Subgroups — #35152953

Order 20224.

1914 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23772420	C₂	1	2	yes	maximal, complemented
2	#23772405	C₂	1	2	yes	maximal, complemented
3	#23772405	C₂	1	4	yes	maximal, complemented
4	#23772387	C₂	1	4	yes	maximal, complemented
5	#23772376	C₂	1	2	yes	maximal, complemented
6	#23772367	C₂	1	2	yes	maximal, complemented
7	#23772349	C₂	1	1	yes	maximal, characteristic, complemented
8	#23772335	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×#11929608	C₂	1	1	yes	maximal, characteristic, complemented
10	#23772127	C₂	1	2	yes	maximal, complemented
11	#23772104	C₂	1	2	yes	maximal, complemented
12	C₂×#19098641	C₂	1	1	yes	maximal, characteristic, complemented
13	#23772066	C₂	1	1	yes	maximal, characteristic, complemented
14	#23772058	C₂	1	2	yes	maximal, complemented
15	C₄×#14579168	C₂	1	1	yes	maximal, characteristic, complemented
16	#23771819	C₂	1	2	yes	maximal, complemented
17	C₇₉×#3475	C₂	1	1	yes	maximal, characteristic
18	C₂×#14579168	C₂²	1	1	yes	characteristic
19	C₂×#14579168	C₂²	1	1	yes	characteristic
20	C₂²×#11929608	C₂²	1	2	yes	—
21	C₂²×#11929608	C₂²	1	2	yes	—
22	#19098694	C₂²	1	2	yes	complemented
23	#19098694	C₂²	1	2	yes	complemented
24	#19098694	C₂²	1	2	yes	complemented
25	#19098694	C₂²	1	4	yes	complemented
26	Q₈×C₇₉⋊C₈	C₂²	1	2	yes	complemented
27	Q₈×C₇₉⋊C₈	C₂²	1	2	yes	complemented
28	Q₈×C₇₉⋊C₈	C₂²	1	2	yes	complemented
29	#19098641	C₂²	1	1	yes	characteristic
30	#19098641	C₂²	1	2	yes	—
31	#19098641	C₂²	1	1	yes	characteristic
32	#19098641	C₂²	1	1	yes	characteristic
33	#19098641	C₂²	1	2	yes	—
34	#19098641	C₂²	1	1	yes	characteristic
35	#19098641	C₂²	1	2	yes	—
36	#19098641	C₂²	1	4	yes	complemented
37	#19098641	C₂²	1	4	yes	complemented
38	#19098641	C₂²	1	4	yes	complemented
39	#19098635	C₂²	1	4	yes	—
40	#19098635	C₂²	1	4	yes	complemented
41	#19098635	C₂²	1	4	yes	complemented
42	#19098635	C₂²	1	4	yes	complemented
43	#19098635	C₂²	1	4	yes	complemented
44	D₄×C₇₉⋊C₈	C₂²	1	2	yes	—
45	D₄×C₇₉⋊C₈	C₂²	1	4	yes	complemented
46	#19098624	C₂²	1	4	yes	complemented
47	#19098624	C₂²	1	4	yes	complemented
48	#19098624	C₂²	1	4	yes	complemented
49	#19098620	C₂²	1	4	yes	complemented
50	#19098620	C₂²	1	2	yes	complemented
51	#19098616	C₂²	1	4	yes	complemented
52	#19098616	C₂²	1	2	yes	complemented
53	#19098590	C₂²	1	2	yes	—
54	#19098590	C₂²	1	2	yes	—
55	#19098587	C₂²	1	1	yes	characteristic
56	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
57	#19098530	C₂²	1	2	yes	—
58	#19098527	C₂²	1	2	yes	—
59	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
60	#19098519	C₂²	1	1	yes	characteristic
61	#19098519	C₂²	1	2	yes	—
62	#19098519	C₂²	1	1	yes	characteristic
63	#19098519	C₂²	1	2	yes	—
64	#19098519	C₂²	1	2	yes	—
65	#19098519	C₂²	1	4	yes	complemented
66	#19098519	C₂²	1	4	yes	complemented
67	#19098519	C₂²	1	2	yes	complemented
68	#19098519	C₂²	1	2	yes	complemented
69	C₄×#11929608	C₂²	1	1	yes	characteristic
70	C₄×#11929608	C₂²	1	4	yes	complemented
71	C₄×#11929608	C₂²	1	2	yes	complemented
72	C₄×#11929608	C₂²	1	4	yes	complemented
73	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
74	C₂×C₄×C₇₉⋊C₈	C₂²	1	2	yes	complemented
75	#556×C₇₉	C₄	1	1	yes	characteristic
76	#555×C₇₉	C₄	1	1	yes	characteristic
77	#554×C₇₉	C₄	1	1	yes	characteristic
78	#553×C₇₉	C₄	1	2	yes	—
79	#552×C₇₉	C₄	1	2	yes	—
80	#552×C₇₉	C₄	1	2	yes	—
81	#551×C₇₉	C₄	1	4	yes	—
82	#547×C₇₉	C₄	1	1	yes	characteristic
83	#546×C₇₉	C₄	1	2	yes	—
84	#533×C₇₉	C₂²	1	1	yes	characteristic
85	#529×C₇₉	C₂²	1	2	yes	—
86	#529×C₇₉	C₂²	1	4	yes	—
87	#525×C₇₉	C₂²	1	2	yes	—
88	C₄×#41×C₇₉	C₂²	1	2	yes	—
89	C₄×#41×C₇₉	C₂²	1	1	yes	characteristic
90	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
91	C₂×#117×C₇₉	C₂²	1	2	yes	—
92	#14579168	—	2	4	no	—
93	#14579168	—	2	4	no	—
94	C₂×#11929608	—	2	8	no	—
95	C₂×#11929608	—	2	8	no	—
96	C₂×#11929608	C₂³	1	4	yes	—
97	C₂×#11929608	C₂³	1	2	yes	—
98	C₂×#11929608	C₂³	1	2	yes	—
99	C₂×#11929608	C₂³	1	2	yes	—
100	C₂×#11929608	C₂³	1	2	yes	—
101	C₂×#11929608	C₂³	1	2	yes	—
102	C₂×#11929608	C₂³	1	2	yes	—
103	C₂×#11929608	C₂³	1	1	yes	characteristic
104	C₂×#11929608	C₂³	1	2	yes	—
105	C₂×#11929608	C₂³	1	1	yes	characteristic
106	C₂²×C₇₉⋊C₈	C₂³	1	4	yes	—
107	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
108	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
109	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
110	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
111	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
112	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
113	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
114	C₄⋊(C₇₉⋊C₈)	C₂³	1	4	yes	—
115	C₄⋊(C₇₉⋊C₈)	C₂³	1	4	yes	—
116	C₄⋊(C₇₉⋊C₈)	C₂³	1	4	yes	—
117	C₄⋊(C₇₉⋊C₈)	C₂³	1	4	yes	—
118	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
119	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
120	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
121	C₂²⋊(C₇₉⋊C₈)	C₂³	1	4	yes	—
122	C₂²⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
123	C₂²⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
124	C₂²⋊(C₇₉⋊C₈)	C₂³	1	4	yes	—
125	C₂²⋊(C₇₉⋊C₈)	C₂³	1	4	yes	—
126	C₂²⋊(C₇₉⋊C₈)	C₂³	1	4	yes	—
127	C₂²⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
128	C₂²⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
129	#14579072	C₂³	1	4	yes	—
130	#14579072	C₂³	1	2	yes	—
131	#14579072	C₂³	1	2	yes	—
132	#14579072	C₂³	1	4	yes	—
133	#14579072	C₂³	1	4	yes	—
134	#14579072	C₂³	1	2	yes	—
135	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
136	C₄×C₇₉⋊C₈	C₂³	1	4	yes	—
137	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
138	C₄×C₇₉⋊C₈	C₂³	1	4	yes	—
139	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
140	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
141	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
142	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
143	C₄×C₇₉⋊C₈	C₂³	1	4	yes	—
144	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
145	C₂×#41×C₇₉	C₂×C₄	1	2	yes	—
146	C₂×#41×C₇₉	C₂³	1	1	yes	characteristic
147	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
148	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
149	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
150	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
151	#126×C₇₉	C₂×C₄	1	4	yes	—
152	#126×C₇₉	C₂×C₄	1	4	yes	—
153	#126×C₇₉	C₂×C₄	1	4	yes	—
154	#125×C₇₉	C₂×C₄	1	4	yes	—
155	#125×C₇₉	C₂×C₄	1	2	yes	—
156	#125×C₇₉	C₂×C₄	1	2	yes	—
157	#124×C₇₉	C₂×C₄	1	2	yes	—
158	#124×C₇₉	C₂×C₄	1	4	yes	—
159	#123×C₇₉	C₂×C₄	1	4	yes	—
160	#123×C₇₉	C₂×C₄	1	4	yes	—
161	#123×C₇₉	C₂×C₄	1	4	yes	—
162	#123×C₇₉	C₂×C₄	1	4	yes	—
163	C₂²⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
164	C₂²⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
165	C₂²⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
166	C₂²⋊Q₈×C₇₉	C₂×C₄	1	4	yes	—
167	C₂²⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
168	C₂²⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
169	#121×C₇₉	C₂×C₄	1	2	yes	—
170	#121×C₇₉	C₂×C₄	1	2	yes	—
171	#121×C₇₉	C₂×C₄	1	4	yes	—
172	#121×C₇₉	C₂×C₄	1	2	yes	—
173	#120×C₇₉	C₂×C₄	1	4	yes	—
174	C₄×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
175	C₄×Q₈×C₇₉	C₂×C₄	1	2	yes	—
176	C₄×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
177	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
178	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
179	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
180	C₄×D₄×C₇₉	C₂×C₄	1	2	yes	—
181	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
182	C₄×D₄×C₇₉	C₂×C₄	1	2	yes	—
183	C₄×D₄×C₇₉	C₂×C₄	1	2	yes	—
184	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
185	C₄×D₄×C₇₉	C₂×C₄	1	2	yes	—
186	C₄×D₄×C₇₉	C₂×C₄	1	4	yes	—
187	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
188	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
189	C₄×D₄×C₇₉	C₂³	1	4	yes	—
190	C₄×D₄×C₇₉	C₂³	1	2	yes	—
191	C₄×D₄×C₇₉	C₂³	1	4	yes	—
192	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
193	#117×C₇₉	C₂×C₄	1	4	yes	—
194	#117×C₇₉	C₂×C₄	1	2	yes	—
195	#117×C₇₉	C₂×C₄	1	2	yes	—
196	#117×C₇₉	C₂×C₄	1	4	yes	—
197	#117×C₇₉	C₂×C₄	1	2	yes	—
198	#117×C₇₉	C₂³	1	4	yes	—
199	#117×C₇₉	C₂³	1	2	yes	—
200	#117×C₇₉	C₂³	1	1	yes	characteristic
201	#117×C₇₉	C₂³	1	2	yes	—
202	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
203	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
204	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
205	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	4	yes	—
206	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
207	C₂×C₄²×C₇₉	C₂³	1	4	yes	—
208	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
210	#11929608	—	2	8	no	—
211	#11929608	—	2	4	no	—
212	#11929608	—	2	4	no	—
213	#11929608	—	2	4	no	—
214	#11929608	—	2	4	no	—
215	#11929608	—	2	4	no	—
216	#11929608	—	2	4	no	—
217	#11929608	—	2	4	no	—
218	#11929608	—	2	2	no	—
219	#11929608	#41	1	4	yes	complemented
220	C₂×C₇₉⋊C₈	—	2	8	no	—
221	C₂×C₇₉⋊C₈	—	2	4	no	—
222	C₂×C₇₉⋊C₈	—	2	4	no	—
223	C₂×C₇₉⋊C₈	—	2	4	no	—
224	C₂×C₇₉⋊C₈	—	2	2	no	—
225	C₂×C₇₉⋊C₈	#41	1	4	yes	complemented
226	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
227	C₂×C₇₉⋊C₈	C₂⁴	1	2	yes	—
228	C₂×C₇₉⋊C₈	C₂⁴	1	2	yes	—
229	C₂×C₇₉⋊C₈	C₂⁴	1	4	yes	—
230	C₂×C₇₉⋊C₈	C₂⁴	1	2	yes	—
231	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
232	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
233	C₂×C₇₉⋊C₈	C₂⁴	1	2	yes	—
234	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
235	C₂⁴×C₇₉	C₂²×C₄	1	2	yes	—
236	#41×C₇₉	—	2	2	no	—
237	#41×C₇₉	—	2	2	no	—
238	#41×C₇₉	—	4	4	no	—
239	C₂×Q₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
240	C₂×Q₈×C₇₉	C₂²×C₄	1	2	yes	—
241	C₂×Q₈×C₇₉	C₂²×C₄	1	2	yes	—
242	C₂×D₄×C₇₉	—	4	2	no	—
243	C₂×D₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
244	C₂×D₄×C₇₉	C₂²×C₄	1	2	yes	—
245	C₂×D₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
246	C₂×D₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
247	C₂×D₄×C₇₉	C₂²×C₄	1	4	yes	—
248	C₂×D₄×C₇₉	C₂²×C₄	1	2	yes	—
249	C₂×D₄×C₇₉	C₂²×C₄	1	4	yes	—
250	C₂²×C₄×C₇₉	—	2	4	no	—
251	C₂²×C₄×C₇₉	—	2	4	no	—
252	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
253	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
254	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
255	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
256	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
257	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
258	C₂²×C₄×C₇₉	C₂²×C₄	1	4	yes	—
259	C₂²×C₄×C₇₉	C₂²×C₄	1	4	yes	—
260	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
261	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
265	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
266	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
267	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
268	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
269	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
270	C₄⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
271	C₄⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
272	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
273	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
274	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
275	C₄⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
276	C₄⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
277	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
278	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
279	C₄⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
280	C₄⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
281	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
282	C₂²⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
283	C₂²⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
284	C₂²⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
285	C₂²⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
286	C₂²⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
287	C₂²⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
288	C₂²⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
289	C₂²⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
290	C₂²⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
291	C₂²⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
292	C₂²⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
293	C₂²⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
294	C₂²⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
295	C₂²⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
296	C₄²×C₇₉	C₂²×C₄	1	4	yes	—
297	C₄²×C₇₉	C₂²×C₄	1	4	yes	—
298	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
299	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
300	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
301	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
302	C₄²×C₇₉	C₂⁴	1	2	yes	—
303	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
304	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
305	C₄²×C₇₉	C₂⁴	1	4	yes	—
306	C₂³×C₇₉	—	2	4	no	—
307	C₂³×C₇₉	—	4	2	no	—
308	C₂³×C₇₉	—	4	2	no	—
309	C₂³×C₇₉	C₂³×C₄	1	2	yes	—
310	C₂³×C₇₉	C₂³×C₄	1	2	yes	—
311	C₂³×C₇₉	C₂³×C₄	1	2	yes	—
312	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
313	Q₈×C₇₉	—	2	2	no	—
314	Q₈×C₇₉	—	2	4	no	—
315	Q₈×C₇₉	—	4	2	no	—
316	D₄×C₇₉	—	2	4	no	—
317	D₄×C₇₉	—	2	2	no	—
318	D₄×C₇₉	—	2	2	no	—
319	D₄×C₇₉	—	2	2	no	—
320	D₄×C₇₉	—	4	2	no	—
321	D₄×C₇₉	—	4	4	no	—
322	D₄×C₇₉	—	4	4	no	—
323	C₂×C₄×C₇₉	—	2	4	no	—
324	C₂×C₄×C₇₉	—	2	4	no	—
325	C₂×C₄×C₇₉	—	2	4	no	—
326	C₂×C₄×C₇₉	—	2	2	no	—
327	C₂×C₄×C₇₉	—	2	4	no	—
328	C₂×C₄×C₇₉	—	2	2	no	—
329	C₂×C₄×C₇₉	—	2	2	no	—
330	C₂×C₄×C₇₉	—	2	2	no	—
331	C₂×C₄×C₇₉	—	2	2	no	—
332	C₂×C₄×C₇₉	—	2	2	no	—
333	C₂×C₄×C₇₉	—	2	2	no	—
334	C₂×C₄×C₇₉	—	4	2	no	—
335	C₂×C₄×C₇₉	—	4	4	no	—
336	C₂×C₄×C₇₉	—	4	1	no	—
337	C₂×C₄×C₇₉	—	4	4	no	—
338	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
339	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
340	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
341	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
342	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
343	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
344	C₂×C₄×C₇₉	C₂³×C₄	1	4	yes	—
345	C₂×C₄×C₇₉	C₂³×C₄	1	4	yes	—
346	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
347	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
348	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
349	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
350	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
351	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
352	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
353	C₇₉⋊C₈	—	2	1	no	—
354	C₇₉⋊C₈	—	2	4	no	—
355	C₇₉⋊C₈	—	2	2	no	—
356	C₇₉⋊C₈	—	2	2	no	—
357	C₇₉⋊C₈	—	2	2	no	—
358	C₇₉⋊C₈	—	2	1	no	—
359	C₇₉⋊C₈	C₂×#41	1	4	yes	—
360	C₇₉⋊C₈	C₂×#41	1	2	yes	—
361	C₇₉⋊C₈	C₂×#41	1	2	yes	—
362	C₂²×C₇₉	—	2	1	no	—
363	C₂²×C₇₉	—	2	1	no	—
364	C₂²×C₇₉	—	2	2	no	—
365	C₂²×C₇₉	—	2	2	no	—
366	C₂²×C₇₉	—	2	2	no	—
367	C₂²×C₇₉	—	2	2	no	—
368	C₂²×C₇₉	—	2	2	no	—
369	C₂²×C₇₉	—	2	2	no	—
370	C₂²×C₇₉	—	2	2	no	—
371	C₂²×C₇₉	—	2	2	no	—
372	C₂²×C₇₉	—	2	2	no	—
373	C₂²×C₇₉	—	8	4	no	—
374	C₂²×C₇₉	C₄×#41	1	2	yes	—
375	C₂²×C₇₉	C₂⁴×C₄	1	1	yes	characteristic
376	C₄×C₇₉	—	2	2	no	—
377	C₄×C₇₉	—	2	2	no	—
378	C₄×C₇₉	—	2	2	no	—
379	C₄×C₇₉	—	2	2	no	—
380	C₄×C₇₉	—	2	1	no	—
381	C₄×C₇₉	—	2	4	no	—
382	C₄×C₇₉	—	2	1	no	—
383	C₄×C₇₉	—	2	2	no	—
384	C₄×C₇₉	—	2	4	no	—
385	C₄×C₇₉	—	2	1	no	—
386	C₄×C₇₉	C₄×#41	1	2	yes	—
387	C₄×C₇₉	#568	1	2	yes	—
388	C₄×C₇₉	C₂²×#41	1	1	yes	characteristic
389	C₄×C₇₉	C₂²×#41	1	1	yes	characteristic
390	#60217	—	79	1	no	maximal, Sylow
391	C₂×C₇₉	—	2	2	no	—
392	C₂×C₇₉	—	4	2	no	—
393	C₂×C₇₉	—	4	2	no	—
394	C₂×C₇₉	—	4	2	no	—
395	C₂×C₇₉	C₂×C₄×#41	1	1	yes	characteristic
396	C₂×C₇₉	C₂×#568	1	1	yes	characteristic
397	C₂×C₇₉	#3573	1	1	yes	characteristic
398	#3475	D₇₉	1	1	yes	characteristic
399	#2971	—	79	2	no	—
400	#2969	—	79	2	no	—
401	#2969	—	79	4	no	—
402	#2967	—	79	4	no	—
403	#2966	—	79	2	no	—
404	#2965	—	79	2	no	—
405	#2962	—	79	1	no	—
406	#2960	—	79	1	no	—
407	D₄×M₁₆	—	79	1	no	—
408	#2933	—	79	2	no	—
409	#2930	—	79	2	no	—
410	C₂×#436	—	79	1	no	—
411	#2925	—	79	1	no	—
412	#2924	—	79	2	no	—
413	C₄×#131	—	79	1	no	—
414	#2873	—	79	2	no	—
415	C₇₉	#60217	1	1	yes	characteristic, complemented, Sylow
416	C₂×#131	—	79	1	no	—
417	C₂×#131	—	79	1	no	—
418	C₂²×M₁₆	—	79	2	no	—
419	C₂²×M₁₆	—	79	2	no	—
420	#556	Dic₇₉	1	1	yes	characteristic
421	#555	Dic₇₉	1	1	yes	characteristic
422	#554	Dic₇₉	1	1	yes	characteristic
423	#553	Dic₇₉	1	2	yes	—
424	#552	Dic₇₉	1	2	yes	—
425	#552	Dic₇₉	1	2	yes	—
426	#551	Dic₇₉	1	4	yes	—
427	#547	Dic₇₉	1	1	yes	characteristic
428	#546	Dic₇₉	1	2	yes	—
429	#533	C₂×D₇₉	1	1	yes	characteristic
430	#529	C₂×D₇₉	1	2	yes	—
431	#529	C₂×D₇₉	1	4	yes	—
432	#525	C₂×D₇₉	1	2	yes	—
433	C₄×#41	C₂×D₇₉	1	1	yes	characteristic
434	C₄×#41	C₂×D₇₉	1	2	yes	—
435	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
436	C₂×#117	C₂×D₇₉	1	2	yes	—
437	#446	—	79	2	no	—
438	#446	—	79	2	no	—
439	#446	—	79	2	no	—
440	#446	—	79	4	no	—
441	C₈×Q₈	—	79	2	no	—
442	C₈×Q₈	—	79	2	no	—
443	C₈×Q₈	—	79	2	no	—
444	#436	—	79	1	no	—
445	#436	—	79	1	no	—
446	#436	—	79	2	no	—
447	#436	—	79	1	no	—
448	#436	—	79	2	no	—
449	#436	—	79	1	no	—
450	#436	—	79	2	no	—
451	#436	—	79	4	no	—
452	#436	—	79	4	no	—
453	#436	—	79	4	no	—
454	#435	—	79	4	no	—
455	#435	—	79	4	no	—
456	#435	—	79	4	no	—
457	#435	—	79	4	no	—
458	#435	—	79	4	no	—
459	C₈×D₄	—	79	2	no	—
460	C₈×D₄	—	79	4	no	—
461	#433	—	79	4	no	—
462	#433	—	79	4	no	—
463	#433	—	79	4	no	—
464	#432	—	79	4	no	—
465	#432	—	79	2	no	—
466	#431	—	79	4	no	—
467	#431	—	79	2	no	—
468	#424	—	79	2	no	—
469	#424	—	79	2	no	—
470	#423	—	79	1	no	—
471	C₂×C₄⋊C₈	—	79	1	no	—
472	#408	—	79	2	no	—
473	#407	—	79	2	no	—
474	C₂×C₂²⋊C₈	—	79	2	no	—
475	#405	—	79	1	no	—
476	#405	—	79	2	no	—
477	#405	—	79	2	no	—
478	#405	—	79	2	no	—
479	#405	—	79	4	no	—
480	#405	—	79	4	no	—
481	#405	—	79	1	no	—
482	#405	—	79	2	no	—
483	#405	—	79	2	no	—
484	C₄×M₁₆	—	79	4	no	—
485	C₄×M₁₆	—	79	4	no	—
486	C₄×M₁₆	—	79	1	no	—
487	C₄×M₁₆	—	79	2	no	—
488	C₂×C₄×C₈	—	79	1	no	—
489	C₂×C₄×C₈	—	79	2	no	—
490	C₂×#41	C₂×Dic₇₉	1	2	yes	—
491	C₂×#41	C₂²×D₇₉	1	1	yes	characteristic
492	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
493	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
494	#131	—	158	4	no	—
495	#131	—	158	4	no	—
496	C₂×M₁₆	—	79	1	no	—
497	C₂×M₁₆	—	79	2	no	—
498	C₂×M₁₆	—	79	4	no	—
499	C₂×M₁₆	—	79	2	no	—
500	C₂×M₁₆	—	79	2	no	—
501	C₂×M₁₆	—	79	2	no	—
502	C₂×M₁₆	—	79	2	no	—
503	C₂×M₁₆	—	79	1	no	—
504	C₂×M₁₆	—	79	2	no	—
505	C₂×M₁₆	—	79	2	no	—
506	C₂×M₁₆	—	158	8	no	—
507	C₂×M₁₆	—	158	8	no	—
508	C₂²×C₈	—	79	1	no	—
509	C₂²×C₈	—	79	2	no	—
510	C₂²×C₈	—	79	4	no	—
511	C₂²×C₈	—	79	1	no	—
512	C₂²×C₈	—	79	2	no	—
513	C₂²×C₈	—	79	2	no	—
514	C₄⋊Q₈	C₂×Dic₇₉	1	1	yes	characteristic
515	C₄⋊Q₈	C₂×Dic₇₉	1	1	yes	characteristic
516	#126	C₂×Dic₇₉	1	4	yes	—
517	#126	C₂×Dic₇₉	1	4	yes	—
518	#126	C₂×Dic₇₉	1	4	yes	—
519	#125	C₂×Dic₇₉	1	4	yes	—
520	#125	C₂×Dic₇₉	1	2	yes	—
521	#125	C₂×Dic₇₉	1	2	yes	—
522	#124	C₂×Dic₇₉	1	2	yes	—
523	#124	C₂×Dic₇₉	1	4	yes	—
524	#123	C₂×Dic₇₉	1	4	yes	—
525	#123	C₂×Dic₇₉	1	4	yes	—
526	#123	C₂×Dic₇₉	1	4	yes	—
527	#123	C₂×Dic₇₉	1	4	yes	—
528	C₂²⋊Q₈	C₂×Dic₇₉	1	2	yes	—
529	C₂²⋊Q₈	C₂×Dic₇₉	1	2	yes	—
530	C₂²⋊Q₈	C₂×Dic₇₉	1	2	yes	—
531	C₂²⋊Q₈	C₂×Dic₇₉	1	4	yes	—
532	C₂²⋊Q₈	C₂×Dic₇₉	1	2	yes	—
533	C₂²⋊Q₈	C₂×Dic₇₉	1	2	yes	—
534	#121	C₂×Dic₇₉	1	2	yes	—
535	#121	C₂×Dic₇₉	1	2	yes	—
536	#121	C₂×Dic₇₉	1	4	yes	—
537	#121	C₂×Dic₇₉	1	2	yes	—
538	#120	C₂×Dic₇₉	1	4	yes	—
539	C₄×Q₈	C₂×Dic₇₉	1	1	yes	characteristic
540	C₄×Q₈	C₂×Dic₇₉	1	2	yes	—
541	C₄×Q₈	C₂×Dic₇₉	1	1	yes	characteristic
542	C₄×Q₈	C₂²×D₇₉	1	2	yes	—
543	C₄×Q₈	C₂²×D₇₉	1	2	yes	—
544	C₄×D₄	C₂×Dic₇₉	1	1	yes	characteristic
545	C₄×D₄	C₂×Dic₇₉	1	2	yes	—
546	C₄×D₄	C₂×Dic₇₉	1	1	yes	characteristic
547	C₄×D₄	C₂×Dic₇₉	1	2	yes	—
548	C₄×D₄	C₂×Dic₇₉	1	2	yes	—
549	C₄×D₄	C₂×Dic₇₉	1	1	yes	characteristic
550	C₄×D₄	C₂×Dic₇₉	1	2	yes	—
551	C₄×D₄	C₂×Dic₇₉	1	4	yes	—
552	C₄×D₄	C₂×Dic₇₉	1	1	yes	characteristic
553	C₄×D₄	C₂²×D₇₉	1	1	yes	characteristic
554	C₄×D₄	C₂²×D₇₉	1	1	yes	characteristic
555	C₄×D₄	C₂²×D₇₉	1	2	yes	—
556	C₄×D₄	C₂²×D₇₉	1	4	yes	—
557	C₄×D₄	C₂²×D₇₉	1	4	yes	—
558	#117	C₂×Dic₇₉	1	4	yes	—
559	#117	C₂×Dic₇₉	1	2	yes	—
560	#117	C₂×Dic₇₉	1	2	yes	—
561	#117	C₂×Dic₇₉	1	4	yes	—
562	#117	C₂×Dic₇₉	1	2	yes	—
563	#117	C₂²×D₇₉	1	1	yes	characteristic
564	#117	C₂²×D₇₉	1	2	yes	—
565	#117	C₂²×D₇₉	1	4	yes	—
566	#117	C₂²×D₇₉	1	2	yes	—
567	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
568	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
569	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
570	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	4	yes	—
571	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
572	C₂×C₄²	C₂²×D₇₉	1	4	yes	—
573	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
574	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
575	C₄⋊C₈	—	79	1	no	—
576	C₄⋊C₈	—	79	1	no	—
577	C₄⋊C₈	—	79	2	no	—
578	C₄⋊C₈	—	79	2	no	—
579	C₄⋊C₈	—	79	2	no	—
580	C₄⋊C₈	—	79	4	no	—
581	C₄⋊C₈	—	79	4	no	—
582	C₄⋊C₈	—	79	4	no	—
583	C₄⋊C₈	—	79	4	no	—
584	C₂²⋊C₈	—	79	2	no	—
585	C₂²⋊C₈	—	79	2	no	—
586	C₂²⋊C₈	—	79	2	no	—
587	C₂²⋊C₈	—	79	2	no	—
588	C₂²⋊C₈	—	79	4	no	—
589	C₂²⋊C₈	—	79	4	no	—
590	C₂²⋊C₈	—	79	4	no	—
591	C₂²⋊C₈	—	79	4	no	—
592	#97	—	79	2	no	—
593	#97	—	79	4	no	—
594	#97	—	79	2	no	—
595	#97	—	79	2	no	—
596	#97	—	79	4	no	—
597	#97	—	79	4	no	—
598	C₄×C₈	—	79	1	no	—
599	C₄×C₈	—	79	2	no	—
600	C₄×C₈	—	79	2	no	—
601	C₄×C₈	—	79	1	no	—
602	C₄×C₈	—	79	2	no	—
603	C₄×C₈	—	79	1	no	—
604	C₄×C₈	—	79	1	no	—
605	C₄×C₈	—	79	4	no	—
606	C₄×C₈	—	79	4	no	—
607	C₄×C₈	—	79	4	no	—
608	C₂⁴	C₂²×Dic₇₉	1	2	yes	—
609	#41	—	2	2	no	—
610	#41	—	2	2	no	—
611	#41	—	4	4	no	—
612	C₂×Q₈	C₂²×Dic₇₉	1	2	yes	—
613	C₂×Q₈	C₂²×Dic₇₉	1	1	yes	characteristic
614	C₂×Q₈	C₂²×Dic₇₉	1	2	yes	—
615	C₂×D₄	—	4	2	no	—
616	C₂×D₄	C₂²×Dic₇₉	1	1	yes	characteristic
617	C₂×D₄	C₂²×Dic₇₉	1	1	yes	characteristic
618	C₂×D₄	C₂²×Dic₇₉	1	2	yes	—
619	C₂×D₄	C₂²×Dic₇₉	1	1	yes	characteristic
620	C₂×D₄	C₂²×Dic₇₉	1	4	yes	—
621	C₂×D₄	C₂²×Dic₇₉	1	2	yes	—
622	C₂×D₄	C₂²×Dic₇₉	1	4	yes	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
626	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
627	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
628	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
629	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
630	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
631	C₂²×C₄	C₂²×Dic₇₉	1	4	yes	—
632	C₂²×C₄	C₂²×Dic₇₉	1	4	yes	—
633	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
634	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
635	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
636	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
637	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
638	M₁₆	—	79	4	no	—
639	M₁₆	—	158	4	no	—
640	M₁₆	—	158	4	no	—
641	M₁₆	—	158	4	no	—
642	M₁₆	—	158	4	no	—
643	M₁₆	—	158	8	no	—
644	M₁₆	—	158	4	no	—
645	M₁₆	—	158	4	no	—
646	M₁₆	—	158	4	no	—
647	M₁₆	—	158	2	no	—
648	C₂×C₈	—	79	4	no	—
649	C₂×C₈	—	79	1	no	—
650	C₂×C₈	—	79	1	no	—
651	C₂×C₈	—	79	2	no	—
652	C₂×C₈	—	79	1	no	—
653	C₂×C₈	—	79	2	no	—
654	C₂×C₈	—	79	1	no	—
655	C₂×C₈	—	79	2	no	—
656	C₂×C₈	—	79	4	no	—
657	C₂×C₈	—	79	2	no	—
658	C₂×C₈	—	158	8	no	—
659	C₂×C₈	—	158	4	no	—
660	C₂×C₈	—	158	4	no	—
661	C₂×C₈	—	158	4	no	—
662	C₂×C₈	—	158	2	no	—
663	C₄⋊C₄	C₂²×Dic₇₉	1	1	yes	characteristic
664	C₄⋊C₄	C₂²×Dic₇₉	1	1	yes	characteristic
665	C₄⋊C₄	C₂²×Dic₇₉	1	2	yes	—
666	C₄⋊C₄	C₂²×Dic₇₉	1	2	yes	—
667	C₄⋊C₄	C₂²×Dic₇₉	1	4	yes	—
668	C₄⋊C₄	C₂²×Dic₇₉	1	4	yes	—
669	C₄⋊C₄	C₂²×Dic₇₉	1	1	yes	characteristic
670	C₄⋊C₄	C₂²×Dic₇₉	1	1	yes	characteristic
671	C₄⋊C₄	C₂²×Dic₇₉	1	2	yes	—
672	C₄⋊C₄	C₂²×Dic₇₉	1	2	yes	—
673	C₄⋊C₄	C₂²×Dic₇₉	1	2	yes	—
674	C₄⋊C₄	C₂²×Dic₇₉	1	4	yes	—
675	C₄⋊C₄	C₂²×Dic₇₉	1	2	yes	—
676	C₄⋊C₄	C₂²×Dic₇₉	1	4	yes	—
677	C₄⋊C₄	C₂²×Dic₇₉	1	4	yes	—
678	C₄⋊C₄	C₂²×Dic₇₉	1	4	yes	—
679	C₄⋊C₄	C₂²×Dic₇₉	1	2	yes	—
680	C₂²⋊C₄	C₂²×Dic₇₉	1	2	yes	—
681	C₂²⋊C₄	C₂²×Dic₇₉	1	4	yes	—
682	C₂²⋊C₄	C₂²×Dic₇₉	1	4	yes	—
683	C₂²⋊C₄	C₂²×Dic₇₉	1	4	yes	—
684	C₂²⋊C₄	C₂²×Dic₇₉	1	2	yes	—
685	C₂²⋊C₄	C₂²×Dic₇₉	1	2	yes	—
686	C₂²⋊C₄	C₂²×Dic₇₉	1	2	yes	—
687	C₂²⋊C₄	C₂²×Dic₇₉	1	2	yes	—
688	C₂²⋊C₄	C₂²×Dic₇₉	1	2	yes	—
689	C₂²⋊C₄	C₂²×Dic₇₉	1	2	yes	—
690	C₂²⋊C₄	C₂²×Dic₇₉	1	4	yes	—
691	C₂²⋊C₄	C₂²×Dic₇₉	1	4	yes	—
692	C₂²⋊C₄	C₂²×Dic₇₉	1	4	yes	—
693	C₂²⋊C₄	C₂²×Dic₇₉	1	4	yes	—
694	C₄²	C₂²×Dic₇₉	1	4	yes	—
695	C₄²	C₂²×Dic₇₉	1	4	yes	—
696	C₄²	C₂²×Dic₇₉	1	2	yes	—
697	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
698	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
699	C₄²	C₂²×Dic₇₉	1	2	yes	—
700	C₄²	C₂³×D₇₉	1	2	yes	—
701	C₄²	C₂³×D₇₉	1	1	yes	characteristic
702	C₄²	C₂³×D₇₉	1	1	yes	characteristic
703	C₄²	C₂³×D₇₉	1	4	yes	—
704	C₂³	—	2	4	no	—
705	C₂³	—	4	2	no	—
706	C₂³	—	4	2	no	—
707	C₂³	C₂³×Dic₇₉	1	2	yes	—
708	C₂³	C₂³×Dic₇₉	1	2	yes	—
709	C₂³	C₂³×Dic₇₉	1	2	yes	—
710	C₂³	C₂³×Dic₇₉	1	1	yes	characteristic
711	Q₈	—	2	2	no	—
712	Q₈	—	2	4	no	—
713	Q₈	—	4	2	no	—
714	D₄	—	2	4	no	—
715	D₄	—	2	2	no	—
716	D₄	—	2	2	no	—
717	D₄	—	2	2	no	—
718	D₄	—	4	2	no	—
719	D₄	—	4	4	no	—
720	D₄	—	4	4	no	—
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	4	no	—
723	C₂×C₄	—	2	4	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	4	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	4	2	no	—
733	C₂×C₄	—	4	4	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	4	no	—
736	C₂×C₄	C₂³×Dic₇₉	1	2	yes	—
737	C₂×C₄	C₂³×Dic₇₉	1	2	yes	—
738	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
739	C₂×C₄	C₂³×Dic₇₉	1	2	yes	—
740	C₂×C₄	C₂³×Dic₇₉	1	2	yes	—
741	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
742	C₂×C₄	C₂³×Dic₇₉	1	4	yes	—
743	C₂×C₄	C₂³×Dic₇₉	1	4	yes	—
744	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
745	C₂×C₄	C₂³×Dic₇₉	1	2	yes	—
746	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
747	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
748	C₂×C₄	#41×D₇₉	1	2	yes	—
749	C₂×C₄	#41×D₇₉	1	2	yes	—
750	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
751	C₈	—	79	2	no	—
752	C₈	—	79	2	no	—
753	C₈	—	79	4	no	—
754	C₈	—	158	1	no	—
755	C₈	—	158	4	no	—
756	C₈	—	158	2	no	—
757	C₈	—	158	2	no	—
758	C₈	—	158	2	no	—
759	C₈	—	158	1	no	—
760	C₂²	—	2	1	no	—
761	C₂²	—	2	1	no	—
762	C₂²	—	2	2	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	2	2	no	—
765	C₂²	—	2	2	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	2	no	—
768	C₂²	—	2	2	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	8	4	no	—
772	C₂²	#41×Dic₇₉	1	2	yes	—
773	C₂²	C₂⁴×Dic₇₉	1	1	yes	characteristic
774	C₄	—	2	2	no	—
775	C₄	—	2	1	no	—
776	C₄	—	2	4	no	—
777	C₄	—	2	1	no	—
778	C₄	—	2	2	no	—
779	C₄	—	2	4	no	—
780	C₄	—	2	1	no	—
781	C₄	—	2	2	no	—
782	C₄	—	2	2	no	—
783	C₄	—	2	2	no	—
784	C₄	#41×Dic₇₉	1	2	yes	—
785	C₄	#19099330	1	2	yes	—
786	C₄	C₂×#41×D₇₉	1	1	yes	characteristic
787	C₄	C₂×#41×D₇₉	1	1	yes	characteristic
788	C₂	—	2	2	no	—
789	C₂	—	4	2	no	—
790	C₂	—	4	2	no	—
791	C₂	—	4	2	no	—
792	C₂	C₂×#41×Dic₇₉	1	1	yes	characteristic
793	C₂	C₂×#19099330	1	1	yes	characteristic
794	C₂	#23778112	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₇₉
commutator, socle	C₂²×C₇₉	C₂⁴×C₄
Fitting, prime radical	C₇₉×#3475	C₂
cosocle	C₂×C₄×C₇₉	C₂⁵
hypercenter	#3475	D₇₉
hypocenter	C₇₉	#60217
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ #3475

Complements

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

N	H ≅ G/N	type
1. #23772420	C₂	semidirect
2. #23772405	C₂	semidirect
3. #23772405	C₂	semidirect
4. #23772387	C₂	semidirect
5. #23772376	C₂	semidirect
6. #23772367	C₂	semidirect
7. #23772349	C₂	semidirect
8. #23772335	C₂	semidirect
9. D₄×#11929608	C₂	semidirect
10. #23772127	C₂	semidirect
11. #23772104	C₂	semidirect
12. C₂×#19098641	C₂	semidirect
13. #23772066	C₂	semidirect
14. #23772058	C₂	semidirect
15. C₄×#14579168	C₂	semidirect
16. #23771819	C₂	semidirect
22. #19098694	C₂²	semidirect
23. #19098694	C₂²	semidirect
24. #19098694	C₂²	semidirect
25. #19098694	C₂²	semidirect
26. Q₈×C₇₉⋊C₈	C₂²	semidirect
27. Q₈×C₇₉⋊C₈	C₂²	semidirect
28. Q₈×C₇₉⋊C₈	C₂²	semidirect
36. #19098641	C₂²	semidirect
37. #19098641	C₂²	semidirect
38. #19098641	C₂²	semidirect
40. #19098635	C₂²	semidirect
41. #19098635	C₂²	semidirect
42. #19098635	C₂²	semidirect
43. #19098635	C₂²	semidirect
45. D₄×C₇₉⋊C₈	C₂²	semidirect
46. #19098624	C₂²	semidirect
47. #19098624	C₂²	semidirect
48. #19098624	C₂²	semidirect
49. #19098620	C₂²	semidirect
50. #19098620	C₂²	semidirect
51. #19098616	C₂²	semidirect
52. #19098616	C₂²	semidirect
65. #19098519	C₂²	semidirect
66. #19098519	C₂²	semidirect
67. #19098519	C₂²	semidirect
68. #19098519	C₂²	semidirect
70. C₄×#11929608	C₂²	semidirect
71. C₄×#11929608	C₂²	semidirect
72. C₄×#11929608	C₂²	semidirect
74. C₂×C₄×C₇₉⋊C₈	C₂²	semidirect
219. #11929608	#41	semidirect
225. C₂×C₇₉⋊C₈	#41	semidirect
415. C₇₉	#60217	semidirect

Maximal subgroups

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

subgroup	index
#23772420	2
#23772405	2
#23772387	2
#23772376	2
#23772367	2
#23772349	2
#23772335	2
D₄×#11929608	2
#23772127	2
#23772104	2
C₂×#19098641	2
#23772066	2
#23772058	2
C₄×#14579168	2
#23771819	2
C₇₉×#3475	2
#60217	79