Subgroups — #35158501

Order 20224.

1860 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23777150	C₂	1	2	yes	maximal, complemented
2	#23774112	C₂	1	2	yes	maximal, complemented
3	#23774105	C₂	1	2	yes	maximal, complemented
4	#23774062	C₂	1	2	yes	maximal, complemented
5	#23774061	C₂	1	2	yes	maximal, complemented
6	#23774059	C₂	1	1	yes	maximal, characteristic, complemented
7	#23774052	C₂	1	1	yes	maximal, characteristic, complemented
8	#23774032	C₂	1	1	yes	maximal, characteristic, complemented
9	#23773987	C₂	1	1	yes	maximal, characteristic, complemented
10	#23773983	C₂	1	1	yes	maximal, characteristic, complemented
11	#23773968	C₂	1	1	yes	maximal, characteristic, complemented
12	#23773967	C₂	1	1	yes	maximal, characteristic, complemented
13	#23773933	C₂	1	1	yes	maximal, characteristic, complemented
14	#23773890	C₂	1	1	yes	maximal, characteristic, complemented
15	#23773762	C₂	1	2	yes	maximal, complemented
16	#23773025	C₂	1	2	yes	maximal, complemented
17	#23772979	C₂	1	1	yes	maximal, characteristic
18	#467×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#23772270	C₂	1	1	yes	maximal, characteristic, complemented
20	#23772263	C₂	1	1	yes	maximal, characteristic, complemented
21	#23772240	C₂	1	2	yes	maximal, complemented
22	#405×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₉×#3175	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14579190	C₂²	1	2	yes	—
25	C₂×#14579180	C₂²	1	1	yes	characteristic
26	C₂×Q₁₆×D₇₉	C₂²	1	1	yes	characteristic
27	C₂×M₁₆×D₇₉	C₂²	1	1	yes	characteristic
28	C₂²×C₈×D₇₉	C₂²	1	1	yes	characteristic
29	#19099282	—	2	2	no	—
30	#19099267	—	2	2	no	—
31	#19099250	—	2	2	no	—
32	#19099249	—	2	2	no	—
33	#19099249	—	2	2	no	—
34	#19099247	—	2	2	no	—
35	#19099243	—	2	2	no	—
36	#19099241	—	2	2	no	—
37	#19099190	C₂²	1	2	yes	—
38	#19099180	C₂²	1	2	yes	—
39	#19099175	C₂²	1	2	yes	—
40	#19099173	C₂²	1	2	yes	—
41	#19099133	C₂²	1	2	yes	—
42	#19099118	C₂²	1	2	yes	—
43	#19099117	C₂²	1	2	yes	—
44	#19099095	C₂²	1	2	yes	—
45	#19099092	C₂²	1	2	yes	—
46	#19099073	C₂²	1	2	yes	—
47	C₂²⋊Q₈×D₇₉	C₂²	1	2	yes	—
48	#19099042	C₂²	1	2	yes	—
49	#19099039	C₂²	1	2	yes	—
50	#117×D₇₉	C₂²	1	1	yes	characteristic
51	#19098971	C₂²	1	2	yes	complemented
52	#19098969	C₂²	1	2	yes	complemented
53	#19098967	C₂²	1	1	yes	characteristic, complemented
54	#19098965	C₂²	1	1	yes	characteristic, complemented
55	#19098964	C₂²	1	1	yes	characteristic, complemented
56	#19098958	C₂²	1	2	yes	complemented
57	#19098954	C₂²	1	2	yes	complemented
58	#19098946	C₂²	1	1	yes	characteristic, complemented
59	#19098943	C₂²	1	1	yes	characteristic, complemented
60	#19098941	C₂²	1	1	yes	characteristic, complemented
61	#19098932	C₂²	1	2	yes	complemented
62	#19098930	C₂²	1	2	yes	complemented
63	#19098921	C₂²	1	2	yes	complemented
64	#19098917	C₂²	1	2	yes	complemented
65	#19098916	C₂²	1	2	yes	complemented
66	#19098915	C₂²	1	2	yes	complemented
67	#19098912	C₂²	1	2	yes	complemented
68	#19098821	C₂²	1	2	yes	—
69	#19098819	C₂²	1	2	yes	—
70	#19098807	C₂²	1	2	yes	—
71	#19098805	C₂²	1	1	yes	characteristic
72	#19098805	C₂²	1	1	yes	characteristic
73	#19098805	C₂²	1	2	yes	—
74	#19098804	C₂²	1	1	yes	characteristic
75	#19098804	C₂²	1	1	yes	characteristic
76	#19098803	C₂²	1	2	yes	—
77	#19098803	C₂²	1	2	yes	—
78	#19098802	C₂²	1	2	yes	—
79	#19098801	C₂²	1	1	yes	characteristic
80	#19098796	C₂²	1	1	yes	characteristic
81	#19098791	C₂²	1	2	yes	—
82	#19098791	C₂²	1	2	yes	—
83	#19098790	C₂²	1	2	yes	—
84	#19098789	C₂²	1	2	yes	—
85	#19098671	C₂²	1	2	yes	complemented
86	#19098668	C₂²	1	2	yes	complemented
87	#19098667	C₂²	1	2	yes	complemented
88	#19098667	C₂²	1	2	yes	complemented
89	#19098663	C₂²	1	2	yes	complemented
90	#19098660	C₂²	1	2	yes	complemented
91	#19098660	C₂²	1	2	yes	complemented
92	C₄×Dic₃₁₆	C₂²	1	1	yes	characteristic, complemented
93	C₄×Dic₃₁₆	C₂²	1	1	yes	characteristic, complemented
94	Q₁₆×Dic₇₉	C₂²	1	1	yes	characteristic, complemented
95	#19098657	C₂²	1	2	yes	complemented
96	#19098657	C₂²	1	1	yes	characteristic, complemented
97	#19098657	C₂²	1	1	yes	characteristic, complemented
98	C₄×#11929614	C₂²	1	2	yes	complemented
99	SD₁₆×Dic₇₉	C₂²	1	2	yes	complemented
100	C₄×#11929612	C₂²	1	2	yes	complemented
101	D₈×Dic₇₉	C₂²	1	1	yes	characteristic, complemented
102	#19098604	C₂²	1	2	yes	—
103	#19098600	C₂²	1	1	yes	characteristic
104	#107×D₇₉	C₂²	1	1	yes	characteristic
105	#19098570	C₂²	1	2	yes	—
106	#19098561	C₂²	1	2	yes	—
107	#19098556	C₂²	1	2	yes	—
108	#103×D₇₉	C₂²	1	2	yes	—
109	#19098521	C₂²	1	1	yes	characteristic
110	#19098520	C₂²	1	1	yes	characteristic
111	#19098520	C₂²	1	1	yes	characteristic
112	#19098519	C₂²	1	1	yes	characteristic
113	#19098518	C₂²	1	1	yes	characteristic
114	#19098517	C₂²	1	1	yes	characteristic
115	#19098517	C₂²	1	1	yes	characteristic
116	#97×D₇₉	C₂²	1	1	yes	characteristic
117	#97×D₇₉	C₂²	1	1	yes	characteristic
118	C₄×C₈×D₇₉	C₂²	1	1	yes	characteristic
119	C₄×C₈×D₇₉	C₂²	1	1	yes	characteristic
120	#542×C₇₉	C₂²	1	2	yes	—
121	#500×C₇₉	C₂²	1	1	yes	characteristic, complemented
122	#495×C₇₉	C₂²	1	1	yes	characteristic, complemented
123	#489×C₇₉	C₂²	1	2	yes	complemented
124	#468×C₇₉	C₂²	1	2	yes	—
125	#467×C₇₉	C₂²	1	1	yes	characteristic
126	#466×C₇₉	C₂²	1	1	yes	characteristic
127	#440×C₇₉	C₂²	1	2	yes	complemented
128	C₄×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic, complemented
129	C₄×D₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
130	#405×C₇₉	C₂²	1	1	yes	characteristic
131	C₂×#11929623	C₂³	1	2	yes	—
132	C₂×Q₈×D₇₉	C₂³	1	2	yes	—
133	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
134	#14579190	—	2	8	no	—
135	#14579180	—	2	4	no	—
136	C₂×Dic₃₁₆	C₂³	1	1	yes	characteristic
137	C₂×Dic₃₁₆	C₂³	1	1	yes	characteristic
138	C₂×Dic₃₁₆	C₂³	1	2	yes	—
139	C₂×#11929614	C₂³	1	2	yes	—
140	C₂×#11929614	C₂³	1	2	yes	—
141	Q₁₆×D₇₉	—	2	4	no	—
142	C₂×#11929612	C₂³	1	2	yes	—
143	C₂×#11929612	C₂³	1	2	yes	—
144	C₂×#11929608	C₂³	1	1	yes	characteristic
145	C₂×#11929607	C₂³	1	1	yes	characteristic
146	C₂×#11929607	C₂³	1	1	yes	characteristic
147	M₁₆×D₇₉	—	2	4	no	—
148	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
149	C₂×C₈×D₇₉	—	2	4	no	—
150	C₂×C₈×D₇₉	C₂³	1	1	yes	characteristic
151	C₂×C₈×D₇₉	C₂³	1	1	yes	characteristic
152	C₂×C₈×D₇₉	C₂³	1	1	yes	characteristic
153	C₂×C₈×D₇₉	C₂³	1	1	yes	characteristic
154	C₂×C₈×D₇₉	C₂³	1	1	yes	characteristic
155	C₂×C₈×D₇₉	C₂³	1	1	yes	characteristic
156	#14579161	C₂³	1	2	yes	—
157	#14579160	C₂³	1	2	yes	—
158	#14579159	—	2	2	no	—
159	#14579159	C₂³	1	2	yes	—
160	#14579154	—	2	2	no	—
161	#14579154	—	2	2	no	—
162	#14579154	—	2	2	no	—
163	#14579154	—	2	2	no	—
164	#14579154	—	2	2	no	—
165	#14579154	—	2	2	no	—
166	#14579154	—	2	2	no	—
167	#14579153	C₂³	1	2	yes	—
168	#14579152	—	2	2	no	—
169	#14579152	—	2	2	no	—
170	#14579152	C₂³	1	2	yes	—
171	#14579151	—	2	2	no	—
172	#14579151	—	2	2	no	—
173	#14579151	—	2	2	no	—
174	#14579151	—	2	2	no	—
175	#14579151	—	2	2	no	—
176	#14579148	—	2	2	no	—
177	#14579148	C₂³	1	2	yes	—
178	#14579143	—	2	2	no	—
179	#14579143	—	2	2	no	—
180	#14579143	—	2	2	no	—
181	#14579143	—	2	2	no	—
182	#14579143	—	2	2	no	—
183	#14579142	—	2	2	no	—
184	#14579141	C₂³	1	2	yes	—
185	#14579141	C₂³	1	2	yes	—
186	#14579140	C₂³	1	2	yes	—
187	#14579140	C₂³	1	2	yes	—
188	#14579139	—	2	2	no	—
189	#14579139	—	2	2	no	—
190	#14579139	—	2	2	no	—
191	#14579138	—	2	2	no	—
192	#14579138	—	2	2	no	—
193	#14579138	—	2	2	no	—
194	#14579138	—	2	2	no	—
195	#14579137	—	2	2	no	—
196	#14579137	—	2	2	no	—
197	#14579137	C₂³	1	2	yes	—
198	#14579132	C₂³	1	2	yes	—
199	#14579129	—	2	2	no	—
200	Q₈×Dic₇₉	—	2	2	no	—
201	Q₈×Dic₇₉	C₂³	1	2	yes	—
202	C₄×Dic₁₅₈	—	2	2	no	—
203	C₄×Dic₁₅₈	—	2	2	no	—
204	C₄×Dic₁₅₈	C₂³	1	2	yes	—
205	C₄×Dic₁₅₈	C₂³	1	2	yes	—
206	#14579126	—	2	2	no	—
207	#14579126	C₂³	1	2	yes	—
208	#14579126	C₂³	1	2	yes	—
209	D₄×Dic₇₉	—	2	2	no	—
210	D₄×Dic₇₉	C₂³	1	2	yes	—
211	C₄×C₂²⋊D₇₉	—	2	2	no	—
212	C₄×C₂²⋊D₇₉	—	2	2	no	—
213	(C₂²⋊D₇₉)⋊C₄	—	2	2	no	—
214	(C₂²⋊D₇₉)⋊C₄	—	2	2	no	—
215	(C₂²⋊D₇₉)⋊C₄	—	2	2	no	—
216	#14579120	—	2	2	no	—
217	#14579120	C₂³	1	1	yes	characteristic
218	#14579119	—	2	2	no	—
219	#14579119	—	2	2	no	—
220	#14579119	D₄	1	1	yes	characteristic
221	#14579119	D₄	1	1	yes	characteristic
222	#14579119	C₂³	1	2	yes	—
223	#14579118	—	2	2	no	—
224	#14579118	—	2	2	no	—
225	#14579118	C₂³	1	1	yes	characteristic
226	#14579118	C₂³	1	1	yes	characteristic
227	#14579117	—	2	2	no	—
228	#14579117	—	2	2	no	—
229	#14579117	D₄	1	1	yes	characteristic
230	#14579117	D₄	1	1	yes	characteristic
231	C₂×Dic₇₉⋊C₄	—	2	2	no	—
232	C₄⋊C₄×D₇₉	—	2	2	no	—
233	C₄⋊C₄×D₇₉	D₄	1	1	yes	characteristic
234	C₄⋊C₄×D₇₉	D₄	1	1	yes	characteristic
235	C₄⋊C₄×D₇₉	C₂³	1	2	yes	—
236	C₂²⋊C₄×D₇₉	—	2	2	no	—
237	C₂²⋊C₄×D₇₉	D₄	1	1	yes	characteristic
238	C₂²⋊C₄×D₇₉	D₄	1	1	yes	characteristic
239	C₄²×D₇₉	C₂³	1	1	yes	characteristic
240	C₄²×D₇₉	C₂³	1	1	yes	characteristic
241	#14579095	C₂³	1	1	yes	characteristic
242	#14579095	C₂³	1	1	yes	characteristic
243	#14579094	C₂³	1	2	yes	—
244	#14579094	C₂³	1	2	yes	—
245	#14579093	C₂³	1	2	yes	—
246	#14579092	C₂³	1	2	yes	—
247	#14579092	C₂³	1	2	yes	—
248	#14579086	C₂³	1	2	yes	—
249	#14579086	C₂³	1	2	yes	—
250	#14579086	C₂³	1	2	yes	—
251	#14579086	C₂³	1	2	yes	—
252	#14579085	C₂³	1	2	yes	—
253	#14579085	C₂³	1	2	yes	—
254	#14579084	C₂³	1	2	yes	—
255	#14579084	C₂³	1	2	yes	—
256	#14579084	C₂³	1	2	yes	—
257	#14579084	C₂³	1	2	yes	—
258	#14579082	C₂³	1	2	yes	—
259	#14579082	C₂³	1	2	yes	—
260	#14579072	C₂³	1	1	yes	characteristic
261	#14579072	C₂³	1	1	yes	characteristic
262	#14579071	C₂³	1	1	yes	characteristic
263	#14579071	C₂³	1	1	yes	characteristic
264	#14579071	C₂³	1	1	yes	characteristic
265	#14579071	C₂³	1	1	yes	characteristic
266	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
267	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
268	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
269	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
270	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
271	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
272	C₂×Q₁₆×C₇₉	C₂³	1	1	yes	characteristic
273	C₂×SD₁₆×C₇₉	C₂³	1	2	yes	—
274	C₂×D₈×C₇₉	C₂³	1	1	yes	characteristic
275	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
276	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
277	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
278	#126×C₇₉	—	2	2	no	—
279	#124×C₇₉	—	2	2	no	—
280	#124×C₇₉	C₂³	1	2	yes	—
281	#123×C₇₉	—	2	2	no	—
282	C₂²⋊Q₈×C₇₉	—	2	2	no	—
283	C₂²⋊Q₈×C₇₉	C₂³	1	2	yes	—
284	#121×C₇₉	C₂³	1	2	yes	—
285	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
286	C₄×D₄×C₇₉	C₂³	1	2	yes	—
287	#117×C₇₉	C₂³	1	1	yes	characteristic
288	#107×C₇₉	C₂³	1	1	yes	characteristic
289	#107×C₇₉	C₂³	1	1	yes	characteristic
290	#107×C₇₉	C₂³	1	2	yes	—
291	#103×C₇₉	C₂³	1	2	yes	—
292	#103×C₇₉	C₂³	1	2	yes	—
293	#102×C₇₉	C₂³	1	2	yes	—
294	#102×C₇₉	C₂³	1	2	yes	—
295	#97×C₇₉	C₂³	1	1	yes	characteristic
296	#97×C₇₉	C₂³	1	1	yes	characteristic
297	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
298	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
299	C₂³×D₇₉	C₂×D₄	1	1	yes	characteristic
300	#11929623	—	2	4	no	—
301	#11929623	—	2	4	no	—
302	C₂×Dic₁₅₈	—	2	2	no	—
303	C₂×Dic₁₅₈	—	2	2	no	—
304	C₂×Dic₁₅₈	C₂⁴	1	2	yes	—
305	C₂×Dic₁₅₈	C₂⁴	1	2	yes	—
306	Q₈×D₇₉	—	2	4	no	—
307	Q₈×D₇₉	—	2	4	no	—
308	C₂×C₂²⋊D₇₉	—	2	2	no	—
309	C₂×C₂²⋊D₇₉	—	2	2	no	—
310	C₂²×Dic₇₉	—	2	2	no	—
311	C₂²×Dic₇₉	—	2	2	no	—
312	C₂²×Dic₇₉	C₂×D₄	1	1	yes	characteristic
313	C₂×C₄×D₇₉	—	2	2	no	—
314	C₂×C₄×D₇₉	—	2	2	no	—
315	C₂×C₄×D₇₉	—	2	2	no	—
316	C₂×C₄×D₇₉	—	2	2	no	—
317	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
318	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
319	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
320	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
321	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
322	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
323	C₂×C₄×D₇₉	C₂⁴	1	1	yes	characteristic
324	C₂×C₄×D₇₉	C₂⁴	1	1	yes	characteristic
325	Dic₃₁₆	—	2	2	no	—
326	Dic₃₁₆	—	2	2	no	—
327	Dic₃₁₆	—	2	4	no	—
328	#11929614	—	2	4	no	—
329	#11929614	—	2	4	no	—
330	#11929612	—	2	4	no	—
331	#11929612	—	2	4	no	—
332	#11929608	—	2	2	no	—
333	#11929607	—	2	2	no	—
334	#11929607	#41	1	4	yes	—
335	C₂×C₇₉⋊C₈	—	2	2	no	—
336	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
337	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
338	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
339	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
340	C₈×D₇₉	—	2	2	no	—
341	C₈×D₇₉	—	2	2	no	—
342	C₈×D₇₉	—	2	2	no	—
343	C₈×D₇₉	—	2	2	no	—
344	C₈×D₇₉	—	2	2	no	—
345	C₈×D₇₉	#41	1	4	yes	—
346	C₄⋊Dic₇₉	—	2	2	no	—
347	C₄⋊Dic₇₉	—	2	2	no	—
348	C₄⋊Dic₇₉	—	2	2	no	—
349	C₄⋊Dic₇₉	—	2	2	no	—
350	C₄⋊Dic₇₉	—	2	2	no	—
351	C₄⋊Dic₇₉	—	2	2	no	—
352	C₄⋊Dic₇₉	C₂×D₄	1	1	yes	characteristic
353	C₄⋊Dic₇₉	C₂×D₄	1	1	yes	characteristic
354	C₄⋊Dic₇₉	C₂⁴	1	2	yes	—
355	C₄⋊Dic₇₉	C₂⁴	1	2	yes	—
356	Dic₇₉⋊C₄	—	2	2	no	—
357	Dic₇₉⋊C₄	—	2	2	no	—
358	Dic₇₉⋊C₄	—	2	2	no	—
359	Dic₇₉⋊C₄	—	2	2	no	—
360	Dic₇₉⋊C₄	—	2	2	no	—
361	Dic₇₉⋊C₄	—	2	2	no	—
362	Dic₇₉⋊C₄	—	2	2	no	—
363	Dic₇₉⋊C₄	—	2	2	no	—
364	Dic₇₉⋊C₄	—	2	2	no	—
365	Dic₇₉⋊C₄	—	2	2	no	—
366	Dic₇₉⋊C₄	—	2	2	no	—
367	Dic₇₉⋊C₄	—	2	2	no	—
368	Dic₇₉⋊C₄	—	2	2	no	—
369	Dic₇₉⋊C₄	—	2	2	no	—
370	Dic₇₉⋊C₄	C₂×D₄	1	1	yes	characteristic
371	Dic₇₉⋊C₄	C₂×D₄	1	1	yes	characteristic
372	Dic₇₉⋊C₄	C₂×D₄	1	1	yes	characteristic
373	Dic₇₉⋊C₄	C₂×D₄	1	1	yes	characteristic
374	C₂²⋊Dic₇₉	—	2	2	no	—
375	C₂²⋊Dic₇₉	—	2	2	no	—
376	C₂²⋊Dic₇₉	—	2	2	no	—
377	C₂²⋊Dic₇₉	—	2	2	no	—
378	C₂²⋊Dic₇₉	—	2	2	no	—
379	C₂²⋊Dic₇₉	—	2	2	no	—
380	C₂²⋊Dic₇₉	C₂×D₄	1	1	yes	characteristic
381	C₂²⋊Dic₇₉	C₂×D₄	1	1	yes	characteristic
382	(C₂×D₇₉)⋊C₄	—	2	2	no	—
383	(C₂×D₇₉)⋊C₄	—	2	2	no	—
384	(C₂×D₇₉)⋊C₄	—	2	2	no	—
385	(C₂×D₇₉)⋊C₄	—	2	2	no	—
386	(C₂×D₇₉)⋊C₄	C₂×D₄	1	1	yes	characteristic
387	(C₂×D₇₉)⋊C₄	C₂×D₄	1	1	yes	characteristic
388	(C₂×D₇₉)⋊C₄	C₂×D₄	1	1	yes	characteristic
389	(C₂×D₇₉)⋊C₄	C₂×D₄	1	1	yes	characteristic
390	C₄×Dic₇₉	—	2	2	no	—
391	C₄×Dic₇₉	—	2	2	no	—
392	C₄×Dic₇₉	—	2	2	no	—
393	C₄×Dic₇₉	—	2	2	no	—
394	C₄×Dic₇₉	—	2	2	no	—
395	C₄×Dic₇₉	—	2	2	no	—
396	C₄×Dic₇₉	C₂×D₄	1	1	yes	characteristic
397	C₄×Dic₇₉	C₂×D₄	1	1	yes	characteristic
398	C₄×Dic₇₉	C₂×D₄	1	1	yes	characteristic
399	C₄×Dic₇₉	C₂×D₄	1	1	yes	characteristic
400	C₄×Dic₇₉	C₂⁴	1	1	yes	characteristic
401	C₄×Dic₇₉	C₂⁴	1	1	yes	characteristic
402	C₂×Q₈×C₇₉	—	2	2	no	—
403	C₂×Q₈×C₇₉	C₂⁴	1	2	yes	—
404	C₂×D₄×C₇₉	—	2	2	no	—
405	C₂×D₄×C₇₉	C₂⁴	1	2	yes	—
406	C₂²×C₄×C₇₉	—	2	2	no	—
407	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
408	Q₁₆×C₇₉	—	2	2	no	—
409	SD₁₆×C₇₉	—	2	4	no	—
410	D₈×C₇₉	—	2	2	no	—
411	M₁₆×C₇₉	—	2	2	no	—
412	C₂×C₈×C₇₉	—	2	2	no	—
413	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
414	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
415	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
416	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₇₉	—	2	2	no	—
418	C₄⋊C₄×C₇₉	—	2	2	no	—
419	C₄⋊C₄×C₇₉	—	2	2	no	—
420	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
421	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
422	C₄⋊C₄×C₇₉	C₂⁴	1	2	yes	—
423	C₄⋊C₄×C₇₉	C₂⁴	1	2	yes	—
424	C₂²⋊C₄×C₇₉	—	2	2	no	—
425	C₂²⋊C₄×C₇₉	—	2	2	no	—
426	C₂²⋊C₄×C₇₉	—	2	2	no	—
427	C₂²⋊C₄×C₇₉	—	2	2	no	—
428	C₂²⋊C₄×C₇₉	—	2	2	no	—
429	C₂²⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
430	C₂²⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
431	C₄²×C₇₉	—	2	2	no	—
432	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
433	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
434	C₂³×C₇₉	—	2	2	no	—
435	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
436	C₂²×D₇₉	—	2	2	no	—
437	C₂²×D₇₉	—	2	2	no	—
438	C₂²×D₇₉	—	4	1	no	—
439	C₂²×D₇₉	C₂²×D₄	1	1	yes	characteristic
440	C₂²×D₇₉	C₂²×D₄	1	1	yes	characteristic
441	Q₈×C₇₉	—	2	2	no	—
442	Q₈×C₇₉	—	2	2	no	—
443	Q₈×C₇₉	—	8	2	no	—
444	D₄×C₇₉	—	2	2	no	—
445	D₄×C₇₉	—	2	2	no	—
446	D₄×C₇₉	—	8	2	no	—
447	C₂×C₄×C₇₉	—	2	1	no	—
448	C₂×C₄×C₇₉	—	2	1	no	—
449	C₂×C₄×C₇₉	—	2	2	no	—
450	C₂×C₄×C₇₉	—	2	2	no	—
451	C₂×C₄×C₇₉	—	2	2	no	—
452	C₂×C₄×C₇₉	—	8	2	no	—
453	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
459	C₂²⋊D₇₉	—	4	4	no	—
460	C₂²⋊D₇₉	—	4	4	no	—
461	C₂×Dic₇₉	—	2	2	no	—
462	C₂×Dic₇₉	—	2	2	no	—
463	C₂×Dic₇₉	—	2	2	no	—
464	C₂×Dic₇₉	—	2	2	no	—
465	C₂×Dic₇₉	—	2	2	no	—
466	C₂×Dic₇₉	—	4	4	no	—
467	C₂×Dic₇₉	—	8	2	no	—
468	C₂×Dic₇₉	C₂²×D₄	1	1	yes	characteristic
469	C₂×Dic₇₉	C₂²×D₄	1	1	yes	characteristic
470	C₂×Dic₇₉	C₂²×D₄	1	1	yes	characteristic
471	C₂×Dic₇₉	C₂²×D₄	1	1	yes	characteristic
472	C₂×Dic₇₉	C₂²×D₄	1	1	yes	characteristic
473	C₂×Dic₇₉	C₂²×D₄	1	1	yes	characteristic
474	C₄×D₇₉	—	2	2	no	—
475	C₄×D₇₉	—	2	2	no	—
476	C₄×D₇₉	—	2	2	no	—
477	C₄×D₇₉	—	2	1	no	—
478	C₄×D₇₉	—	2	1	no	—
479	C₄×D₇₉	—	2	2	no	—
480	C₄×D₇₉	—	4	1	no	—
481	C₄×D₇₉	—	4	1	no	—
482	C₄×D₇₉	—	4	4	no	—
483	C₄×D₇₉	—	8	2	no	—
484	C₄×D₇₉	C₂×#41	1	2	yes	—
485	C₄×D₇₉	C₂×#41	1	2	yes	—
486	Dic₁₅₈	—	2	2	no	—
487	Dic₁₅₈	—	2	2	no	—
488	Dic₁₅₈	—	2	2	no	—
489	Dic₁₅₈	—	2	2	no	—
490	Dic₁₅₈	—	4	4	no	—
491	Dic₁₅₈	—	8	2	no	—
492	C₈×C₇₉	—	2	1	no	—
493	C₈×C₇₉	—	2	1	no	—
494	C₈×C₇₉	C₂×#41	1	2	yes	—
495	C₈×C₇₉	C₂×#41	1	2	yes	—
496	C₇₉⋊C₈	—	2	1	no	—
497	C₇₉⋊C₈	—	2	1	no	—
498	C₇₉⋊C₈	C₂×#41	1	2	yes	—
499	C₇₉⋊C₈	C₂×#41	1	2	yes	—
500	C₂²×C₇₉	—	2	1	no	—
501	C₂²×C₇₉	—	2	1	no	—
502	C₂²×C₇₉	—	2	1	no	—
503	C₂²×C₇₉	—	4	2	no	—
504	C₂²×C₇₉	—	4	2	no	—
505	C₂²×C₇₉	—	4	2	no	—
506	C₂²×C₇₉	C₂³×D₄	1	1	yes	characteristic
507	C₂×D₇₉	—	2	1	no	—
508	C₂×D₇₉	—	2	1	no	—
509	C₂×D₇₉	—	2	1	no	—
510	C₂×D₇₉	—	2	1	no	—
511	C₂×D₇₉	—	4	4	no	—
512	C₂×D₇₉	#532	1	2	yes	—
513	C₂×D₇₉	#578	1	2	yes	—
514	C₄×C₇₉	—	2	1	no	—
515	C₄×C₇₉	—	2	1	no	—
516	C₄×C₇₉	—	2	1	no	—
517	C₄×C₇₉	—	2	1	no	—
518	C₄×C₇₉	—	2	1	no	—
519	C₄×C₇₉	—	4	2	no	—
520	C₄×C₇₉	—	4	2	no	—
521	C₄×C₇₉	—	4	2	no	—
522	C₄×C₇₉	C₂²×#41	1	1	yes	characteristic
523	C₄×C₇₉	C₂²×#41	1	1	yes	characteristic
524	Dic₇₉	—	2	1	no	—
525	Dic₇₉	—	2	1	no	—
526	Dic₇₉	—	2	1	no	—
527	Dic₇₉	—	2	1	no	—
528	Dic₇₉	—	2	1	no	—
529	Dic₇₉	—	4	2	no	—
530	Dic₇₉	—	4	2	no	—
531	Dic₇₉	—	4	2	no	—
532	Dic₇₉	—	4	2	no	—
533	Dic₇₉	#532	1	2	yes	—
534	#60708	—	79	1	no	maximal, Sylow
535	C₂×C₇₉	—	4	1	no	—
536	C₂×C₇₉	—	8	2	no	—
537	C₂×C₇₉	C₂×#532	1	1	yes	characteristic
538	C₂×C₇₉	C₂×#578	1	1	yes	characteristic
539	C₂×C₇₉	#3584	1	1	yes	characteristic
540	D₇₉	—	2	2	no	—
541	D₇₉	—	2	2	no	—
542	#3495	—	79	2	no	—
543	#3181	—	79	2	no	—
544	#3181	—	79	2	no	—
545	#3178	—	79	2	no	—
546	#3178	—	79	2	no	—
547	#3177	—	79	1	no	—
548	#3177	—	79	1	no	—
549	#3175	—	79	1	no	—
550	#3175	D₇₉	1	1	yes	characteristic, complemented
551	#3170	—	79	1	no	—
552	#3170	—	79	1	no	—
553	#3168	—	79	1	no	—
554	#3168	—	79	1	no	—
555	#3164	—	79	1	no	—
556	#3156	—	79	1	no	—
557	#3137	—	79	2	no	—
558	#3056	—	79	2	no	—
559	#3050	—	79	1	no	—
560	C₂×#467	—	79	1	no	—
561	#2951	—	79	1	no	—
562	#2950	—	79	1	no	—
563	#2947	—	79	2	no	—
564	C₂×#405	—	79	1	no	—
565	C₇₉	#60708	1	1	yes	characteristic, complemented, Sylow
566	C₂×#137	—	79	2	no	—
567	C₂×#135	—	79	1	no	—
568	C₂²×Q₁₆	—	79	1	no	—
569	C₂²×M₁₆	—	79	1	no	—
570	C₂³×C₈	—	79	1	no	—
571	#556	—	158	2	no	—
572	#554	—	158	2	no	—
573	#552	—	158	2	no	—
574	#552	—	158	2	no	—
575	#552	—	158	2	no	—
576	#552	—	158	2	no	—
577	#551	—	158	2	no	—
578	#551	—	158	2	no	—
579	#544	—	79	2	no	—
580	#542	—	79	2	no	—
581	#542	C₂×D₇₉	1	2	yes	—
582	#541	—	79	2	no	—
583	#541	—	79	2	no	—
584	#536	—	79	2	no	—
585	#533	—	79	2	no	—
586	#533	—	79	2	no	—
587	#529	—	79	2	no	—
588	#529	—	79	2	no	—
589	#525	—	79	2	no	—
590	C₂×C₂²⋊Q₈	—	79	2	no	—
591	#520	—	79	2	no	—
592	#519	—	79	2	no	—
593	C₂×#117	—	79	1	no	—
594	#501	—	79	2	no	—
595	#501	—	79	2	no	—
596	#500	—	79	1	no	—
597	#500	C₂×D₇₉	1	1	yes	characteristic, complemented
598	#499	—	79	1	no	—
599	#499	—	79	1	no	—
600	#497	—	79	2	no	—
601	#497	—	79	2	no	—
602	#495	—	79	1	no	—
603	#495	C₂×D₇₉	1	1	yes	characteristic, complemented
604	#494	—	79	1	no	—
605	#494	—	79	1	no	—
606	#491	—	79	2	no	—
607	#491	—	79	2	no	—
608	#489	—	79	2	no	—
609	#489	C₂×D₇₉	1	2	yes	complemented
610	#488	—	79	2	no	—
611	#488	—	79	2	no	—
612	#487	—	79	2	no	—
613	#487	—	79	2	no	—
614	#470	—	79	2	no	—
615	#470	—	79	2	no	—
616	#468	—	79	2	no	—
617	#468	C₂×D₇₉	1	2	yes	—
618	#467	—	79	1	no	—
619	#467	—	79	1	no	—
620	#467	—	79	1	no	—
621	#467	—	79	2	no	—
622	#467	—	79	1	no	—
623	#467	—	79	1	no	—
624	#467	—	79	2	no	—
625	#467	—	79	2	no	—
626	#467	—	79	2	no	—
627	#467	C₂×D₇₉	1	1	yes	characteristic
628	#466	—	79	1	no	—
629	#466	C₂×D₇₉	1	1	yes	characteristic
630	#465	—	79	2	no	—
631	#465	—	79	2	no	—
632	#465	—	79	2	no	—
633	#465	—	79	2	no	—
634	#441	—	79	2	no	—
635	#441	—	79	2	no	—
636	#441	—	79	2	no	—
637	#441	—	79	2	no	—
638	#440	—	79	2	no	—
639	#440	—	79	2	no	—
640	#440	—	79	2	no	—
641	#440	C₂×D₇₉	1	2	yes	complemented
642	C₄×Q₁₆	—	79	1	no	—
643	C₄×Q₁₆	—	79	2	no	—
644	C₄×Q₁₆	—	79	1	no	—
645	C₄×Q₁₆	—	79	1	no	—
646	C₄×Q₁₆	—	79	2	no	—
647	C₄×Q₁₆	—	79	1	no	—
648	C₄×Q₁₆	—	79	1	no	—
649	C₄×Q₁₆	C₂×D₇₉	1	1	yes	characteristic, complemented
650	C₄×SD₁₆	—	79	2	no	—
651	C₄×SD₁₆	—	79	2	no	—
652	C₄×D₈	—	79	1	no	—
653	C₄×D₈	C₂×D₇₉	1	1	yes	characteristic, complemented
654	#428	—	79	2	no	—
655	#427	—	79	1	no	—
656	C₂×#107	—	79	1	no	—
657	#419	—	79	2	no	—
658	#417	—	79	2	no	—
659	#416	—	79	2	no	—
660	C₂×#103	—	79	2	no	—
661	#405	—	79	1	no	—
662	#405	—	79	1	no	—
663	#405	—	79	1	no	—
664	#405	—	79	1	no	—
665	#405	—	79	1	no	—
666	#405	—	79	1	no	—
667	#405	—	79	1	no	—
668	#405	C₂×D₇₉	1	1	yes	characteristic
669	C₂×#97	—	79	1	no	—
670	C₂×#97	—	79	1	no	—
671	C₂×C₄×C₈	—	79	1	no	—
672	C₂×C₄×C₈	—	79	1	no	—
673	C₂×#41	—	79	2	no	—
674	C₂²×Q₈	—	79	2	no	—
675	C₂³×C₄	—	79	1	no	—
676	#137	—	158	8	no	—
677	#135	—	158	4	no	—
678	C₂×Q₁₆	—	79	2	no	—
679	C₂×Q₁₆	—	79	2	no	—
680	C₂×Q₁₆	—	79	1	no	—
681	C₂×Q₁₆	—	79	1	no	—
682	C₂×Q₁₆	—	79	2	no	—
683	C₂×Q₁₆	—	158	4	no	—
684	C₂×Q₁₆	C₂²×D₇₉	1	1	yes	characteristic
685	C₂×SD₁₆	—	79	2	no	—
686	C₂×SD₁₆	—	79	2	no	—
687	C₂×SD₁₆	C₂²×D₇₉	1	2	yes	—
688	C₂×D₈	C₂²×D₇₉	1	1	yes	characteristic
689	C₂×M₁₆	—	79	1	no	—
690	C₂×M₁₆	—	79	1	no	—
691	C₂×M₁₆	—	79	1	no	—
692	C₂×M₁₆	—	158	4	no	—
693	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
694	C₂²×C₈	—	79	1	no	—
695	C₂²×C₈	—	79	1	no	—
696	C₂²×C₈	—	79	1	no	—
697	C₂²×C₈	—	79	1	no	—
698	C₂²×C₈	—	79	1	no	—
699	C₂²×C₈	—	79	1	no	—
700	C₂²×C₈	—	79	1	no	—
701	C₂²×C₈	—	158	4	no	—
702	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
703	C₄⋊Q₈	—	79	2	no	—
704	C₄⋊Q₈	—	79	2	no	—
705	C₄⋊Q₈	—	79	2	no	—
706	C₄⋊Q₈	—	158	2	no	—
707	C₄⋊Q₈	C₂²×D₇₉	1	2	yes	—
708	#126	—	2	2	no	—
709	#126	—	158	2	no	—
710	#126	—	158	2	no	—
711	#126	—	158	2	no	—
712	#126	—	158	2	no	—
713	#126	—	158	2	no	—
714	#126	—	158	2	no	—
715	#126	—	158	2	no	—
716	#125	—	79	2	no	—
717	#125	—	79	2	no	—
718	#125	—	158	2	no	—
719	#125	—	158	2	no	—
720	#125	—	158	2	no	—
721	#125	—	158	2	no	—
722	#125	—	158	2	no	—
723	#125	—	158	2	no	—
724	#125	—	158	2	no	—
725	#124	—	2	2	no	—
726	#124	—	79	2	no	—
727	#124	—	158	2	no	—
728	#124	C₂²×D₇₉	1	2	yes	—
729	#123	—	2	2	no	—
730	#123	—	158	2	no	—
731	#123	—	158	2	no	—
732	#123	—	158	2	no	—
733	#123	—	158	2	no	—
734	#123	—	158	2	no	—
735	#123	—	158	2	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	—	79	2	no	—
738	C₂²⋊Q₈	—	79	2	no	—
739	C₂²⋊Q₈	—	79	2	no	—
740	C₂²⋊Q₈	—	79	2	no	—
741	C₂²⋊Q₈	—	79	2	no	—
742	C₂²⋊Q₈	—	158	2	no	—
743	C₂²⋊Q₈	—	158	2	no	—
744	C₂²⋊Q₈	—	158	2	no	—
745	C₂²⋊Q₈	—	158	2	no	—
746	C₂²⋊Q₈	—	158	2	no	—
747	C₂²⋊Q₈	—	158	2	no	—
748	C₂²⋊Q₈	—	158	2	no	—
749	C₂²⋊Q₈	—	158	2	no	—
750	C₂²⋊Q₈	—	158	2	no	—
751	C₂²⋊Q₈	C₂²×D₇₉	1	2	yes	—
752	#121	—	79	2	no	—
753	#121	C₂²×D₇₉	1	2	yes	—
754	#120	—	158	2	no	—
755	C₄×Q₈	—	79	2	no	—
756	C₄×Q₈	—	79	2	no	—
757	C₄×Q₈	—	79	2	no	—
758	C₄×Q₈	—	79	2	no	—
759	C₄×Q₈	—	79	2	no	—
760	C₄×Q₈	—	158	2	no	—
761	C₄×Q₈	—	158	2	no	—
762	C₄×Q₈	—	158	2	no	—
763	C₄×Q₈	—	158	2	no	—
764	C₄×Q₈	C₂²×D₇₉	1	2	yes	—
765	C₄×D₄	—	79	2	no	—
766	C₄×D₄	—	158	2	no	—
767	C₄×D₄	—	158	2	no	—
768	C₄×D₄	—	158	2	no	—
769	C₄×D₄	—	158	2	no	—
770	C₄×D₄	—	158	2	no	—
771	C₄×D₄	—	158	2	no	—
772	C₄×D₄	C₂²×D₇₉	1	2	yes	—
773	#117	—	79	1	no	—
774	#117	—	79	1	no	—
775	#117	—	79	1	no	—
776	#117	—	79	1	no	—
777	#117	—	79	1	no	—
778	#117	—	79	1	no	—
779	#117	—	79	1	no	—
780	#117	—	79	2	no	—
781	#117	—	158	2	no	—
782	#117	—	158	2	no	—
783	#117	—	158	2	no	—
784	#117	—	158	2	no	—
785	#117	—	158	2	no	—
786	#117	—	158	2	no	—
787	#117	—	158	2	no	—
788	#117	C₂²×D₇₉	1	1	yes	characteristic
789	C₂×C₄⋊C₄	—	79	1	no	—
790	C₂×C₄⋊C₄	—	79	1	no	—
791	C₂×C₄⋊C₄	—	79	2	no	—
792	C₂×C₄⋊C₄	—	158	2	no	—
793	C₂×C₄⋊C₄	—	158	2	no	—
794	C₂×C₂²⋊C₄	—	79	1	no	—
795	C₂×C₂²⋊C₄	—	79	1	no	—
796	C₂×C₂²⋊C₄	—	158	2	no	—
797	C₂×C₄²	—	79	1	no	—
798	C₂×C₄²	—	79	1	no	—
799	#107	—	79	1	no	—
800	#107	—	79	1	no	—
801	#107	—	79	2	no	—
802	#107	—	79	2	no	—
803	#107	C₂²×D₇₉	1	1	yes	characteristic
804	#107	C₂²×D₇₉	1	1	yes	characteristic
805	#107	C₂²×D₇₉	1	2	yes	—
806	#106	—	79	2	no	—
807	#106	—	79	2	no	—
808	#106	—	79	2	no	—
809	#103	—	79	2	no	—
810	#103	—	79	2	no	—
811	#103	—	79	2	no	—
812	#103	—	79	2	no	—
813	#103	—	79	2	no	—
814	#103	—	79	2	no	—
815	#103	—	79	2	no	—
816	#103	—	79	2	no	—
817	#103	—	79	2	no	—
818	#103	—	79	2	no	—
819	#103	C₂²×D₇₉	1	2	yes	—
820	#103	C₂²×D₇₉	1	2	yes	—
821	#102	—	79	2	no	—
822	#102	—	79	2	no	—
823	#102	C₂²×D₇₉	1	2	yes	—
824	#102	C₂²×D₇₉	1	2	yes	—
825	#97	—	79	1	no	—
826	#97	—	79	1	no	—
827	#97	—	79	1	no	—
828	#97	—	79	1	no	—
829	#97	—	79	1	no	—
830	#97	—	79	1	no	—
831	#97	C₂²×D₇₉	1	1	yes	characteristic
832	#97	C₂²×D₇₉	1	1	yes	characteristic
833	C₄×C₈	—	79	1	no	—
834	C₄×C₈	—	79	1	no	—
835	C₄×C₈	—	79	1	no	—
836	C₄×C₈	—	79	1	no	—
837	C₄×C₈	—	79	1	no	—
838	C₄×C₈	—	79	1	no	—
839	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
840	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
841	C₂⁴	—	79	1	no	—
842	#41	—	158	4	no	—
843	#41	—	158	4	no	—
844	C₂×Q₈	—	2	2	no	—
845	C₂×Q₈	—	79	2	no	—
846	C₂×Q₈	—	79	2	no	—
847	C₂×Q₈	—	158	2	no	—
848	C₂×Q₈	—	158	2	no	—
849	C₂×Q₈	—	158	4	no	—
850	C₂×Q₈	—	158	4	no	—
851	C₂×Q₈	C₂³×D₇₉	1	2	yes	—
852	C₂×D₄	—	2	2	no	—
853	C₂×D₄	—	158	2	no	—
854	C₂×D₄	—	158	2	no	—
855	C₂×D₄	C₂³×D₇₉	1	2	yes	—
856	C₂²×C₄	—	2	2	no	—
857	C₂²×C₄	—	79	1	no	—
858	C₂²×C₄	—	79	1	no	—
859	C₂²×C₄	—	79	1	no	—
860	C₂²×C₄	—	79	1	no	—
861	C₂²×C₄	—	79	1	no	—
862	C₂²×C₄	—	79	1	no	—
863	C₂²×C₄	—	79	1	no	—
864	C₂²×C₄	—	79	1	no	—
865	C₂²×C₄	—	79	1	no	—
866	C₂²×C₄	—	158	2	no	—
867	C₂²×C₄	—	158	2	no	—
868	C₂²×C₄	—	158	2	no	—
869	C₂²×C₄	—	158	2	no	—
870	C₂²×C₄	—	158	2	no	—
871	C₂²×C₄	—	158	2	no	—
872	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
873	Q₁₆	—	2	2	no	—
874	Q₁₆	—	158	4	no	—
875	Q₁₆	—	158	4	no	—
876	Q₁₆	—	158	2	no	—
877	Q₁₆	—	158	2	no	—
878	Q₁₆	—	158	4	no	—
879	SD₁₆	—	2	4	no	—
880	SD₁₆	—	158	4	no	—
881	SD₁₆	—	158	4	no	—
882	D₈	—	2	2	no	—
883	M₁₆	—	2	2	no	—
884	M₁₆	—	79	4	no	—
885	M₁₆	—	158	2	no	—
886	M₁₆	—	158	2	no	—
887	C₂×C₈	—	2	2	no	—
888	C₂×C₈	—	79	1	no	—
889	C₂×C₈	—	79	1	no	—
890	C₂×C₈	—	79	4	no	—
891	C₂×C₈	—	79	1	no	—
892	C₂×C₈	—	79	1	no	—
893	C₂×C₈	—	158	2	no	—
894	C₂×C₈	—	158	2	no	—
895	C₂×C₈	—	158	2	no	—
896	C₂×C₈	—	158	2	no	—
897	C₂×C₈	—	158	2	no	—
898	C₂×C₈	—	158	2	no	—
899	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
900	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
901	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
902	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	79	1	no	—
907	C₄⋊C₄	—	79	1	no	—
908	C₄⋊C₄	—	79	1	no	—
909	C₄⋊C₄	—	79	1	no	—
910	C₄⋊C₄	—	79	1	no	—
911	C₄⋊C₄	—	79	1	no	—
912	C₄⋊C₄	—	79	2	no	—
913	C₄⋊C₄	—	79	2	no	—
914	C₄⋊C₄	—	158	2	no	—
915	C₄⋊C₄	—	158	2	no	—
916	C₄⋊C₄	—	158	2	no	—
917	C₄⋊C₄	—	158	2	no	—
918	C₄⋊C₄	—	158	2	no	—
919	C₄⋊C₄	—	158	2	no	—
920	C₄⋊C₄	—	158	2	no	—
921	C₄⋊C₄	—	158	2	no	—
922	C₄⋊C₄	—	158	2	no	—
923	C₄⋊C₄	—	158	2	no	—
924	C₄⋊C₄	—	158	2	no	—
925	C₄⋊C₄	—	158	2	no	—
926	C₄⋊C₄	—	158	2	no	—
927	C₄⋊C₄	—	158	2	no	—
928	C₄⋊C₄	—	158	2	no	—
929	C₄⋊C₄	—	158	2	no	—
930	C₄⋊C₄	—	158	2	no	—
931	C₄⋊C₄	—	158	2	no	—
932	C₄⋊C₄	—	158	2	no	—
933	C₄⋊C₄	—	158	2	no	—
934	C₄⋊C₄	D₄×D₇₉	1	1	yes	characteristic
935	C₄⋊C₄	D₄×D₇₉	1	1	yes	characteristic
936	C₄⋊C₄	C₂³×D₇₉	1	2	yes	—
937	C₄⋊C₄	C₂³×D₇₉	1	2	yes	—
938	C₂²⋊C₄	—	2	2	no	—
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	79	1	no	—
944	C₂²⋊C₄	—	79	1	no	—
945	C₂²⋊C₄	—	79	1	no	—
946	C₂²⋊C₄	—	79	1	no	—
947	C₂²⋊C₄	—	79	1	no	—
948	C₂²⋊C₄	—	79	1	no	—
949	C₂²⋊C₄	—	158	2	no	—
950	C₂²⋊C₄	—	158	2	no	—
951	C₂²⋊C₄	—	158	2	no	—
952	C₂²⋊C₄	—	158	2	no	—
953	C₂²⋊C₄	—	158	2	no	—
954	C₂²⋊C₄	—	158	2	no	—
955	C₂²⋊C₄	—	158	2	no	—
956	C₂²⋊C₄	—	158	2	no	—
957	C₂²⋊C₄	—	158	2	no	—
958	C₂²⋊C₄	—	158	2	no	—
959	C₂²⋊C₄	D₄×D₇₉	1	1	yes	characteristic
960	C₂²⋊C₄	D₄×D₇₉	1	1	yes	characteristic
961	C₄²	—	2	2	no	—
962	C₄²	—	79	1	no	—
963	C₄²	—	79	1	no	—
964	C₄²	—	79	1	no	—
965	C₄²	—	79	1	no	—
966	C₄²	—	79	1	no	—
967	C₄²	—	79	1	no	—
968	C₄²	—	158	2	no	—
969	C₄²	—	158	2	no	—
970	C₄²	—	158	2	no	—
971	C₄²	—	158	2	no	—
972	C₄²	—	158	2	no	—
973	C₄²	—	158	2	no	—
974	C₄²	C₂³×D₇₉	1	1	yes	characteristic
975	C₄²	C₂³×D₇₉	1	1	yes	characteristic
976	C₂³	—	2	2	no	—
977	C₂³	—	316	1	no	—
978	C₂³	—	79	1	no	—
979	C₂³	—	79	1	no	—
980	C₂³	—	158	2	no	—
981	C₂³	—	158	2	no	—
982	C₂³	C₂×D₄×D₇₉	1	1	yes	characteristic
983	Q₈	—	2	2	no	—
984	Q₈	—	2	2	no	—
985	Q₈	—	8	2	no	—
986	Q₈	—	316	4	no	—
987	Q₈	—	632	2	no	—
988	Q₈	—	158	2	no	—
989	Q₈	—	158	2	no	—
990	Q₈	—	158	2	no	—
991	Q₈	—	158	2	no	—
992	D₄	—	2	2	no	—
993	D₄	—	2	2	no	—
994	D₄	—	8	2	no	—
995	D₄	—	316	4	no	—
996	D₄	—	316	4	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	8	2	no	—
1003	C₂×C₄	—	316	1	no	—
1004	C₂×C₄	—	316	1	no	—
1005	C₂×C₄	—	316	4	no	—
1006	C₂×C₄	—	316	4	no	—
1007	C₂×C₄	—	79	1	no	—
1008	C₂×C₄	—	79	2	no	—
1009	C₂×C₄	—	79	2	no	—
1010	C₂×C₄	—	79	1	no	—
1011	C₂×C₄	—	79	1	no	—
1012	C₂×C₄	—	79	1	no	—
1013	C₂×C₄	—	79	1	no	—
1014	C₂×C₄	—	79	1	no	—
1015	C₂×C₄	—	632	2	no	—
1016	C₂×C₄	—	632	2	no	—
1017	C₂×C₄	—	158	2	no	—
1018	C₂×C₄	—	158	2	no	—
1019	C₂×C₄	—	158	2	no	—
1020	C₂×C₄	—	158	2	no	—
1021	C₂×C₄	—	158	2	no	—
1022	C₂×C₄	—	158	2	no	—
1023	C₂×C₄	—	158	2	no	—
1024	C₂×C₄	—	158	2	no	—
1025	C₂×C₄	—	158	2	no	—
1026	C₂×C₄	—	158	1	no	—
1027	C₂×C₄	—	158	1	no	—
1028	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
1029	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
1030	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
1031	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
1032	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
1033	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
1034	C₈	—	2	1	no	—
1035	C₈	—	2	1	no	—
1036	C₈	—	79	2	no	—
1037	C₈	—	79	2	no	—
1038	C₈	—	158	1	no	—
1039	C₈	—	158	1	no	—
1040	C₈	#41×D₇₉	1	2	yes	—
1041	C₈	#41×D₇₉	1	2	yes	—
1042	C₂²	—	2	1	no	—
1043	C₂²	—	2	1	no	—
1044	C₂²	—	2	1	no	—
1045	C₂²	—	4	2	no	—
1046	C₂²	—	4	2	no	—
1047	C₂²	—	4	2	no	—
1048	C₂²	—	316	4	no	—
1049	C₂²	—	79	2	no	—
1050	C₂²	—	79	2	no	—
1051	C₂²	—	158	1	no	—
1052	C₂²	—	158	1	no	—
1053	C₂²	—	158	1	no	—
1054	C₂²	—	158	1	no	—
1055	C₂²	C₂²×D₄×D₇₉	1	1	yes	characteristic
1056	C₄	—	2	1	no	—
1057	C₄	—	2	1	no	—
1058	C₄	—	2	1	no	—
1059	C₄	—	2	1	no	—
1060	C₄	—	2	1	no	—
1061	C₄	—	4	2	no	—
1062	C₄	—	4	2	no	—
1063	C₄	—	4	2	no	—
1064	C₄	—	316	2	no	—
1065	C₄	—	316	2	no	—
1066	C₄	—	316	2	no	—
1067	C₄	—	316	2	no	—
1068	C₄	—	79	2	no	—
1069	C₄	—	158	1	no	—
1070	C₄	—	158	1	no	—
1071	C₄	—	158	1	no	—
1072	C₄	—	158	1	no	—
1073	C₄	—	158	1	no	—
1074	C₄	C₂×#41×D₇₉	1	1	yes	characteristic
1075	C₄	C₂×#41×D₇₉	1	1	yes	characteristic
1076	C₂	—	4	1	no	—
1077	C₂	—	8	2	no	—
1078	C₂	—	158	2	no	—
1079	C₂	—	158	2	no	—
1080	C₂	#532×D₇₉	1	1	yes	characteristic
1081	C₂	#578×D₇₉	1	1	yes	characteristic
1082	C₂	#23778168	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₇₉
commutator, cosocle	C₂×C₄×C₇₉	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₉
Fitting	C₇₉×#3175	C₂
socle	C₂²×C₇₉	C₂³×D₄
prime radical	#23772979	C₂
hypercenter	#3175	D₇₉
hypocenter	C₇₉	#60708
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3175

Complements

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

N	H ≅ G/N	type
1. #23777150	C₂	semidirect
2. #23774112	C₂	semidirect
3. #23774105	C₂	semidirect
4. #23774062	C₂	semidirect
5. #23774061	C₂	semidirect
6. #23774059	C₂	semidirect
7. #23774052	C₂	semidirect
8. #23774032	C₂	semidirect
9. #23773987	C₂	semidirect
10. #23773983	C₂	semidirect
11. #23773968	C₂	semidirect
12. #23773967	C₂	semidirect
13. #23773933	C₂	semidirect
14. #23773890	C₂	semidirect
15. #23773762	C₂	semidirect
16. #23773025	C₂	semidirect
18. #467×D₇₉	C₂	semidirect
19. #23772270	C₂	semidirect
20. #23772263	C₂	semidirect
21. #23772240	C₂	semidirect
22. #405×D₇₉	C₂	semidirect
23. C₇₉×#3175	C₂	semidirect
51. #19098971	C₂²	semidirect
52. #19098969	C₂²	semidirect
53. #19098967	C₂²	semidirect
54. #19098965	C₂²	semidirect
55. #19098964	C₂²	semidirect
56. #19098958	C₂²	semidirect
57. #19098954	C₂²	semidirect
58. #19098946	C₂²	semidirect
59. #19098943	C₂²	semidirect
60. #19098941	C₂²	semidirect
61. #19098932	C₂²	semidirect
62. #19098930	C₂²	semidirect
63. #19098921	C₂²	semidirect
64. #19098917	C₂²	semidirect
65. #19098916	C₂²	semidirect
66. #19098915	C₂²	semidirect
67. #19098912	C₂²	semidirect
85. #19098671	C₂²	semidirect
86. #19098668	C₂²	semidirect
87. #19098667	C₂²	semidirect
88. #19098667	C₂²	semidirect
89. #19098663	C₂²	semidirect
90. #19098660	C₂²	semidirect
91. #19098660	C₂²	semidirect
92. C₄×Dic₃₁₆	C₂²	semidirect
93. C₄×Dic₃₁₆	C₂²	semidirect
94. Q₁₆×Dic₇₉	C₂²	semidirect
95. #19098657	C₂²	semidirect
96. #19098657	C₂²	semidirect
97. #19098657	C₂²	semidirect
98. C₄×#11929614	C₂²	semidirect
99. SD₁₆×Dic₇₉	C₂²	semidirect
100. C₄×#11929612	C₂²	semidirect
101. D₈×Dic₇₉	C₂²	semidirect
121. #500×C₇₉	C₂²	semidirect
122. #495×C₇₉	C₂²	semidirect
123. #489×C₇₉	C₂²	semidirect
127. #440×C₇₉	C₂²	semidirect
128. C₄×Q₁₆×C₇₉	C₂²	semidirect
129. C₄×D₈×C₇₉	C₂²	semidirect
550. #3175	D₇₉	semidirect
565. C₇₉	#60708	semidirect
597. #500	C₂×D₇₉	semidirect
603. #495	C₂×D₇₉	semidirect
609. #489	C₂×D₇₉	semidirect
641. #440	C₂×D₇₉	semidirect
649. C₄×Q₁₆	C₂×D₇₉	semidirect
653. C₄×D₈	C₂×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23777150	2
#23774112	2
#23774105	2
#23774062	2
#23774061	2
#23774059	2
#23774052	2
#23774032	2
#23773987	2
#23773983	2
#23773968	2
#23773967	2
#23773933	2
#23773890	2
#23773762	2
#23773025	2
#23772979	2
#467×D₇₉	2
#23772270	2
#23772263	2
#23772240	2
#405×D₇₉	2
C₇₉×#3175	2
#60708	79