Subgroups — #34441728

Order 20224.

646 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23776534	C₂	1	1	yes	maximal, characteristic
2	#23772285	C₂	1	1	yes	maximal, characteristic, complemented
3	#23765298	C₂	1	4	yes	maximal, complemented
4	#23765291	C₂	1	4	yes	maximal, complemented
5	C₂×#19098387	C₂	1	1	yes	maximal, characteristic, complemented
6	#23765147	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#19098373	C₂	1	1	yes	maximal, characteristic, complemented
8	#23765005	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#2957	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#14579183	C₂²	1	1	yes	characteristic
11	#19099043	—	2	1	no	—
12	#19099004	C₄	1	2	yes	complemented
13	#19099003	C₂²	1	2	yes	—
14	#19098999	C₄	1	2	yes	complemented
15	#19098998	C₂²	1	2	yes	—
16	#19098993	C₄	1	4	yes	complemented
17	C₂×#14579101	C₂²	1	1	yes	characteristic
18	C₂×#14579101	C₂²	1	1	yes	characteristic
19	#19098676	C₂²	1	2	yes	complemented
20	#19098671	C₂²	1	2	yes	complemented
21	C₄×#11929613	—	2	2	no	—
22	C₂×#14579093	C₂²	1	1	yes	characteristic
23	#19098565	—	2	1	no	—
24	#19098387	C₂²	1	4	yes	complemented
25	#19098378	C₂²	1	2	yes	complemented
26	#19098375	C₂²	1	2	yes	complemented
27	#19098373	C₂²	1	4	yes	—
28	#19098341	C₂²	1	4	yes	complemented
29	C₂×#135×C₇₉	C₂²	1	1	yes	characteristic
30	#568×C₇₉	—	2	1	no	—
31	#444×C₇₉	C₂²	1	4	yes	—
32	#443×C₇₉	—	2	2	no	—
33	C₂×#108×C₇₉	C₂²	1	1	yes	characteristic
34	#421×C₇₉	—	2	1	no	—
35	#405×C₇₉	C₂²	1	1	yes	characteristic
36	C₂×#11929624	—	2	1	no	—
37	#14579183	—	2	1	no	—
38	#14579183	—	2	1	no	—
39	#14579183	C₂×C₄	1	2	yes	—
40	#14579183	C₂×C₄	1	2	yes	—
41	C₂×Dic₃₁₆	C₂³	1	1	yes	characteristic
42	C₂×#11929613	—	2	1	no	—
43	C₂×D₆₃₂	C₂³	1	1	yes	characteristic
44	C₄×Dic₁₅₈	—	2	2	no	—
45	C₄×D₃₁₆	—	2	2	no	—
46	(C₂²⋊D₇₉)⋊C₄	—	4	2	no	—
47	#14579119	—	4	1	no	—
48	C₂×C₄⋊Dic₇₉	—	2	1	no	—
49	C₄⋊C₄×D₇₉	—	4	1	no	—
50	#14579107	C₂×C₄	1	4	yes	complemented
51	#14579105	C₂×C₄	1	4	yes	complemented
52	#14579104	C₂×C₄	1	4	yes	complemented
53	#14579102	C₂×C₄	1	4	yes	complemented
54	#14579101	—	2	1	no	—
55	#14579101	C₂×C₄	1	2	yes	complemented
56	#14579101	C₂³	1	2	yes	—
57	#14579101	C₂³	1	2	yes	—
58	C₂×C₇₉⋊C₁₆	—	2	1	no	—
59	C₂×C₇₉⋊C₁₆	C₂×C₄	1	2	yes	complemented
60	#14579093	—	2	1	no	—
61	#14579093	C₂³	1	2	yes	—
62	#14579086	—	2	2	no	—
63	#14579083	—	2	2	no	—
64	C₂×#41×C₇₉	—	2	1	no	—
65	#135×C₇₉	—	2	1	no	—
66	#135×C₇₉	—	2	1	no	—
67	#135×C₇₉	C₂×C₄	1	2	yes	complemented
68	#135×C₇₉	C₂³	1	2	yes	—
69	C₂×Q₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic, complemented
70	C₂×SD₁₆×C₇₉	—	2	1	no	—
71	C₂×D₈×C₇₉	C₂×C₄	1	1	yes	characteristic, complemented
72	#131×C₇₉	—	2	4	no	—
73	#131×C₇₉	—	4	2	no	—
74	C₂×M₁₆×C₇₉	—	2	1	no	—
75	C₂×M₁₆×C₇₉	—	4	2	no	—
76	C₂×M₁₆×C₇₉	D₄	1	1	yes	characteristic
77	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
78	#117×C₇₉	D₄	1	1	yes	characteristic
79	#108×C₇₉	—	2	1	no	—
80	#108×C₇₉	C₂³	1	2	yes	—
81	#104×C₇₉	—	2	4	no	—
82	#97×C₇₉	C₂³	1	2	yes	—
83	C₄×C₈×C₇₉	D₄	1	2	yes	—
84	#11929624	—	2	2	no	—
85	#11929624	—	2	2	no	—
86	#11929624	—	4	1	no	—
87	#11929624	—	4	1	no	—
88	C₂×Dic₁₅₈	—	2	1	no	—
89	C₂×D₃₁₆	—	2	1	no	—
90	C₂×C₂²⋊D₇₉	—	4	1	no	—
91	C₂²×Dic₇₉	—	4	1	no	—
92	C₂×C₄×D₇₉	—	4	2	no	—
93	C₂×C₄×D₇₉	—	4	1	no	—
94	Dic₃₁₆	—	2	1	no	—
95	Dic₃₁₆	C₂²×C₄	1	2	yes	—
96	#11929613	—	2	2	no	—
97	#11929613	—	2	2	no	—
98	D₆₃₂	—	2	1	no	—
99	D₆₃₂	C₂²×C₄	1	2	yes	—
100	C₄⋊Dic₇₉	—	2	2	no	—
101	C₄⋊Dic₇₉	—	4	1	no	—
102	Dic₇₉⋊C₄	—	4	2	no	—
103	(C₂×D₇₉)⋊C₄	—	4	2	no	—
104	C₄×Dic₇₉	—	4	2	no	—
105	C₇₉⋊C₁₆	—	2	2	no	—
106	C₇₉⋊C₁₆	C₂²×C₄	1	4	yes	—
107	#41×C₇₉	—	2	2	no	—
108	#41×C₇₉	—	2	2	no	—
109	#41×C₇₉	—	4	1	no	—
110	#41×C₇₉	—	4	1	no	—
111	C₂×Q₈×C₇₉	—	2	1	no	—
112	C₂×D₄×C₇₉	—	2	1	no	—
113	C₂×D₄×C₇₉	—	4	1	no	—
114	C₂²×C₄×C₇₉	—	4	1	no	—
115	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
116	Q₁₆×C₇₉	—	2	1	no	—
117	Q₁₆×C₇₉	C₂²×C₄	1	2	yes	—
118	SD₁₆×C₇₉	—	2	2	no	—
119	SD₁₆×C₇₉	—	2	2	no	—
120	D₈×C₇₉	—	2	1	no	—
121	D₈×C₇₉	C₂²×C₄	1	2	yes	—
122	M₁₆×C₇₉	—	2	1	no	—
123	M₁₆×C₇₉	—	2	1	no	—
124	M₁₆×C₇₉	—	2	2	no	—
125	M₁₆×C₇₉	—	4	4	no	—
126	M₁₆×C₇₉	—	4	1	no	—
127	C₂×C₈×C₇₉	—	4	4	no	—
128	C₂×C₈×C₇₉	—	4	1	no	—
129	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
132	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₇₉	#41	1	1	yes	characteristic
134	C₂×C₈×C₇₉	#41	1	1	yes	characteristic
135	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
136	C₄⋊C₄×C₇₉	—	2	1	no	—
137	C₂²⋊C₄×C₇₉	—	2	1	no	—
138	C₄²×C₇₉	C₂×D₄	1	2	yes	—
139	C₂³×C₇₉	—	4	1	no	—
140	C₂³×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
141	C₂²×D₇₉	—	4	1	no	—
142	Q₈×C₇₉	—	2	2	no	—
143	Q₈×C₇₉	—	4	1	no	—
144	D₄×C₇₉	—	2	2	no	—
145	D₄×C₇₉	—	4	2	no	—
146	D₄×C₇₉	—	4	2	no	—
147	D₄×C₇₉	—	4	1	no	—
148	C₂×C₄×C₇₉	—	2	2	no	—
149	C₂×C₄×C₇₉	—	4	1	no	—
150	C₂×C₄×C₇₉	—	4	2	no	—
151	C₂×C₄×C₇₉	—	4	2	no	—
152	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
155	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
156	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
157	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
158	C₂²⋊D₇₉	—	4	2	no	—
159	C₂²⋊D₇₉	—	4	2	no	—
160	C₂×Dic₇₉	—	4	1	no	—
161	C₂×Dic₇₉	—	4	2	no	—
162	C₂×Dic₇₉	—	16	1	no	—
163	D₃₁₆	—	2	2	no	—
164	D₃₁₆	—	4	1	no	—
165	C₄×D₇₉	—	4	2	no	—
166	C₄×D₇₉	—	4	2	no	—
167	C₄×D₇₉	—	16	2	no	—
168	Dic₁₅₈	—	2	2	no	—
169	Dic₁₅₈	—	4	1	no	—
170	C₈×C₇₉	—	2	2	no	—
171	C₈×C₇₉	—	4	2	no	—
172	C₈×C₇₉	C₄×D₄	1	1	yes	characteristic
173	C₈×C₇₉	C₄×D₄	1	1	yes	characteristic
174	C₈×C₇₉	C₂³×C₄	1	1	yes	characteristic
175	C₈×C₇₉	C₂×#41	1	1	yes	characteristic
176	C₂²×C₇₉	—	4	1	no	—
177	C₂²×C₇₉	—	4	2	no	—
178	C₂²×C₇₉	—	16	1	no	—
179	C₂²×C₇₉	#442	1	1	yes	characteristic
180	C₂²×C₇₉	#442	1	1	yes	characteristic
181	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
182	C₂×D₇₉	—	4	2	no	—
183	C₂×D₇₉	—	8	1	no	—
184	C₂×D₇₉	—	8	1	no	—
185	C₄×C₇₉	—	4	2	no	—
186	C₄×C₇₉	—	4	2	no	—
187	C₄×C₇₉	#442	1	1	yes	characteristic
188	C₄×C₇₉	#442	1	1	yes	characteristic
189	C₄×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
190	C₄×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
191	Dic₇₉	—	4	2	no	—
192	Dic₇₉	—	8	2	no	—
193	#33469	—	79	1	no	maximal, Sylow
194	C₂×C₇₉	—	2	1	no	—
195	C₂×C₇₉	—	2	1	no	—
196	C₂×C₇₉	—	2	1	no	—
197	C₂×C₇₉	—	8	2	no	—
198	C₂×C₇₉	C₂×#442	1	1	yes	characteristic
199	D₇₉	—	8	2	no	—
200	#3414	—	79	1	no	—
201	#2957	D₇₉	1	1	yes	characteristic, complemented
202	#2952	—	79	1	no	—
203	AGL(1,ℤ/16)	—	79	4	no	—
204	#2180	—	79	4	no	—
205	C₂×#365	—	79	1	no	—
206	#2148	—	79	1	no	—
207	C₂×#360	—	79	1	no	—
208	#2110	—	79	1	no	—
209	C₇₉	#33469	1	1	yes	characteristic, complemented, Sylow
210	C₂×#135	—	79	1	no	—
211	C₂×#135	C₂×D₇₉	1	1	yes	characteristic
212	#568	—	2	1	no	—
213	#520	—	158	1	no	—
214	#510	—	79	2	no	—
215	#510	—	79	2	no	—
216	#509	—	79	2	no	—
217	#509	—	79	2	no	—
218	#508	—	79	4	no	—
219	C₂×M₃₂	—	79	1	no	—
220	C₂×M₃₂	—	79	1	no	—
221	#444	C₂×D₇₉	1	4	yes	—
222	#443	—	2	2	no	—
223	#442	—	79	2	no	—
224	#441	—	79	2	no	—
225	C₄×SD₁₆	—	158	2	no	—
226	C₂×#108	C₂×D₇₉	1	1	yes	characteristic
227	C₂×#106	—	79	1	no	—
228	#421	—	2	1	no	—
229	#417	—	158	1	no	—
230	#405	C₂×D₇₉	1	1	yes	characteristic
231	#365	—	79	4	no	—
232	#362	—	79	2	no	—
233	#361	—	79	2	no	—
234	#360	—	79	4	no	—
235	#347	—	79	4	no	—
236	C₂×#41	—	2	1	no	—
237	C₂×#41	—	158	1	no	—
238	#135	—	2	1	no	—
239	#135	—	2	1	no	—
240	#135	—	79	2	no	—
241	#135	—	79	2	no	—
242	#135	—	158	1	no	—
243	#135	—	158	1	no	—
244	#135	C₄×D₇₉	1	2	yes	complemented
245	#135	C₂²×D₇₉	1	2	yes	—
246	C₂×Q₁₆	—	79	1	no	—
247	C₂×Q₁₆	C₄×D₇₉	1	1	yes	characteristic, complemented
248	C₂×SD₁₆	—	2	1	no	—
249	C₂×SD₁₆	—	158	1	no	—
250	C₂×D₈	—	79	1	no	—
251	C₂×D₈	C₄×D₇₉	1	1	yes	characteristic, complemented
252	#131	—	2	4	no	—
253	#131	—	4	2	no	—
254	C₂×M₁₆	—	2	1	no	—
255	C₂×M₁₆	—	4	2	no	—
256	C₂×M₁₆	C₂²⋊D₇₉	1	1	yes	characteristic
257	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
258	C₄×Q₈	—	158	2	no	—
259	C₄×D₄	—	316	2	no	—
260	C₄×D₄	—	158	2	no	—
261	#117	—	316	1	no	—
262	#117	C₂²⋊D₇₉	1	1	yes	characteristic
263	C₂×C₄⋊C₄	—	316	1	no	—
264	C₂×C₄⋊C₄	—	158	1	no	—
265	Q₃₂	—	79	4	no	—
266	SD₃₂	—	79	4	no	—
267	SD₃₂	—	79	4	no	—
268	D₁₆	—	79	4	no	—
269	M₃₂	—	79	2	no	—
270	M₃₂	—	79	2	no	—
271	M₃₂	—	79	2	no	—
272	M₃₂	—	158	1	no	—
273	C₂×C₁₆	—	79	2	no	—
274	C₂×C₁₆	—	158	1	no	—
275	#108	—	2	1	no	—
276	#108	C₂²×D₇₉	1	2	yes	—
277	#106	—	79	2	no	—
278	#106	—	158	1	no	—
279	#104	—	2	4	no	—
280	#103	—	158	2	no	—
281	#102	—	158	2	no	—
282	#97	C₂²×D₇₉	1	2	yes	—
283	C₄×C₈	C₂²⋊D₇₉	1	2	yes	—
284	#41	—	2	2	no	—
285	#41	—	2	2	no	—
286	#41	—	4	1	no	—
287	#41	—	4	1	no	—
288	#41	—	316	1	no	—
289	#41	—	316	1	no	—
290	#41	—	158	2	no	—
291	#41	—	158	2	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	158	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	316	1	no	—
297	C₂×D₄	—	158	1	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	—	316	2	no	—
300	C₂²×C₄	—	316	1	no	—
301	C₂²×C₄	—	316	1	no	—
302	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
303	Q₁₆	—	2	1	no	—
304	Q₁₆	—	79	2	no	—
305	Q₁₆	—	158	1	no	—
306	Q₁₆	C₂×C₄×D₇₉	1	2	yes	—
307	SD₁₆	—	2	2	no	—
308	SD₁₆	—	2	2	no	—
309	SD₁₆	—	158	2	no	—
310	SD₁₆	—	158	2	no	—
311	D₈	—	2	1	no	—
312	D₈	—	79	2	no	—
313	D₈	—	158	1	no	—
314	D₈	C₂×C₄×D₇₉	1	2	yes	—
315	M₁₆	—	2	1	no	—
316	M₁₆	—	2	1	no	—
317	M₁₆	—	2	2	no	—
318	M₁₆	—	4	4	no	—
319	M₁₆	—	4	1	no	—
320	C₂×C₈	—	4	4	no	—
321	C₂×C₈	—	4	1	no	—
322	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
323	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
324	C₂×C₈	C₂×C₂²⋊D₇₉	1	2	yes	—
325	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
326	C₂×C₈	#11929624	1	1	yes	characteristic
327	C₂×C₈	#11929624	1	1	yes	characteristic
328	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	316	2	no	—
331	C₄⋊C₄	—	316	1	no	—
332	C₄⋊C₄	—	158	2	no	—
333	C₂²⋊C₄	—	2	1	no	—
334	C₂²⋊C₄	—	316	2	no	—
335	C₄²	—	316	2	no	—
336	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
337	C₁₆	—	79	4	no	—
338	C₁₆	—	158	2	no	—
339	C₂³	—	4	1	no	—
340	C₂³	—	316	1	no	—
341	C₂³	#14579186	1	1	yes	characteristic
342	Q₈	—	2	2	no	—
343	Q₈	—	4	1	no	—
344	Q₈	—	316	1	no	—
345	Q₈	—	158	2	no	—
346	D₄	—	2	2	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	1	no	—
350	D₄	—	316	2	no	—
351	D₄	—	316	2	no	—
352	D₄	—	316	1	no	—
353	D₄	—	158	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	316	1	no	—
359	C₂×C₄	—	316	2	no	—
360	C₂×C₄	—	316	2	no	—
361	C₂×C₄	—	316	2	no	—
362	C₂×C₄	—	1264	2	no	—
363	C₂×C₄	—	1264	1	no	—
364	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
365	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
366	C₂×C₄	#14579186	1	1	yes	characteristic
367	C₂×C₄	#14579187	1	1	yes	characteristic
368	C₂×C₄	#14579187	1	1	yes	characteristic
369	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
370	C₈	—	2	2	no	—
371	C₈	—	4	2	no	—
372	C₈	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
373	C₈	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
374	C₈	C₂²×C₄×D₇₉	1	1	yes	characteristic
375	C₈	C₂×#11929624	1	1	yes	characteristic
376	C₂²	—	4	1	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	16	1	no	—
379	C₂²	—	316	2	no	—
380	C₂²	—	632	1	no	—
381	C₂²	—	632	1	no	—
382	C₂²	#19098673	1	1	yes	characteristic
383	C₂²	#19098673	1	1	yes	characteristic
384	C₂²	C₂×#14579186	1	1	yes	characteristic
385	C₄	—	4	2	no	—
386	C₄	—	4	2	no	—
387	C₄	—	316	2	no	—
388	C₄	—	632	2	no	—
389	C₄	#19098673	1	1	yes	characteristic
390	C₄	#19098673	1	1	yes	characteristic
391	C₄	C₂×C₄×C₂²⋊D₇₉	1	1	yes	characteristic
392	C₄	C₂×#14579187	1	1	yes	characteristic
393	C₂	—	2	1	no	—
394	C₂	—	2	1	no	—
395	C₂	—	2	1	no	—
396	C₂	—	8	2	no	—
397	C₂	—	632	2	no	—
398	C₂	C₂×#19098673	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×#19098673
commutator	C₈×C₇₉	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₇₉
Fitting	C₇₉×#2957	C₂
socle	C₂×C₇₉	C₂×#442
prime radical	#23776534	C₂
cosocle	C₂×C₈×C₇₉	C₂⁴
hypercenter	#2957	D₇₉
hypocenter	C₇₉	#33469
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #405 ◁ #2957

Complements

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

N	H ≅ G/N	type
2. #23772285	C₂	semidirect
3. #23765298	C₂	semidirect
4. #23765291	C₂	semidirect
5. C₂×#19098387	C₂	semidirect
6. #23765147	C₂	semidirect
7. C₂×#19098373	C₂	semidirect
8. #23765005	C₂	semidirect
9. C₇₉×#2957	C₂	semidirect
12. #19099004	C₄	semidirect
14. #19098999	C₄	semidirect
16. #19098993	C₄	semidirect
19. #19098676	C₂²	semidirect
20. #19098671	C₂²	semidirect
24. #19098387	C₂²	semidirect
25. #19098378	C₂²	semidirect
26. #19098375	C₂²	semidirect
28. #19098341	C₂²	semidirect
50. #14579107	C₂×C₄	semidirect
51. #14579105	C₂×C₄	semidirect
52. #14579104	C₂×C₄	semidirect
53. #14579102	C₂×C₄	semidirect
55. #14579101	C₂×C₄	semidirect
59. C₂×C₇₉⋊C₁₆	C₂×C₄	semidirect
67. #135×C₇₉	C₂×C₄	semidirect
69. C₂×Q₁₆×C₇₉	C₂×C₄	semidirect
71. C₂×D₈×C₇₉	C₂×C₄	semidirect
201. #2957	D₇₉	semidirect
209. C₇₉	#33469	semidirect
244. #135	C₄×D₇₉	semidirect
247. C₂×Q₁₆	C₄×D₇₉	semidirect
251. C₂×D₈	C₄×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23776534	2
#23772285	2
#23765298	2
#23765291	2
C₂×#19098387	2
#23765147	2
C₂×#19098373	2
#23765005	2
C₇₉×#2957	2
#33469	79