	4	no	—
351	#11929607	—	2	2	no	—
352	#11929607	—	2	4	no	—
353	#11929607	—	2	4	no	—
354	#11929607	—	2	2	no	—
355	#11929607	—	2	4	no	—
356	#11929607	—	2	4	no	—
357	#11929607	—	2	2	no	—
358	#11929607	#41	1	4	yes	complemented
359	C₂×C₇₉⋊C₈	—	2	4	no	—
360	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
361	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
362	C₂×C₇₉⋊C₈	C₂⁴	1	2	yes	—
363	C₂×C₇₉⋊C₈	C₂⁴	1	2	yes	—
364	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
365	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
366	C₈×D₇₉	—	2	4	no	—
367	C₈×D₇₉	—	2	2	no	—
368	C₈×D₇₉	—	2	2	no	—
369	C₈×D₇₉	—	2	2	no	—
370	C₈×D₇₉	#41	1	4	yes	complemented
371	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
372	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
373	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
374	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
375	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
376	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
377	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
378	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
379	Dic₇₉⋊C₄	C₂²×C₄	1	1	yes	characteristic
380	Dic₇₉⋊C₄	C₂²×C₄	1	1	yes	characteristic
381	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
382	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
383	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
384	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
385	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
386	Dic₇₉⋊C₄	C₂²×C₄	1	1	yes	characteristic
387	Dic₇₉⋊C₄	C₂²×C₄	1	1	yes	characteristic
388	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
389	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
390	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
391	C₂²⋊Dic₇₉	C₂²×C₄	1	2	yes	—
392	C₂²⋊Dic₇₉	C₂²×C₄	1	2	yes	—
393	C₂²⋊Dic₇₉	C₂²×C₄	1	2	yes	—
394	C₂²⋊Dic₇₉	C₂²×C₄	1	2	yes	—
395	C₂²⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
396	C₂²⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
397	C₂²⋊Dic₇₉	C₂²×C₄	1	2	yes	—
398	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	1	yes	characteristic
399	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	1	yes	characteristic
400	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
401	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
402	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
403	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
404	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
405	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	1	yes	characteristic
406	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	1	yes	characteristic
407	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
408	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
409	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
410	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
411	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
412	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
413	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
414	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
415	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
416	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
417	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
418	C₄×Dic₇₉	C₂⁴	1	1	yes	characteristic
419	C₄×Dic₇₉	C₂⁴	1	1	yes	characteristic
420	C₄×Dic₇₉	C₂⁴	1	2	yes	—
421	C₂×Q₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
422	C₂×D₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
423	C₂×D₄×C₇₉	C₂²×C₄	1	2	yes	—
424	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
425	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
426	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
427	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
428	M₁₆×C₇₉	—	2	4	no	—
429	C₂×C₈×C₇₉	—	2	4	no	—
430	C₂×C₈×C₇₉	—	2	2	no	—
431	C₂×C₈×C₇₉	—	2	2	no	—
432	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
433	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
434	C₂×C₈×C₇₉	C₂⁴	1	2	yes	—
435	C₂×C₈×C₇₉	C₂⁴	1	2	yes	—
436	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
437	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
438	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
439	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
440	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
441	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
442	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
443	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
444	C₂²⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
445	C₂²⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
446	C₂²⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
447	C₂²⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
448	C₂²⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
449	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
450	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
451	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
452	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
453	C₄²×C₇₉	C₂⁴	1	2	yes	—
454	C₂³×C₇₉	C₂³×C₄	1	2	yes	—
455	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
456	C₂²×D₇₉	—	2	4	no	—
457	C₂²×D₇₉	—	4	2	no	—
458	C₂²×D₇₉	—	4	2	no	—
459	C₂²×D₇₉	C₂³×C₄	1	1	yes	characteristic
460	C₂²×D₇₉	C₂³×C₄	1	2	yes	—
461	C₂²×D₇₉	C₂³×C₄	1	1	yes	characteristic
462	Q₈×C₇₉	—	2	2	no	—
463	D₄×C₇₉	—	2	2	no	—
464	D₄×C₇₉	—	4	2	no	—
465	C₂×C₄×C₇₉	—	2	2	no	—
466	C₂×C₄×C₇₉	—	2	2	no	—
467	C₂×C₄×C₇₉	—	2	2	no	—
468	C₂×C₄×C₇₉	—	2	1	no	—
469	C₂×C₄×C₇₉	—	2	1	no	—
470	C₂×C₄×C₇₉	—	4	1	no	—
471	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
472	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
473	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
474	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
475	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
476	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
477	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
478	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
479	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
480	C₂²⋊D₇₉	—	2	2	no	—
481	C₂²⋊D₇₉	—	2	2	no	—
482	C₂²⋊D₇₉	—	4	2	no	—
483	C₂²⋊D₇₉	—	4	2	no	—
484	C₂²⋊D₇₉	—	4	2	no	—
485	C₂×Dic₇₉	—	2	4	no	—
486	C₂×Dic₇₉	C₂³×C₄	1	2	yes	—
487	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
488	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
489	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
490	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
491	C₂×Dic₇₉	C₂³×C₄	1	2	yes	—
492	C₂×Dic₇₉	C₂³×C₄	1	2	yes	—
493	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
494	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
495	D₃₁₆	—	2	2	no	—
496	D₃₁₆	—	2	2	no	—
497	D₃₁₆	—	4	2	no	—
498	C₄×D₇₉	—	2	4	no	—
499	C₄×D₇₉	—	2	2	no	—
500	C₄×D₇₉	—	2	2	no	—
501	C₄×D₇₉	—	2	1	no	—
502	C₄×D₇₉	—	2	1	no	—
503	C₄×D₇₉	—	2	2	no	—
504	C₄×D₇₉	—	2	2	no	—
505	C₄×D₇₉	—	2	4	no	—
506	C₄×D₇₉	—	4	2	no	—
507	C₄×D₇₉	—	4	1	no	—
508	C₄×D₇₉	—	4	1	no	—
509	C₄×D₇₉	—	4	2	no	—
510	C₄×D₇₉	—	4	2	no	—
511	C₄×D₇₉	—	4	2	no	—
512	C₄×D₇₉	C₂×#41	1	2	yes	—
513	C₄×D₇₉	C₂×#41	1	2	yes	—
514	Dic₁₅₈	—	2	2	no	—
515	Dic₁₅₈	—	2	2	no	—
516	Dic₁₅₈	—	4	2	no	—
517	C₈×C₇₉	—	2	1	no	—
518	C₈×C₇₉	—	2	2	no	—
519	C₈×C₇₉	—	2	2	no	—
520	C₈×C₇₉	—	2	1	no	—
521	C₈×C₇₉	C₂×#41	1	2	yes	—
522	C₈×C₇₉	C₂×#41	1	2	yes	—
523	C₇₉⋊C₈	—	2	2	no	—
524	C₇₉⋊C₈	—	2	1	no	—
525	C₇₉⋊C₈	—	2	1	no	—
526	C₇₉⋊C₈	—	2	2	no	—
527	C₇₉⋊C₈	C₂×#41	1	2	yes	—
528	C₇₉⋊C₈	C₂×#41	1	2	yes	—
529	C₂²×C₇₉	—	2	1	no	—
530	C₂²×C₇₉	—	2	2	no	—
531	C₂²×C₇₉	—	2	1	no	—
532	C₂²×C₇₉	—	2	2	no	—
533	C₂²×C₇₉	—	2	2	no	—
534	C₂²×C₇₉	—	2	1	no	—
535	C₂²×C₇₉	C₂⁴×C₄	1	1	yes	characteristic
536	C₂×D₇₉	—	2	1	no	—
537	C₂×D₇₉	—	2	1	no	—
538	C₂×D₇₉	—	2	1	no	—
539	C₂×D₇₉	—	2	2	no	—
540	C₂×D₇₉	—	2	2	no	—
541	C₂×D₇₉	—	2	1	no	—
542	C₂×D₇₉	—	2	1	no	—
543	C₂×D₇₉	—	2	2	no	—
544	C₂×D₇₉	—	8	4	no	—
545	C₂×D₇₉	C₄×#41	1	2	yes	—
546	C₄×C₇₉	—	2	1	no	—
547	C₄×C₇₉	—	2	2	no	—
548	C₄×C₇₉	—	2	1	no	—
549	C₄×C₇₉	—	2	2	no	—
550	C₄×C₇₉	—	2	1	no	—
551	C₄×C₇₉	—	2	1	no	—
552	C₄×C₇₉	—	2	2	no	—
553	C₄×C₇₉	#568	1	2	yes	—
554	C₄×C₇₉	C₂²×#41	1	1	yes	characteristic
555	C₄×C₇₉	C₂²×#41	1	1	yes	characteristic
556	Dic₇₉	—	2	1	no	—
557	Dic₇₉	—	2	2	no	—
558	Dic₇₉	—	2	1	no	—
559	Dic₇₉	—	2	2	no	—
560	Dic₇₉	—	2	1	no	—
561	Dic₇₉	—	2	2	no	—
562	Dic₇₉	—	2	1	no	—
563	Dic₇₉	—	2	1	no	—
564	Dic₇₉	C₄×#41	1	2	yes	—
565	#60217	—	79	1	no	maximal, Sylow
566	C₂×C₇₉	—	4	2	no	—
567	C₂×C₇₉	—	4	1	no	—
568	C₂×C₇₉	C₂×C₄×#41	1	1	yes	characteristic
569	C₂×C₇₉	C₂×#568	1	1	yes	characteristic
570	C₂×C₇₉	#3573	1	1	yes	characteristic
571	D₇₉	—	2	2	no	—
572	D₇₉	—	4	1	no	—
573	D₇₉	—	4	2	no	—
574	#3475	—	79	1	no	—
575	#2971	—	79	1	no	—
576	#2971	—	79	1	no	—
577	#2969	—	79	1	no	—
578	#2969	—	79	2	no	—
579	#2969	—	79	2	no	—
580	#2969	—	79	1	no	—
581	#2967	—	79	2	no	—
582	#2967	—	79	2	no	—
583	#2966	—	79	1	no	—
584	#2966	D₇₉	1	1	yes	characteristic, complemented
585	#2965	—	79	1	no	—
586	#2965	—	79	1	no	—
587	#2962	—	79	1	no	—
588	#2960	—	79	1	no	—
589	D₄×M₁₆	—	79	1	no	—
590	#2933	—	79	2	no	—
591	#2930	—	79	2	no	—
592	C₂×#436	—	79	1	no	—
593	#2925	—	79	1	no	—
594	#2924	—	79	2	no	—
595	C₄×#131	—	79	1	no	—
596	#2873	—	79	2	no	—
597	C₇₉	#60217	1	1	yes	characteristic, complemented, Sylow
598	C₂×#131	—	79	1	no	—
599	C₂×#131	—	79	1	no	—
600	C₂²×M₁₆	—	79	2	no	—
601	C₂²×M₁₆	—	79	2	no	—
602	#556	—	79	1	no	—
603	#555	—	79	1	no	—
604	#554	—	79	1	no	—
605	#553	—	79	2	no	—
606	#552	—	79	2	no	—
607	#552	—	79	1	no	—
608	#552	—	79	1	no	—
609	#551	—	79	2	no	—
610	#551	—	79	2	no	—
611	#547	—	79	1	no	—
612	#546	—	79	1	no	—
613	#546	—	79	1	no	—
614	#533	—	79	1	no	—
615	#529	—	79	1	no	—
616	#529	—	79	2	no	—
617	#529	—	79	2	no	—
618	#529	C₂×D₇₉	1	1	yes	characteristic
619	#525	—	79	2	no	—
620	C₄×#41	—	79	1	no	—
621	C₄×#41	—	79	1	no	—
622	C₄×#41	—	79	1	no	—
623	C₂×C₄×D₄	—	79	1	no	—
624	C₂×#117	—	79	2	no	—
625	#446	—	79	1	no	—
626	#446	—	79	2	no	—
627	#446	—	79	2	no	—
628	#446	—	79	1	no	—
629	#446	—	79	1	no	—
630	#446	—	79	2	no	—
631	#446	C₂×D₇₉	1	1	yes	characteristic, complemented
632	C₈×Q₈	—	79	1	no	—
633	C₈×Q₈	—	79	2	no	—
634	C₈×Q₈	—	79	1	no	—
635	C₈×Q₈	—	79	1	no	—
636	C₈×Q₈	C₂×D₇₉	1	1	yes	characteristic, complemented
637	#436	—	79	2	no	—
638	#436	—	79	1	no	—
639	#436	—	79	2	no	—
640	#436	—	79	1	no	—
641	#436	—	79	1	no	—
642	#436	—	79	2	no	—
643	#436	—	79	2	no	—
644	#436	—	79	2	no	—
645	#436	—	79	2	no	—
646	#436	—	79	2	no	—
647	#436	—	79	1	no	—
648	#436	—	79	1	no	—
649	#436	—	79	2	no	—
650	#436	C₂×D₇₉	1	1	yes	characteristic
651	#435	—	79	2	no	—
652	#435	—	79	2	no	—
653	#435	—	79	2	no	—
654	#435	—	79	2	no	—
655	#435	—	79	2	no	—
656	#435	—	79	2	no	—
657	#435	—	79	2	no	—
658	#435	—	79	2	no	—
659	#435	—	79	2	no	—
660	#435	C₂×D₇₉	1	2	yes	complemented
661	C₈×D₄	—	79	1	no	—
662	C₈×D₄	—	79	2	no	—
663	C₈×D₄	C₂×D₇₉	1	1	yes	characteristic
664	C₈×D₄	C₂×D₇₉	1	2	yes	complemented
665	#433	—	79	2	no	—
666	#433	—	79	2	no	—
667	#433	—	79	2	no	—
668	#433	—	79	2	no	—
669	#433	—	79	2	no	—
670	#433	C₂×D₇₉	1	2	yes	complemented
671	#432	—	79	2	no	—
672	#432	—	79	1	no	—
673	#432	—	79	2	no	—
674	#432	C₂×D₇₉	1	1	yes	characteristic, complemented
675	#431	—	79	1	no	—
676	#431	—	79	2	no	—
677	#431	—	79	1	no	—
678	#431	—	79	2	no	—
679	#424	—	79	2	no	—
680	#424	—	79	2	no	—
681	#423	—	79	1	no	—
682	C₂×C₄⋊C₈	—	79	1	no	—
683	#408	—	79	2	no	—
684	#407	—	79	2	no	—
685	C₂×C₂²⋊C₈	—	79	2	no	—
686	#405	—	79	2	no	—
687	#405	—	79	2	no	—
688	#405	—	79	1	no	—
689	#405	—	79	1	no	—
690	#405	—	79	2	no	—
691	#405	—	79	2	no	—
692	#405	—	79	2	no	—
693	#405	—	79	1	no	—
694	#405	—	79	2	no	—
695	#405	—	79	1	no	—
696	#405	—	79	1	no	—
697	#405	—	79	1	no	—
698	#405	C₂×D₇₉	1	2	yes	complemented
699	C₄×M₁₆	—	79	1	no	—
700	C₄×M₁₆	—	79	2	no	—
701	C₄×M₁₆	—	79	2	no	—
702	C₄×M₁₆	—	79	2	no	—
703	C₄×M₁₆	—	79	2	no	—
704	C₄×M₁₆	—	79	1	no	—
705	C₄×M₁₆	—	79	1	no	—
706	C₂×C₄×C₈	—	79	1	no	—
707	C₂×C₄×C₈	—	79	1	no	—
708	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic, complemented
709	C₂×#41	—	79	1	no	—
710	C₂×#41	—	79	1	no	—
711	C₂×#41	—	79	1	no	—
712	C₂²×D₄	—	79	1	no	—
713	C₂³×C₄	—	79	2	no	—
714	#131	—	158	4	no	—
715	#131	—	158	4	no	—
716	C₂×M₁₆	—	79	2	no	—
717	C₂×M₁₆	—	79	1	no	—
718	C₂×M₁₆	—	79	1	no	—
719	C₂×M₁₆	—	79	1	no	—
720	C₂×M₁₆	—	79	2	no	—
721	C₂×M₁₆	—	79	2	no	—
722	C₂×M₁₆	—	79	2	no	—
723	C₂×M₁₆	—	79	2	no	—
724	C₂×M₁₆	—	79	2	no	—
725	C₂×M₁₆	—	79	1	no	—
726	C₂×M₁₆	—	79	1	no	—
727	C₂×M₁₆	—	79	1	no	—
728	C₂×M₁₆	—	158	8	no	—
729	C₂×M₁₆	—	158	8	no	—
730	C₂×M₁₆	C₂²×D₇₉	1	2	yes	—
731	C₂²×C₈	—	79	1	no	—
732	C₂²×C₈	—	79	2	no	—
733	C₂²×C₈	—	79	2	no	—
734	C₂²×C₈	—	79	1	no	—
735	C₂²×C₈	—	79	1	no	—
736	C₂²×C₈	—	79	1	no	—
737	C₂²×C₈	C₂²×D₇₉	1	2	yes	—
738	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
739	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
740	C₄⋊Q₈	—	79	1	no	—
741	C₄⋊Q₈	—	79	1	no	—
742	#126	—	79	2	no	—
743	#126	—	79	2	no	—
744	#126	—	79	2	no	—
745	#126	—	79	2	no	—
746	#126	—	79	2	no	—
747	#126	C₄×D₇₉	1	2	yes	—
748	#125	—	79	2	no	—
749	#125	—	79	2	no	—
750	#125	—	79	1	no	—
751	#125	—	79	2	no	—
752	#125	C₄×D₇₉	1	1	yes	characteristic
753	#124	—	79	1	no	—
754	#124	—	79	2	no	—
755	#124	—	79	2	no	—
756	#124	C₄×D₇₉	1	1	yes	characteristic
757	#123	—	79	2	no	—
758	#123	—	79	2	no	—
759	#123	—	79	2	no	—
760	#123	—	79	2	no	—
761	#123	—	79	2	no	—
762	#123	—	79	2	no	—
763	#123	—	79	2	no	—
764	#123	C₄×D₇₉	1	2	yes	—
765	C₂²⋊Q₈	—	79	1	no	—
766	C₂²⋊Q₈	—	79	2	no	—
767	C₂²⋊Q₈	—	79	1	no	—
768	C₂²⋊Q₈	—	79	2	no	—
769	C₂²⋊Q₈	—	79	2	no	—
770	C₂²⋊Q₈	—	79	1	no	—
771	C₂²⋊Q₈	—	79	2	no	—
772	C₂²⋊Q₈	—	79	2	no	—
773	C₂²⋊Q₈	C₄×D₇₉	1	1	yes	characteristic
774	#121	—	79	2	no	—
775	#121	—	79	2	no	—
776	#121	—	79	1	no	—
777	#121	—	79	2	no	—
778	#121	—	79	2	no	—
779	#121	C₄×D₇₉	1	1	yes	characteristic
780	#120	—	79	2	no	—
781	#120	—	79	2	no	—
782	C₄×Q₈	—	79	1	no	—
783	C₄×Q₈	—	79	1	no	—
784	C₄×Q₈	—	79	1	no	—
785	C₄×Q₈	—	79	1	no	—
786	C₄×Q₈	—	79	1	no	—
787	C₄×Q₈	—	79	2	no	—
788	C₄×Q₈	C₂²×D₇₉	1	1	yes	characteristic
789	C₄×D₄	—	79	1	no	—
790	C₄×D₄	—	79	1	no	—
791	C₄×D₄	—	79	1	no	—
792	C₄×D₄	—	79	1	no	—
793	C₄×D₄	—	79	2	no	—
794	C₄×D₄	—	79	1	no	—
795	C₄×D₄	—	79	2	no	—
796	C₄×D₄	—	79	2	no	—
797	C₄×D₄	—	79	2	no	—
798	C₄×D₄	—	79	1	no	—
799	C₄×D₄	—	79	1	no	—
800	C₄×D₄	—	79	2	no	—
801	C₄×D₄	—	79	2	no	—
802	C₄×D₄	—	79	1	no	—
803	C₄×D₄	—	79	1	no	—
804	C₄×D₄	—	79	1	no	—
805	C₄×D₄	—	79	1	no	—
806	C₄×D₄	—	79	2	no	—
807	C₄×D₄	C₂²×D₇₉	1	1	yes	characteristic
808	C₄×D₄	C₂²×D₇₉	1	2	yes	—
809	#117	—	79	1	no	—
810	#117	—	79	2	no	—
811	#117	—	79	1	no	—
812	#117	—	79	2	no	—
813	#117	—	79	2	no	—
814	#117	—	79	2	no	—
815	#117	—	79	1	no	—
816	#117	—	79	2	no	—
817	#117	—	79	2	no	—
818	#117	—	79	2	no	—
819	#117	—	79	1	no	—
820	#117	—	79	2	no	—
821	#117	—	79	1	no	—
822	#117	C₂²×D₇₉	1	2	yes	—
823	C₂×C₄⋊C₄	—	79	2	no	—
824	C₂×C₄⋊C₄	—	79	2	no	—
825	C₂×C₄⋊C₄	—	79	1	no	—
826	C₂×C₂²⋊C₄	—	79	2	no	—
827	C₂×C₂²⋊C₄	—	79	2	no	—
828	C₂×C₂²⋊C₄	—	79	2	no	—
829	C₂×C₄²	—	79	2	no	—
830	C₂×C₄²	—	79	2	no	—
831	C₂×C₄²	—	79	1	no	—
832	C₂×C₄²	—	79	1	no	—
833	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
834	C₄⋊C₈	—	79	2	no	—
835	C₄⋊C₈	—	79	2	no	—
836	C₄⋊C₈	—	79	2	no	—
837	C₄⋊C₈	—	79	2	no	—
838	C₄⋊C₈	—	79	2	no	—
839	C₄⋊C₈	—	79	2	no	—
840	C₄⋊C₈	—	79	1	no	—
841	C₄⋊C₈	—	79	1	no	—
842	C₄⋊C₈	—	79	2	no	—
843	C₄⋊C₈	—	79	2	no	—
844	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
845	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
846	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
847	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
848	C₂²⋊C₈	—	79	2	no	—
849	C₂²⋊C₈	—	79	2	no	—
850	C₂²⋊C₈	—	79	2	no	—
851	C₂²⋊C₈	—	79	2	no	—
852	C₂²⋊C₈	—	79	2	no	—
853	C₂²⋊C₈	—	79	2	no	—
854	C₂²⋊C₈	—	79	2	no	—
855	C₂²⋊C₈	—	79	2	no	—
856	C₂²⋊C₈	—	79	2	no	—
857	C₂²⋊C₈	C₂²×D₇₉	1	2	yes	—
858	C₂²⋊C₈	C₂²×D₇₉	1	2	yes	—
859	C₂²⋊C₈	C₂²×D₇₉	1	2	yes	—
860	#97	—	79	1	no	—
861	#97	—	79	2	no	—
862	#97	—	79	1	no	—
863	#97	—	79	1	no	—
864	#97	—	79	2	no	—
865	#97	—	79	1	no	—
866	#97	—	79	2	no	—
867	#97	—	79	1	no	—
868	#97	—	79	1	no	—
869	#97	—	79	2	no	—
870	#97	C₂²×D₇₉	1	2	yes	—
871	#97	C₂²×D₇₉	1	2	yes	—
872	C₄×C₈	—	79	1	no	—
873	C₄×C₈	—	79	1	no	—
874	C₄×C₈	—	79	1	no	—
875	C₄×C₈	—	79	1	no	—
876	C₄×C₈	—	79	2	no	—
877	C₄×C₈	—	79	2	no	—
878	C₄×C₈	—	79	2	no	—
879	C₄×C₈	—	79	1	no	—
880	C₄×C₈	—	79	1	no	—
881	C₄×C₈	—	79	2	no	—
882	C₄×C₈	—	79	2	no	—
883	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
884	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
885	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
886	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
887	C₄×C₈	C₂²×D₇₉	1	2	yes	—
888	C₂⁴	—	79	2	no	—
889	#41	—	316	2	no	—
890	#41	—	316	2	no	—
891	#41	—	158	2	no	—
892	#41	—	158	2	no	—
893	C₂×Q₈	—	79	2	no	—
894	C₂×Q₈	—	79	1	no	—
895	C₂×Q₈	—	79	1	no	—
896	C₂×Q₈	C₂×C₄×D₇₉	1	1	yes	characteristic
897	C₂×D₄	—	316	2	no	—
898	C₂×D₄	—	79	2	no	—
899	C₂×D₄	—	79	2	no	—
900	C₂×D₄	—	79	2	no	—
901	C₂×D₄	—	79	1	no	—
902	C₂×D₄	—	79	1	no	—
903	C₂×D₄	—	79	2	no	—
904	C₂×D₄	—	79	1	no	—
905	C₂×D₄	—	79	1	no	—
906	C₂×D₄	C₂×C₄×D₇₉	1	1	yes	characteristic
907	C₂×D₄	C₂×C₄×D₇₉	1	2	yes	—
908	C₂²×C₄	—	79	1	no	—
909	C₂²×C₄	—	79	2	no	—
910	C₂²×C₄	—	79	2	no	—
911	C₂²×C₄	—	79	2	no	—
912	C₂²×C₄	—	79	2	no	—
913	C₂²×C₄	—	79	1	no	—
914	C₂²×C₄	—	79	1	no	—
915	C₂²×C₄	—	79	2	no	—
916	C₂²×C₄	—	79	2	no	—
917	C₂²×C₄	—	79	1	no	—
918	C₂²×C₄	—	79	1	no	—
919	C₂²×C₄	—	79	1	no	—
920	C₂²×C₄	—	79	2	no	—
921	C₂²×C₄	—	79	2	no	—
922	C₂²×C₄	—	158	4	no	—
923	C₂²×C₄	—	158	4	no	—
924	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
925	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
926	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
927	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
928	M₁₆	—	2	4	no	—
929	M₁₆	—	79	4	no	—
930	M₁₆	—	158	4	no	—
931	M₁₆	—	158	4	no	—
932	M₁₆	—	158	2	no	—
933	M₁₆	—	158	4	no	—
934	M₁₆	—	158	2	no	—
935	M₁₆	—	158	4	no	—
936	M₁₆	—	158	2	no	—
937	M₁₆	—	158	2	no	—
938	M₁₆	—	158	4	no	—
939	M₁₆	—	158	4	no	—
940	M₁₆	—	158	2	no	—
941	C₂×C₈	—	2	4	no	—
942	C₂×C₈	—	2	2	no	—
943	C₂×C₈	—	2	2	no	—
944	C₂×C₈	—	79	1	no	—
945	C₂×C₈	—	79	1	no	—
946	C₂×C₈	—	79	4	no	—
947	C₂×C₈	—	79	1	no	—
948	C₂×C₈	—	79	1	no	—
949	C₂×C₈	—	79	2	no	—
950	C₂×C₈	—	79	2	no	—
951	C₂×C₈	—	158	2	no	—
952	C₂×C₈	—	158	4	no	—
953	C₂×C₈	—	158	2	no	—
954	C₂×C₈	—	158	4	no	—
955	C₂×C₈	—	158	2	no	—
956	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
957	C₂×C₈	C₂³×D₇₉	1	2	yes	—
958	C₂×C₈	C₂³×D₇₉	1	2	yes	—
959	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
960	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
961	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
962	C₄⋊C₄	—	79	1	no	—
963	C₄⋊C₄	—	79	1	no	—
964	C₄⋊C₄	—	79	2	no	—
965	C₄⋊C₄	—	79	2	no	—
966	C₄⋊C₄	—	79	2	no	—
967	C₄⋊C₄	—	79	1	no	—
968	C₄⋊C₄	—	79	2	no	—
969	C₄⋊C₄	—	79	2	no	—
970	C₄⋊C₄	—	79	1	no	—
971	C₄⋊C₄	—	79	2	no	—
972	C₄⋊C₄	—	79	2	no	—
973	C₄⋊C₄	—	79	2	no	—
974	C₄⋊C₄	—	79	1	no	—
975	C₄⋊C₄	—	79	2	no	—
976	C₄⋊C₄	—	79	2	no	—
977	C₄⋊C₄	—	79	1	no	—
978	C₄⋊C₄	—	79	1	no	—
979	C₄⋊C₄	—	79	2	no	—
980	C₄⋊C₄	—	79	1	no	—
981	C₄⋊C₄	—	79	2	no	—
982	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
983	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
984	C₄⋊C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
985	C₄⋊C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
986	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
987	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
988	C₂²⋊C₄	—	79	2	no	—
989	C₂²⋊C₄	—	79	2	no	—
990	C₂²⋊C₄	—	79	2	no	—
991	C₂²⋊C₄	—	79	1	no	—
992	C₂²⋊C₄	—	79	2	no	—
993	C₂²⋊C₄	—	79	1	no	—
994	C₂²⋊C₄	—	79	2	no	—
995	C₂²⋊C₄	—	79	1	no	—
996	C₂²⋊C₄	—	79	1	no	—
997	C₂²⋊C₄	—	79	2	no	—
998	C₂²⋊C₄	—	79	2	no	—
999	C₂²⋊C₄	—	79	2	no	—
1000	C₂²⋊C₄	—	79	2	no	—
1001	C₂²⋊C₄	—	79	2	no	—
1002	C₂²⋊C₄	—	79	2	no	—
1003	C₂²⋊C₄	—	79	1	no	—
1004	C₂²⋊C₄	—	79	2	no	—
1005	C₂²⋊C₄	—	79	1	no	—
1006	C₂²⋊C₄	—	79	2	no	—
1007	C₂²⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
1008	C₂²⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
1009	C₂²⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
1010	C₂²⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
1011	C₂²⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
1012	C₄²	—	79	1	no	—
1013	C₄²	—	79	1	no	—
1014	C₄²	—	79	2	no	—
1015	C₄²	—	79	2	no	—
1016	C₄²	—	79	2	no	—
1017	C₄²	—	79	2	no	—
1018	C₄²	—	79	2	no	—
1019	C₄²	—	79	1	no	—
1020	C₄²	—	79	1	no	—
1021	C₄²	—	79	1	no	—
1022	C₄²	—	79	1	no	—
1023	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
1024	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
1025	C₄²	C₂³×D₇₉	1	1	yes	characteristic
1026	C₄²	C₂³×D₇₉	1	1	yes	characteristic
1027	C₄²	C₂³×D₇₉	1	2	yes	—
1028	C₂³	—	316	2	no	—
1029	C₂³	—	316	2	no	—
1030	C₂³	—	79	1	no	—
1031	C₂³	—	79	1	no	—
1032	C₂³	—	79	2	no	—
1033	C₂³	—	158	4	no	—
1034	C₂³	C₂²×C₄×D₇₉	1	2	yes	—
1035	C₂³	C₂²×C₄×D₇₉	1	1	yes	characteristic
1036	Q₈	—	2	2	no	—
1037	Q₈	—	316	2	no	—
1038	Q₈	—	158	2	no	—
1039	Q₈	—	158	2	no	—
1040	D₄	—	2	2	no	—
1041	D₄	—	4	2	no	—
1042	D₄	—	316	2	no	—
1043	D₄	—	316	2	no	—
1044	D₄	—	316	2	no	—
1045	D₄	—	316	2	no	—
1046	D₄	—	158	2	no	—
1047	D₄	—	158	2	no	—
1048	D₄	—	158	2	no	—
1049	D₄	—	158	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	4	1	no	—
1056	C₂×C₄	—	316	2	no	—
1057	C₂×C₄	—	316	2	no	—
1058	C₂×C₄	—	316	1	no	—
1059	C₂×C₄	—	316	2	no	—
1060	C₂×C₄	—	316	1	no	—
1061	C₂×C₄	—	316	2	no	—
1062	C₂×C₄	—	79	1	no	—
1063	C₂×C₄	—	79	2	no	—
1064	C₂×C₄	—	79	2	no	—
1065	C₂×C₄	—	79	1	no	—
1066	C₂×C₄	—	79	1	no	—
1067	C₂×C₄	—	79	2	no	—
1068	C₂×C₄	—	79	1	no	—
1069	C₂×C₄	—	79	2	no	—
1070	C₂×C₄	—	79	2	no	—
1071	C₂×C₄	—	79	1	no	—
1072	C₂×C₄	—	79	1	no	—
1073	C₂×C₄	—	158	4	no	—
1074	C₂×C₄	—	158	4	no	—
1075	C₂×C₄	—	158	4	no	—
1076	C₂×C₄	—	158	2	no	—
1077	C₂×C₄	—	158	2	no	—
1078	C₂×C₄	—	158	1	no	—
1079	C₂×C₄	—	158	1	no	—
1080	C₂×C₄	—	158	2	no	—
1081	C₂×C₄	—	158	2	no	—
1082	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
1083	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
1084	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
1085	C₂×C₄	C₂²×C₄×D₇₉	1	2	yes	—
1086	C₂×C₄	C₂²×C₄×D₇₉	1	2	yes	—
1087	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
1088	C₂×C₄	C₂²×C₄×D₇₉	1	2	yes	—
1089	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
1090	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
1091	C₈	—	2	1	no	—
1092	C₈	—	2	2	no	—
1093	C₈	—	2	1	no	—
1094	C₈	—	2	2	no	—
1095	C₈	—	79	2	no	—
1096	C₈	—	79	2	no	—
1097	C₈	—	158	2	no	—
1098	C₈	—	158	1	no	—
1099	C₈	—	158	2	no	—
1100	C₈	—	158	1	no	—
1101	C₈	#41×D₇₉	1	2	yes	—
1102	C₈	#41×D₇₉	1	2	yes	—
1103	C₂²	—	2	1	no	—
1104	C₂²	—	2	2	no	—
1105	C₂²	—	2	1	no	—
1106	C₂²	—	2	2	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	2	1	no	—
1109	C₂²	—	79	2	no	—
1110	C₂²	—	632	4	no	—
1111	C₂²	—	158	2	no	—
1112	C₂²	—	158	1	no	—
1113	C₂²	—	158	2	no	—
1114	C₂²	—	158	1	no	—
1115	C₂²	—	158	2	no	—
1116	C₂²	—	158	1	no	—
1117	C₂²	—	158	1	no	—
1118	C₂²	—	158	1	no	—
1119	C₂²	C₂³×C₄×D₇₉	1	1	yes	characteristic
1120	C₄	—	2	1	no	—
1121	C₄	—	2	2	no	—
1122	C₄	—	2	1	no	—
1123	C₄	—	2	1	no	—
1124	C₄	—	2	2	no	—
1125	C₄	—	2	2	no	—
1126	C₄	—	2	1	no	—
1127	C₄	—	79	2	no	—
1128	C₄	—	158	1	no	—
1129	C₄	—	158	2	no	—
1130	C₄	—	158	1	no	—
1131	C₄	—	158	1	no	—
1132	C₄	—	158	2	no	—
1133	C₄	—	158	1	no	—
1134	C₄	—	158	2	no	—
1135	C₄	—	158	1	no	—
1136	C₄	#19099328	1	2	yes	—
1137	C₄	C₂×#41×D₇₉	1	1	yes	characteristic
1138	C₄	C₂×#41×D₇₉	1	1	yes	characteristic
1139	C₂	—	4	2	no	—
1140	C₂	—	4	1	no	—
1141	C₂	—	316	2	no	—
1142	C₂	—	316	1	no	—
1143	C₂	—	158	2	no	—
1144	C₂	C₄×#41×D₇₉	1	1	yes	characteristic
1145	C₂	C₂×#19099328	1	1	yes	characteristic
1146	C₂	#23778111	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₇₉
commutator, socle	C₂²×C₇₉	C₂⁴×C₄
Fitting	C₇₉×#2966	C₂
prime radical	#23776956	C₂
cosocle	C₂×C₄×C₇₉	C₂⁵
hypercenter	#2966	D₇₉
hypocenter	C₇₉	#60217
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ #2966

Complements

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

N	H ≅ G/N	type
2. #23772419	C₂	semidirect
3. #23772417	C₂	semidirect
4. #23772405	C₂	semidirect
5. #23772402	C₂	semidirect
6. #23772401	C₂	semidirect
7. #23772401	C₂	semidirect
8. #23772382	C₂	semidirect
9. #23772381	C₂	semidirect
10. #23772378	C₂	semidirect
11. #23772366	C₂	semidirect
12. #23772365	C₂	semidirect
13. #23772342	C₂	semidirect
14. #23772331	C₂	semidirect
15. D₄×#11929607	C₂	semidirect
16. #23772120	C₂	semidirect
17. #23772098	C₂	semidirect
18. #436×D₇₉	C₂	semidirect
19. #23772067	C₂	semidirect
20. #23772056	C₂	semidirect
21. C₄×#14579167	C₂	semidirect
22. #23771816	C₂	semidirect
23. C₇₉×#2966	C₂	semidirect
50. #19098694	C₂²	semidirect
51. #19098693	C₂²	semidirect
52. #19098693	C₂²	semidirect
53. #19098693	C₂²	semidirect
54. #19098692	C₂²	semidirect
55. #19098691	C₂²	semidirect
56. Q₈×C₇₉⋊C₈	C₂²	semidirect
57. #19098687	C₂²	semidirect
58. #19098687	C₂²	semidirect
59. #19098687	C₂²	semidirect
62. #19098642	C₂²	semidirect
64. #19098641	C₂²	semidirect
67. #19098640	C₂²	semidirect
70. #19098638	C₂²	semidirect
71. #19098638	C₂²	semidirect
72. #19098638	C₂²	semidirect
73. #19098636	C₂²	semidirect
74. #19098635	C₂²	semidirect
76. #19098634	C₂²	semidirect
77. #19098634	C₂²	semidirect
78. #19098634	C₂²	semidirect
79. #19098633	C₂²	semidirect
80. #19098632	C₂²	semidirect
83. (C₂²⋊D₇₉)⋊C₈	C₂²	semidirect
84. #19098625	C₂²	semidirect
85. #19098624	C₂²	semidirect
86. #19098621	C₂²	semidirect
87. #19098621	C₂²	semidirect
88. #19098621	C₂²	semidirect
89. #19098619	C₂²	semidirect
90. #19098619	C₂²	semidirect
91. #19098618	C₂²	semidirect
92. #19098616	C₂²	semidirect
93. #19098615	C₂²	semidirect
94. #19098615	C₂²	semidirect
95. #19098614	C₂²	semidirect
103. #19098521	C₂²	semidirect
106. #19098519	C₂²	semidirect
107. #19098518	C₂²	semidirect
108. #19098518	C₂²	semidirect
109. #19098518	C₂²	semidirect
113. #19098517	C₂²	semidirect
114. #19098517	C₂²	semidirect
115. C₄×#11929608	C₂²	semidirect
116. #19098515	C₂²	semidirect
117. #19098515	C₂²	semidirect
119. C₄×#11929607	C₂²	semidirect
120. C₄×#11929607	C₂²	semidirect
121. C₄×#11929607	C₂²	semidirect
123. C₄×C₈×D₇₉	C₂²	semidirect
125. #446×C₇₉	C₂²	semidirect
126. C₈×Q₈×C₇₉	C₂²	semidirect
128. #435×C₇₉	C₂²	semidirect
130. C₈×D₄×C₇₉	C₂²	semidirect
131. #433×C₇₉	C₂²	semidirect
132. #432×C₇₉	C₂²	semidirect
133. #405×C₇₉	C₂²	semidirect
134. C₂×C₄×C₈×C₇₉	C₂²	semidirect
358. #11929607	#41	semidirect
370. C₈×D₇₉	#41	semidirect
584. #2966	D₇₉	semidirect
597. C₇₉	#60217	semidirect
631. #446	C₂×D₇₉	semidirect
636. C₈×Q₈	C₂×D₇₉	semidirect
660. #435	C₂×D₇₉	semidirect
664. C₈×D₄	C₂×D₇₉	semidirect
670. #433	C₂×D₇₉	semidirect
674. #432	C₂×D₇₉	semidirect
698. #405	C₂×D₇₉	semidirect
708. C₂×C₄×C₈	C₂×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23776956	2
#23772419	2
#23772417	2
#23772405	2
#23772402	2
#23772401	2
#23772382	2
#23772381	2
#23772378	2
#23772366	2
#23772365	2
#23772342	2
#23772331	2
D₄×#11929607	2
#23772120	2
#23772098	2
#436×D₇₉	2
#23772067	2
#23772056	2
C₄×#14579167	2
#23771816	2
C₇₉×#2966	2
#60217	79