Subgroups — #34189346

Order 20224.

714 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	C₂×#19098937	C₂	1	1	yes	maximal, characteristic
2	C₂×#19098763	C₂	1	1	yes	maximal, characteristic
3	#23764327	C₂	1	1	yes	maximal, characteristic
4	C₂×#19098312	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₈⋊(C₇₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	#23761241	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#2567	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#11929611	—	2	2	no	—
9	C₂²×#11929611	—	2	1	no	—
10	C₂×#14579158	C₂²	1	1	yes	characteristic
11	#19098937	—	2	2	no	—
12	#19098937	—	2	2	no	—
13	#19098763	—	2	2	no	—
14	#19098763	—	2	2	no	—
15	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×#14579081	—	2	1	no	—
18	C₂×#14579081	—	2	2	no	—
19	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
20	#19098312	—	2	2	no	—
21	Q₈⋊(C₇₉⋊C₈)	—	2	2	no	—
22	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
24	#395×C₇₉	—	2	2	no	—
25	#391×C₇₉	—	2	1	no	—
26	#389×C₇₉	—	2	2	no	—
27	#384×C₇₉	—	2	1	no	—
28	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
29	C₂²×D₃₁₆	—	2	1	no	—
30	C₂²×D₃₁₆	—	2	1	no	—
31	C₂²×D₃₁₆	—	2	1	no	—
32	C₂×#11929611	—	2	8	no	—
33	C₂×#11929611	—	2	4	no	—
34	C₂×#11929611	—	4	8	no	—
35	C₂×#11929611	—	4	2	no	—
36	C₂×#11929611	—	4	2	no	—
37	C₂²×C₇₉⋊C₈	—	2	1	no	—
38	C₂²×C₇₉⋊C₈	—	2	1	no	—
39	C₂²×C₇₉⋊C₈	—	2	1	no	—
40	#14579158	—	2	1	no	—
41	#14579158	—	2	1	no	—
42	#14579158	—	2	1	no	—
43	#14579158	D₄	1	2	yes	—
44	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
45	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
46	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
47	C₄⋊(C₇₉⋊C₈)	D₄	1	2	yes	—
48	#14579081	—	2	4	no	—
49	#14579081	—	4	4	no	—
50	C₄×C₇₉⋊C₈	—	2	1	no	—
51	C₄×C₇₉⋊C₈	D₄	1	2	yes	—
52	C₂²×Q₈×C₇₉	D₄	1	1	yes	characteristic
53	C₂²×Q₈×C₇₉	D₄	1	2	yes	—
54	C₄⋊Q₈×C₇₉	—	2	1	no	—
55	C₄⋊Q₈×C₇₉	—	2	1	no	—
56	C₄⋊Q₈×C₇₉	—	2	1	no	—
57	C₄⋊Q₈×C₇₉	—	2	1	no	—
58	C₄×Q₈×C₇₉	—	2	1	no	—
59	C₄×Q₈×C₇₉	—	2	1	no	—
60	C₄×Q₈×C₇₉	—	2	1	no	—
61	C₄×Q₈×C₇₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
66	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₇₉	D₄	1	2	yes	—
68	C₂×C₄²×C₇₉	—	2	1	no	—
69	C₂×C₄²×C₇₉	—	2	1	no	—
70	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
71	#95×C₇₉	—	2	4	no	—
72	#95×C₇₉	—	2	1	no	—
73	C₂³×D₇₉	—	4	1	no	—
74	C₂×D₃₁₆	—	2	2	no	—
75	C₂×D₃₁₆	—	2	2	no	—
76	C₂×D₃₁₆	—	2	2	no	—
77	C₂×D₃₁₆	—	4	4	no	—
78	C₂×D₃₁₆	—	4	1	no	—
79	C₂×D₃₁₆	—	4	1	no	—
80	C₂×D₃₁₆	—	4	1	no	—
81	C₂×D₃₁₆	—	4	2	no	—
82	C₂×D₃₁₆	—	4	1	no	—
83	C₂×D₃₁₆	—	4	1	no	—
84	C₂×D₃₁₆	—	4	1	no	—
85	C₂×D₃₁₆	—	4	1	no	—
86	C₂×D₃₁₆	—	4	2	no	—
87	#11929611	—	4	8	no	—
88	#11929611	—	4	16	no	—
89	C₂×C₇₉⋊C₈	—	2	4	no	—
90	C₂×C₇₉⋊C₈	—	2	2	no	—
91	C₂×C₇₉⋊C₈	—	2	2	no	—
92	C₂×C₇₉⋊C₈	—	4	1	no	—
93	C₂×C₇₉⋊C₈	—	4	1	no	—
94	C₂×C₇₉⋊C₈	—	4	2	no	—
95	C₂×C₇₉⋊C₈	—	4	1	no	—
96	C₂×Q₈×C₇₉	—	2	1	no	—
97	C₂×Q₈×C₇₉	—	2	1	no	—
98	C₂×Q₈×C₇₉	—	2	2	no	—
99	C₂×Q₈×C₇₉	—	2	1	no	—
100	C₂×Q₈×C₇₉	—	2	2	no	—
101	C₂×Q₈×C₇₉	—	2	1	no	—
102	C₂×Q₈×C₇₉	—	2	1	no	—
103	C₂×Q₈×C₇₉	—	4	4	no	—
104	C₂×Q₈×C₇₉	SD₁₆	1	2	yes	complemented
105	C₂²×C₄×C₇₉	—	2	1	no	—
106	C₂²×C₄×C₇₉	—	2	2	no	—
107	C₂²×C₄×C₇₉	—	2	2	no	—
108	C₂²×C₄×C₇₉	—	2	1	no	—
109	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
112	C₄⋊C₄×C₇₉	—	2	2	no	—
113	C₄⋊C₄×C₇₉	—	2	1	no	—
114	C₄⋊C₄×C₇₉	—	2	1	no	—
115	C₄⋊C₄×C₇₉	—	4	1	no	—
116	C₄⋊C₄×C₇₉	—	4	1	no	—
117	C₄⋊C₄×C₇₉	—	4	1	no	—
118	C₄⋊C₄×C₇₉	—	4	1	no	—
119	C₄⋊C₄×C₇₉	—	4	1	no	—
120	C₄⋊C₄×C₇₉	—	4	1	no	—
121	C₄⋊C₄×C₇₉	—	8	4	no	—
122	C₄⋊C₄×C₇₉	SD₁₆	1	4	yes	complemented
123	C₄²×C₇₉	—	4	1	no	—
124	C₄²×C₇₉	—	4	1	no	—
125	C₄²×C₇₉	—	4	1	no	—
126	C₄²×C₇₉	—	4	1	no	—
127	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₇₉	#41	1	1	yes	characteristic
131	C₂³×C₇₉	#120	1	1	yes	characteristic
132	C₂²×D₇₉	—	4	2	no	—
133	C₂²×D₇₉	—	8	1	no	—
134	C₂²×D₇₉	—	8	2	no	—
135	C₂²×D₇₉	—	8	1	no	—
136	C₂²×D₇₉	—	8	2	no	—
137	Q₈×C₇₉	—	2	2	no	—
138	Q₈×C₇₉	—	2	2	no	—
139	Q₈×C₇₉	—	4	4	no	—
140	Q₈×C₇₉	—	4	1	no	—
141	Q₈×C₇₉	—	4	1	no	—
142	Q₈×C₇₉	—	8	2	no	—
143	C₂×C₄×C₇₉	—	2	2	no	—
144	C₂×C₄×C₇₉	—	2	4	no	—
145	C₂×C₄×C₇₉	—	2	2	no	—
146	C₂×C₄×C₇₉	—	4	1	no	—
147	C₂×C₄×C₇₉	—	4	2	no	—
148	C₂×C₄×C₇₉	—	4	1	no	—
149	C₂×C₄×C₇₉	—	4	2	no	—
150	C₂×C₄×C₇₉	—	4	1	no	—
151	C₂×C₄×C₇₉	—	4	2	no	—
152	C₂×C₄×C₇₉	—	4	2	no	—
153	C₂×C₄×C₇₉	—	4	4	no	—
154	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
155	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
156	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
157	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
158	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
159	C₂×C₄×C₇₉	#127	1	1	yes	characteristic
160	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
161	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
162	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
163	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
164	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
165	C₂×C₄×C₇₉	#137	1	2	yes	—
166	D₃₁₆	—	4	4	no	—
167	D₃₁₆	—	4	2	no	—
168	D₃₁₆	—	4	2	no	—
169	D₃₁₆	—	4	4	no	—
170	D₃₁₆	—	8	2	no	—
171	D₃₁₆	—	8	1	no	—
172	D₃₁₆	—	8	1	no	—
173	D₃₁₆	—	8	1	no	—
174	D₃₁₆	—	8	1	no	—
175	C₇₉⋊C₈	—	2	4	no	—
176	C₇₉⋊C₈	—	4	2	no	—
177	C₇₉⋊C₈	—	8	1	no	—
178	C₂²×C₇₉	#392	1	1	yes	characteristic
179	C₂²×C₇₉	#448	1	2	yes	—
180	C₂²×C₇₉	#448	1	1	yes	characteristic
181	C₂²×C₇₉	#449	1	1	yes	characteristic
182	C₂²×C₇₉	#453	1	2	yes	—
183	C₂×D₇₉	—	8	2	no	—
184	C₂×D₇₉	—	8	2	no	—
185	C₂×D₇₉	—	8	2	no	—
186	C₂×D₇₉	—	16	2	no	—
187	C₂×D₇₉	—	16	2	no	—
188	C₄×C₇₉	—	2	1	no	—
189	C₄×C₇₉	—	2	1	no	—
190	C₄×C₇₉	—	4	4	no	—
191	C₄×C₇₉	—	4	2	no	—
192	C₄×C₇₉	—	8	1	no	—
193	C₄×C₇₉	—	8	2	no	—
194	C₄×C₇₉	#450	1	1	yes	characteristic
195	C₄×C₇₉	#452	1	1	yes	characteristic
196	C₄×C₇₉	#461	1	2	yes	—
197	C₄×C₇₉	#465	1	1	yes	characteristic
198	C₄×C₇₉	#468	1	1	yes	characteristic
199	C₄×C₇₉	#492	1	1	yes	characteristic
200	C₄×C₇₉	#497	1	1	yes	characteristic
201	#10049	—	79	1	no	maximal, Sylow
202	C₂×C₇₉	#1622	1	2	yes	—
203	C₂×C₇₉	#1623	1	2	yes	—
204	C₂×C₇₉	#2000	1	1	yes	characteristic
205	C₂×C₇₉	#2002	1	1	yes	characteristic
206	C₂×C₇₉	#2013	1	1	yes	characteristic
207	D₇₉	—	16	2	no	—
208	C₂×#492	—	79	1	no	—
209	C₂×#460	—	79	1	no	—
210	#2567	D₇₉	1	1	yes	characteristic, complemented
211	#1982	—	79	1	no	—
212	C₂×#333	—	79	1	no	—
213	C₂×Q₈⋊C₈	—	79	1	no	—
214	#1279	—	79	1	no	—
215	C₇₉	#10049	1	1	yes	characteristic, complemented, Sylow
216	C₂²×SD₁₆	—	158	2	no	—
217	C₂²×SD₁₆	—	158	1	no	—
218	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
219	C₂×#127	—	79	1	no	—
220	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
221	#492	—	158	2	no	—
222	#492	—	158	2	no	—
223	#460	—	158	2	no	—
224	#460	—	158	2	no	—
225	C₂×C₄⋊C₈	—	79	1	no	—
226	C₂×C₄⋊C₈	—	79	1	no	—
227	C₂×#102	—	158	2	no	—
228	C₂×#102	—	158	1	no	—
229	C₂×C₄×C₈	—	79	1	no	—
230	#395	—	2	2	no	—
231	#391	—	2	1	no	—
232	#389	—	2	2	no	—
233	#384	—	2	1	no	—
234	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
235	#333	—	158	2	no	—
236	Q₈⋊C₈	—	158	2	no	—
237	C₂²×Q₈	C₂²⋊D₇₉	1	1	yes	characteristic
238	C₂²×Q₈	C₂²⋊D₇₉	1	2	yes	—
239	C₂²×D₄	—	158	1	no	—
240	C₂²×D₄	—	158	1	no	—
241	C₂²×D₄	—	158	1	no	—
242	C₂×SD₁₆	—	316	2	no	—
243	C₂×SD₁₆	—	316	2	no	—
244	C₂×SD₁₆	—	316	8	no	—
245	C₂×SD₁₆	—	158	4	no	—
246	C₂×SD₁₆	—	158	8	no	—
247	C₂²×C₈	—	158	1	no	—
248	C₂²×C₈	—	158	1	no	—
249	C₂²×C₈	—	158	1	no	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	—	2	1	no	—
252	C₄⋊Q₈	—	2	1	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	#127	—	79	2	no	—
255	#127	—	158	1	no	—
256	#127	—	158	1	no	—
257	#127	—	158	1	no	—
258	C₄×Q₈	—	2	1	no	—
259	C₄×Q₈	—	2	1	no	—
260	C₄×Q₈	—	2	1	no	—
261	C₄×Q₈	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	4	no	—
266	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	1	yes	characteristic
267	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	2	yes	—
268	C₂×C₄²	—	2	1	no	—
269	C₂×C₄²	—	2	1	no	—
270	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
271	C₄⋊C₈	—	79	2	no	—
272	C₄⋊C₈	—	158	1	no	—
273	C₄⋊C₈	—	158	1	no	—
274	C₄⋊C₈	—	158	1	no	—
275	#102	—	316	4	no	—
276	#102	—	158	4	no	—
277	C₄×C₈	—	79	2	no	—
278	C₄×C₈	—	158	1	no	—
279	#95	—	2	4	no	—
280	#95	—	2	1	no	—
281	C₂⁴	—	316	1	no	—
282	C₂×Q₈	—	2	1	no	—
283	C₂×Q₈	—	2	1	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	2	1	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	1	no	—
288	C₂×Q₈	—	2	1	no	—
289	C₂×Q₈	—	4	4	no	—
290	C₂×Q₈	#11929611	1	2	yes	complemented
291	C₂×D₄	—	316	4	no	—
292	C₂×D₄	—	316	1	no	—
293	C₂×D₄	—	316	1	no	—
294	C₂×D₄	—	316	1	no	—
295	C₂×D₄	—	316	2	no	—
296	C₂×D₄	—	316	1	no	—
297	C₂×D₄	—	316	1	no	—
298	C₂×D₄	—	316	1	no	—
299	C₂×D₄	—	316	2	no	—
300	C₂×D₄	—	316	1	no	—
301	C₂×D₄	—	158	2	no	—
302	C₂×D₄	—	158	2	no	—
303	C₂×D₄	—	158	2	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
310	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
311	SD₁₆	—	316	8	no	—
312	SD₁₆	—	316	16	no	—
313	C₂×C₈	—	316	1	no	—
314	C₂×C₈	—	316	1	no	—
315	C₂×C₈	—	316	1	no	—
316	C₂×C₈	—	316	2	no	—
317	C₂×C₈	—	158	2	no	—
318	C₂×C₈	—	158	4	no	—
319	C₂×C₈	—	158	2	no	—
320	C₄⋊C₄	—	2	2	no	—
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	—	4	1	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	—	8	4	no	—
330	C₄⋊C₄	#11929611	1	4	yes	complemented
331	C₄²	—	4	1	no	—
332	C₄²	—	4	1	no	—
333	C₄²	—	4	1	no	—
334	C₄²	—	4	1	no	—
335	C₄²	D₄×D₇₉	1	1	yes	characteristic
336	C₄²	D₄×D₇₉	1	1	yes	characteristic
337	C₄²	D₄×D₇₉	1	1	yes	characteristic
338	C₄²	#11929623	1	1	yes	characteristic
339	C₂³	—	316	2	no	—
340	C₂³	—	632	2	no	—
341	C₂³	—	632	1	no	—
342	C₂³	—	632	1	no	—
343	C₂³	—	632	2	no	—
344	C₂³	#14579130	1	1	yes	characteristic
345	Q₈	—	2	2	no	—
346	Q₈	—	2	2	no	—
347	Q₈	—	4	4	no	—
348	Q₈	—	4	1	no	—
349	Q₈	—	4	1	no	—
350	Q₈	—	8	2	no	—
351	D₄	—	316	4	no	—
352	D₄	—	316	2	no	—
353	D₄	—	316	2	no	—
354	D₄	—	316	4	no	—
355	D₄	—	632	2	no	—
356	D₄	—	632	1	no	—
357	D₄	—	632	1	no	—
358	D₄	—	632	1	no	—
359	D₄	—	632	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	#14579129	1	1	yes	characteristic
372	C₂×C₄	#14579129	1	1	yes	characteristic
373	C₂×C₄	#14579132	1	1	yes	characteristic
374	C₂×C₄	#14579133	1	1	yes	characteristic
375	C₂×C₄	#14579133	1	1	yes	characteristic
376	C₂×C₄	#14579157	1	1	yes	characteristic
377	C₂×C₄	C₂×#11929611	1	2	yes	—
378	C₂×C₄	C₂×#11929611	1	1	yes	characteristic
379	C₂×C₄	#14579181	1	1	yes	characteristic
380	C₂×C₄	#14579186	1	1	yes	characteristic
381	C₂×C₄	#14579192	1	2	yes	—
382	C₂×C₄	#14579192	1	1	yes	characteristic
383	C₈	—	316	2	no	—
384	C₈	—	632	1	no	—
385	C₈	—	158	4	no	—
386	C₂²	—	632	2	no	—
387	C₂²	—	632	2	no	—
388	C₂²	—	632	2	no	—
389	C₂²	—	1264	2	no	—
390	C₂²	—	1264	2	no	—
391	C₂²	#19098471	1	1	yes	characteristic
392	C₂²	#19098702	1	2	yes	—
393	C₂²	#19098702	1	1	yes	characteristic
394	C₂²	#19098708	1	1	yes	characteristic
395	C₂²	#19098731	1	2	yes	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	4	4	no	—
399	C₄	—	4	2	no	—
400	C₄	—	8	2	no	—
401	C₄	—	8	1	no	—
402	C₄	#19098713	1	1	yes	characteristic
403	C₄	#19098723	1	1	yes	characteristic
404	C₄	#19098765	1	2	yes	—
405	C₄	#19098794	1	1	yes	characteristic
406	C₄	#19098811	1	1	yes	characteristic
407	C₄	#19098937	1	1	yes	characteristic
408	C₄	#19098955	1	1	yes	characteristic
409	C₂	—	1264	2	no	—
410	C₂	#23762472	1	2	yes	—
411	C₂	#23762478	1	2	yes	—
412	C₂	#23764401	1	1	yes	characteristic
413	C₂	#23764413	1	1	yes	characteristic
414	C₂	#23764483	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#14579130
commutator, cosocle	C₂×C₄²×C₇₉	C₂³
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#2567	C₂
socle	C₂³×C₇₉	#120
prime radical	C₂×#14579158	C₂²
hypercenter	#2567	D₇₉
hypocenter	C₇₉	#10049
LCS	G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2567

Complements

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

N	H ≅ G/N	type
4. C₂×#19098312	C₂	semidirect
5. C₂×Q₈⋊(C₇₉⋊C₈)	C₂	semidirect
6. #23761241	C₂	semidirect
7. C₇₉×#2567	C₂	semidirect
104. C₂×Q₈×C₇₉	SD₁₆	semidirect
122. C₄⋊C₄×C₇₉	SD₁₆	semidirect
210. #2567	D₇₉	semidirect
215. C₇₉	#10049	semidirect
290. C₂×Q₈	#11929611	semidirect
330. C₄⋊C₄	#11929611	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098937	2
C₂×#19098763	2
#23764327	2
C₂×#19098312	2
C₂×Q₈⋊(C₇₉⋊C₈)	2
#23761241	2
C₇₉×#2567	2
#10049	79