Subgroups — C₇₉×#3296 #23760918

Order 10112.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#552×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#546×C₇₉	C₂	1	1	yes	maximal, characteristic
3	#488×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#483×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#482×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#478×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#467×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#465×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#464×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#452×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#450×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×SD₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈×D₄×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#416×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#102×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₇₉	C₂²	1	1	yes	characteristic
17	C₂²×D₄×C₇₉	C₂²	1	1	yes	characteristic
18	C₂×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic, complemented
19	C₂×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
21	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
22	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
23	#126×C₇₉	—	2	1	no	—
24	#125×C₇₉	—	2	1	no	—
25	#125×C₇₉	C₂²	1	1	yes	characteristic, complemented
26	#124×C₇₉	C₂²	1	1	yes	characteristic
27	#123×C₇₉	—	2	1	no	—
28	#123×C₇₉	—	2	1	no	—
29	C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
30	C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
31	C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
32	#121×C₇₉	—	2	1	no	—
33	#121×C₇₉	C₂²	1	1	yes	characteristic
34	#120×C₇₉	—	2	1	no	—
35	C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
36	C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
37	C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
38	#117×C₇₉	—	2	1	no	—
39	#117×C₇₉	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
42	#107×C₇₉	C₂²	1	1	yes	characteristic, complemented
43	#106×C₇₉	C₂²	1	1	yes	characteristic, complemented
44	#106×C₇₉	C₂²	1	1	yes	characteristic, complemented
45	C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
46	#103×C₇₉	C₂²	1	1	yes	characteristic, complemented
47	#103×C₇₉	C₂²	1	1	yes	characteristic, complemented
48	#103×C₇₉	C₂²	1	1	yes	characteristic, complemented
49	#103×C₇₉	C₂²	1	1	yes	characteristic, complemented
50	#102×C₇₉	C₂²	1	1	yes	characteristic
51	#102×C₇₉	C₂²	1	1	yes	characteristic
52	#102×C₇₉	C₂²	1	1	yes	characteristic
53	#102×C₇₉	C₂²	1	1	yes	characteristic
54	#102×C₇₉	C₂²	1	1	yes	characteristic
55	#102×C₇₉	C₂²	1	1	yes	characteristic
56	C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
57	C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
59	C₂⁴×C₇₉	—	2	1	no	—
60	#41×C₇₉	—	2	2	no	—
61	#41×C₇₉	—	4	1	no	—
62	C₂×Q₈×C₇₉	C₂³	1	1	yes	characteristic
63	C₂×Q₈×C₇₉	C₂³	1	1	yes	characteristic
64	C₂×D₄×C₇₉	—	2	2	no	—
65	C₂×D₄×C₇₉	—	2	1	no	—
66	C₂×D₄×C₇₉	—	2	1	no	—
67	C₂×D₄×C₇₉	—	2	1	no	—
68	C₂×D₄×C₇₉	—	4	1	no	—
69	C₂×D₄×C₇₉	D₄	1	1	yes	characteristic
70	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
71	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
72	C₂²×C₄×C₇₉	—	2	1	no	—
73	C₂²×C₄×C₇₉	—	2	1	no	—
74	C₂²×C₄×C₇₉	—	2	1	no	—
75	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
76	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
77	Q₁₆×C₇₉	—	4	1	no	—
78	SD₁₆×C₇₉	—	2	2	no	—
79	SD₁₆×C₇₉	—	4	1	no	—
80	C₂×C₈×C₇₉	—	4	1	no	—
81	C₂×C₈×C₇₉	—	4	1	no	—
82	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
83	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
84	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
85	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
86	C₄⋊C₄×C₇₉	—	2	1	no	—
87	C₄⋊C₄×C₇₉	—	2	1	no	—
88	C₄⋊C₄×C₇₉	—	2	1	no	—
89	C₄⋊C₄×C₇₉	—	2	1	no	—
90	C₄⋊C₄×C₇₉	—	2	1	no	—
91	C₄⋊C₄×C₇₉	—	2	1	no	—
92	C₄⋊C₄×C₇₉	—	2	1	no	—
93	C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
94	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
95	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
96	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
97	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
98	C₂²⋊C₄×C₇₉	—	2	1	no	—
99	C₂²⋊C₄×C₇₉	—	2	1	no	—
100	C₂²⋊C₄×C₇₉	—	2	1	no	—
101	C₂²⋊C₄×C₇₉	—	2	1	no	—
102	C₂²⋊C₄×C₇₉	—	2	1	no	—
103	C₂²⋊C₄×C₇₉	—	2	1	no	—
104	C₂²⋊C₄×C₇₉	—	2	1	no	—
105	C₂²⋊C₄×C₇₉	—	2	1	no	—
106	C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
107	C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
108	C₄²×C₇₉	—	2	1	no	—
109	C₄²×C₇₉	—	2	1	no	—
110	C₄²×C₇₉	C₂³	1	1	yes	characteristic
111	C₂³×C₇₉	—	2	1	no	—
112	C₂³×C₇₉	—	2	1	no	—
113	C₂³×C₇₉	—	4	2	no	—
114	C₂³×C₇₉	—	4	2	no	—
115	C₂³×C₇₉	—	8	1	no	—
116	C₂³×C₇₉	C₂×D₄	1	1	yes	characteristic
117	C₂³×C₇₉	C₂×D₄	1	1	yes	characteristic
118	Q₈×C₇₉	—	2	1	no	—
119	Q₈×C₇₉	—	2	1	no	—
120	Q₈×C₇₉	—	2	1	no	—
121	Q₈×C₇₉	—	2	1	no	—
122	D₄×C₇₉	—	2	2	no	—
123	D₄×C₇₉	—	2	1	no	—
124	D₄×C₇₉	—	2	1	no	—
125	D₄×C₇₉	—	2	1	no	—
126	D₄×C₇₉	—	4	2	no	—
127	D₄×C₇₉	—	4	2	no	—
128	D₄×C₇₉	—	8	1	no	—
129	D₄×C₇₉	#41	1	2	yes	—
130	C₂×C₄×C₇₉	—	2	1	no	—
131	C₂×C₄×C₇₉	—	2	1	no	—
132	C₂×C₄×C₇₉	—	2	1	no	—
133	C₂×C₄×C₇₉	—	2	1	no	—
134	C₂×C₄×C₇₉	—	2	1	no	—
135	C₂×C₄×C₇₉	—	2	1	no	—
136	C₂×C₄×C₇₉	—	2	1	no	—
137	C₂×C₄×C₇₉	—	2	1	no	—
138	C₂×C₄×C₇₉	—	2	1	no	—
139	C₂×C₄×C₇₉	—	2	1	no	—
140	C₂×C₄×C₇₉	—	4	2	no	—
141	C₂×C₄×C₇₉	—	4	2	no	—
142	C₂×C₄×C₇₉	—	8	1	no	—
143	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
144	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
145	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
146	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
147	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
148	C₈×C₇₉	—	2	1	no	—
149	C₈×C₇₉	—	2	1	no	—
150	C₈×C₇₉	—	2	1	no	—
151	C₈×C₇₉	—	2	1	no	—
152	C₂²×C₇₉	—	2	1	no	—
153	C₂²×C₇₉	—	2	1	no	—
154	C₂²×C₇₉	—	2	1	no	—
155	C₂²×C₇₉	—	2	2	no	—
156	C₂²×C₇₉	—	2	1	no	—
157	C₂²×C₇₉	—	2	1	no	—
158	C₂²×C₇₉	—	4	1	no	—
159	C₂²×C₇₉	—	4	1	no	—
160	C₂²×C₇₉	—	4	1	no	—
161	C₂²×C₇₉	—	4	1	no	—
162	C₂²×C₇₉	—	4	1	no	—
163	C₂²×C₇₉	—	8	4	no	—
164	C₂²×C₇₉	#135	1	2	yes	—
165	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
166	C₄×C₇₉	—	2	1	no	—
167	C₄×C₇₉	—	2	1	no	—
168	C₄×C₇₉	—	2	1	no	—
169	C₄×C₇₉	—	2	1	no	—
170	C₄×C₇₉	—	4	1	no	—
171	C₄×C₇₉	—	4	1	no	—
172	C₄×C₇₉	—	4	1	no	—
173	C₄×C₇₉	—	4	1	no	—
174	C₄×C₇₉	—	4	1	no	—
175	C₄×C₇₉	—	4	1	no	—
176	C₄×C₇₉	C₂×#41	1	1	yes	characteristic
177	C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
178	C₂×C₇₉	—	2	2	no	—
179	C₂×C₇₉	—	4	1	no	—
180	C₂×C₇₉	—	4	2	no	—
181	C₂×C₇₉	—	8	1	no	—
182	C₂×C₇₉	#546	1	1	yes	characteristic
183	C₂×C₇₉	C₂×#135	1	1	yes	characteristic
184	C₂×C₇₉	#577	1	1	yes	characteristic
185	#3296	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₇₉	#3296	1	1	yes	characteristic, direct product factor, Sylow
187	#552	C₂×C₇₉	1	1	yes	characteristic, complemented
188	#546	C₂×C₇₉	1	1	yes	characteristic
189	#488	C₂×C₇₉	1	1	yes	characteristic, complemented
190	#483	C₂×C₇₉	1	1	yes	characteristic, complemented
191	#482	C₂×C₇₉	1	1	yes	characteristic, complemented
192	#478	C₂×C₇₉	1	1	yes	characteristic, complemented
193	#467	C₂×C₇₉	1	1	yes	characteristic, complemented
194	#465	C₂×C₇₉	1	1	yes	characteristic, complemented
195	#464	C₂×C₇₉	1	1	yes	characteristic, complemented
196	#452	C₂×C₇₉	1	1	yes	characteristic, complemented
197	#450	C₂×C₇₉	1	1	yes	characteristic, complemented
198	C₄×SD₁₆	C₂×C₇₉	1	1	yes	characteristic, complemented
199	C₈×D₄	C₂×C₇₉	1	1	yes	characteristic, complemented
200	#416	C₂×C₇₉	1	1	yes	characteristic, complemented
201	C₂×#102	C₂×C₇₉	1	1	yes	characteristic, complemented
202	C₂×#41	C₂²×C₇₉	1	1	yes	characteristic
203	C₂²×D₄	C₂²×C₇₉	1	1	yes	characteristic
204	C₂×Q₁₆	C₂²×C₇₉	1	1	yes	characteristic, complemented
205	C₂×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
206	C₂×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
207	C₂²×C₈	C₂²×C₇₉	1	1	yes	characteristic
208	C₂²×C₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
209	#126	—	2	1	no	—
210	#125	—	2	1	no	—
211	#125	C₂²×C₇₉	1	1	yes	characteristic, complemented
212	#124	C₂²×C₇₉	1	1	yes	characteristic
213	#123	—	2	1	no	—
214	#123	—	2	1	no	—
215	C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
216	C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
217	C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
218	#121	—	2	1	no	—
219	#121	C₂²×C₇₉	1	1	yes	characteristic
220	#120	—	2	1	no	—
221	C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
222	C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
223	C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
224	#117	—	2	1	no	—
225	#117	C₂²×C₇₉	1	1	yes	characteristic, complemented
226	C₂×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
227	C₂×C₂²⋊C₄	—	2	1	no	—
228	#107	C₂²×C₇₉	1	1	yes	characteristic, complemented
229	#106	C₂²×C₇₉	1	1	yes	characteristic, complemented
230	#106	C₂²×C₇₉	1	1	yes	characteristic, complemented
231	C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
232	#103	C₂²×C₇₉	1	1	yes	characteristic, complemented
233	#103	C₂²×C₇₉	1	1	yes	characteristic, complemented
234	#103	C₂²×C₇₉	1	1	yes	characteristic, complemented
235	#103	C₂²×C₇₉	1	1	yes	characteristic, complemented
236	#102	C₂²×C₇₉	1	1	yes	characteristic
237	#102	C₂²×C₇₉	1	1	yes	characteristic
238	#102	C₂²×C₇₉	1	1	yes	characteristic
239	#102	C₂²×C₇₉	1	1	yes	characteristic
240	#102	C₂²×C₇₉	1	1	yes	characteristic
241	#102	C₂²×C₇₉	1	1	yes	characteristic
242	C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
243	C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
244	C₄×C₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
245	C₂⁴	—	2	1	no	—
246	#41	—	2	2	no	—
247	#41	—	4	1	no	—
248	C₂×Q₈	C₂³×C₇₉	1	1	yes	characteristic
249	C₂×Q₈	C₂³×C₇₉	1	1	yes	characteristic
250	C₂×D₄	—	2	2	no	—
251	C₂×D₄	—	2	1	no	—
252	C₂×D₄	—	2	1	no	—
253	C₂×D₄	—	2	1	no	—
254	C₂×D₄	—	4	1	no	—
255	C₂×D₄	D₄×C₇₉	1	1	yes	characteristic
256	C₂×D₄	C₂³×C₇₉	1	1	yes	characteristic
257	C₂×D₄	C₂³×C₇₉	1	1	yes	characteristic
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	—	2	1	no	—
260	C₂²×C₄	—	2	1	no	—
261	C₂²×C₄	C₂³×C₇₉	1	1	yes	characteristic
262	C₂²×C₄	C₂³×C₇₉	1	1	yes	characteristic
263	Q₁₆	—	4	1	no	—
264	SD₁₆	—	2	2	no	—
265	SD₁₆	—	4	1	no	—
266	C₂×C₈	—	4	1	no	—
267	C₂×C₈	—	4	1	no	—
268	C₂×C₈	C₂³×C₇₉	1	1	yes	characteristic
269	C₂×C₈	C₂³×C₇₉	1	1	yes	characteristic
270	C₂×C₈	C₂³×C₇₉	1	1	yes	characteristic
271	C₂×C₈	C₂³×C₇₉	1	1	yes	characteristic
272	C₄⋊C₄	—	2	1	no	—
273	C₄⋊C₄	—	2	1	no	—
274	C₄⋊C₄	—	2	1	no	—
275	C₄⋊C₄	—	2	1	no	—
276	C₄⋊C₄	—	2	1	no	—
277	C₄⋊C₄	—	2	1	no	—
278	C₄⋊C₄	—	2	1	no	—
279	C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
280	C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
281	C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
282	C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
283	C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
284	C₂²⋊C₄	—	2	1	no	—
285	C₂²⋊C₄	—	2	1	no	—
286	C₂²⋊C₄	—	2	1	no	—
287	C₂²⋊C₄	—	2	1	no	—
288	C₂²⋊C₄	—	2	1	no	—
289	C₂²⋊C₄	—	2	1	no	—
290	C₂²⋊C₄	—	2	1	no	—
291	C₂²⋊C₄	—	2	1	no	—
292	C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
293	C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
294	C₄²	—	2	1	no	—
295	C₄²	—	2	1	no	—
296	C₄²	C₂³×C₇₉	1	1	yes	characteristic
297	C₂³	—	2	1	no	—
298	C₂³	—	2	1	no	—
299	C₂³	—	4	2	no	—
300	C₂³	—	4	2	no	—
301	C₂³	—	8	1	no	—
302	C₂³	C₂×D₄×C₇₉	1	1	yes	characteristic
303	C₂³	C₂×D₄×C₇₉	1	1	yes	characteristic
304	Q₈	—	2	1	no	—
305	Q₈	—	2	1	no	—
306	Q₈	—	2	1	no	—
307	Q₈	—	2	1	no	—
308	D₄	—	2	2	no	—
309	D₄	—	2	1	no	—
310	D₄	—	2	1	no	—
311	D₄	—	2	1	no	—
312	D₄	—	4	2	no	—
313	D₄	—	4	2	no	—
314	D₄	—	8	1	no	—
315	D₄	#41×C₇₉	1	2	yes	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	8	1	no	—
329	C₂×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
330	C₂×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
331	C₂×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
332	C₂×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
333	C₂×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
334	C₈	—	2	1	no	—
335	C₈	—	2	1	no	—
336	C₈	—	2	1	no	—
337	C₈	—	2	1	no	—
338	C₂²	—	2	1	no	—
339	C₂²	—	2	1	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	4	1	no	—
345	C₂²	—	4	1	no	—
346	C₂²	—	4	1	no	—
347	C₂²	—	4	1	no	—
348	C₂²	—	4	1	no	—
349	C₂²	—	8	4	no	—
350	C₂²	#135×C₇₉	1	2	yes	—
351	C₂²	C₂²×D₄×C₇₉	1	1	yes	characteristic
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	4	1	no	—
357	C₄	—	4	1	no	—
358	C₄	—	4	1	no	—
359	C₄	—	4	1	no	—
360	C₄	—	4	1	no	—
361	C₄	—	4	1	no	—
362	C₄	C₂×#41×C₇₉	1	1	yes	characteristic
363	C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
364	C₂	—	2	2	no	—
365	C₂	—	4	1	no	—
366	C₂	—	4	2	no	—
367	C₂	—	8	1	no	—
368	C₂	#546×C₇₉	1	1	yes	characteristic
369	C₂	C₂×#135×C₇₉	1	1	yes	characteristic
370	C₂	#577×C₇₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₇₉
prime radical	#546×C₇₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ C₄×D₄×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #552×C₇₉	C₂	semidirect
3. #488×C₇₉	C₂	semidirect
4. #483×C₇₉	C₂	semidirect
5. #482×C₇₉	C₂	semidirect
6. #478×C₇₉	C₂	semidirect
7. #467×C₇₉	C₂	semidirect
8. #465×C₇₉	C₂	semidirect
9. #464×C₇₉	C₂	semidirect
10. #452×C₇₉	C₂	semidirect
11. #450×C₇₉	C₂	semidirect
12. C₄×SD₁₆×C₇₉	C₂	semidirect
13. C₈×D₄×C₇₉	C₂	semidirect
14. #416×C₇₉	C₂	semidirect
15. C₂×#102×C₇₉	C₂	semidirect
18. C₂×Q₁₆×C₇₉	C₂²	semidirect
22. C₂²×C₈×C₇₉	C₂²	semidirect
25. #125×C₇₉	C₂²	semidirect
31. C₂²⋊Q₈×C₇₉	C₂²	semidirect
35. C₄×Q₈×C₇₉	C₂²	semidirect
39. #117×C₇₉	C₂²	semidirect
42. #107×C₇₉	C₂²	semidirect
43. #106×C₇₉	C₂²	semidirect
44. #106×C₇₉	C₂²	semidirect
45. C₄⋊C₈×C₇₉	C₂²	semidirect
46. #103×C₇₉	C₂²	semidirect
47. #103×C₇₉	C₂²	semidirect
48. #103×C₇₉	C₂²	semidirect
49. #103×C₇₉	C₂²	semidirect
57. C₂²⋊C₈×C₇₉	C₂²	semidirect
58. C₄×C₈×C₇₉	C₂²	semidirect
185. #3296	C₇₉	direct (N × H)
186. C₇₉	#3296	direct (N × H)
187. #552	C₂×C₇₉	semidirect
189. #488	C₂×C₇₉	semidirect
190. #483	C₂×C₇₉	semidirect
191. #482	C₂×C₇₉	semidirect
192. #478	C₂×C₇₉	semidirect
193. #467	C₂×C₇₉	semidirect
194. #465	C₂×C₇₉	semidirect
195. #464	C₂×C₇₉	semidirect
196. #452	C₂×C₇₉	semidirect
197. #450	C₂×C₇₉	semidirect
198. C₄×SD₁₆	C₂×C₇₉	semidirect
199. C₈×D₄	C₂×C₇₉	semidirect
200. #416	C₂×C₇₉	semidirect
201. C₂×#102	C₂×C₇₉	semidirect
204. C₂×Q₁₆	C₂²×C₇₉	semidirect
208. C₂²×C₈	C₂²×C₇₉	semidirect
211. #125	C₂²×C₇₉	semidirect
217. C₂²⋊Q₈	C₂²×C₇₉	semidirect
221. C₄×Q₈	C₂²×C₇₉	semidirect
225. #117	C₂²×C₇₉	semidirect
228. #107	C₂²×C₇₉	semidirect
229. #106	C₂²×C₇₉	semidirect
230. #106	C₂²×C₇₉	semidirect
231. C₄⋊C₈	C₂²×C₇₉	semidirect
232. #103	C₂²×C₇₉	semidirect
233. #103	C₂²×C₇₉	semidirect
234. #103	C₂²×C₇₉	semidirect
235. #103	C₂²×C₇₉	semidirect
243. C₂²⋊C₈	C₂²×C₇₉	semidirect
244. C₄×C₈	C₂²×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
#552×C₇₉	2
#546×C₇₉	2
#488×C₇₉	2
#483×C₇₉	2
#482×C₇₉	2
#478×C₇₉	2
#467×C₇₉	2
#465×C₇₉	2
#464×C₇₉	2
#452×C₇₉	2
#450×C₇₉	2
C₄×SD₁₆×C₇₉	2
C₈×D₄×C₇₉	2
#416×C₇₉	2
C₂×#102×C₇₉	2
#3296	79

Subgroups — C79×#3296 #23760918

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#3296 #23760918