Subgroups — #34443327

Order 20224.

612 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₆₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	#23765595	C₂	1	1	yes	maximal, characteristic, complemented
3	#23765578	C₂	1	1	yes	maximal, characteristic, complemented
4	#23765554	C₂	1	2	yes	maximal, complemented
5	#23765452	C₂	1	2	yes	maximal, complemented
6	#23765328	C₂	1	1	yes	maximal, characteristic, complemented
7	#23765311	C₂	1	1	yes	maximal, characteristic
8	#23765274	C₂	1	2	yes	maximal, complemented
9	#23765262	C₂	1	2	yes	maximal, complemented
10	#23765203	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#3168	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₆₃₂	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₃₁₆	—	2	1	no	—
14	C₂×#14579104	C₂²	1	2	yes	—
15	C₂×#14579102	C₂²	1	2	yes	—
16	C₄×D₆₃₂	—	2	1	no	—
17	C₄×D₆₃₂	—	2	1	no	—
18	C₄×D₆₃₂	C₂²	1	2	yes	—
19	C₄×D₆₃₂	C₂²	1	2	yes	—
20	C₂×#14579095	C₂²	1	1	yes	characteristic
21	C₂×#14579083	—	2	1	no	—
22	#19098390	C₂²	1	2	yes	complemented
23	#19098388	C₂²	1	2	yes	complemented
24	C₄⋊(C₇₉⋊C₁₆)	C₂²	1	2	yes	complemented
25	#19098367	C₂²	1	2	yes	complemented
26	#19098364	C₂²	1	2	yes	complemented
27	#19098363	C₂²	1	2	yes	—
28	#19098363	C₂²	1	2	yes	—
29	C₂²⋊(C₇₉⋊C₁₆)	C₂²	1	1	yes	characteristic
30	C₂²⋊(C₇₉⋊C₁₆)	C₂²	1	1	yes	characteristic
31	#19098339	C₂²	1	2	yes	complemented
32	#529×C₇₉	—	2	1	no	—
33	#499×C₇₉	C₂²	1	1	yes	characteristic, complemented
34	#495×C₇₉	C₂²	1	1	yes	characteristic, complemented
35	#488×C₇₉	—	2	1	no	—
36	#467×C₇₉	C₂²	1	1	yes	characteristic
37	#466×C₇₉	C₂²	1	1	yes	characteristic
38	#465×C₇₉	—	2	1	no	—
39	C₄×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic, complemented
40	C₄×SD₁₆×C₇₉	—	2	1	no	—
41	C₄×D₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
43	C₂²×D₃₁₆	—	2	1	no	—
44	C₂²×C₄×D₇₉	—	4	1	no	—
45	C₂×D₆₃₂	—	2	1	no	—
46	C₂×D₆₃₂	—	2	4	no	—
47	C₂×D₆₃₂	C₂³	1	2	yes	—
48	C₄×D₃₁₆	—	2	2	no	—
49	C₄×D₃₁₆	—	2	2	no	—
50	C₄×D₃₁₆	—	4	1	no	—
51	C₄×D₃₁₆	—	4	1	no	—
52	C₂×C₄⋊Dic₇₉	—	2	1	no	—
53	C₂×(C₂×D₇₉)⋊C₄	—	4	1	no	—
54	#14579104	—	2	4	no	—
55	#14579102	—	2	4	no	—
56	C₂×C₇₉⋊C₁₆	C₂³	1	2	yes	—
57	C₂×C₇₉⋊C₁₆	C₂³	1	2	yes	—
58	#14579095	—	2	1	no	—
59	#14579095	C₂³	1	2	yes	—
60	#14579083	—	2	2	no	—
61	#14579083	—	2	2	no	—
62	C₂×Q₁₆×C₇₉	C₂³	1	1	yes	characteristic
63	C₂×SD₁₆×C₇₉	—	2	1	no	—
64	C₂×D₈×C₇₉	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
66	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
67	#126×C₇₉	—	4	1	no	—
68	#125×C₇₉	—	2	1	no	—
69	#124×C₇₉	—	2	1	no	—
70	#123×C₇₉	—	4	1	no	—
71	C₂²⋊Q₈×C₇₉	—	2	1	no	—
72	#121×C₇₉	—	2	1	no	—
73	C₄×Q₈×C₇₉	—	2	1	no	—
74	C₄×D₄×C₇₉	—	2	1	no	—
75	C₄×D₄×C₇₉	—	4	1	no	—
76	#117×C₇₉	—	4	1	no	—
77	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
78	#107×C₇₉	C₂³	1	1	yes	characteristic
79	#107×C₇₉	C₂³	1	1	yes	characteristic
80	#106×C₇₉	—	2	1	no	—
81	#103×C₇₉	—	2	1	no	—
82	#103×C₇₉	—	2	1	no	—
83	#102×C₇₉	—	2	1	no	—
84	#102×C₇₉	—	2	1	no	—
85	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
86	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
87	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
89	C₂³×D₇₉	—	4	1	no	—
90	C₂×D₃₁₆	—	2	4	no	—
91	C₂×D₃₁₆	—	2	2	no	—
92	C₂×D₃₁₆	—	4	2	no	—
93	C₂×D₃₁₆	—	4	1	no	—
94	C₂²×Dic₇₉	—	4	1	no	—
95	C₂×C₄×D₇₉	—	4	2	no	—
96	C₂×C₄×D₇₉	—	4	2	no	—
97	C₂×C₄×D₇₉	—	8	4	no	—
98	D₆₃₂	—	2	4	no	—
99	D₆₃₂	—	2	2	no	—
100	D₆₃₂	#41	1	4	yes	—
101	C₄⋊Dic₇₉	—	2	2	no	—
102	C₄⋊Dic₇₉	—	4	1	no	—
103	(C₂×D₇₉)⋊C₄	—	4	2	no	—
104	(C₂×D₇₉)⋊C₄	—	4	2	no	—
105	C₇₉⋊C₁₆	—	2	2	no	—
106	C₇₉⋊C₁₆	—	2	2	no	—
107	C₂×Q₈×C₇₉	—	2	1	no	—
108	C₂×D₄×C₇₉	—	2	1	no	—
109	C₂×D₄×C₇₉	—	4	1	no	—
110	C₂²×C₄×C₇₉	—	4	1	no	—
111	C₂²×C₄×C₇₉	D₈	1	1	yes	characteristic
112	C₂²×C₄×C₇₉	D₈	1	1	yes	characteristic
113	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
114	Q₁₆×C₇₉	—	2	2	no	—
115	SD₁₆×C₇₉	—	4	2	no	—
116	D₈×C₇₉	—	2	2	no	—
117	C₂×C₈×C₇₉	—	2	2	no	—
118	C₂×C₈×C₇₉	—	4	1	no	—
119	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
123	C₄⋊C₄×C₇₉	—	2	1	no	—
124	C₄⋊C₄×C₇₉	—	2	1	no	—
125	C₄⋊C₄×C₇₉	—	4	1	no	—
126	C₄⋊C₄×C₇₉	—	4	1	no	—
127	C₄⋊C₄×C₇₉	—	4	1	no	—
128	C₄⋊C₄×C₇₉	—	4	1	no	—
129	C₂²⋊C₄×C₇₉	—	4	1	no	—
130	C₂²⋊C₄×C₇₉	—	4	1	no	—
131	C₂²⋊C₄×C₇₉	—	4	1	no	—
132	C₂²⋊C₄×C₇₉	—	4	1	no	—
133	C₂²⋊C₄×C₇₉	—	4	1	no	—
134	C₄²×C₇₉	—	4	1	no	—
135	C₄²×C₇₉	D₈	1	1	yes	characteristic
136	C₄²×C₇₉	D₈	1	1	yes	characteristic
137	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
139	C₂³×C₇₉	—	4	1	no	—
140	C₂³×C₇₉	C₂×D₈	1	1	yes	characteristic
141	C₂²×D₇₉	—	4	4	no	—
142	C₂²×D₇₉	—	4	2	no	—
143	C₂²×D₇₉	—	8	2	no	—
144	C₂²×D₇₉	—	8	2	no	—
145	Q₈×C₇₉	—	4	1	no	—
146	Q₈×C₇₉	—	4	1	no	—
147	D₄×C₇₉	—	4	1	no	—
148	D₄×C₇₉	—	4	1	no	—
149	D₄×C₇₉	—	8	2	no	—
150	C₂×C₄×C₇₉	—	2	2	no	—
151	C₂×C₄×C₇₉	—	2	1	no	—
152	C₂×C₄×C₇₉	—	2	1	no	—
153	C₂×C₄×C₇₉	—	4	1	no	—
154	C₂×C₄×C₇₉	—	4	1	no	—
155	C₂×C₄×C₇₉	—	4	1	no	—
156	C₂×C₄×C₇₉	—	4	1	no	—
157	C₂×C₄×C₇₉	—	8	2	no	—
158	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
159	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
160	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
161	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
162	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
163	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
164	C₂×Dic₇₉	—	4	2	no	—
165	C₂×Dic₇₉	—	8	2	no	—
166	D₃₁₆	—	2	4	no	—
167	D₃₁₆	—	4	4	no	—
168	D₃₁₆	—	4	2	no	—
169	C₄×D₇₉	—	8	4	no	—
170	C₄×D₇₉	—	8	4	no	—
171	C₈×C₇₉	—	2	1	no	—
172	C₈×C₇₉	—	2	1	no	—
173	C₈×C₇₉	—	2	1	no	—
174	C₈×C₇₉	C₂×#41	1	2	yes	—
175	C₂²×C₇₉	—	2	1	no	—
176	C₂²×C₇₉	—	2	1	no	—
177	C₂²×C₇₉	—	8	1	no	—
178	C₂²×C₇₉	—	8	1	no	—
179	C₂²×C₇₉	—	8	1	no	—
180	C₂²×C₇₉	#509	1	2	yes	—
181	C₂²×C₇₉	C₂²×D₈	1	1	yes	characteristic
182	C₂×D₇₉	—	4	4	no	—
183	C₂×D₇₉	—	8	8	no	—
184	C₂×D₇₉	—	8	2	no	—
185	C₂×D₇₉	—	8	2	no	—
186	C₄×C₇₉	—	2	1	no	—
187	C₄×C₇₉	—	2	1	no	—
188	C₄×C₇₉	—	2	1	no	—
189	C₄×C₇₉	—	2	1	no	—
190	C₄×C₇₉	—	2	1	no	—
191	C₄×C₇₉	—	8	1	no	—
192	C₄×C₇₉	—	8	1	no	—
193	C₄×C₇₉	—	8	1	no	—
194	C₄×C₇₉	#525	1	1	yes	characteristic
195	C₄×C₇₉	#575	1	1	yes	characteristic
196	Dic₇₉	—	8	2	no	—
197	#33674	—	79	1	no	maximal, Sylow
198	C₂×C₇₉	—	2	2	no	—
199	C₂×C₇₉	—	16	1	no	—
200	C₂×C₇₉	#3100	1	1	yes	characteristic
201	C₂×C₇₉	C₂×#509	1	1	yes	characteristic
202	C₂×C₇₉	#3414	1	1	yes	characteristic
203	D₇₉	—	8	4	no	—
204	#3168	D₇₉	1	1	yes	characteristic, complemented
205	C₂×C₄×D₈	—	79	1	no	—
206	#2235	—	79	1	no	—
207	#2232	—	79	1	no	—
208	#2228	—	79	2	no	—
209	#2210	—	79	2	no	—
210	#2187	—	79	1	no	—
211	#2184	—	79	1	no	—
212	#2177	—	79	2	no	—
213	#2175	—	79	2	no	—
214	#2163	—	79	1	no	—
215	C₇₉	#33674	1	1	yes	characteristic, complemented, Sylow
216	C₂²×D₈	—	79	1	no	—
217	#529	—	2	1	no	—
218	C₂×C₄×D₄	—	158	1	no	—
219	C₂×SD₃₂	—	79	2	no	—
220	C₂×D₁₆	—	79	2	no	—
221	#499	C₂×D₇₉	1	1	yes	characteristic, complemented
222	#495	C₂×D₇₉	1	1	yes	characteristic, complemented
223	#488	—	2	1	no	—
224	#467	C₂×D₇₉	1	1	yes	characteristic
225	#466	C₂×D₇₉	1	1	yes	characteristic
226	#465	—	2	1	no	—
227	C₄×Q₁₆	C₂×D₇₉	1	1	yes	characteristic, complemented
228	C₄×SD₁₆	—	2	1	no	—
229	C₄×D₈	—	79	2	no	—
230	C₄×D₈	—	79	2	no	—
231	C₄×D₈	—	158	1	no	—
232	C₄×D₈	—	158	1	no	—
233	C₄×D₈	C₂×D₇₉	1	1	yes	characteristic, complemented
234	C₂×#107	—	79	1	no	—
235	C₂×#102	—	158	1	no	—
236	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
237	#367	—	79	2	no	—
238	#366	—	79	2	no	—
239	C₄⋊C₁₆	—	79	2	no	—
240	#358	—	79	2	no	—
241	#357	—	79	2	no	—
242	#357	—	79	2	no	—
243	#357	—	79	2	no	—
244	C₂²⋊C₁₆	—	79	1	no	—
245	C₂²⋊C₁₆	—	79	1	no	—
246	#346	—	79	2	no	—
247	C₂²×D₄	—	158	1	no	—
248	C₂³×C₄	—	316	1	no	—
249	C₂×Q₁₆	C₂²×D₇₉	1	1	yes	characteristic
250	C₂×SD₁₆	—	2	1	no	—
251	C₂×D₈	—	79	2	no	—
252	C₂×D₈	—	158	4	no	—
253	C₂×D₈	—	158	1	no	—
254	C₂×D₈	C₂²×D₇₉	1	1	yes	characteristic
255	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
256	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
257	#126	—	4	1	no	—
258	#125	—	2	1	no	—
259	#124	—	2	1	no	—
260	#123	—	4	1	no	—
261	C₂²⋊Q₈	—	2	1	no	—
262	#121	—	2	1	no	—
263	C₄×Q₈	—	2	1	no	—
264	C₄×D₄	—	2	1	no	—
265	C₄×D₄	—	4	1	no	—
266	C₄×D₄	—	316	1	no	—
267	C₄×D₄	—	316	1	no	—
268	C₄×D₄	—	158	2	no	—
269	C₄×D₄	—	158	2	no	—
270	#117	—	4	1	no	—
271	C₂×C₄⋊C₄	—	158	1	no	—
272	C₂×C₂²⋊C₄	—	316	1	no	—
273	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
274	SD₃₂	—	158	4	no	—
275	D₁₆	—	158	4	no	—
276	C₂×C₁₆	—	79	2	no	—
277	C₂×C₁₆	—	79	2	no	—
278	#107	—	79	2	no	—
279	#107	—	158	1	no	—
280	#107	C₂²×D₇₉	1	1	yes	characteristic
281	#107	C₂²×D₇₉	1	1	yes	characteristic
282	#106	—	2	1	no	—
283	#103	—	2	1	no	—
284	#103	—	2	1	no	—
285	#102	—	2	1	no	—
286	#102	—	2	1	no	—
287	#102	—	158	2	no	—
288	#102	—	158	2	no	—
289	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
290	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
291	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
292	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
293	C₂⁴	—	316	1	no	—
294	C₂×Q₈	—	2	1	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	316	2	no	—
298	C₂×D₄	—	316	1	no	—
299	C₂×D₄	—	158	4	no	—
300	C₂×D₄	—	158	2	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	—	316	1	no	—
303	C₂²×C₄	—	316	2	no	—
304	C₂²×C₄	—	316	2	no	—
305	C₂²×C₄	—	632	4	no	—
306	C₂²×C₄	#11929609	1	1	yes	characteristic
307	C₂²×C₄	#11929609	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
309	Q₁₆	—	2	2	no	—
310	SD₁₆	—	4	2	no	—
311	D₈	—	2	2	no	—
312	D₈	—	79	4	no	—
313	D₈	—	158	4	no	—
314	D₈	—	158	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	4	1	no	—
317	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
318	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
319	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
320	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	316	1	no	—
328	C₄⋊C₄	—	158	2	no	—
329	C₂²⋊C₄	—	4	1	no	—
330	C₂²⋊C₄	—	4	1	no	—
331	C₂²⋊C₄	—	4	1	no	—
332	C₂²⋊C₄	—	4	1	no	—
333	C₂²⋊C₄	—	4	1	no	—
334	C₂²⋊C₄	—	316	2	no	—
335	C₂²⋊C₄	—	316	2	no	—
336	C₄²	—	4	1	no	—
337	C₄²	#11929609	1	1	yes	characteristic
338	C₄²	#11929609	1	1	yes	characteristic
339	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
340	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
341	C₁₆	—	158	2	no	—
342	C₁₆	—	158	2	no	—
343	C₂³	—	4	1	no	—
344	C₂³	—	316	4	no	—
345	C₂³	—	316	2	no	—
346	C₂³	—	632	2	no	—
347	C₂³	—	632	2	no	—
348	C₂³	C₂×#11929609	1	1	yes	characteristic
349	Q₈	—	4	1	no	—
350	Q₈	—	4	1	no	—
351	D₄	—	4	1	no	—
352	D₄	—	4	1	no	—
353	D₄	—	8	2	no	—
354	D₄	—	316	4	no	—
355	D₄	—	316	2	no	—
356	D₄	—	158	4	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	8	2	no	—
365	C₂×C₄	—	316	2	no	—
366	C₂×C₄	—	632	4	no	—
367	C₂×C₄	—	632	4	no	—
368	C₂×C₄	—	632	2	no	—
369	C₂×C₄	C₂×#11929609	1	1	yes	characteristic
370	C₂×C₄	C₂×#11929609	1	1	yes	characteristic
371	C₂×C₄	C₂×#11929609	1	1	yes	characteristic
372	C₂×C₄	C₂×#11929609	1	1	yes	characteristic
373	C₂×C₄	C₂×#11929609	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	2	1	no	—
378	C₈	#41×D₇₉	1	2	yes	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	8	1	no	—
382	C₂²	—	8	1	no	—
383	C₂²	—	8	1	no	—
384	C₂²	—	316	4	no	—
385	C₂²	—	632	8	no	—
386	C₂²	—	632	2	no	—
387	C₂²	—	632	2	no	—
388	C₂²	#19098998	1	2	yes	—
389	C₂²	C₂²×#11929609	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	8	1	no	—
396	C₄	—	8	1	no	—
397	C₄	—	8	1	no	—
398	C₄	—	632	2	no	—
399	C₄	#19099070	1	1	yes	characteristic
400	C₄	#19099361	1	1	yes	characteristic
401	C₂	—	2	2	no	—
402	C₂	—	16	1	no	—
403	C₂	—	632	4	no	—
404	C₂	#23773396	1	1	yes	characteristic
405	C₂	C₂×#19098998	1	1	yes	characteristic
406	C₂	#23776534	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#11929609
commutator, cosocle	C₂×C₈×C₇₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₇₉
Fitting	C₇₉×#3168	C₂
socle	C₂²×C₇₉	C₂²×D₈
prime radical	#23765311	C₂
hypercenter	#3168	D₇₉
hypocenter	C₇₉	#33674
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #3168

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×D₆₃₂	C₂	semidirect
2. #23765595	C₂	semidirect
3. #23765578	C₂	semidirect
4. #23765554	C₂	semidirect
5. #23765452	C₂	semidirect
6. #23765328	C₂	semidirect
8. #23765274	C₂	semidirect
9. #23765262	C₂	semidirect
10. #23765203	C₂	semidirect
11. C₇₉×#3168	C₂	semidirect
22. #19098390	C₂²	semidirect
23. #19098388	C₂²	semidirect
24. C₄⋊(C₇₉⋊C₁₆)	C₂²	semidirect
25. #19098367	C₂²	semidirect
26. #19098364	C₂²	semidirect
31. #19098339	C₂²	semidirect
33. #499×C₇₉	C₂²	semidirect
34. #495×C₇₉	C₂²	semidirect
39. C₄×Q₁₆×C₇₉	C₂²	semidirect
41. C₄×D₈×C₇₉	C₂²	semidirect
204. #3168	D₇₉	semidirect
215. C₇₉	#33674	semidirect
221. #499	C₂×D₇₉	semidirect
222. #495	C₂×D₇₉	semidirect
227. C₄×Q₁₆	C₂×D₇₉	semidirect
233. C₄×D₈	C₂×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₆₃₂	2
#23765595	2
#23765578	2
#23765554	2
#23765452	2
#23765328	2
#23765311	2
#23765274	2
#23765262	2
#23765203	2
C₇₉×#3168	2
#33674	79