Subgroups — #2226×D₇₉ #34442874

Order 20224.

638 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#500×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×D₈×D₇₉	C₂	1	1	yes	maximal, characteristic
3	#23765548	C₂	1	1	yes	maximal, characteristic, complemented
4	#23765547	C₂	1	1	yes	maximal, characteristic, complemented
5	#23765546	C₂	1	2	yes	maximal, complemented
6	#23765545	C₂	1	2	yes	maximal, complemented
7	#23765544	C₂	1	1	yes	maximal, characteristic, complemented
8	#367×D₇₉	C₂	1	2	yes	maximal, complemented
9	C₄⋊C₁₆×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#357×D₇₉	C₂	1	2	yes	maximal
11	C₇₉×#2226	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₈×D₇₉	C₂²	1	1	yes	characteristic
13	C₄⋊Q₈×D₇₉	—	2	1	no	—
14	C₄×D₄×D₇₉	—	2	1	no	—
15	C₂×C₁₆×D₇₉	C₂²	1	2	yes	—
16	#19098968	C₂²	1	1	yes	characteristic, complemented
17	#19098967	—	2	1	no	—
18	#19098967	C₂²	1	2	yes	complemented
19	#19098966	—	2	1	no	—
20	C₄×D₆₃₂	C₂²	1	1	yes	characteristic
21	D₈×Dic₇₉	C₂²	1	1	yes	characteristic
22	#19098645	C₂²	1	1	yes	characteristic
23	C₄×#11929609	—	2	1	no	—
24	#19098643	—	2	1	no	—
25	#107×D₇₉	—	2	1	no	—
26	#107×D₇₉	C₂²	1	2	yes	—
27	#107×D₇₉	C₂²	1	1	yes	characteristic
28	#102×D₇₉	—	2	1	no	—
29	C₄×C₈×D₇₉	C₂²	1	1	yes	characteristic
30	#19098391	C₂²	1	2	yes	complemented
31	#19098390	C₂²	1	2	yes	complemented
32	#19098390	C₂²	1	2	yes	complemented
33	C₄⋊(C₇₉⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
34	Dic₇₉⋊C₁₆	C₂²	1	2	yes	complemented
35	#19098365	C₂²	1	2	yes	—
36	#19098364	C₂²	1	2	yes	—
37	#19098363	C₂²	1	2	yes	—
38	#500×C₇₉	C₂²	1	1	yes	characteristic, complemented
39	C₄×D₈×C₇₉	C₂²	1	1	yes	characteristic
40	#367×C₇₉	C₂²	1	2	yes	complemented
41	C₄⋊C₁₆×C₇₉	C₂²	1	1	yes	characteristic, complemented
42	#357×C₇₉	C₂²	1	2	yes	—
43	C₂×Q₈×D₇₉	—	4	1	no	—
44	C₂×D₄×D₇₉	—	2	1	no	—
45	C₂²×C₄×D₇₉	—	4	1	no	—
46	C₂×D₆₃₂	C₂³	1	1	yes	characteristic
47	C₂×#11929609	—	2	1	no	—
48	D₈×D₇₉	—	2	2	no	—
49	D₈×D₇₉	Q₈	1	4	yes	complemented
50	C₂×C₈×D₇₉	D₄	1	1	yes	characteristic
51	C₂×C₈×D₇₉	C₂³	1	1	yes	characteristic
52	#14579161	—	2	1	no	—
53	#14579160	—	2	2	no	—
54	#14579160	—	4	1	no	—
55	#14579159	—	4	1	no	—
56	C₄×D₃₁₆	—	2	1	no	—
57	D₄×Dic₇₉	—	2	1	no	—
58	#14579123	—	2	1	no	—
59	C₄×C₂²⋊D₇₉	—	4	1	no	—
60	(C₂²⋊D₇₉)⋊C₄	—	4	1	no	—
61	C₄⋊C₄×D₇₉	—	2	1	no	—
62	C₄⋊C₄×D₇₉	—	2	2	no	—
63	C₄⋊C₄×D₇₉	—	4	1	no	—
64	C₂²⋊C₄×D₇₉	—	4	1	no	—
65	C₄²×D₇₉	D₄	1	1	yes	characteristic
66	C₂×C₇₉⋊C₁₆	C₂³	1	2	yes	—
67	C₁₆×D₇₉	—	2	4	no	—
68	#14579095	—	2	1	no	—
69	#14579095	C₂³	1	1	yes	characteristic
70	#14579095	C₂³	1	2	yes	—
71	#14579094	—	2	1	no	—
72	#14579094	—	2	2	no	—
73	#14579094	—	2	2	no	—
74	#14579083	—	2	1	no	—
75	#14579082	—	2	1	no	—
76	#14579081	—	2	1	no	—
77	C₄×C₇₉⋊C₈	D₄	1	1	yes	characteristic
78	C₈×Dic₇₉	D₄	1	1	yes	characteristic
79	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
80	C₂×D₈×C₇₉	C₂³	1	1	yes	characteristic
81	C₄⋊Q₈×C₇₉	—	2	1	no	—
82	C₄×D₄×C₇₉	—	2	1	no	—
83	C₂×C₁₆×C₇₉	C₂³	1	2	yes	—
84	#107×C₇₉	—	2	1	no	—
85	#107×C₇₉	C₂³	1	1	yes	characteristic
86	#107×C₇₉	C₂³	1	2	yes	—
87	#102×C₇₉	—	2	1	no	—
88	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
89	C₂³×D₇₉	—	4	1	no	—
90	C₂×Dic₁₅₈	—	4	2	no	—
91	C₂×Dic₁₅₈	—	4	1	no	—
92	Q₈×D₇₉	—	8	4	no	—
93	C₂×D₃₁₆	—	2	1	no	—
94	C₂×C₂²⋊D₇₉	—	4	1	no	—
95	D₄×D₇₉	—	2	4	no	—
96	D₄×D₇₉	—	4	2	no	—
97	C₂²×Dic₇₉	—	4	1	no	—
98	C₂×C₄×D₇₉	—	4	1	no	—
99	C₂×C₄×D₇₉	—	4	2	no	—
100	C₂×C₄×D₇₉	—	4	1	no	—
101	C₂×C₄×D₇₉	—	4	1	no	—
102	C₂×C₄×D₇₉	—	8	4	no	—
103	C₂×C₄×D₇₉	D₈	1	1	yes	characteristic
104	C₂×C₄×D₇₉	D₈	1	1	yes	characteristic
105	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
106	D₆₃₂	—	2	1	no	—
107	D₆₃₂	C₂×Q₈	1	2	yes	complemented
108	#11929609	—	2	4	no	—
109	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
110	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
111	C₈×D₇₉	—	2	2	no	—
112	C₈×D₇₉	C₂×Q₈	1	2	yes	—
113	C₈×D₇₉	#41	1	2	yes	—
114	C₄⋊Dic₇₉	—	2	1	no	—
115	C₄⋊Dic₇₉	—	2	2	no	—
116	C₄⋊Dic₇₉	—	4	1	no	—
117	Dic₇₉⋊C₄	—	4	1	no	—
118	Dic₇₉⋊C₄	—	4	2	no	—
119	Dic₇₉⋊C₄	—	4	2	no	—
120	C₂²⋊Dic₇₉	—	4	1	no	—
121	(C₂×D₇₉)⋊C₄	—	4	1	no	—
122	(C₂×D₇₉)⋊C₄	—	4	1	no	—
123	C₄×Dic₇₉	D₈	1	1	yes	characteristic
124	C₄×Dic₇₉	D₈	1	1	yes	characteristic
125	C₄×Dic₇₉	C₂×D₄	1	1	yes	characteristic
126	C₇₉⋊C₁₆	—	2	2	no	—
127	C₂×Q₈×C₇₉	—	4	1	no	—
128	C₂×D₄×C₇₉	—	2	1	no	—
129	C₂²×C₄×C₇₉	—	4	1	no	—
130	D₈×C₇₉	—	2	1	no	—
131	D₈×C₇₉	C₂×Q₈	1	2	yes	complemented
132	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
134	C₄⋊C₄×C₇₉	—	2	1	no	—
135	C₄⋊C₄×C₇₉	—	2	2	no	—
136	C₄⋊C₄×C₇₉	—	4	1	no	—
137	C₂²⋊C₄×C₇₉	—	4	1	no	—
138	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
139	C₁₆×C₇₉	—	2	2	no	—
140	C₂³×C₇₉	—	4	1	no	—
141	C₂²×D₇₉	—	4	1	no	—
142	C₂²×D₇₉	—	4	4	no	—
143	C₂²×D₇₉	—	8	2	no	—
144	C₂²×D₇₉	—	8	2	no	—
145	C₂²×D₇₉	C₂×D₈	1	1	yes	characteristic
146	Q₈×C₇₉	—	8	2	no	—
147	D₄×C₇₉	—	2	2	no	—
148	D₄×C₇₉	—	4	1	no	—
149	C₂×C₄×C₇₉	—	4	1	no	—
150	C₂×C₄×C₇₉	—	4	2	no	—
151	C₂×C₄×C₇₉	—	8	2	no	—
152	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
153	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
154	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
155	C₂²⋊D₇₉	—	4	4	no	—
156	C₂×Dic₇₉	—	4	1	no	—
157	C₂×Dic₇₉	—	4	2	no	—
158	C₂×Dic₇₉	—	8	2	no	—
159	C₂×Dic₇₉	C₂×D₈	1	1	yes	characteristic
160	C₂×Dic₇₉	C₂×D₈	1	1	yes	characteristic
161	C₂×Dic₇₉	C₂×D₈	1	1	yes	characteristic
162	D₃₁₆	—	2	2	no	—
163	D₃₁₆	—	4	1	no	—
164	C₄×D₇₉	—	2	2	no	—
165	C₄×D₇₉	—	8	2	no	—
166	C₄×D₇₉	—	8	4	no	—
167	C₄×D₇₉	—	8	2	no	—
168	C₄×D₇₉	—	8	2	no	—
169	C₄×D₇₉	SD₃₂	1	4	yes	—
170	C₄×D₇₉	C₂²⋊Q₈	1	2	yes	—
171	C₄×D₇₉	#137	1	2	yes	—
172	Dic₁₅₈	—	8	4	no	—
173	Dic₁₅₈	—	8	2	no	—
174	C₈×C₇₉	—	2	1	no	—
175	C₈×C₇₉	C₂²×Q₈	1	1	yes	characteristic
176	C₈×C₇₉	C₂×#41	1	1	yes	characteristic
177	C₇₉⋊C₈	—	2	1	no	—
178	C₇₉⋊C₈	C₂²⋊Q₈	1	2	yes	—
179	C₂²×C₇₉	—	4	2	no	—
180	C₂²×C₇₉	—	8	1	no	—
181	C₂²×C₇₉	—	8	1	no	—
182	C₂²×C₇₉	C₂²×D₈	1	1	yes	characteristic
183	C₂×D₇₉	—	4	2	no	—
184	C₂×D₇₉	—	8	1	no	—
185	C₂×D₇₉	—	8	1	no	—
186	C₂×D₇₉	—	8	8	no	—
187	C₂×D₇₉	#474	1	2	yes	—
188	C₂×D₇₉	C₂×SD₃₂	1	2	yes	—
189	C₂×D₇₉	#509	1	2	yes	—
190	C₄×C₇₉	—	2	1	no	—
191	C₄×C₇₉	—	8	1	no	—
192	C₄×C₇₉	—	8	2	no	—
193	C₄×C₇₉	C₂×SD₃₂	1	2	yes	—
194	C₄×C₇₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
195	C₄×C₇₉	C₂×#137	1	1	yes	characteristic
196	Dic₇₉	—	2	1	no	—
197	Dic₇₉	—	8	1	no	—
198	Dic₇₉	—	8	2	no	—
199	Dic₇₉	#474	1	2	yes	—
200	Dic₇₉	C₂×SD₃₂	1	2	yes	—
201	C₂×#2226	—	79	1	no	maximal, Sylow
202	C₂×C₇₉	—	8	2	no	—
203	C₂×C₇₉	C₂×#474	1	1	yes	characteristic
204	C₂×C₇₉	C₂²×SD₃₂	1	1	yes	characteristic
205	C₂×C₇₉	C₂×#509	1	1	yes	characteristic
206	D₇₉	—	8	2	no	—
207	D₇₉	#2226	1	4	yes	direct product factor
208	C₂×#500	—	79	1	no	—
209	C₂×C₄×D₈	—	79	1	no	—
210	#2226	—	79	1	no	—
211	#2226	—	79	1	no	—
212	#2226	—	79	2	no	—
213	#2226	—	79	1	no	—
214	#2226	—	79	2	no	—
215	#2226	D₇₉	1	1	yes	characteristic, direct product factor
216	C₂×#367	—	79	2	no	—
217	C₂×C₄⋊C₁₆	—	79	1	no	—
218	C₂×#357	—	79	2	no	—
219	C₇₉	C₂×#2226	1	1	yes	characteristic, complemented, Sylow
220	C₂²×D₈	—	79	1	no	—
221	C₂×C₄⋊Q₈	—	158	1	no	—
222	C₂×C₄×D₄	—	158	1	no	—
223	C₂²×C₁₆	—	79	2	no	—
224	#500	—	79	2	no	—
225	#500	—	79	1	no	—
226	#500	—	158	1	no	—
227	#500	—	158	1	no	—
228	#500	C₂×D₇₉	1	1	yes	characteristic, complemented
229	C₄×D₈	—	79	1	no	—
230	C₄×D₈	—	79	1	no	—
231	C₄×D₈	—	79	1	no	—
232	C₄×D₈	—	158	1	no	—
233	C₄×D₈	—	158	1	no	—
234	C₄×D₈	C₂×D₇₉	1	1	yes	characteristic
235	C₂×#107	—	79	2	no	—
236	C₂×#107	—	79	1	no	—
237	C₂×#107	—	158	1	no	—
238	C₂×#102	—	158	1	no	—
239	C₂×C₄×C₈	—	79	1	no	—
240	#367	—	79	2	no	—
241	#367	—	79	2	no	—
242	#367	—	79	2	no	—
243	#367	C₂×D₇₉	1	2	yes	complemented
244	C₄⋊C₁₆	—	79	2	no	—
245	C₄⋊C₁₆	—	79	1	no	—
246	C₄⋊C₁₆	C₂×D₇₉	1	1	yes	characteristic, complemented
247	#357	—	79	2	no	—
248	#357	—	79	2	no	—
249	#357	—	79	2	no	—
250	#357	C₂×D₇₉	1	2	yes	—
251	C₂²×Q₈	—	316	1	no	—
252	C₂²×D₄	—	158	1	no	—
253	C₂³×C₄	—	316	1	no	—
254	C₂×D₈	—	79	4	no	—
255	C₂×D₈	—	79	1	no	—
256	C₂×D₈	—	158	2	no	—
257	C₂×D₈	—	158	1	no	—
258	C₂×D₈	C₂²×D₇₉	1	1	yes	characteristic
259	C₂²×C₈	—	79	1	no	—
260	C₂²×C₈	—	79	1	no	—
261	C₄⋊Q₈	—	2	1	no	—
262	C₄⋊Q₈	—	316	1	no	—
263	C₄⋊Q₈	—	316	1	no	—
264	C₄⋊Q₈	—	158	2	no	—
265	C₄⋊Q₈	—	158	1	no	—
266	C₄×D₄	—	2	1	no	—
267	C₄×D₄	—	316	1	no	—
268	C₄×D₄	—	316	1	no	—
269	C₄×D₄	—	158	1	no	—
270	C₄×D₄	—	158	1	no	—
271	C₄×D₄	—	158	1	no	—
272	C₂×C₄⋊C₄	—	316	1	no	—
273	C₂×C₄⋊C₄	—	158	1	no	—
274	C₂×C₄⋊C₄	—	158	2	no	—
275	C₂×C₂²⋊C₄	—	316	1	no	—
276	C₂×C₄²	—	79	1	no	—
277	C₂×C₁₆	—	79	2	no	—
278	C₂×C₁₆	—	158	4	no	—
279	C₂×C₁₆	C₂²×D₇₉	1	2	yes	—
280	#107	—	2	1	no	—
281	#107	—	79	2	no	—
282	#107	—	79	1	no	—
283	#107	—	158	1	no	—
284	#107	—	158	2	no	—
285	#107	—	158	2	no	—
286	#107	—	158	1	no	—
287	#107	C₂²×D₇₉	1	2	yes	—
288	#107	C₂²×D₇₉	1	1	yes	characteristic
289	#102	—	2	1	no	—
290	#102	—	158	1	no	—
291	#102	—	158	1	no	—
292	#102	—	158	1	no	—
293	C₄×C₈	—	79	1	no	—
294	C₄×C₈	—	79	1	no	—
295	C₄×C₈	—	79	1	no	—
296	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
297	C₂⁴	—	316	1	no	—
298	C₂×Q₈	—	4	1	no	—
299	C₂×Q₈	—	316	2	no	—
300	C₂×Q₈	—	316	1	no	—
301	C₂×Q₈	—	632	4	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	316	2	no	—
304	C₂×D₄	—	316	1	no	—
305	C₂×D₄	—	158	4	no	—
306	C₂×D₄	—	158	1	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	—	316	1	no	—
309	C₂²×C₄	—	316	2	no	—
310	C₂²×C₄	—	316	1	no	—
311	C₂²×C₄	—	316	1	no	—
312	C₂²×C₄	—	316	1	no	—
313	C₂²×C₄	—	79	1	no	—
314	C₂²×C₄	—	79	1	no	—
315	C₂²×C₄	—	79	1	no	—
316	C₂²×C₄	—	632	4	no	—
317	D₈	—	2	1	no	—
318	D₈	—	79	2	no	—
319	D₈	—	158	4	no	—
320	D₈	—	158	1	no	—
321	D₈	Q₈×D₇₉	1	2	yes	complemented
322	C₂×C₈	—	79	1	no	—
323	C₂×C₈	—	79	2	no	—
324	C₂×C₈	—	79	2	no	—
325	C₂×C₈	—	79	1	no	—
326	C₂×C₈	—	158	2	no	—
327	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
328	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	4	1	no	—
332	C₄⋊C₄	—	316	2	no	—
333	C₄⋊C₄	—	316	1	no	—
334	C₄⋊C₄	—	316	2	no	—
335	C₄⋊C₄	—	316	1	no	—
336	C₄⋊C₄	—	158	1	no	—
337	C₄⋊C₄	—	158	2	no	—
338	C₂²⋊C₄	—	4	1	no	—
339	C₂²⋊C₄	—	316	1	no	—
340	C₂²⋊C₄	—	316	1	no	—
341	C₂²⋊C₄	—	316	1	no	—
342	C₄²	—	79	1	no	—
343	C₄²	—	79	1	no	—
344	C₄²	—	79	1	no	—
345	C₄²	D₄×D₇₉	1	1	yes	characteristic
346	C₁₆	—	2	2	no	—
347	C₁₆	—	158	2	no	—
348	C₂³	—	4	1	no	—
349	C₂³	—	316	4	no	—
350	C₂³	—	316	1	no	—
351	C₂³	—	79	1	no	—
352	C₂³	—	632	2	no	—
353	C₂³	—	632	2	no	—
354	Q₈	—	8	2	no	—
355	Q₈	—	632	2	no	—
356	Q₈	—	632	4	no	—
357	D₄	—	2	2	no	—
358	D₄	—	4	1	no	—
359	D₄	—	316	4	no	—
360	D₄	—	316	1	no	—
361	D₄	—	158	2	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	8	2	no	—
365	C₂×C₄	—	316	1	no	—
366	C₂×C₄	—	316	2	no	—
367	C₂×C₄	—	79	1	no	—
368	C₂×C₄	—	79	1	no	—
369	C₂×C₄	—	79	4	no	—
370	C₂×C₄	—	79	2	no	—
371	C₂×C₄	—	79	2	no	—
372	C₂×C₄	—	79	1	no	—
373	C₂×C₄	—	632	2	no	—
374	C₂×C₄	—	632	2	no	—
375	C₂×C₄	—	632	4	no	—
376	C₂×C₄	—	632	2	no	—
377	C₂×C₄	—	632	2	no	—
378	C₂×C₄	—	158	2	no	—
379	C₂×C₄	D₈×D₇₉	1	1	yes	characteristic
380	C₂×C₄	D₈×D₇₉	1	1	yes	characteristic
381	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
382	C₈	—	2	1	no	—
383	C₈	—	79	2	no	—
384	C₈	—	158	1	no	—
385	C₈	C₂×Q₈×D₇₉	1	1	yes	characteristic
386	C₈	#41×D₇₉	1	1	yes	characteristic
387	C₂²	—	4	2	no	—
388	C₂²	—	8	1	no	—
389	C₂²	—	8	1	no	—
390	C₂²	—	316	2	no	—
391	C₂²	—	79	2	no	—
392	C₂²	—	79	2	no	—
393	C₂²	—	79	2	no	—
394	C₂²	—	632	8	no	—
395	C₂²	—	632	1	no	—
396	C₂²	—	632	1	no	—
397	C₂²	C₂×D₈×D₇₉	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	8	2	no	—
400	C₄	—	8	1	no	—
401	C₄	—	79	2	no	—
402	C₄	—	79	2	no	—
403	C₄	—	632	2	no	—
404	C₄	—	632	1	no	—
405	C₄	—	158	1	no	—
406	C₄	SD₃₂×D₇₉	1	2	yes	—
407	C₄	C₂²⋊Q₈×D₇₉	1	1	yes	characteristic
408	C₄	#137×D₇₉	1	1	yes	characteristic
409	C₂	—	8	2	no	—
410	C₂	—	79	4	no	—
411	C₂	—	632	2	no	—
412	C₂	#474×D₇₉	1	1	yes	characteristic
413	C₂	C₂×SD₃₂×D₇₉	1	1	yes	characteristic
414	C₂	#509×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×#2226	C₂
socle	C₂²×C₇₉	C₂²×D₈
prime radical	C₂×D₈×D₇₉	C₂²
hypercenter	#2226	D₇₉
hypocenter	C₇₉	C₂×#2226
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2226

Complements

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

N	H ≅ G/N	type
1. #500×D₇₉	C₂	semidirect
3. #23765548	C₂	semidirect
4. #23765547	C₂	semidirect
5. #23765546	C₂	semidirect
6. #23765545	C₂	semidirect
7. #23765544	C₂	semidirect
8. #367×D₇₉	C₂	semidirect
9. C₄⋊C₁₆×D₇₉	C₂	semidirect
11. C₇₉×#2226	C₂	semidirect
16. #19098968	C₂²	semidirect
18. #19098967	C₂²	semidirect
30. #19098391	C₂²	semidirect
31. #19098390	C₂²	semidirect
32. #19098390	C₂²	semidirect
33. C₄⋊(C₇₉⋊C₁₆)	C₂²	semidirect
34. Dic₇₉⋊C₁₆	C₂²	semidirect
38. #500×C₇₉	C₂²	semidirect
40. #367×C₇₉	C₂²	semidirect
41. C₄⋊C₁₆×C₇₉	C₂²	semidirect
49. D₈×D₇₉	Q₈	semidirect
107. D₆₃₂	C₂×Q₈	semidirect
131. D₈×C₇₉	C₂×Q₈	semidirect
207. D₇₉	#2226	direct (N × H)
215. #2226	D₇₉	direct (N × H)
219. C₇₉	C₂×#2226	semidirect
228. #500	C₂×D₇₉	semidirect
243. #367	C₂×D₇₉	semidirect
246. C₄⋊C₁₆	C₂×D₇₉	semidirect
321. D₈	Q₈×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
#500×D₇₉	2
C₄×D₈×D₇₉	2
#23765548	2
#23765547	2
#23765546	2
#23765545	2
#23765544	2
#367×D₇₉	2
C₄⋊C₁₆×D₇₉	2
#357×D₇₉	2
C₇₉×#2226	2
C₂×#2226	79

Subgroups — #2226×D79 #34442874

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2226×D₇₉ #34442874