Subgroups — C₇₉×#3118 #23760740

Order 10112.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#542×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#518×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#485×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#482×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#476×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#474×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#463×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#463×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#450×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#447×C₇₉	C₂	1	1	yes	maximal, characteristic
11	#442×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#440×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×SD₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×D₈×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#433×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₄×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
18	C₂×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
19	C₂×D₈×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×D₈×C₇₉	C₂²	1	1	yes	characteristic
21	C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
22	#126×C₇₉	—	2	1	no	—
23	#124×C₇₉	—	2	1	no	—
24	#124×C₇₉	C₂²	1	1	yes	characteristic, complemented
25	#123×C₇₉	—	2	1	no	—
26	C₂²⋊Q₈×C₇₉	—	2	1	no	—
27	C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
28	#121×C₇₉	C₂²	1	1	yes	characteristic
29	C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
30	C₄×D₄×C₇₉	—	2	1	no	—
31	C₄×D₄×C₇₉	—	2	1	no	—
32	C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
33	C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
34	C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
35	C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
36	C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
37	#117×C₇₉	C₂²	1	1	yes	characteristic
38	#117×C₇₉	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
40	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
41	#107×C₇₉	C₂²	1	1	yes	characteristic, complemented
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	C₄⋊C₈×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	#102×C₇₉	C₂²	1	1	yes	characteristic
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, complemented
54	#102×C₇₉	C₂²	1	1	yes	characteristic, complemented
55	C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
56	C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
57	#97×C₇₉	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
59	C₂⁴×C₇₉	—	2	1	no	—
60	C₂×Q₈×C₇₉	—	2	1	no	—
61	C₂×Q₈×C₇₉	C₂³	1	1	yes	characteristic
62	C₂×D₄×C₇₉	—	2	2	no	—
63	C₂×D₄×C₇₉	—	2	2	no	—
64	C₂×D₄×C₇₉	—	2	1	no	—
65	C₂×D₄×C₇₉	—	2	1	no	—
66	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
67	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
68	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₇₉	—	2	1	no	—
70	C₂²×C₄×C₇₉	—	2	1	no	—
71	C₂²×C₄×C₇₉	—	2	1	no	—
72	C₂²×C₄×C₇₉	—	2	1	no	—
73	C₂²×C₄×C₇₉	—	2	1	no	—
74	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
75	SD₁₆×C₇₉	—	2	2	no	—
76	SD₁₆×C₇₉	—	2	2	no	—
77	D₈×C₇₉	—	2	2	no	—
78	D₈×C₇₉	—	2	2	no	—
79	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
80	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
81	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
82	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
83	C₄⋊C₄×C₇₉	—	2	1	no	—
84	C₄⋊C₄×C₇₉	—	2	1	no	—
85	C₄⋊C₄×C₇₉	—	2	1	no	—
86	C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
87	C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
88	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
89	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
90	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
91	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
92	C₂²⋊C₄×C₇₉	—	2	1	no	—
93	C₂²⋊C₄×C₇₉	—	2	1	no	—
94	C₂²⋊C₄×C₇₉	—	2	1	no	—
95	C₂²⋊C₄×C₇₉	—	2	1	no	—
96	C₂²⋊C₄×C₇₉	—	2	1	no	—
97	C₂²⋊C₄×C₇₉	—	2	1	no	—
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	D₄	1	1	yes	characteristic
103	C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
104	C₄²×C₇₉	—	2	1	no	—
105	C₄²×C₇₉	—	2	1	no	—
106	C₄²×C₇₉	C₂³	1	1	yes	characteristic
107	C₄²×C₇₉	C₂³	1	1	yes	characteristic
108	C₂³×C₇₉	—	2	4	no	—
109	C₂³×C₇₉	—	2	1	no	—
110	C₂³×C₇₉	—	2	1	no	—
111	C₂³×C₇₉	—	2	1	no	—
112	C₂³×C₇₉	—	8	1	no	—
113	C₂³×C₇₉	—	8	1	no	—
114	C₂³×C₇₉	C₂×D₄	1	1	yes	characteristic
115	Q₈×C₇₉	—	2	1	no	—
116	Q₈×C₇₉	—	2	1	no	—
117	Q₈×C₇₉	—	8	1	no	—
118	D₄×C₇₉	—	2	4	no	—
119	D₄×C₇₉	—	2	1	no	—
120	D₄×C₇₉	—	2	1	no	—
121	D₄×C₇₉	—	2	1	no	—
122	D₄×C₇₉	—	2	1	no	—
123	D₄×C₇₉	—	8	1	no	—
124	D₄×C₇₉	#41	1	2	yes	—
125	D₄×C₇₉	#41	1	2	yes	—
126	C₂×C₄×C₇₉	—	2	1	no	—
127	C₂×C₄×C₇₉	—	2	1	no	—
128	C₂×C₄×C₇₉	—	2	1	no	—
129	C₂×C₄×C₇₉	—	2	1	no	—
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	—	8	1	no	—
134	C₂×C₄×C₇₉	—	8	1	no	—
135	C₂×C₄×C₇₉	—	8	1	no	—
136	C₂×C₄×C₇₉	—	8	1	no	—
137	C₂×C₄×C₇₉	—	8	1	no	—
138	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
139	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
140	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
141	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
142	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
144	C₈×C₇₉	—	2	1	no	—
145	C₈×C₇₉	—	2	1	no	—
146	C₈×C₇₉	—	2	1	no	—
147	C₈×C₇₉	—	2	1	no	—
148	C₂²×C₇₉	—	2	1	no	—
149	C₂²×C₇₉	—	2	2	no	—
150	C₂²×C₇₉	—	2	2	no	—
151	C₂²×C₇₉	—	2	1	no	—
152	C₂²×C₇₉	—	2	1	no	—
153	C₂²×C₇₉	—	4	1	no	—
154	C₂²×C₇₉	—	4	1	no	—
155	C₂²×C₇₉	—	4	1	no	—
156	C₂²×C₇₉	—	4	1	no	—
157	C₂²×C₇₉	—	4	1	no	—
158	C₂²×C₇₉	—	4	1	no	—
159	C₂²×C₇₉	—	4	1	no	—
160	C₂²×C₇₉	—	8	4	no	—
161	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
162	C₄×C₇₉	—	2	1	no	—
163	C₄×C₇₉	—	2	1	no	—
164	C₄×C₇₉	—	2	1	no	—
165	C₄×C₇₉	—	2	1	no	—
166	C₄×C₇₉	—	2	1	no	—
167	C₄×C₇₉	—	4	1	no	—
168	C₄×C₇₉	—	4	1	no	—
169	C₄×C₇₉	—	4	1	no	—
170	C₄×C₇₉	—	4	1	no	—
171	C₄×C₇₉	—	4	1	no	—
172	C₄×C₇₉	C₂×#41	1	1	yes	characteristic
173	C₄×C₇₉	C₂×#41	1	1	yes	characteristic
174	C₂×C₇₉	—	4	1	no	—
175	C₂×C₇₉	—	4	2	no	—
176	C₂×C₇₉	—	4	2	no	—
177	C₂×C₇₉	—	8	1	no	—
178	C₂×C₇₉	#525	1	1	yes	characteristic
179	C₂×C₇₉	#576	1	1	yes	characteristic
180	C₂×C₇₉	#577	1	1	yes	characteristic
181	#3118	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₇₉	#3118	1	1	yes	characteristic, direct product factor, Sylow
183	#542	C₂×C₇₉	1	1	yes	characteristic, complemented
184	#518	C₂×C₇₉	1	1	yes	characteristic, complemented
185	#485	C₂×C₇₉	1	1	yes	characteristic, complemented
186	#482	C₂×C₇₉	1	1	yes	characteristic, complemented
187	#476	C₂×C₇₉	1	1	yes	characteristic, complemented
188	#474	C₂×C₇₉	1	1	yes	characteristic, complemented
189	#463	C₂×C₇₉	1	1	yes	characteristic, complemented
190	#463	C₂×C₇₉	1	1	yes	characteristic, complemented
191	#450	C₂×C₇₉	1	1	yes	characteristic, complemented
192	#447	C₂×C₇₉	1	1	yes	characteristic
193	#442	C₂×C₇₉	1	1	yes	characteristic, complemented
194	#440	C₂×C₇₉	1	1	yes	characteristic, complemented
195	C₄×SD₁₆	C₂×C₇₉	1	1	yes	characteristic, complemented
196	C₄×D₈	C₂×C₇₉	1	1	yes	characteristic, complemented
197	#433	C₂×C₇₉	1	1	yes	characteristic, complemented
198	C₂²×D₄	C₂²×C₇₉	1	1	yes	characteristic
199	C₂×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
200	C₂×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
201	C₂×D₈	C₂²×C₇₉	1	1	yes	characteristic
202	C₂×D₈	C₂²×C₇₉	1	1	yes	characteristic
203	C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
204	#126	—	2	1	no	—
205	#124	—	2	1	no	—
206	#124	C₂²×C₇₉	1	1	yes	characteristic, complemented
207	#123	—	2	1	no	—
208	C₂²⋊Q₈	—	2	1	no	—
209	C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
210	#121	C₂²×C₇₉	1	1	yes	characteristic
211	C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
212	C₄×D₄	—	2	1	no	—
213	C₄×D₄	—	2	1	no	—
214	C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
215	C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
216	C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
217	C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
218	C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic, complemented
219	#117	C₂²×C₇₉	1	1	yes	characteristic
220	#117	C₂²×C₇₉	1	1	yes	characteristic
221	C₂×C₂²⋊C₄	—	2	1	no	—
222	C₂×C₂²⋊C₄	—	2	1	no	—
223	#107	C₂²×C₇₉	1	1	yes	characteristic, complemented
224	#107	C₂²×C₇₉	1	1	yes	characteristic, complemented
225	#106	C₂²×C₇₉	1	1	yes	characteristic, complemented
226	#106	C₂²×C₇₉	1	1	yes	characteristic, complemented
227	C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
228	C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
229	#103	C₂²×C₇₉	1	1	yes	characteristic, complemented
230	#103	C₂²×C₇₉	1	1	yes	characteristic, complemented
231	#102	C₂²×C₇₉	1	1	yes	characteristic
232	#102	C₂²×C₇₉	1	1	yes	characteristic
233	#102	C₂²×C₇₉	1	1	yes	characteristic
234	#102	C₂²×C₇₉	1	1	yes	characteristic
235	#102	C₂²×C₇₉	1	1	yes	characteristic, complemented
236	#102	C₂²×C₇₉	1	1	yes	characteristic, complemented
237	C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
238	C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
239	#97	C₂²×C₇₉	1	1	yes	characteristic, complemented
240	C₄×C₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
241	C₂⁴	—	2	1	no	—
242	C₂×Q₈	—	2	1	no	—
243	C₂×Q₈	C₂³×C₇₉	1	1	yes	characteristic
244	C₂×D₄	—	2	2	no	—
245	C₂×D₄	—	2	2	no	—
246	C₂×D₄	—	2	1	no	—
247	C₂×D₄	—	2	1	no	—
248	C₂×D₄	C₂³×C₇₉	1	1	yes	characteristic
249	C₂×D₄	C₂³×C₇₉	1	1	yes	characteristic
250	C₂×D₄	C₂³×C₇₉	1	1	yes	characteristic
251	C₂²×C₄	—	2	1	no	—
252	C₂²×C₄	—	2	1	no	—
253	C₂²×C₄	—	2	1	no	—
254	C₂²×C₄	—	2	1	no	—
255	C₂²×C₄	—	2	1	no	—
256	C₂²×C₄	C₂³×C₇₉	1	1	yes	characteristic
257	SD₁₆	—	2	2	no	—
258	SD₁₆	—	2	2	no	—
259	D₈	—	2	2	no	—
260	D₈	—	2	2	no	—
261	C₂×C₈	C₂³×C₇₉	1	1	yes	characteristic
262	C₂×C₈	C₂³×C₇₉	1	1	yes	characteristic
263	C₂×C₈	C₂³×C₇₉	1	1	yes	characteristic
264	C₂×C₈	C₂³×C₇₉	1	1	yes	characteristic
265	C₄⋊C₄	—	2	1	no	—
266	C₄⋊C₄	—	2	1	no	—
267	C₄⋊C₄	—	2	1	no	—
268	C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
269	C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
270	C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
271	C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
272	C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
273	C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
274	C₂²⋊C₄	—	2	1	no	—
275	C₂²⋊C₄	—	2	1	no	—
276	C₂²⋊C₄	—	2	1	no	—
277	C₂²⋊C₄	—	2	1	no	—
278	C₂²⋊C₄	—	2	1	no	—
279	C₂²⋊C₄	—	2	1	no	—
280	C₂²⋊C₄	—	2	1	no	—
281	C₂²⋊C₄	—	2	1	no	—
282	C₂²⋊C₄	—	2	1	no	—
283	C₂²⋊C₄	—	2	1	no	—
284	C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
285	C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
286	C₄²	—	2	1	no	—
287	C₄²	—	2	1	no	—
288	C₄²	C₂³×C₇₉	1	1	yes	characteristic
289	C₄²	C₂³×C₇₉	1	1	yes	characteristic
290	C₂³	—	2	4	no	—
291	C₂³	—	2	1	no	—
292	C₂³	—	2	1	no	—
293	C₂³	—	2	1	no	—
294	C₂³	—	8	1	no	—
295	C₂³	—	8	1	no	—
296	C₂³	C₂×D₄×C₇₉	1	1	yes	characteristic
297	Q₈	—	2	1	no	—
298	Q₈	—	2	1	no	—
299	Q₈	—	8	1	no	—
300	D₄	—	2	4	no	—
301	D₄	—	2	1	no	—
302	D₄	—	2	1	no	—
303	D₄	—	2	1	no	—
304	D₄	—	2	1	no	—
305	D₄	—	8	1	no	—
306	D₄	#41×C₇₉	1	2	yes	—
307	D₄	#41×C₇₉	1	2	yes	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	8	1	no	—
316	C₂×C₄	—	8	1	no	—
317	C₂×C₄	—	8	1	no	—
318	C₂×C₄	—	8	1	no	—
319	C₂×C₄	—	8	1	no	—
320	C₂×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
321	C₂×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
322	C₂×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
323	C₂×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
324	C₂×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
325	C₂×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
326	C₈	—	2	1	no	—
327	C₈	—	2	1	no	—
328	C₈	—	2	1	no	—
329	C₈	—	2	1	no	—
330	C₂²	—	2	1	no	—
331	C₂²	—	2	2	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	1	no	—
334	C₂²	—	2	1	no	—
335	C₂²	—	4	1	no	—
336	C₂²	—	4	1	no	—
337	C₂²	—	4	1	no	—
338	C₂²	—	4	1	no	—
339	C₂²	—	4	1	no	—
340	C₂²	—	4	1	no	—
341	C₂²	—	4	1	no	—
342	C₂²	—	8	4	no	—
343	C₂²	C₂²×D₄×C₇₉	1	1	yes	characteristic
344	C₄	—	2	1	no	—
345	C₄	—	2	1	no	—
346	C₄	—	2	1	no	—
347	C₄	—	2	1	no	—
348	C₄	—	2	1	no	—
349	C₄	—	4	1	no	—
350	C₄	—	4	1	no	—
351	C₄	—	4	1	no	—
352	C₄	—	4	1	no	—
353	C₄	—	4	1	no	—
354	C₄	C₂×#41×C₇₉	1	1	yes	characteristic
355	C₄	C₂×#41×C₇₉	1	1	yes	characteristic
356	C₂	—	4	1	no	—
357	C₂	—	4	2	no	—
358	C₂	—	4	2	no	—
359	C₂	—	8	1	no	—
360	C₂	#525×C₇₉	1	1	yes	characteristic
361	C₂	#576×C₇₉	1	1	yes	characteristic
362	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	#447×C₇₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ #117×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #542×C₇₉	C₂	semidirect
2. #518×C₇₉	C₂	semidirect
3. #485×C₇₉	C₂	semidirect
4. #482×C₇₉	C₂	semidirect
5. #476×C₇₉	C₂	semidirect
6. #474×C₇₉	C₂	semidirect
7. #463×C₇₉	C₂	semidirect
8. #463×C₇₉	C₂	semidirect
9. #450×C₇₉	C₂	semidirect
11. #442×C₇₉	C₂	semidirect
12. #440×C₇₉	C₂	semidirect
13. C₄×SD₁₆×C₇₉	C₂	semidirect
14. C₄×D₈×C₇₉	C₂	semidirect
15. #433×C₇₉	C₂	semidirect
21. C₄⋊Q₈×C₇₉	C₂²	semidirect
24. #124×C₇₉	C₂²	semidirect
29. C₄×Q₈×C₇₉	C₂²	semidirect
36. C₄×D₄×C₇₉	C₂²	semidirect
41. #107×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. C₄⋊C₈×C₇₉	C₂²	semidirect
47. #103×C₇₉	C₂²	semidirect
48. #103×C₇₉	C₂²	semidirect
53. #102×C₇₉	C₂²	semidirect
54. #102×C₇₉	C₂²	semidirect
57. #97×C₇₉	C₂²	semidirect
58. C₄×C₈×C₇₉	C₂²	semidirect
181. #3118	C₇₉	direct (N × H)
182. C₇₉	#3118	direct (N × H)
183. #542	C₂×C₇₉	semidirect
184. #518	C₂×C₇₉	semidirect
185. #485	C₂×C₇₉	semidirect
186. #482	C₂×C₇₉	semidirect
187. #476	C₂×C₇₉	semidirect
188. #474	C₂×C₇₉	semidirect
189. #463	C₂×C₇₉	semidirect
190. #463	C₂×C₇₉	semidirect
191. #450	C₂×C₇₉	semidirect
193. #442	C₂×C₇₉	semidirect
194. #440	C₂×C₇₉	semidirect
195. C₄×SD₁₆	C₂×C₇₉	semidirect
196. C₄×D₈	C₂×C₇₉	semidirect
197. #433	C₂×C₇₉	semidirect
203. C₄⋊Q₈	C₂²×C₇₉	semidirect
206. #124	C₂²×C₇₉	semidirect
211. C₄×Q₈	C₂²×C₇₉	semidirect
218. C₄×D₄	C₂²×C₇₉	semidirect
223. #107	C₂²×C₇₉	semidirect
224. #107	C₂²×C₇₉	semidirect
225. #106	C₂²×C₇₉	semidirect
226. #106	C₂²×C₇₉	semidirect
227. C₄⋊C₈	C₂²×C₇₉	semidirect
228. C₄⋊C₈	C₂²×C₇₉	semidirect
229. #103	C₂²×C₇₉	semidirect
230. #103	C₂²×C₇₉	semidirect
235. #102	C₂²×C₇₉	semidirect
236. #102	C₂²×C₇₉	semidirect
239. #97	C₂²×C₇₉	semidirect
240. 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
#542×C₇₉	2
#518×C₇₉	2
#485×C₇₉	2
#482×C₇₉	2
#476×C₇₉	2
#474×C₇₉	2
#463×C₇₉	2
#450×C₇₉	2
#447×C₇₉	2
#442×C₇₉	2
#440×C₇₉	2
C₄×SD₁₆×C₇₉	2
C₄×D₈×C₇₉	2
#433×C₇₉	2
#3118	79

Subgroups — C79×#3118 #23760740

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#3118 #23760740