Subgroups — #2216×D₇₉ #34442689

Order 20224.

702 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₃₂×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₆×D₇₉	C₂	1	1	yes	maximal, characteristic
3	#467×D₇₉	C₂	1	2	yes	maximal
4	#23765492	C₂	1	1	yes	maximal, characteristic, complemented
5	#23765491	C₂	1	1	yes	maximal, characteristic, complemented
6	#23765490	C₂	1	2	yes	maximal, complemented
7	#23765489	C₂	1	2	yes	maximal, complemented
8	#23765488	C₂	1	1	yes	maximal, characteristic, complemented
9	#366×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#358×D₇₉	C₂	1	2	yes	maximal, complemented
11	C₇₉×#2216	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×D₇₉	C₂²	1	2	yes	—
13	C₂²×C₈×D₇₉	C₂²	1	1	yes	characteristic
14	C₂²⋊Q₈×D₇₉	—	2	2	no	—
15	C₂×Dic₆₃₂	C₂²	1	1	yes	characteristic, complemented
16	C₂×#14579107	C₂²	1	2	yes	complemented
17	Q₃₂×D₇₉	—	2	4	no	—
18	C₂²×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₁₆×D₇₉	—	2	4	no	—
20	C₂×C₁₆×D₇₉	C₂²	1	1	yes	characteristic
21	C₂×C₁₆×D₇₉	C₂²	1	1	yes	characteristic
22	C₂×C₁₆×D₇₉	C₂²	1	1	yes	characteristic
23	C₂×C₁₆×D₇₉	C₂²	1	1	yes	characteristic
24	#19098805	C₂²	1	2	yes	—
25	#19098804	C₂²	1	2	yes	—
26	#19098803	—	2	2	no	—
27	#19098802	—	2	2	no	—
28	#19098801	C₂²	1	2	yes	—
29	#107×D₇₉	C₂²	1	2	yes	—
30	#103×D₇₉	—	2	2	no	—
31	#19098389	C₂²	1	1	yes	characteristic, complemented
32	#19098388	C₂²	1	2	yes	complemented
33	#19098368	C₂²	1	2	yes	complemented
34	#19098367	C₂²	1	2	yes	complemented
35	#19098366	C₂²	1	2	yes	complemented
36	C₂×Q₃₂×C₇₉	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
38	#467×C₇₉	C₂²	1	2	yes	—
39	#366×C₇₉	C₂²	1	1	yes	characteristic, complemented
40	#358×C₇₉	C₂²	1	2	yes	complemented
41	C₂×Q₈×D₇₉	—	2	2	no	—
42	C₂²×C₄×D₇₉	D₄	1	1	yes	characteristic
43	C₂×Dic₃₁₆	C₂³	1	2	yes	—
44	C₂×#11929614	—	2	2	no	—
45	Q₁₆×D₇₉	—	2	4	no	—
46	Q₁₆×D₇₉	—	2	4	no	—
47	C₂²×C₇₉⋊C₈	D₄	1	1	yes	characteristic
48	C₂×C₈×D₇₉	—	2	2	no	—
49	C₂×C₈×D₇₉	—	2	2	no	—
50	C₂×C₈×D₇₉	D₄	1	1	yes	characteristic
51	C₂×C₈×D₇₉	D₄	1	1	yes	characteristic
52	C₂×C₈×D₇₉	C₂³	1	1	yes	characteristic
53	C₂×C₈×D₇₉	C₂³	1	1	yes	characteristic
54	#14579141	—	2	2	no	—
55	#14579140	—	2	2	no	—
56	#14579139	—	4	2	no	—
57	#14579138	—	4	2	no	—
58	#14579137	—	2	2	no	—
59	C₄⋊C₄×D₇₉	—	2	2	no	—
60	C₄⋊C₄×D₇₉	—	4	2	no	—
61	C₂²⋊C₄×D₇₉	—	4	2	no	—
62	Dic₆₃₂	—	2	2	no	—
63	#14579107	—	2	4	no	—
64	C₂×C₇₉⋊C₁₆	—	2	2	no	—
65	C₂×C₇₉⋊C₁₆	C₂³	1	1	yes	characteristic
66	C₂×C₇₉⋊C₁₆	C₂³	1	1	yes	characteristic
67	C₁₆×D₇₉	—	2	2	no	—
68	C₁₆×D₇₉	—	2	2	no	—
69	C₁₆×D₇₉	—	2	2	no	—
70	C₁₆×D₇₉	D₄	1	4	yes	—
71	#14579095	C₂³	1	2	yes	—
72	#14579094	—	2	2	no	—
73	#14579086	—	2	2	no	—
74	#14579085	—	2	2	no	—
75	#14579084	—	2	2	no	—
76	C₂×Q₁₆×C₇₉	C₂³	1	2	yes	—
77	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
78	C₂²⋊Q₈×C₇₉	—	2	2	no	—
79	Q₃₂×C₇₉	—	2	2	no	—
80	C₂×C₁₆×C₇₉	—	2	2	no	—
81	C₂×C₁₆×C₇₉	C₂³	1	1	yes	characteristic
82	C₂×C₁₆×C₇₉	C₂³	1	1	yes	characteristic
83	#107×C₇₉	C₂³	1	2	yes	—
84	#103×C₇₉	—	2	2	no	—
85	C₂³×D₇₉	D₈	1	1	yes	characteristic
86	C₂×Dic₁₅₈	—	2	2	no	—
87	C₂×Dic₁₅₈	—	4	2	no	—
88	Q₈×D₇₉	—	4	4	no	—
89	Q₈×D₇₉	—	4	4	no	—
90	C₂²×Dic₇₉	D₈	1	1	yes	characteristic
91	C₂×C₄×D₇₉	—	2	2	no	—
92	C₂×C₄×D₇₉	—	2	2	no	—
93	C₂×C₄×D₇₉	—	4	2	no	—
94	C₂×C₄×D₇₉	—	4	2	no	—
95	C₂×C₄×D₇₉	D₈	1	1	yes	characteristic
96	C₂×C₄×D₇₉	D₈	1	1	yes	characteristic
97	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
98	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
99	Dic₃₁₆	—	2	2	no	—
100	Dic₃₁₆	—	2	2	no	—
101	#11929614	—	4	4	no	—
102	C₂×C₇₉⋊C₈	—	2	2	no	—
103	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
104	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
105	C₈×D₇₉	—	2	2	no	—
106	C₈×D₇₉	—	2	1	no	—
107	C₈×D₇₉	—	2	1	no	—
108	C₈×D₇₉	—	2	2	no	—
109	C₈×D₇₉	C₂×D₄	1	2	yes	—
110	C₈×D₇₉	#41	1	2	yes	—
111	C₄⋊Dic₇₉	—	2	2	no	—
112	C₄⋊Dic₇₉	—	4	2	no	—
113	Dic₇₉⋊C₄	—	4	2	no	—
114	Dic₇₉⋊C₄	—	4	2	no	—
115	Dic₇₉⋊C₄	—	4	2	no	—
116	C₂²⋊Dic₇₉	—	4	2	no	—
117	(C₂×D₇₉)⋊C₄	—	4	2	no	—
118	(C₂×D₇₉)⋊C₄	—	4	2	no	—
119	C₇₉⋊C₁₆	—	2	1	no	—
120	C₇₉⋊C₁₆	C₂×D₄	1	2	yes	—
121	C₂×Q₈×C₇₉	—	2	2	no	—
122	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
123	Q₁₆×C₇₉	—	2	2	no	—
124	Q₁₆×C₇₉	—	2	2	no	—
125	C₂×C₈×C₇₉	—	2	1	no	—
126	C₂×C₈×C₇₉	—	2	1	no	—
127	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
129	C₄⋊C₄×C₇₉	—	2	2	no	—
130	C₄⋊C₄×C₇₉	—	4	2	no	—
131	C₂²⋊C₄×C₇₉	—	4	2	no	—
132	C₁₆×C₇₉	—	2	1	no	—
133	C₁₆×C₇₉	C₂×D₄	1	2	yes	—
134	C₂³×C₇₉	C₂×D₈	1	1	yes	characteristic
135	C₂²×D₇₉	—	2	2	no	—
136	C₂²×D₇₉	—	2	2	no	—
137	C₂²×D₇₉	Q₃₂	1	4	yes	complemented
138	C₂²×D₇₉	C₂×D₈	1	1	yes	characteristic
139	C₂²×D₇₉	C₂×D₈	1	1	yes	characteristic
140	Q₈×C₇₉	—	4	2	no	—
141	Q₈×C₇₉	—	4	2	no	—
142	C₂×C₄×C₇₉	—	2	1	no	—
143	C₂×C₄×C₇₉	—	2	1	no	—
144	C₂×C₄×C₇₉	—	4	2	no	—
145	C₂×C₄×C₇₉	—	4	2	no	—
146	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
147	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
148	C₂×Dic₇₉	—	2	2	no	—
149	C₂×Dic₇₉	—	4	2	no	—
150	C₂×Dic₇₉	—	4	2	no	—
151	C₂×Dic₇₉	C₂×D₈	1	1	yes	characteristic
152	C₂×Dic₇₉	C₂×D₈	1	1	yes	characteristic
153	C₄×D₇₉	—	2	2	no	—
154	C₄×D₇₉	—	2	1	no	—
155	C₄×D₇₉	—	2	1	no	—
156	C₄×D₇₉	—	2	2	no	—
157	C₄×D₇₉	—	8	4	no	—
158	C₄×D₇₉	—	8	4	no	—
159	C₄×D₇₉	#121	1	2	yes	—
160	C₄×D₇₉	#135	1	2	yes	—
161	Dic₁₅₈	—	4	2	no	—
162	Dic₁₅₈	—	4	2	no	—
163	Dic₁₅₈	—	8	4	no	—
164	C₈×C₇₉	—	2	1	no	—
165	C₈×C₇₉	C₂²×D₄	1	1	yes	characteristic
166	C₈×C₇₉	C₂×#41	1	1	yes	characteristic
167	C₇₉⋊C₈	—	2	1	no	—
168	C₇₉⋊C₈	#121	1	2	yes	—
169	C₂²×C₇₉	—	2	1	no	—
170	C₂²×C₇₉	—	2	1	no	—
171	C₂²×C₇₉	C₂×Q₃₂	1	2	yes	complemented
172	C₂²×C₇₉	C₂²×D₈	1	1	yes	characteristic
173	C₂×D₇₉	—	2	1	no	—
174	C₂×D₇₉	—	2	1	no	—
175	C₂×D₇₉	—	2	8	no	—
176	C₂×D₇₉	#466	1	2	yes	—
177	C₂×D₇₉	C₂×Q₃₂	1	2	yes	—
178	C₂×D₇₉	C₂×Q₃₂	1	2	yes	complemented
179	C₂×D₇₉	#508	1	2	yes	—
180	C₄×C₇₉	—	2	1	no	—
181	C₄×C₇₉	—	8	2	no	—
182	C₄×C₇₉	—	8	2	no	—
183	C₄×C₇₉	C₂×#121	1	1	yes	characteristic
184	C₄×C₇₉	C₂×#135	1	1	yes	characteristic
185	Dic₇₉	—	2	1	no	—
186	Dic₇₉	—	8	2	no	—
187	Dic₇₉	—	8	2	no	—
188	Dic₇₉	#466	1	2	yes	—
189	C₂×#2216	—	79	1	no	maximal, Sylow
190	C₂×C₇₉	—	2	2	no	—
191	C₂×C₇₉	C₂×#466	1	1	yes	characteristic
192	C₂×C₇₉	C₂²×Q₃₂	1	1	yes	characteristic
193	C₂×C₇₉	C₂×#508	1	1	yes	characteristic
194	D₇₉	—	2	2	no	—
195	D₇₉	#2216	1	4	yes	direct product factor
196	C₂²×Q₃₂	—	79	1	no	—
197	C₂³×C₁₆	—	79	1	no	—
198	C₂×#467	—	79	2	no	—
199	#2216	—	79	1	no	—
200	#2216	—	79	1	no	—
201	#2216	—	79	2	no	—
202	#2216	—	79	1	no	—
203	#2216	—	79	2	no	—
204	#2216	D₇₉	1	1	yes	characteristic, direct product factor
205	C₂×#366	—	79	1	no	—
206	C₂×#358	—	79	2	no	—
207	C₇₉	C₂×#2216	1	1	yes	characteristic, complemented, Sylow
208	C₂²×Q₁₆	—	79	2	no	—
209	C₂³×C₈	—	79	1	no	—
210	C₂×C₂²⋊Q₈	—	158	2	no	—
211	C₂×Q₃₂	—	79	2	no	—
212	C₂×Q₃₂	—	79	1	no	—
213	C₂×Q₃₂	—	158	4	no	—
214	C₂×Q₃₂	C₂×D₇₉	1	1	yes	characteristic, complemented
215	C₂²×C₁₆	—	79	1	no	—
216	C₂²×C₁₆	—	79	1	no	—
217	C₂²×C₁₆	—	79	1	no	—
218	C₂²×C₁₆	—	79	1	no	—
219	C₂²×C₁₆	—	79	1	no	—
220	C₂²×C₁₆	—	158	4	no	—
221	C₂²×C₁₆	C₂×D₇₉	1	1	yes	characteristic
222	#467	—	79	2	no	—
223	#467	—	79	2	no	—
224	#467	—	79	2	no	—
225	#467	—	158	2	no	—
226	#467	—	158	2	no	—
227	#467	C₂×D₇₉	1	2	yes	—
228	C₂×#107	—	79	2	no	—
229	C₂×#103	—	158	2	no	—
230	#366	—	79	1	no	—
231	#366	—	79	2	no	—
232	#366	C₂×D₇₉	1	1	yes	characteristic, complemented
233	#358	—	79	2	no	—
234	#358	—	79	2	no	—
235	#358	—	79	2	no	—
236	#358	C₂×D₇₉	1	2	yes	complemented
237	C₂²×Q₈	—	158	2	no	—
238	C₂³×C₄	—	79	1	no	—
239	C₂×Q₁₆	—	79	2	no	—
240	C₂×Q₁₆	—	158	4	no	—
241	C₂×Q₁₆	—	158	4	no	—
242	C₂×Q₁₆	—	158	2	no	—
243	C₂×Q₁₆	C₂²×D₇₉	1	2	yes	—
244	C₂²×C₈	—	79	1	no	—
245	C₂²×C₈	—	79	1	no	—
246	C₂²×C₈	—	79	1	no	—
247	C₂²×C₈	—	79	1	no	—
248	C₂²×C₈	—	79	1	no	—
249	C₂²×C₈	—	158	2	no	—
250	C₂²×C₈	—	158	2	no	—
251	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
252	C₂²⋊Q₈	—	2	2	no	—
253	C₂²⋊Q₈	—	316	2	no	—
254	C₂²⋊Q₈	—	316	2	no	—
255	C₂²⋊Q₈	—	158	2	no	—
256	C₂²⋊Q₈	—	158	2	no	—
257	C₂²⋊Q₈	—	158	2	no	—
258	C₂×C₄⋊C₄	—	316	2	no	—
259	C₂×C₄⋊C₄	—	158	2	no	—
260	C₂×C₂²⋊C₄	—	316	2	no	—
261	Q₃₂	—	2	2	no	—
262	Q₃₂	—	158	4	no	—
263	Q₃₂	—	158	2	no	—
264	C₂×C₁₆	—	2	2	no	—
265	C₂×C₁₆	—	79	1	no	—
266	C₂×C₁₆	—	79	4	no	—
267	C₂×C₁₆	—	79	1	no	—
268	C₂×C₁₆	—	158	2	no	—
269	C₂×C₁₆	—	158	2	no	—
270	C₂×C₁₆	—	158	2	no	—
271	C₂×C₁₆	—	158	2	no	—
272	C₂×C₁₆	C₂²×D₇₉	1	1	yes	characteristic
273	C₂×C₁₆	C₂²×D₇₉	1	1	yes	characteristic
274	#107	—	79	2	no	—
275	#107	—	158	2	no	—
276	#107	C₂²×D₇₉	1	2	yes	—
277	#103	—	2	2	no	—
278	#103	—	158	2	no	—
279	#103	—	158	2	no	—
280	#103	—	158	2	no	—
281	C₂⁴	—	79	1	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	316	2	no	—
284	C₂×Q₈	—	316	4	no	—
285	C₂×Q₈	—	316	4	no	—
286	C₂×Q₈	—	158	2	no	—
287	C₂²×C₄	—	316	2	no	—
288	C₂²×C₄	—	316	2	no	—
289	C₂²×C₄	—	79	1	no	—
290	C₂²×C₄	—	79	1	no	—
291	C₂²×C₄	—	79	1	no	—
292	C₂²×C₄	—	79	1	no	—
293	C₂²×C₄	—	79	1	no	—
294	C₂²×C₄	—	158	2	no	—
295	C₂²×C₄	—	158	2	no	—
296	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
297	Q₁₆	—	2	2	no	—
298	Q₁₆	—	2	2	no	—
299	Q₁₆	—	316	4	no	—
300	Q₁₆	—	158	2	no	—
301	Q₁₆	—	158	2	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	79	1	no	—
305	C₂×C₈	—	79	2	no	—
306	C₂×C₈	—	79	2	no	—
307	C₂×C₈	—	79	1	no	—
308	C₂×C₈	—	158	2	no	—
309	C₂×C₈	—	158	2	no	—
310	C₂×C₈	—	158	2	no	—
311	C₂×C₈	—	158	1	no	—
312	C₂×C₈	—	158	1	no	—
313	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
314	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₄⋊C₄	—	316	2	no	—
318	C₄⋊C₄	—	316	2	no	—
319	C₄⋊C₄	—	316	2	no	—
320	C₄⋊C₄	—	316	2	no	—
321	C₄⋊C₄	—	158	2	no	—
322	C₂²⋊C₄	—	4	2	no	—
323	C₂²⋊C₄	—	316	2	no	—
324	C₂²⋊C₄	—	316	2	no	—
325	C₂²⋊C₄	—	316	2	no	—
326	C₁₆	—	2	1	no	—
327	C₁₆	—	79	2	no	—
328	C₁₆	—	158	1	no	—
329	C₁₆	D₄×D₇₉	1	2	yes	—
330	C₂³	—	79	1	no	—
331	C₂³	—	79	4	no	—
332	C₂³	—	79	1	no	—
333	C₂³	—	158	2	no	—
334	C₂³	—	158	2	no	—
335	C₂³	D₈×D₇₉	1	1	yes	characteristic
336	Q₈	—	4	2	no	—
337	Q₈	—	4	2	no	—
338	Q₈	—	316	2	no	—
339	Q₈	—	316	2	no	—
340	Q₈	—	632	4	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	316	2	no	—
346	C₂×C₄	—	316	2	no	—
347	C₂×C₄	—	79	1	no	—
348	C₂×C₄	—	79	2	no	—
349	C₂×C₄	—	79	2	no	—
350	C₂×C₄	—	79	1	no	—
351	C₂×C₄	—	632	4	no	—
352	C₂×C₄	—	632	4	no	—
353	C₂×C₄	—	158	2	no	—
354	C₂×C₄	—	158	2	no	—
355	C₂×C₄	—	158	2	no	—
356	C₂×C₄	—	158	1	no	—
357	C₂×C₄	—	158	1	no	—
358	C₂×C₄	D₈×D₇₉	1	1	yes	characteristic
359	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
360	C₈	—	2	1	no	—
361	C₈	—	79	2	no	—
362	C₈	—	158	1	no	—
363	C₈	C₂×D₄×D₇₉	1	1	yes	characteristic
364	C₈	#41×D₇₉	1	1	yes	characteristic
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	79	2	no	—
368	C₂²	—	79	2	no	—
369	C₂²	—	79	2	no	—
370	C₂²	—	79	2	no	—
371	C₂²	—	158	8	no	—
372	C₂²	—	158	1	no	—
373	C₂²	—	158	1	no	—
374	C₂²	Q₃₂×D₇₉	1	2	yes	complemented
375	C₂²	C₂×D₈×D₇₉	1	1	yes	characteristic
376	C₄	—	2	1	no	—
377	C₄	—	8	2	no	—
378	C₄	—	8	2	no	—
379	C₄	—	79	2	no	—
380	C₄	—	632	2	no	—
381	C₄	—	632	2	no	—
382	C₄	—	158	1	no	—
383	C₄	#121×D₇₉	1	1	yes	characteristic
384	C₄	#135×D₇₉	1	1	yes	characteristic
385	C₂	—	2	2	no	—
386	C₂	—	79	4	no	—
387	C₂	—	158	2	no	—
388	C₂	#466×D₇₉	1	1	yes	characteristic
389	C₂	C₂×Q₃₂×D₇₉	1	1	yes	characteristic
390	C₂	#508×D₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₈×D₇₉
commutator, cosocle	C₂×C₈×C₇₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₇₉
Fitting	C₇₉×#2216	C₂
socle	C₂²×C₇₉	C₂²×D₈
prime radical	C₂³×D₇₉	D₈
hypercenter	#2216	D₇₉
hypocenter	C₇₉	C₂×#2216
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2216

Complements

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

N	H ≅ G/N	type
1. C₂×Q₃₂×D₇₉	C₂	semidirect
4. #23765492	C₂	semidirect
5. #23765491	C₂	semidirect
6. #23765490	C₂	semidirect
7. #23765489	C₂	semidirect
8. #23765488	C₂	semidirect
9. #366×D₇₉	C₂	semidirect
10. #358×D₇₉	C₂	semidirect
11. C₇₉×#2216	C₂	semidirect
15. C₂×Dic₆₃₂	C₂²	semidirect
16. C₂×#14579107	C₂²	semidirect
31. #19098389	C₂²	semidirect
32. #19098388	C₂²	semidirect
33. #19098368	C₂²	semidirect
34. #19098367	C₂²	semidirect
35. #19098366	C₂²	semidirect
36. C₂×Q₃₂×C₇₉	C₂²	semidirect
39. #366×C₇₉	C₂²	semidirect
40. #358×C₇₉	C₂²	semidirect
137. C₂²×D₇₉	Q₃₂	semidirect
171. C₂²×C₇₉	C₂×Q₃₂	semidirect
178. C₂×D₇₉	C₂×Q₃₂	semidirect
195. D₇₉	#2216	direct (N × H)
204. #2216	D₇₉	direct (N × H)
207. C₇₉	C₂×#2216	semidirect
214. C₂×Q₃₂	C₂×D₇₉	semidirect
232. #366	C₂×D₇₉	semidirect
236. #358	C₂×D₇₉	semidirect
374. C₂²	Q₃₂×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₃₂×D₇₉	2
C₂²×C₁₆×D₇₉	2
#467×D₇₉	2
#23765492	2
#23765491	2
#23765490	2
#23765489	2
#23765488	2
#366×D₇₉	2
#358×D₇₉	2
C₇₉×#2216	2
C₂×#2216	79

Subgroups — #2216×D79 #34442689

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2216×D₇₉ #34442689