Subgroups — #121×C₇₉⋊C₈ #34294298

Order 20224.

1222 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₇₉⋊C₈	C₂	1	2	yes	maximal, complemented
2	C₂×D₄×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#23764195	C₂	1	1	yes	maximal, characteristic, complemented
5	#23764119	C₂	1	1	yes	maximal, characteristic, complemented
6	#23764008	C₂	1	2	yes	maximal, complemented
7	#23763693	C₂	1	2	yes	maximal, complemented
8	#23763380	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄⋊C₄×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²⋊C₄×C₇₉⋊C₈	C₂	1	2	yes	maximal, complemented
11	C₄×#121×C₇₉	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
13	C₂³×C₇₉⋊C₈	C₂²	1	2	yes	—
14	C₂³×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
15	D₄×C₇₉⋊C₈	—	2	8	no	—
16	D₄×C₇₉⋊C₈	—	2	4	no	—
17	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
18	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
21	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
22	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
23	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
24	C₂×C₄×C₇₉⋊C₈	—	2	4	no	—
25	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₇₉⋊C₈	C₂²	1	2	yes	—
27	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
30	#19098318	C₂²	1	2	yes	—
31	#19098318	C₂²	1	2	yes	—
32	#19098318	C₂²	1	2	yes	—
33	C₂×#121×C₇₉	C₄	1	1	yes	characteristic
34	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	—
36	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
37	#390×C₇₉	C₄	1	1	yes	characteristic
38	#389×C₇₉	C₄	1	1	yes	characteristic
39	#388×C₇₉	C₄	1	2	yes	—
40	#386×C₇₉	C₄	1	2	yes	—
41	#380×C₇₉	C₄	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
43	C₄×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
44	C₂²×C₇₉⋊C₈	—	2	2	no	—
45	C₂²×C₇₉⋊C₈	—	2	2	no	—
46	C₂²×C₇₉⋊C₈	—	2	2	no	—
47	C₂²×C₇₉⋊C₈	—	2	2	no	—
48	C₂²×C₇₉⋊C₈	—	2	2	no	—
49	C₂²×C₇₉⋊C₈	—	2	4	no	—
50	C₂²×C₇₉⋊C₈	—	2	4	no	—
51	C₂²×C₇₉⋊C₈	—	2	4	no	—
52	C₂²×C₇₉⋊C₈	D₄	1	4	yes	complemented
53	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
54	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
55	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
56	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
59	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
60	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
61	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
62	C₂²⋊(C₇₉⋊C₈)	—	2	4	no	—
63	C₂²⋊(C₇₉⋊C₈)	—	2	4	no	—
64	C₂²⋊(C₇₉⋊C₈)	—	2	4	no	—
65	C₂²⋊(C₇₉⋊C₈)	—	2	4	no	—
66	C₄×C₇₉⋊C₈	—	2	2	no	—
67	C₄×C₇₉⋊C₈	—	2	4	no	—
68	C₄×C₇₉⋊C₈	—	2	2	no	—
69	C₄×C₇₉⋊C₈	—	2	2	no	—
70	C₄×C₇₉⋊C₈	D₄	1	4	yes	complemented
71	C₂²×D₄×C₇₉	C₂×C₄	1	2	yes	—
72	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
73	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
74	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
75	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
76	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
77	#121×C₇₉	C₈	1	8	yes	complemented
78	C₄×D₄×C₇₉	—	2	4	no	—
79	C₄×D₄×C₇₉	—	2	4	no	—
80	C₄×D₄×C₇₉	—	2	2	no	—
81	C₄×D₄×C₇₉	—	2	2	no	—
82	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
84	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
86	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
87	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
88	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
89	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
90	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
91	C₂×C₄²×C₇₉	—	2	2	no	—
92	C₂×C₄²×C₇₉	—	2	2	no	—
93	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
97	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
98	#95×C₇₉	C₂×C₄	1	2	yes	—
99	#95×C₇₉	C₂×C₄	1	2	yes	—
100	#95×C₇₉	C₂×C₄	1	2	yes	—
101	C₂×C₇₉⋊C₈	—	2	8	no	—
102	C₂×C₇₉⋊C₈	—	2	8	no	—
103	C₂×C₇₉⋊C₈	—	2	1	no	—
104	C₂×C₇₉⋊C₈	—	2	1	no	—
105	C₂×C₇₉⋊C₈	—	2	2	no	—
106	C₂×C₇₉⋊C₈	—	2	2	no	—
107	C₂×C₇₉⋊C₈	—	2	2	no	—
108	C₂×C₇₉⋊C₈	—	2	1	no	—
109	C₂×C₇₉⋊C₈	—	2	1	no	—
110	C₂×C₇₉⋊C₈	—	2	1	no	—
111	C₂×C₇₉⋊C₈	—	2	1	no	—
112	C₂×C₇₉⋊C₈	—	2	2	no	—
113	C₂×C₇₉⋊C₈	—	2	2	no	—
114	C₂×C₇₉⋊C₈	—	2	2	no	—
115	C₂×C₇₉⋊C₈	—	4	8	no	—
116	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
117	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
118	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
119	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
120	C₂×C₇₉⋊C₈	#41	1	2	yes	—
121	C₂×C₇₉⋊C₈	#41	1	2	yes	—
122	C₂⁴×C₇₉	C₂²×C₄	1	2	yes	—
123	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
124	C₂×D₄×C₇₉	—	2	4	no	—
125	C₂×D₄×C₇₉	—	2	4	no	—
126	C₂×D₄×C₇₉	—	2	2	no	—
127	C₂×D₄×C₇₉	—	2	2	no	—
128	C₂×D₄×C₇₉	C₂×C₈	1	8	yes	complemented
129	C₂×D₄×C₇₉	C₂×C₈	1	4	yes	complemented
130	C₂²×C₄×C₇₉	—	2	2	no	—
131	C₂²×C₄×C₇₉	—	2	2	no	—
132	C₂²×C₄×C₇₉	—	2	2	no	—
133	C₂²×C₄×C₇₉	—	2	2	no	—
134	C₂²×C₄×C₇₉	—	2	2	no	—
135	C₂²×C₄×C₇₉	—	2	1	no	—
136	C₂²×C₄×C₇₉	—	2	1	no	—
137	C₂²×C₄×C₇₉	—	2	1	no	—
138	C₂²×C₄×C₇₉	—	2	1	no	—
139	C₂²×C₄×C₇₉	—	2	2	no	—
140	C₂²×C₄×C₇₉	—	2	2	no	—
141	C₂²×C₄×C₇₉	—	2	2	no	—
142	C₂²×C₄×C₇₉	—	2	2	no	—
143	C₂²×C₄×C₇₉	—	2	2	no	—
144	C₂²×C₄×C₇₉	—	2	2	no	—
145	C₂²×C₄×C₇₉	C₂×C₈	1	4	yes	complemented
146	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
147	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
148	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
152	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₇₉	#41	1	2	yes	—
156	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
157	C₄⋊C₄×C₇₉	—	2	4	no	—
158	C₄⋊C₄×C₇₉	—	2	2	no	—
159	C₄⋊C₄×C₇₉	—	2	2	no	—
160	C₄⋊C₄×C₇₉	C₂×C₈	1	4	yes	complemented
161	C₂²⋊C₄×C₇₉	—	2	4	no	—
162	C₂²⋊C₄×C₇₉	—	2	4	no	—
163	C₂²⋊C₄×C₇₉	—	2	4	no	—
164	C₂²⋊C₄×C₇₉	—	2	4	no	—
165	C₂²⋊C₄×C₇₉	C₂×C₈	1	8	yes	complemented
166	C₄²×C₇₉	—	2	2	no	—
167	C₄²×C₇₉	—	2	2	no	—
168	C₄²×C₇₉	—	2	1	no	—
169	C₄²×C₇₉	—	2	2	no	—
170	C₄²×C₇₉	—	2	1	no	—
171	C₄²×C₇₉	—	2	2	no	—
172	C₄²×C₇₉	C₂×D₄	1	2	yes	—
173	C₄²×C₇₉	#41	1	2	yes	—
174	C₂³×C₇₉	—	2	1	no	—
175	C₂³×C₇₉	—	2	1	no	—
176	C₂³×C₇₉	—	2	1	no	—
177	C₂³×C₇₉	—	2	1	no	—
178	C₂³×C₇₉	—	2	2	no	—
179	C₂³×C₇₉	—	2	2	no	—
180	C₂³×C₇₉	—	2	2	no	—
181	C₂³×C₇₉	—	2	2	no	—
182	C₂³×C₇₉	—	2	2	no	—
183	C₂³×C₇₉	—	2	2	no	—
184	C₂³×C₇₉	C₄×D₄	1	2	yes	—
185	C₂³×C₇₉	C₂²×C₈	1	4	yes	—
186	C₂³×C₇₉	C₂²×C₈	1	2	yes	—
187	C₂³×C₇₉	#131	1	2	yes	—
188	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
189	D₄×C₇₉	—	2	16	no	—
190	D₄×C₇₉	—	2	8	no	—
191	C₂×C₄×C₇₉	—	2	8	no	—
192	C₂×C₄×C₇₉	—	2	1	no	—
193	C₂×C₄×C₇₉	—	2	1	no	—
194	C₂×C₄×C₇₉	—	2	1	no	—
195	C₂×C₄×C₇₉	—	2	2	no	—
196	C₂×C₄×C₇₉	—	2	1	no	—
197	C₂×C₄×C₇₉	—	2	1	no	—
198	C₂×C₄×C₇₉	—	2	1	no	—
199	C₂×C₄×C₇₉	—	2	1	no	—
200	C₂×C₄×C₇₉	—	2	1	no	—
201	C₂×C₄×C₇₉	—	2	2	no	—
202	C₂×C₄×C₇₉	—	2	2	no	—
203	C₂×C₄×C₇₉	—	2	2	no	—
204	C₂×C₄×C₇₉	—	2	2	no	—
205	C₂×C₄×C₇₉	—	2	2	no	—
206	C₂×C₄×C₇₉	—	2	8	no	—
207	C₂×C₄×C₇₉	—	2	2	no	—
208	C₂×C₄×C₇₉	—	2	2	no	—
209	C₂×C₄×C₇₉	—	2	2	no	—
210	C₂×C₄×C₇₉	—	2	2	no	—
211	C₂×C₄×C₇₉	—	2	2	no	—
212	C₂×C₄×C₇₉	—	2	2	no	—
213	C₂×C₄×C₇₉	—	4	2	no	—
214	C₂×C₄×C₇₉	—	4	2	no	—
215	C₂×C₄×C₇₉	—	4	2	no	—
216	C₂×C₄×C₇₉	—	4	2	no	—
217	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
218	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
219	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
220	C₂×C₄×C₇₉	C₂²×C₈	1	2	yes	—
221	C₂×C₄×C₇₉	C₂²×C₈	1	4	yes	—
222	C₂×C₄×C₇₉	C₂²×C₈	1	2	yes	—
223	C₂×C₄×C₇₉	#131	1	2	yes	—
224	C₂×C₄×C₇₉	#131	1	2	yes	—
225	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
228	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
229	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
230	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
231	C₇₉⋊C₈	—	2	2	no	—
232	C₇₉⋊C₈	—	2	2	no	—
233	C₇₉⋊C₈	—	2	2	no	—
234	C₇₉⋊C₈	—	4	2	no	—
235	C₇₉⋊C₈	—	4	2	no	—
236	C₇₉⋊C₈	#121	1	4	yes	direct product factor
237	C₂²×C₇₉	—	2	2	no	—
238	C₂²×C₇₉	—	2	2	no	—
239	C₂²×C₇₉	—	2	2	no	—
240	C₂²×C₇₉	—	2	2	no	—
241	C₂²×C₇₉	—	2	2	no	—
242	C₂²×C₇₉	—	2	2	no	—
243	C₂²×C₇₉	—	2	4	no	—
244	C₂²×C₇₉	—	2	4	no	—
245	C₂²×C₇₉	—	2	4	no	—
246	C₂²×C₇₉	—	4	2	no	—
247	C₂²×C₇₉	—	4	2	no	—
248	C₂²×C₇₉	—	4	2	no	—
249	C₂²×C₇₉	—	4	2	no	—
250	C₂²×C₇₉	C₈×D₄	1	4	yes	complemented
251	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
252	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
253	C₂²×C₇₉	C₄×#41	1	1	yes	characteristic
254	C₂²×C₇₉	C₂³×C₈	1	1	yes	characteristic
255	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
256	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
257	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
258	C₄×C₇₉	—	2	2	no	—
259	C₄×C₇₉	—	2	4	no	—
260	C₄×C₇₉	—	2	2	no	—
261	C₄×C₇₉	—	2	2	no	—
262	C₄×C₇₉	—	2	2	no	—
263	C₄×C₇₉	—	4	2	no	—
264	C₄×C₇₉	—	4	2	no	—
265	C₄×C₇₉	C₈×D₄	1	4	yes	complemented
266	C₄×C₇₉	C₂×#121	1	1	yes	characteristic
267	C₄×C₇₉	#525	1	1	yes	characteristic
268	C₄×C₇₉	#529	1	1	yes	characteristic
269	C₄×C₇₉	#532	1	1	yes	characteristic
270	C₈×#121	—	79	1	no	maximal, Sylow
271	C₂×C₇₉	—	2	4	no	—
272	C₂×C₇₉	—	4	4	no	—
273	C₂×C₇₉	C₄×#121	1	1	yes	characteristic
274	C₂×C₇₉	C₂×C₈×D₄	1	1	yes	characteristic
275	C₂×C₇₉	C₂×C₈×D₄	1	1	yes	characteristic
276	C₂×C₇₉	#2929	1	1	yes	characteristic
277	C₂×C₇₉	#2931	1	1	yes	characteristic
278	C₂×C₇₉	C₈×#41	1	1	yes	characteristic
279	C₂×C₇₉	#2966	1	1	yes	characteristic
280	C₂×C₈×D₄	—	79	2	no	—
281	C₂×C₈×D₄	—	79	1	no	—
282	C₂²×C₄×C₈	—	79	1	no	—
283	C₄×#121	D₇₉	1	1	yes	characteristic
284	#1954	—	79	1	no	—
285	#1939	—	79	1	no	—
286	#1923	—	79	2	no	—
287	#1869	—	79	2	no	—
288	#1797	—	79	1	no	—
289	C₈×C₄⋊C₄	—	79	1	no	—
290	C₈×C₂²⋊C₄	—	79	2	no	—
291	C₇₉	C₈×#121	1	1	yes	characteristic, complemented, Sylow
292	C₂³×C₈	—	79	1	no	—
293	C₂³×C₈	—	79	1	no	—
294	C₂³×C₈	—	79	2	no	—
295	C₂×#121	Dic₇₉	1	1	yes	characteristic
296	C₂×C₄×D₄	C₂×D₇₉	1	2	yes	—
297	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
298	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
299	C₈×D₄	—	158	4	no	—
300	C₈×D₄	—	158	8	no	—
301	C₂×C₄⋊C₈	—	79	1	no	—
302	C₂×C₄⋊C₈	—	79	1	no	—
303	C₂×C₄⋊C₈	—	79	2	no	—
304	C₂×C₂²⋊C₈	—	79	2	no	—
305	C₂×C₂²⋊C₈	—	79	2	no	—
306	C₂×C₂²⋊C₈	—	79	2	no	—
307	C₂×C₂²⋊C₈	—	79	2	no	—
308	C₂×C₄×C₈	—	79	1	no	—
309	C₂×C₄×C₈	—	79	1	no	—
310	C₂×C₄×C₈	—	79	1	no	—
311	C₂×C₄×C₈	—	79	1	no	—
312	C₂×C₄×C₈	—	79	2	no	—
313	C₂×C₄×C₈	—	158	4	no	—
314	#390	Dic₇₉	1	1	yes	characteristic
315	#389	Dic₇₉	1	1	yes	characteristic
316	#388	Dic₇₉	1	2	yes	—
317	#386	Dic₇₉	1	2	yes	—
318	#380	Dic₇₉	1	1	yes	characteristic
319	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
320	C₄×C₂²⋊C₄	C₂×D₇₉	1	2	yes	—
321	#336	—	79	2	no	—
322	#336	—	79	2	no	—
323	#336	—	79	2	no	—
324	C₂²×D₄	C₂×Dic₇₉	1	2	yes	—
325	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
326	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
327	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
328	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
329	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
330	C₂²×C₈	—	79	1	no	—
331	C₂²×C₈	—	79	4	no	—
332	C₂²×C₈	—	79	1	no	—
333	C₂²×C₈	—	79	1	no	—
334	C₂²×C₈	—	79	1	no	—
335	C₂²×C₈	—	79	2	no	—
336	C₂²×C₈	—	79	2	no	—
337	C₂²×C₈	—	158	4	no	—
338	C₂²×C₈	—	158	4	no	—
339	C₂²×C₈	—	158	4	no	—
340	C₂²×C₈	—	158	2	no	—
341	C₂²×C₈	—	158	2	no	—
342	C₂²×C₈	—	158	2	no	—
343	C₂²×C₈	—	158	2	no	—
344	C₂²×C₈	—	158	2	no	—
345	#121	C₇₉⋊C₈	1	8	yes	direct product factor
346	C₄×D₄	—	2	4	no	—
347	C₄×D₄	—	2	4	no	—
348	C₄×D₄	—	2	2	no	—
349	C₄×D₄	—	2	2	no	—
350	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
352	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
354	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
355	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
356	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
357	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
358	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
359	C₂×C₄²	—	2	2	no	—
360	C₂×C₄²	—	2	2	no	—
361	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
362	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
363	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
364	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
365	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
366	C₄⋊C₈	—	158	4	no	—
367	C₄⋊C₈	—	158	2	no	—
368	C₄⋊C₈	—	158	2	no	—
369	C₂²⋊C₈	—	158	4	no	—
370	C₂²⋊C₈	—	158	4	no	—
371	C₂²⋊C₈	—	158	4	no	—
372	C₂²⋊C₈	—	158	4	no	—
373	C₄×C₈	—	79	4	no	—
374	C₄×C₈	—	158	2	no	—
375	C₄×C₈	—	158	2	no	—
376	C₄×C₈	—	158	4	no	—
377	C₄×C₈	—	158	2	no	—
378	#95	C₂×Dic₇₉	1	2	yes	—
379	#95	C₂×Dic₇₉	1	2	yes	—
380	#95	C₂×Dic₇₉	1	2	yes	—
381	C₂⁴	C₂²×Dic₇₉	1	2	yes	—
382	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
383	C₂×D₄	—	2	4	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	C₂×C₇₉⋊C₈	1	8	yes	complemented
388	C₂×D₄	C₂×C₇₉⋊C₈	1	4	yes	complemented
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	C₂×C₇₉⋊C₈	1	4	yes	complemented
405	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
406	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
407	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
408	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
409	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
410	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
411	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
412	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
413	C₂²×C₄	D₄×D₇₉	1	2	yes	—
414	C₂²×C₄	#11929623	1	2	yes	—
415	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
416	C₂×C₈	—	316	8	no	—
417	C₂×C₈	—	79	2	no	—
418	C₂×C₈	—	79	2	no	—
419	C₂×C₈	—	79	2	no	—
420	C₂×C₈	—	79	2	no	—
421	C₂×C₈	—	79	2	no	—
422	C₂×C₈	—	79	2	no	—
423	C₂×C₈	—	158	2	no	—
424	C₂×C₈	—	158	2	no	—
425	C₂×C₈	—	158	2	no	—
426	C₂×C₈	—	158	2	no	—
427	C₂×C₈	—	158	2	no	—
428	C₂×C₈	—	158	2	no	—
429	C₂×C₈	—	158	8	no	—
430	C₂×C₈	—	158	8	no	—
431	C₂×C₈	—	158	1	no	—
432	C₂×C₈	—	158	1	no	—
433	C₂×C₈	—	158	1	no	—
434	C₂×C₈	—	158	1	no	—
435	C₂×C₈	—	158	1	no	—
436	C₂×C₈	—	158	1	no	—
437	C₄⋊C₄	—	2	4	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	C₂×C₇₉⋊C₈	1	4	yes	complemented
441	C₂²⋊C₄	—	2	4	no	—
442	C₂²⋊C₄	—	2	4	no	—
443	C₂²⋊C₄	—	2	4	no	—
444	C₂²⋊C₄	—	2	4	no	—
445	C₂²⋊C₄	C₂×C₇₉⋊C₈	1	8	yes	complemented
446	C₄²	—	2	1	no	—
447	C₄²	—	2	2	no	—
448	C₄²	—	2	2	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	2	no	—
452	C₄²	D₄×D₇₉	1	2	yes	—
453	C₄²	#11929623	1	2	yes	—
454	C₂³	—	2	1	no	—
455	C₂³	—	2	1	no	—
456	C₂³	—	2	1	no	—
457	C₂³	—	2	1	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	2	2	no	—
464	C₂³	D₄×Dic₇₉	1	2	yes	—
465	C₂³	C₂²×C₇₉⋊C₈	1	4	yes	—
466	C₂³	C₂²×C₇₉⋊C₈	1	2	yes	—
467	C₂³	#14579168	1	2	yes	—
468	C₂³	C₂³×Dic₇₉	1	1	yes	characteristic
469	D₄	—	2	16	no	—
470	D₄	—	2	8	no	—
471	C₂×C₄	—	2	8	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	8	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
498	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
499	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
500	C₂×C₄	C₂²×C₇₉⋊C₈	1	2	yes	—
501	C₂×C₄	C₂²×C₇₉⋊C₈	1	4	yes	—
502	C₂×C₄	C₂²×C₇₉⋊C₈	1	2	yes	—
503	C₂×C₄	#14579168	1	2	yes	—
504	C₂×C₄	#14579168	1	2	yes	—
505	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
506	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
507	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
508	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
509	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
510	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
511	C₈	—	316	2	no	—
512	C₈	—	316	2	no	—
513	C₈	—	79	4	no	—
514	C₈	—	158	2	no	—
515	C₈	—	158	2	no	—
516	C₈	—	158	2	no	—
517	C₂²	—	2	2	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	4	no	—
524	C₂²	—	2	4	no	—
525	C₂²	—	2	4	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	2	no	—
530	C₂²	D₄×C₇₉⋊C₈	1	4	yes	complemented
531	C₂²	C₂×D₄×Dic₇₉	1	1	yes	characteristic
532	C₂²	C₂×D₄×Dic₇₉	1	1	yes	characteristic
533	C₂²	#41×Dic₇₉	1	1	yes	characteristic
534	C₂²	C₂³×C₇₉⋊C₈	1	1	yes	characteristic
535	C₂²	C₂×#14579168	1	1	yes	characteristic
536	C₂²	C₂×#14579168	1	1	yes	characteristic
537	C₂²	C₂×#14579168	1	1	yes	characteristic
538	C₄	—	2	2	no	—
539	C₄	—	2	2	no	—
540	C₄	—	2	4	no	—
541	C₄	—	2	2	no	—
542	C₄	—	2	2	no	—
543	C₄	—	4	2	no	—
544	C₄	—	4	2	no	—
545	C₄	D₄×C₇₉⋊C₈	1	4	yes	complemented
546	C₄	#121×D₇₉	1	1	yes	characteristic
547	C₄	#19099073	1	1	yes	characteristic
548	C₄	#19099094	1	1	yes	characteristic
549	C₄	#19099108	1	1	yes	characteristic
550	C₂	—	2	4	no	—
551	C₂	—	4	4	no	—
552	C₂	#121×Dic₇₉	1	1	yes	characteristic
553	C₂	C₂×D₄×C₇₉⋊C₈	1	1	yes	characteristic
554	C₂	C₂×D₄×C₇₉⋊C₈	1	1	yes	characteristic
555	C₂	#23772095	1	1	yes	characteristic
556	C₂	#23772112	1	1	yes	characteristic
557	C₂	#41×C₇₉⋊C₈	1	1	yes	characteristic
558	C₂	#23772376	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator	C₂²×C₇₉	C₂³×C₈
Fitting	C₄×#121×C₇₉	C₂
socle	C₂³×C₇₉	C₂³×C₄
prime radical	C₂×#121×C₇₉	C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₄×#121	D₇₉
hypocenter	C₇₉	C₈×#121
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#121

Complements

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

N	H ≅ G/N	type
1. C₂×D₄×C₇₉⋊C₈	C₂	semidirect
2. C₂×D₄×C₇₉⋊C₈	C₂	semidirect
3. C₂²×C₄×C₇₉⋊C₈	C₂	semidirect
4. #23764195	C₂	semidirect
5. #23764119	C₂	semidirect
6. #23764008	C₂	semidirect
7. #23763693	C₂	semidirect
8. #23763380	C₂	semidirect
9. C₄⋊C₄×C₇₉⋊C₈	C₂	semidirect
10. C₂²⋊C₄×C₇₉⋊C₈	C₂	semidirect
52. C₂²×C₇₉⋊C₈	D₄	semidirect
70. C₄×C₇₉⋊C₈	D₄	semidirect
77. #121×C₇₉	C₈	semidirect
128. C₂×D₄×C₇₉	C₂×C₈	semidirect
129. C₂×D₄×C₇₉	C₂×C₈	semidirect
145. C₂²×C₄×C₇₉	C₂×C₈	semidirect
160. C₄⋊C₄×C₇₉	C₂×C₈	semidirect
165. C₂²⋊C₄×C₇₉	C₂×C₈	semidirect
236. C₇₉⋊C₈	#121	direct (N × H)
250. C₂²×C₇₉	C₈×D₄	semidirect
265. C₄×C₇₉	C₈×D₄	semidirect
291. C₇₉	C₈×#121	semidirect
345. #121	C₇₉⋊C₈	direct (N × H)
387. C₂×D₄	C₂×C₇₉⋊C₈	semidirect
388. C₂×D₄	C₂×C₇₉⋊C₈	semidirect
404. C₂²×C₄	C₂×C₇₉⋊C₈	semidirect
440. C₄⋊C₄	C₂×C₇₉⋊C₈	semidirect
445. C₂²⋊C₄	C₂×C₇₉⋊C₈	semidirect
530. C₂²	D₄×C₇₉⋊C₈	semidirect
545. C₄	D₄×C₇₉⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×C₇₉⋊C₈	2
C₂²×C₄×C₇₉⋊C₈	2
#23764195	2
#23764119	2
#23764008	2
#23763693	2
#23763380	2
C₄⋊C₄×C₇₉⋊C₈	2
C₂²⋊C₄×C₇₉⋊C₈	2
C₄×#121×C₇₉	2
C₈×#121	79

Subgroups — #121×C79⋊C8 #34294298

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #121×C₇₉⋊C₈ #34294298