Subgroups — C₇₉×#25782 #34137471

Order 20224.

1538 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#495×C₇₉	C₂	1	2	yes	maximal, complemented
3	C₂×#466×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#448×C₇₉	C₂	1	2	yes	maximal, complemented
5	C₇₉×#2436	C₂	1	2	yes	maximal, complemented
6	C₇₉×#2015	C₂	1	4	yes	maximal, complemented
7	C₇₉×#1969	C₂	1	2	yes	maximal, complemented
8	C₈×C₂²⋊C₄×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×Q₈×C₇₉	C₂²	1	2	yes	—
10	C₂²×Q₁₆×C₇₉	—	2	8	no	—
11	C₂²×Q₁₆×C₇₉	—	2	4	no	—
12	C₂²×Q₁₆×C₇₉	C₂²	1	2	yes	—
13	C₂²×Q₁₆×C₇₉	C₂²	1	2	yes	—
14	C₂²×SD₁₆×C₇₉	C₂²	1	4	yes	—
15	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×#124×C₇₉	C₂²	1	4	yes	—
18	C₂×#121×C₇₉	C₂²	1	2	yes	—
19	#495×C₇₉	—	2	8	no	—
20	#466×C₇₉	—	2	4	no	—
21	#448×C₇₉	—	2	8	no	—
22	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
23	C₂×#103×C₇₉	C₂²	1	4	yes	—
24	C₂×#102×C₇₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₇₉	C₂²	1	2	yes	—
27	#393×C₇₉	—	2	4	no	—
28	#391×C₇₉	C₂²	1	4	yes	—
29	#386×C₇₉	—	2	4	no	—
30	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
31	#336×C₇₉	C₂²	1	2	yes	—
32	C₂²×Q₈×C₇₉	—	2	2	no	—
33	C₂²×Q₈×C₇₉	—	2	8	no	—
34	C₂²×Q₈×C₇₉	—	2	4	no	—
35	C₂²×Q₈×C₇₉	—	2	4	no	—
36	C₂²×Q₈×C₇₉	—	4	4	no	—
37	C₂²×Q₈×C₇₉	C₂³	1	4	yes	—
38	C₂²×D₄×C₇₉	—	2	2	no	—
39	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
40	C₂³×C₄×C₇₉	—	2	2	no	—
41	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
42	C₂×Q₁₆×C₇₉	—	2	32	no	—
43	C₂×Q₁₆×C₇₉	—	2	8	no	—
44	C₂×Q₁₆×C₇₉	—	2	4	no	—
45	C₂×Q₁₆×C₇₉	—	2	4	no	—
46	C₂×Q₁₆×C₇₉	—	2	4	no	—
47	C₂×Q₁₆×C₇₉	D₄	1	8	yes	complemented
48	C₂×SD₁₆×C₇₉	—	2	8	no	—
49	C₂×SD₁₆×C₇₉	—	2	8	no	—
50	C₂×SD₁₆×C₇₉	—	4	4	no	—
51	C₂×D₈×C₇₉	—	2	2	no	—
52	C₂×D₈×C₇₉	—	2	4	no	—
53	C₂²×C₈×C₇₉	—	2	4	no	—
54	C₂²×C₈×C₇₉	D₄	1	4	yes	—
55	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
57	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
58	#124×C₇₉	—	2	8	no	—
59	#124×C₇₉	—	4	4	no	—
60	#121×C₇₉	—	2	4	no	—
61	#121×C₇₉	—	2	4	no	—
62	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
63	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₇₉	—	2	8	no	—
65	C₂×C₂²⋊C₄×C₇₉	D₄	1	2	yes	—
66	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
67	#107×C₇₉	—	2	2	no	—
68	#103×C₇₉	—	2	8	no	—
69	#102×C₇₉	—	2	4	no	—
70	C₂²⋊C₈×C₇₉	D₄	1	4	yes	—
71	C₄×C₈×C₇₉	—	2	4	no	—
72	#95×C₇₉	—	2	8	no	—
73	#95×C₇₉	D₄	1	2	yes	—
74	C₂⁴×C₇₉	—	2	2	no	—
75	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
76	C₂×Q₈×C₇₉	—	2	4	no	—
77	C₂×Q₈×C₇₉	—	2	16	no	—
78	C₂×Q₈×C₇₉	—	2	4	no	—
79	C₂×Q₈×C₇₉	—	2	4	no	—
80	C₂×Q₈×C₇₉	—	2	4	no	—
81	C₂×Q₈×C₇₉	—	2	4	no	—
82	C₂×Q₈×C₇₉	—	4	8	no	—
83	C₂×Q₈×C₇₉	—	4	16	no	—
84	C₂×Q₈×C₇₉	—	4	8	no	—
85	C₂×Q₈×C₇₉	—	4	4	no	—
86	C₂×Q₈×C₇₉	C₂×D₄	1	8	yes	—
87	C₂×D₄×C₇₉	—	2	2	no	—
88	C₂×D₄×C₇₉	—	2	2	no	—
89	C₂×D₄×C₇₉	—	2	4	no	—
90	C₂×D₄×C₇₉	—	2	4	no	—
91	C₂×D₄×C₇₉	—	4	4	no	—
92	C₂×D₄×C₇₉	—	4	8	no	—
93	C₂²×C₄×C₇₉	—	2	2	no	—
94	C₂²×C₄×C₇₉	—	2	2	no	—
95	C₂²×C₄×C₇₉	—	2	4	no	—
96	C₂²×C₄×C₇₉	—	2	2	no	—
97	C₂²×C₄×C₇₉	—	4	8	no	—
98	C₂²×C₄×C₇₉	—	4	4	no	—
99	C₂²×C₄×C₇₉	C₂×D₄	1	4	yes	—
100	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
104	Q₁₆×C₇₉	—	2	16	no	—
105	Q₁₆×C₇₉	—	2	16	no	—
106	SD₁₆×C₇₉	—	4	16	no	—
107	D₈×C₇₉	—	4	4	no	—
108	C₂×C₈×C₇₉	—	2	8	no	—
109	C₂×C₈×C₇₉	—	2	2	no	—
110	C₂×C₈×C₇₉	—	2	2	no	—
111	C₂×C₈×C₇₉	—	2	2	no	—
112	C₂×C₈×C₇₉	C₂×D₄	1	4	yes	—
113	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
114	C₂×C₈×C₇₉	C₂×D₄	1	4	yes	—
115	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
116	C₄⋊C₄×C₇₉	—	2	2	no	—
117	C₄⋊C₄×C₇₉	—	2	2	no	—
118	C₂²⋊C₄×C₇₉	—	2	4	no	—
119	C₂²⋊C₄×C₇₉	—	4	16	no	—
120	C₂²⋊C₄×C₇₉	—	4	4	no	—
121	C₄²×C₇₉	—	2	2	no	—
122	C₄²×C₇₉	—	2	2	no	—
123	C₂³×C₇₉	—	2	2	no	—
124	C₂³×C₇₉	—	2	2	no	—
125	C₂³×C₇₉	—	4	2	no	—
126	C₂³×C₇₉	—	4	4	no	—
127	C₂³×C₇₉	—	4	4	no	—
128	C₂³×C₇₉	—	4	4	no	—
129	C₂³×C₇₉	#127	1	2	yes	—
130	C₂³×C₇₉	#135	1	4	yes	—
131	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
132	Q₈×C₇₉	—	2	8	no	—
133	Q₈×C₇₉	—	2	8	no	—
134	Q₈×C₇₉	—	4	16	no	—
135	Q₈×C₇₉	—	4	4	no	—
136	Q₈×C₇₉	—	4	4	no	—
137	D₄×C₇₉	—	4	2	no	—
138	D₄×C₇₉	—	4	2	no	—
139	D₄×C₇₉	—	4	4	no	—
140	D₄×C₇₉	—	8	8	no	—
141	C₂×C₄×C₇₉	—	2	2	no	—
142	C₂×C₄×C₇₉	—	2	2	no	—
143	C₂×C₄×C₇₉	—	2	2	no	—
144	C₂×C₄×C₇₉	—	2	4	no	—
145	C₂×C₄×C₇₉	—	2	4	no	—
146	C₂×C₄×C₇₉	—	2	8	no	—
147	C₂×C₄×C₇₉	—	2	4	no	—
148	C₂×C₄×C₇₉	—	2	4	no	—
149	C₂×C₄×C₇₉	—	4	16	no	—
150	C₂×C₄×C₇₉	—	4	4	no	—
151	C₂×C₄×C₇₉	—	4	4	no	—
152	C₂×C₄×C₇₉	—	4	2	no	—
153	C₂×C₄×C₇₉	—	4	4	no	—
154	C₂×C₄×C₇₉	#127	1	2	yes	—
155	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
157	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₇₉	H(5,𝔽₂)	1	2	yes	—
159	C₈×C₇₉	—	2	2	no	—
160	C₈×C₇₉	—	2	4	no	—
161	C₈×C₇₉	#120	1	4	yes	—
162	C₂²×C₇₉	—	2	2	no	—
163	C₂²×C₇₉	—	2	2	no	—
164	C₂²×C₇₉	—	2	8	no	—
165	C₂²×C₇₉	—	8	2	no	—
166	C₂²×C₇₉	—	8	2	no	—
167	C₂²×C₇₉	—	8	2	no	—
168	C₂²×C₇₉	—	8	8	no	—
169	C₂²×C₇₉	#495	1	4	yes	complemented
170	C₂²×C₇₉	C₂×#127	1	1	yes	characteristic
171	C₂²×C₇₉	D₄²	1	2	yes	—
172	C₂²×C₇₉	C₂×#135	1	2	yes	—
173	C₂²×C₇₉	#578	1	2	yes	—
174	C₄×C₇₉	—	2	2	no	—
175	C₄×C₇₉	—	4	8	no	—
176	C₄×C₇₉	—	4	4	no	—
177	C₄×C₇₉	—	8	2	no	—
178	C₄×C₇₉	C₂×#120	1	1	yes	characteristic
179	C₄×C₇₉	#535	1	1	yes	characteristic
180	C₄×C₇₉	D₄²	1	2	yes	—
181	#25782	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂×C₇₉	—	2	4	no	—
183	C₂×C₇₉	—	16	2	no	—
184	C₂×C₇₉	#2433	1	1	yes	characteristic
185	C₂×C₇₉	C₂×#495	1	1	yes	characteristic
186	C₂×C₇₉	#3156	1	1	yes	characteristic
187	C₂×C₇₉	#3285	1	4	yes	—
188	C₂³×Q₁₆	C₂×C₇₉	1	1	yes	characteristic, complemented
189	C₂×#495	C₂×C₇₉	1	2	yes	complemented
190	C₂×#466	C₂×C₇₉	1	1	yes	characteristic
191	C₂×#448	C₂×C₇₉	1	2	yes	complemented
192	#2436	C₂×C₇₉	1	2	yes	complemented
193	#2015	C₂×C₇₉	1	4	yes	complemented
194	#1969	C₂×C₇₉	1	2	yes	complemented
195	C₈×C₂²⋊C₄	C₂×C₇₉	1	1	yes	characteristic, complemented
196	C₇₉	#25782	1	1	yes	characteristic, direct product factor, Sylow
197	C₂³×Q₈	C₂²×C₇₉	1	2	yes	—
198	C₂²×Q₁₆	—	2	8	no	—
199	C₂²×Q₁₆	—	2	4	no	—
200	C₂²×Q₁₆	C₂²×C₇₉	1	2	yes	—
201	C₂²×Q₁₆	C₂²×C₇₉	1	2	yes	—
202	C₂²×SD₁₆	C₂²×C₇₉	1	4	yes	—
203	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic
204	C₂³×C₈	C₂²×C₇₉	1	1	yes	characteristic
205	C₂×#124	C₂²×C₇₉	1	4	yes	—
206	C₂×#121	C₂²×C₇₉	1	2	yes	—
207	#495	—	2	8	no	—
208	#466	—	2	4	no	—
209	#448	—	2	8	no	—
210	C₂×#107	C₂²×C₇₉	1	1	yes	characteristic
211	C₂×#103	C₂²×C₇₉	1	4	yes	—
212	C₂×#102	C₂²×C₇₉	1	2	yes	—
213	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
214	C₂×C₄×C₈	C₂²×C₇₉	1	2	yes	—
215	#393	—	2	4	no	—
216	#391	C₂²×C₇₉	1	4	yes	—
217	#386	—	2	4	no	—
218	C₄×C₂²⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
219	#336	C₂²×C₇₉	1	2	yes	—
220	C₂²×Q₈	—	2	2	no	—
221	C₂²×Q₈	—	2	8	no	—
222	C₂²×Q₈	—	2	4	no	—
223	C₂²×Q₈	—	2	4	no	—
224	C₂²×Q₈	—	4	4	no	—
225	C₂²×Q₈	C₂³×C₇₉	1	4	yes	—
226	C₂²×D₄	—	2	2	no	—
227	C₂²×D₄	C₂³×C₇₉	1	2	yes	—
228	C₂³×C₄	—	2	2	no	—
229	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
230	C₂×Q₁₆	—	2	32	no	—
231	C₂×Q₁₆	—	2	8	no	—
232	C₂×Q₁₆	—	2	4	no	—
233	C₂×Q₁₆	—	2	4	no	—
234	C₂×Q₁₆	—	2	4	no	—
235	C₂×Q₁₆	D₄×C₇₉	1	8	yes	complemented
236	C₂×SD₁₆	—	2	8	no	—
237	C₂×SD₁₆	—	2	8	no	—
238	C₂×SD₁₆	—	4	4	no	—
239	C₂×D₈	—	2	2	no	—
240	C₂×D₈	—	2	4	no	—
241	C₂²×C₈	—	2	4	no	—
242	C₂²×C₈	D₄×C₇₉	1	4	yes	—
243	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
244	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
245	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
246	#124	—	2	8	no	—
247	#124	—	4	4	no	—
248	#121	—	2	4	no	—
249	#121	—	2	4	no	—
250	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
251	C₂×C₂²⋊C₄	—	2	2	no	—
252	C₂×C₂²⋊C₄	—	2	8	no	—
253	C₂×C₂²⋊C₄	D₄×C₇₉	1	2	yes	—
254	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
255	#107	—	2	2	no	—
256	#103	—	2	8	no	—
257	#102	—	2	4	no	—
258	C₂²⋊C₈	D₄×C₇₉	1	4	yes	—
259	C₄×C₈	—	2	4	no	—
260	#95	—	2	8	no	—
261	#95	D₄×C₇₉	1	2	yes	—
262	C₂⁴	—	2	2	no	—
263	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
264	C₂×Q₈	—	2	4	no	—
265	C₂×Q₈	—	2	16	no	—
266	C₂×Q₈	—	2	4	no	—
267	C₂×Q₈	—	2	4	no	—
268	C₂×Q₈	—	2	4	no	—
269	C₂×Q₈	—	2	4	no	—
270	C₂×Q₈	—	4	8	no	—
271	C₂×Q₈	—	4	16	no	—
272	C₂×Q₈	—	4	8	no	—
273	C₂×Q₈	—	4	4	no	—
274	C₂×Q₈	C₂×D₄×C₇₉	1	8	yes	—
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	2	4	no	—
278	C₂×D₄	—	2	4	no	—
279	C₂×D₄	—	4	4	no	—
280	C₂×D₄	—	4	8	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	4	8	no	—
286	C₂²×C₄	—	4	4	no	—
287	C₂²×C₄	C₂×D₄×C₇₉	1	4	yes	—
288	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
290	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
291	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
292	Q₁₆	—	2	16	no	—
293	Q₁₆	—	2	16	no	—
294	SD₁₆	—	4	16	no	—
295	D₈	—	4	4	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	8	no	—
300	C₂×C₈	C₂×D₄×C₇₉	1	4	yes	—
301	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
302	C₂×C₈	C₂×D₄×C₇₉	1	4	yes	—
303	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₂²⋊C₄	—	2	4	no	—
307	C₂²⋊C₄	—	4	16	no	—
308	C₂²⋊C₄	—	4	4	no	—
309	C₄²	—	2	2	no	—
310	C₄²	—	2	2	no	—
311	C₂³	—	2	2	no	—
312	C₂³	—	2	2	no	—
313	C₂³	—	4	2	no	—
314	C₂³	—	4	4	no	—
315	C₂³	—	4	4	no	—
316	C₂³	—	4	4	no	—
317	C₂³	#127×C₇₉	1	2	yes	—
318	C₂³	#135×C₇₉	1	4	yes	—
319	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
320	Q₈	—	2	8	no	—
321	Q₈	—	2	8	no	—
322	Q₈	—	4	16	no	—
323	Q₈	—	4	4	no	—
324	Q₈	—	4	4	no	—
325	D₄	—	4	2	no	—
326	D₄	—	4	2	no	—
327	D₄	—	4	4	no	—
328	D₄	—	8	8	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	8	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	4	16	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	#127×C₇₉	1	2	yes	—
343	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
344	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
345	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
346	C₂×C₄	H(5,𝔽₂)×C₇₉	1	2	yes	—
347	C₈	—	2	2	no	—
348	C₈	—	2	4	no	—
349	C₈	#120×C₇₉	1	4	yes	—
350	C₂²	—	2	8	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	8	8	no	—
354	C₂²	—	8	2	no	—
355	C₂²	—	8	2	no	—
356	C₂²	—	8	2	no	—
357	C₂²	#495×C₇₉	1	4	yes	complemented
358	C₂²	C₂×#127×C₇₉	1	1	yes	characteristic
359	C₂²	D₄²×C₇₉	1	2	yes	—
360	C₂²	C₂×#135×C₇₉	1	2	yes	—
361	C₂²	#578×C₇₉	1	2	yes	—
362	C₄	—	2	2	no	—
363	C₄	—	4	4	no	—
364	C₄	—	4	8	no	—
365	C₄	—	8	2	no	—
366	C₄	C₂×#120×C₇₉	1	1	yes	characteristic
367	C₄	#535×C₇₉	1	1	yes	characteristic
368	C₄	D₄²×C₇₉	1	2	yes	—
369	C₂	—	2	4	no	—
370	C₂	—	16	2	no	—
371	C₂	C₇₉×#2433	1	1	yes	characteristic
372	C₂	C₂×#495×C₇₉	1	1	yes	characteristic
373	C₂	C₇₉×#3156	1	1	yes	characteristic
374	C₂	C₇₉×#3285	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₂×#466×C₇₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₄×C₂²⋊C₄×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×Q₁₆×C₇₉	C₂	semidirect
2. C₂×#495×C₇₉	C₂	semidirect
4. C₂×#448×C₇₉	C₂	semidirect
5. C₇₉×#2436	C₂	semidirect
6. C₇₉×#2015	C₂	semidirect
7. C₇₉×#1969	C₂	semidirect
8. C₈×C₂²⋊C₄×C₇₉	C₂	semidirect
47. C₂×Q₁₆×C₇₉	D₄	semidirect
169. C₂²×C₇₉	#495	semidirect
181. #25782	C₇₉	direct (N × H)
188. C₂³×Q₁₆	C₂×C₇₉	semidirect
189. C₂×#495	C₂×C₇₉	semidirect
191. C₂×#448	C₂×C₇₉	semidirect
192. #2436	C₂×C₇₉	semidirect
193. #2015	C₂×C₇₉	semidirect
194. #1969	C₂×C₇₉	semidirect
195. C₈×C₂²⋊C₄	C₂×C₇₉	semidirect
196. C₇₉	#25782	direct (N × H)
235. C₂×Q₁₆	D₄×C₇₉	semidirect
357. C₂²	#495×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂³×Q₁₆×C₇₉	2
C₂×#495×C₇₉	2
C₂×#466×C₇₉	2
C₂×#448×C₇₉	2
C₇₉×#2436	2
C₇₉×#2015	2
C₇₉×#1969	2
C₈×C₂²⋊C₄×C₇₉	2
#25782	79

Subgroups — C79×#25782 #34137471

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#25782 #34137471