Subgroups — C₄×#484×C₇₉ #34133264

Order 20224.

976 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#484×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂²⋊Q₈×C₇₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₇₉×#1928	C₂	1	2	yes	maximal, complemented
5	C₇₉×#1921	C₂	1	2	yes	maximal, complemented
6	C₇₉×#1872	C₂	1	1	yes	maximal, characteristic
7	C₇₉×#1852	C₂	1	1	yes	maximal, characteristic
8	C₇₉×#1824	C₂	1	1	yes	maximal, characteristic
9	C₄×#107×C₇₉	C₂	1	2	yes	maximal, complemented
10	C₄×#103×C₇₉	C₂	1	2	yes	maximal, complemented
11	C₄×C₂²⋊C₈×C₇₉	C₂	1	1	yes	maximal, characteristic
12	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₇₉	—	2	1	no	—
17	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
18	#484×C₇₉	C₄	1	8	yes	direct product factor
19	C₂×#107×C₇₉	C₂²	1	2	yes	—
20	C₂×#107×C₇₉	C₂²	1	2	yes	—
21	C₂×#103×C₇₉	C₂²	1	2	yes	—
22	C₂×#103×C₇₉	C₂²	1	2	yes	—
23	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₇₉	C₂²	1	2	yes	—
26	#391×C₇₉	C₂²	1	1	yes	characteristic
27	#389×C₇₉	C₂²	1	1	yes	characteristic
28	#387×C₇₉	—	2	1	no	—
29	#385×C₇₉	—	2	1	no	—
30	#380×C₇₉	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊C₄×C₇₉	—	2	1	no	—
32	C₄×C₄⋊C₄×C₇₉	—	2	1	no	—
33	C₄×C₄⋊C₄×C₇₉	—	2	1	no	—
34	C₄×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
35	C₄×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
36	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
37	C₄×C₂²⋊C₄×C₇₉	—	2	1	no	—
38	C₂×#95×C₇₉	—	2	1	no	—
39	#340×C₇₉	C₂²	1	2	yes	—
40	#340×C₇₉	C₂²	1	2	yes	—
41	#340×C₇₉	C₂²	1	2	yes	—
42	#340×C₇₉	C₂²	1	2	yes	—
43	#336×C₇₉	C₂²	1	2	yes	—
44	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₇₉	—	2	1	no	—
46	C₂³×C₄×C₇₉	—	2	1	no	—
47	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
51	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
52	C₂²⋊Q₈×C₇₉	—	2	2	no	—
53	C₂²⋊Q₈×C₇₉	C₂×C₄	1	4	yes	—
54	C₄×Q₈×C₇₉	—	2	4	no	—
55	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
60	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
68	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
70	C₂×C₄²×C₇₉	—	2	4	no	—
71	C₂×C₄²×C₇₉	—	2	2	no	—
72	C₂×C₄²×C₇₉	—	2	2	no	—
73	C₂×C₄²×C₇₉	—	2	1	no	—
74	C₂×C₄²×C₇₉	—	2	1	no	—
75	C₂×C₄²×C₇₉	—	4	4	no	—
76	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
80	#107×C₇₉	—	2	4	no	—
81	#107×C₇₉	C₂×C₄	1	8	yes	complemented
82	#103×C₇₉	—	2	4	no	—
83	#103×C₇₉	C₂×C₄	1	8	yes	complemented
84	C₂²⋊C₈×C₇₉	—	2	2	no	—
85	C₂²⋊C₈×C₇₉	C₂×C₄	1	4	yes	—
86	C₄×C₈×C₇₉	—	2	4	no	—
87	#95×C₇₉	—	2	2	no	—
88	#95×C₇₉	—	2	2	no	—
89	#95×C₇₉	—	2	1	no	—
90	#95×C₇₉	—	2	1	no	—
91	#95×C₇₉	—	2	1	no	—
92	#95×C₇₉	—	2	1	no	—
93	#95×C₇₉	—	2	1	no	—
94	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
95	C₂×Q₈×C₇₉	—	2	1	no	—
96	C₂×Q₈×C₇₉	—	2	2	no	—
97	C₂×Q₈×C₇₉	—	2	2	no	—
98	C₂×Q₈×C₇₉	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₇₉	—	2	2	no	—
100	C₂²×C₄×C₇₉	—	2	2	no	—
101	C₂²×C₄×C₇₉	—	2	2	no	—
102	C₂²×C₄×C₇₉	—	2	2	no	—
103	C₂²×C₄×C₇₉	—	2	4	no	—
104	C₂²×C₄×C₇₉	—	2	4	no	—
105	C₂²×C₄×C₇₉	—	2	2	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	—	2	1	no	—
110	C₂²×C₄×C₇₉	—	2	2	no	—
111	C₂²×C₄×C₇₉	—	2	1	no	—
112	C₂²×C₄×C₇₉	—	2	1	no	—
113	C₂²×C₄×C₇₉	—	4	1	no	—
114	C₂²×C₄×C₇₉	—	4	2	no	—
115	C₂²×C₄×C₇₉	—	4	2	no	—
116	C₂²×C₄×C₇₉	—	4	2	no	—
117	C₂²×C₄×C₇₉	—	4	2	no	—
118	C₂²×C₄×C₇₉	Q₁₆	1	4	yes	—
119	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₇₉	#41	1	2	yes	—
126	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
127	C₂×C₈×C₇₉	—	2	2	no	—
128	C₂×C₈×C₇₉	—	2	2	no	—
129	C₂×C₈×C₇₉	—	2	2	no	—
130	C₂×C₈×C₇₉	—	2	2	no	—
131	C₂×C₈×C₇₉	—	2	2	no	—
132	C₂×C₈×C₇₉	C₂²×C₄	1	4	yes	—
133	C₄⋊C₄×C₇₉	—	2	4	no	—
134	C₄⋊C₄×C₇₉	—	2	4	no	—
135	C₄⋊C₄×C₇₉	—	2	4	no	—
136	C₄⋊C₄×C₇₉	—	2	2	no	—
137	C₄⋊C₄×C₇₉	—	2	2	no	—
138	C₄⋊C₄×C₇₉	—	2	1	no	—
139	C₄⋊C₄×C₇₉	—	2	2	no	—
140	C₄⋊C₄×C₇₉	—	2	2	no	—
141	C₄⋊C₄×C₇₉	—	4	2	no	—
142	C₄⋊C₄×C₇₉	—	4	2	no	—
143	C₄⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
144	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
145	C₄⋊C₄×C₇₉	#41	1	4	yes	—
146	C₂²⋊C₄×C₇₉	—	2	4	no	—
147	C₂²⋊C₄×C₇₉	—	4	2	no	—
148	C₄²×C₇₉	—	2	2	no	—
149	C₄²×C₇₉	—	2	2	no	—
150	C₄²×C₇₉	—	2	2	no	—
151	C₄²×C₇₉	—	4	4	no	—
152	C₄²×C₇₉	—	4	2	no	—
153	C₄²×C₇₉	—	4	2	no	—
154	C₄²×C₇₉	—	4	4	no	—
155	C₄²×C₇₉	#41	1	4	yes	—
156	C₂³×C₇₉	—	2	1	no	—
157	C₂³×C₇₉	—	2	1	no	—
158	C₂³×C₇₉	—	2	1	no	—
159	C₂³×C₇₉	—	2	1	no	—
160	C₂³×C₇₉	C₄×D₄	1	2	yes	—
161	C₂³×C₇₉	C₂×Q₁₆	1	2	yes	—
162	C₂³×C₇₉	#135	1	2	yes	—
163	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
164	Q₈×C₇₉	—	2	4	no	—
165	Q₈×C₇₉	—	4	2	no	—
166	C₂×C₄×C₇₉	—	2	1	no	—
167	C₂×C₄×C₇₉	—	2	1	no	—
168	C₂×C₄×C₇₉	—	2	1	no	—
169	C₂×C₄×C₇₉	—	2	1	no	—
170	C₂×C₄×C₇₉	—	2	1	no	—
171	C₂×C₄×C₇₉	—	2	1	no	—
172	C₂×C₄×C₇₉	—	2	4	no	—
173	C₂×C₄×C₇₉	—	2	4	no	—
174	C₂×C₄×C₇₉	—	2	8	no	—
175	C₂×C₄×C₇₉	—	2	2	no	—
176	C₂×C₄×C₇₉	—	2	2	no	—
177	C₂×C₄×C₇₉	—	2	4	no	—
178	C₂×C₄×C₇₉	—	2	1	no	—
179	C₂×C₄×C₇₉	—	2	4	no	—
180	C₂×C₄×C₇₉	—	2	1	no	—
181	C₂×C₄×C₇₉	—	2	1	no	—
182	C₂×C₄×C₇₉	—	4	4	no	—
183	C₂×C₄×C₇₉	—	4	8	no	—
184	C₂×C₄×C₇₉	—	4	8	no	—
185	C₂×C₄×C₇₉	—	4	1	no	—
186	C₂×C₄×C₇₉	—	4	1	no	—
187	C₂×C₄×C₇₉	—	4	2	no	—
188	C₂×C₄×C₇₉	—	4	2	no	—
189	C₂×C₄×C₇₉	—	4	2	no	—
190	C₂×C₄×C₇₉	—	4	1	no	—
191	C₂×C₄×C₇₉	—	4	1	no	—
192	C₂×C₄×C₇₉	—	4	2	no	—
193	C₂×C₄×C₇₉	—	4	1	no	—
194	C₂×C₄×C₇₉	—	4	1	no	—
195	C₂×C₄×C₇₉	—	4	1	no	—
196	C₂×C₄×C₇₉	—	4	1	no	—
197	C₂×C₄×C₇₉	—	4	1	no	—
198	C₂×C₄×C₇₉	—	4	1	no	—
199	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
200	C₂×C₄×C₇₉	#123	1	2	yes	—
201	C₂×C₄×C₇₉	#123	1	2	yes	—
202	C₂×C₄×C₇₉	C₂×Q₁₆	1	2	yes	—
203	C₂×C₄×C₇₉	C₂×Q₁₆	1	2	yes	—
204	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
205	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
206	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
207	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
208	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
209	C₈×C₇₉	—	2	4	no	—
210	C₈×C₇₉	—	4	2	no	—
211	C₂²×C₇₉	—	2	2	no	—
212	C₂²×C₇₉	—	2	2	no	—
213	C₂²×C₇₉	—	2	2	no	—
214	C₂²×C₇₉	—	2	2	no	—
215	C₂²×C₇₉	—	2	2	no	—
216	C₂²×C₇₉	—	2	2	no	—
217	C₂²×C₇₉	C₄×Q₁₆	1	4	yes	—
218	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
219	C₂²×C₇₉	C₂×#123	1	1	yes	characteristic
220	C₂²×C₇₉	#525	1	1	yes	characteristic
221	C₂²×C₇₉	C₂²×Q₁₆	1	1	yes	characteristic
222	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
223	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
224	C₂²×C₇₉	#575	1	1	yes	characteristic
225	C₄×C₇₉	—	2	2	no	—
226	C₄×C₇₉	—	2	2	no	—
227	C₄×C₇₉	—	2	2	no	—
228	C₄×C₇₉	—	4	1	no	—
229	C₄×C₇₉	—	4	4	no	—
230	C₄×C₇₉	—	4	2	no	—
231	C₄×C₇₉	—	4	4	no	—
232	C₄×C₇₉	—	4	2	no	—
233	C₄×C₇₉	—	8	1	no	—
234	C₄×C₇₉	—	8	1	no	—
235	C₄×C₇₉	#484	1	4	yes	direct product factor
236	C₄×C₇₉	C₄×#41	1	2	yes	—
237	C₄×C₇₉	#529	1	2	yes	—
238	C₄×#484	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₂×C₇₉	—	2	4	no	—
240	C₂×C₇₉	C₄×#123	1	1	yes	characteristic
241	C₂×C₇₉	C₂×C₄×Q₁₆	1	1	yes	characteristic
242	C₂×C₇₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
243	C₂×C₇₉	C₂×#484	1	1	yes	characteristic
244	C₂×C₇₉	#3091	1	1	yes	characteristic
245	C₂×C₇₉	#3104	1	1	yes	characteristic
246	C₂×C₇₉	#3105	1	1	yes	characteristic
247	C₂×#484	C₂×C₇₉	1	1	yes	characteristic
248	C₄×C₂²⋊Q₈	C₂×C₇₉	1	1	yes	characteristic
249	C₂×C₄×C₄⋊C₄	C₂×C₇₉	1	1	yes	characteristic
250	#1928	C₂×C₇₉	1	2	yes	complemented
251	#1921	C₂×C₇₉	1	2	yes	complemented
252	#1872	C₂×C₇₉	1	1	yes	characteristic
253	#1852	C₂×C₇₉	1	1	yes	characteristic
254	#1824	C₂×C₇₉	1	1	yes	characteristic
255	C₄×#107	C₂×C₇₉	1	2	yes	complemented
256	C₄×#103	C₂×C₇₉	1	2	yes	complemented
257	C₄×C₂²⋊C₈	C₂×C₇₉	1	1	yes	characteristic
258	C₇₉	C₄×#484	1	1	yes	characteristic, direct product factor, Sylow
259	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
260	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
261	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
262	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
263	C₂²×C₄²	—	2	1	no	—
264	C₂²×C₄²	C₂²×C₇₉	1	1	yes	characteristic
265	#484	C₄×C₇₉	1	8	yes	direct product factor
266	C₂×#107	C₂²×C₇₉	1	2	yes	—
267	C₂×#107	C₂²×C₇₉	1	2	yes	—
268	C₂×#103	C₂²×C₇₉	1	2	yes	—
269	C₂×#103	C₂²×C₇₉	1	2	yes	—
270	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
271	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
272	C₂×C₄×C₈	C₂²×C₇₉	1	2	yes	—
273	#391	C₂²×C₇₉	1	1	yes	characteristic
274	#389	C₂²×C₇₉	1	1	yes	characteristic
275	#387	—	2	1	no	—
276	#385	—	2	1	no	—
277	#380	C₂²×C₇₉	1	1	yes	characteristic
278	C₄×C₄⋊C₄	—	2	1	no	—
279	C₄×C₄⋊C₄	—	2	1	no	—
280	C₄×C₄⋊C₄	—	2	1	no	—
281	C₄×C₄⋊C₄	C₂²×C₇₉	1	2	yes	—
282	C₄×C₄⋊C₄	C₂²×C₇₉	1	2	yes	—
283	C₄×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
284	C₄×C₂²⋊C₄	—	2	1	no	—
285	C₂×#95	—	2	1	no	—
286	#340	C₂²×C₇₉	1	2	yes	—
287	#340	C₂²×C₇₉	1	2	yes	—
288	#340	C₂²×C₇₉	1	2	yes	—
289	#340	C₂²×C₇₉	1	2	yes	—
290	#336	C₂²×C₇₉	1	2	yes	—
291	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
292	C₂³×C₄	—	2	1	no	—
293	C₂³×C₄	—	2	1	no	—
294	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
295	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
296	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
297	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
298	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
299	C₂²⋊Q₈	—	2	2	no	—
300	C₂²⋊Q₈	C₂×C₄×C₇₉	1	4	yes	—
301	C₄×Q₈	—	2	4	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	4	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	C₂×C₄×C₇₉	1	4	yes	—
310	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
311	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
313	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
315	C₂×C₂²⋊C₄	—	2	1	no	—
316	C₂×C₂²⋊C₄	—	2	1	no	—
317	C₂×C₄²	—	2	4	no	—
318	C₂×C₄²	—	2	1	no	—
319	C₂×C₄²	—	2	1	no	—
320	C₂×C₄²	—	2	2	no	—
321	C₂×C₄²	—	2	2	no	—
322	C₂×C₄²	—	4	4	no	—
323	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
324	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
325	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
326	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
327	#107	—	2	4	no	—
328	#107	C₂×C₄×C₇₉	1	8	yes	complemented
329	#103	—	2	4	no	—
330	#103	C₂×C₄×C₇₉	1	8	yes	complemented
331	C₂²⋊C₈	—	2	2	no	—
332	C₂²⋊C₈	C₂×C₄×C₇₉	1	4	yes	—
333	C₄×C₈	—	2	4	no	—
334	#95	—	2	2	no	—
335	#95	—	2	2	no	—
336	#95	—	2	1	no	—
337	#95	—	2	1	no	—
338	#95	—	2	1	no	—
339	#95	—	2	1	no	—
340	#95	—	2	1	no	—
341	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	C₂²×C₄×C₇₉	1	2	yes	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	4	1	no	—
361	C₂²×C₄	—	4	2	no	—
362	C₂²×C₄	—	4	2	no	—
363	C₂²×C₄	—	4	2	no	—
364	C₂²×C₄	—	4	2	no	—
365	C₂²×C₄	Q₁₆×C₇₉	1	4	yes	—
366	C₂²×C₄	C₂²×C₄×C₇₉	1	2	yes	—
367	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
372	C₂²×C₄	#41×C₇₉	1	2	yes	—
373	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	C₂²×C₄×C₇₉	1	4	yes	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	4	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	4	2	no	—
389	C₄⋊C₄	—	4	2	no	—
390	C₄⋊C₄	C₂²×C₄×C₇₉	1	4	yes	—
391	C₄⋊C₄	C₂²×C₄×C₇₉	1	2	yes	—
392	C₄⋊C₄	#41×C₇₉	1	4	yes	—
393	C₂²⋊C₄	—	2	4	no	—
394	C₂²⋊C₄	—	4	2	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	4	4	no	—
399	C₄²	—	4	2	no	—
400	C₄²	—	4	4	no	—
401	C₄²	—	4	2	no	—
402	C₄²	#41×C₇₉	1	4	yes	—
403	C₂³	—	2	1	no	—
404	C₂³	—	2	1	no	—
405	C₂³	—	2	1	no	—
406	C₂³	—	2	1	no	—
407	C₂³	C₄×D₄×C₇₉	1	2	yes	—
408	C₂³	C₂×Q₁₆×C₇₉	1	2	yes	—
409	C₂³	#135×C₇₉	1	2	yes	—
410	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
411	Q₈	—	2	4	no	—
412	Q₈	—	4	2	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	8	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	4	4	no	—
430	C₂×C₄	—	4	8	no	—
431	C₂×C₄	—	4	8	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	C₄×D₄×C₇₉	1	2	yes	—
447	C₂×C₄	#123×C₇₉	1	2	yes	—
448	C₂×C₄	#123×C₇₉	1	2	yes	—
449	C₂×C₄	C₂×Q₁₆×C₇₉	1	2	yes	—
450	C₂×C₄	C₂×Q₁₆×C₇₉	1	2	yes	—
451	C₂×C₄	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
452	C₂×C₄	C₂³×C₄×C₇₉	1	1	yes	characteristic
453	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
454	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
455	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
456	C₈	—	2	4	no	—
457	C₈	—	4	2	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	2	2	no	—
464	C₂²	C₄×Q₁₆×C₇₉	1	4	yes	—
465	C₂²	C₂×C₄×D₄×C₇₉	1	1	yes	characteristic
466	C₂²	C₂×#123×C₇₉	1	1	yes	characteristic
467	C₂²	#525×C₇₉	1	1	yes	characteristic
468	C₂²	C₂²×Q₁₆×C₇₉	1	1	yes	characteristic
469	C₂²	C₂×#135×C₇₉	1	1	yes	characteristic
470	C₂²	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
471	C₂²	#575×C₇₉	1	1	yes	characteristic
472	C₄	—	2	2	no	—
473	C₄	—	2	2	no	—
474	C₄	—	2	2	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	1	no	—
477	C₄	—	4	4	no	—
478	C₄	—	4	4	no	—
479	C₄	—	4	2	no	—
480	C₄	—	8	1	no	—
481	C₄	—	8	1	no	—
482	C₄	#484×C₇₉	1	4	yes	direct product factor
483	C₄	C₄×#41×C₇₉	1	2	yes	—
484	C₄	#529×C₇₉	1	2	yes	—
485	C₂	—	2	4	no	—
486	C₂	C₄×#123×C₇₉	1	1	yes	characteristic
487	C₂	C₂×C₄×Q₁₆×C₇₉	1	1	yes	characteristic
488	C₂	C₄×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
489	C₂	C₂×#484×C₇₉	1	1	yes	characteristic
490	C₂	C₇₉×#3091	1	1	yes	characteristic
491	C₂	C₇₉×#3104	1	1	yes	characteristic
492	C₂	C₇₉×#3105	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇₉	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₇₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
socle	C₂³×C₇₉	C₂²×D₄
prime radical	C₂⁴×C₇₉	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇₉ ◁ C₂²×C₄²×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₇₉×#1928	C₂	semidirect
5. C₇₉×#1921	C₂	semidirect
9. C₄×#107×C₇₉	C₂	semidirect
10. C₄×#103×C₇₉	C₂	semidirect
18. #484×C₇₉	C₄	direct (N × H)
81. #107×C₇₉	C₂×C₄	semidirect
83. #103×C₇₉	C₂×C₄	semidirect
235. C₄×C₇₉	#484	direct (N × H)
238. C₄×#484	C₇₉	direct (N × H)
250. #1928	C₂×C₇₉	semidirect
251. #1921	C₂×C₇₉	semidirect
255. C₄×#107	C₂×C₇₉	semidirect
256. C₄×#103	C₂×C₇₉	semidirect
258. C₇₉	C₄×#484	direct (N × H)
265. #484	C₄×C₇₉	direct (N × H)
328. #107	C₂×C₄×C₇₉	semidirect
330. #103	C₂×C₄×C₇₉	semidirect
482. C₄	#484×C₇₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#484×C₇₉	2
C₄×C₂²⋊Q₈×C₇₉	2
C₂×C₄×C₄⋊C₄×C₇₉	2
C₇₉×#1928	2
C₇₉×#1921	2
C₇₉×#1872	2
C₇₉×#1852	2
C₇₉×#1824	2
C₄×#107×C₇₉	2
C₄×#103×C₇₉	2
C₄×C₂²⋊C₈×C₇₉	2
C₄×#484	79

Subgroups — C4×#484×C79 #34133264

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#484×C₇₉ #34133264