Subgroups — #34304791

Order 20224.

1064 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098694	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×Q₈×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#23764341	C₂	1	2	yes	maximal, complemented
4	#23764337	C₂	1	1	yes	maximal, characteristic, complemented
5	#23764337	C₂	1	1	yes	maximal, characteristic, complemented
6	#23764337	C₂	1	2	yes	maximal, complemented
7	#23763384	C₂	1	2	yes	maximal
8	#23763380	C₂	1	1	yes	maximal, characteristic
9	#23763166	C₂	1	2	yes	maximal
10	C₄×C₂²⋊(C₇₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
11	C₂×#533×C₇₉	C₂	1	1	yes	maximal, characteristic
12	#19098694	—	2	4	no	—
13	Q₈×C₇₉⋊C₈	—	2	4	no	—
14	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
17	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
18	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
19	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×#14579072	C₂²	1	2	yes	—
22	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₇₉⋊C₈	C₂²	1	2	yes	—
24	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
25	#19098318	C₂²	1	2	yes	—
26	#19098318	C₂²	1	1	yes	characteristic
27	#19098318	C₂²	1	2	yes	—
28	#19098318	C₂²	1	2	yes	—
29	#19098318	C₂²	1	2	yes	—
30	#19098318	C₂²	1	2	yes	—
31	#19098318	C₂²	1	1	yes	characteristic
32	#533×C₇₉	—	2	4	no	—
33	#533×C₇₉	—	2	4	no	—
34	C₂×C₄⋊Q₈×C₇₉	C₄	1	1	yes	characteristic
35	C₂×C₄⋊Q₈×C₇₉	C₄	1	1	yes	characteristic
36	C₂×#125×C₇₉	C₄	1	2	yes	—
37	C₂×C₂²⋊Q₈×C₇₉	C₄	1	1	yes	characteristic
38	C₂×C₂²⋊Q₈×C₇₉	C₄	1	1	yes	characteristic
39	C₂×C₂²⋊Q₈×C₇₉	C₄	1	2	yes	—
40	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₇₉	C₂²	1	2	yes	—
42	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
43	C₂×#117×C₇₉	C₂²	1	2	yes	—
44	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
45	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
47	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
49	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
50	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
51	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
52	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
53	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
54	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
55	C₂²⋊(C₇₉⋊C₈)	—	2	4	no	—
56	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
57	C₂²⋊(C₇₉⋊C₈)	Q₈	1	4	yes	complemented
58	#14579072	—	2	4	no	—
59	C₄×C₇₉⋊C₈	—	2	2	no	—
60	C₄×C₇₉⋊C₈	—	2	4	no	—
61	C₄×C₇₉⋊C₈	—	2	2	no	—
62	C₂²×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
63	C₂²×Q₈×C₇₉	C₂×C₄	1	2	yes	—
64	C₂²×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
65	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
66	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
67	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
68	C₄⋊Q₈×C₇₉	—	2	4	no	—
69	C₄⋊Q₈×C₇₉	—	2	4	no	—
70	#125×C₇₉	—	2	8	no	—
71	C₂²⋊Q₈×C₇₉	—	2	4	no	—
72	C₂²⋊Q₈×C₇₉	—	2	4	no	—
73	C₂²⋊Q₈×C₇₉	—	2	8	no	—
74	C₄×Q₈×C₇₉	—	2	4	no	—
75	C₄×Q₈×C₇₉	—	2	4	no	—
76	C₄×Q₈×C₇₉	—	2	2	no	—
77	C₄×Q₈×C₇₉	—	2	2	no	—
78	C₄×Q₈×C₇₉	D₄	1	4	yes	—
79	C₄×Q₈×C₇₉	D₄	1	4	yes	—
80	#117×C₇₉	—	2	4	no	—
81	#117×C₇₉	—	2	4	no	—
82	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
83	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
84	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
85	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
86	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
87	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
89	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
90	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
92	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
93	C₂×C₄²×C₇₉	—	2	2	no	—
94	C₂×C₄²×C₇₉	—	2	2	no	—
95	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
99	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
101	C₂×C₇₉⋊C₈	—	2	1	no	—
102	C₂×C₇₉⋊C₈	—	2	1	no	—
103	C₂×C₇₉⋊C₈	—	2	1	no	—
104	C₂×C₇₉⋊C₈	—	2	2	no	—
105	C₂×C₇₉⋊C₈	—	2	1	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	2	no	—
111	C₂×C₇₉⋊C₈	—	2	1	no	—
112	C₂×C₇₉⋊C₈	—	2	1	no	—
113	C₂×C₇₉⋊C₈	—	2	1	no	—
114	C₂×C₇₉⋊C₈	—	2	2	no	—
115	C₂×C₇₉⋊C₈	—	2	1	no	—
116	C₂×C₇₉⋊C₈	—	2	2	no	—
117	C₂×C₇₉⋊C₈	C₂×Q₈	1	2	yes	—
118	C₂×C₇₉⋊C₈	C₂×Q₈	1	2	yes	—
119	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
120	C₂×Q₈×C₇₉	—	2	4	no	—
121	C₂×Q₈×C₇₉	—	2	2	no	—
122	C₂×Q₈×C₇₉	—	2	2	no	—
123	C₂×Q₈×C₇₉	—	2	2	no	—
124	C₂×Q₈×C₇₉	—	2	4	no	—
125	C₂×Q₈×C₇₉	—	2	2	no	—
126	C₂×Q₈×C₇₉	—	2	2	no	—
127	C₂×Q₈×C₇₉	—	4	2	no	—
128	C₂×Q₈×C₇₉	C₂²⋊C₄	1	4	yes	—
129	C₂²×C₄×C₇₉	—	2	1	no	—
130	C₂²×C₄×C₇₉	—	2	1	no	—
131	C₂²×C₄×C₇₉	—	2	1	no	—
132	C₂²×C₄×C₇₉	—	2	1	no	—
133	C₂²×C₄×C₇₉	—	2	2	no	—
134	C₂²×C₄×C₇₉	—	2	2	no	—
135	C₂²×C₄×C₇₉	—	2	2	no	—
136	C₂²×C₄×C₇₉	—	2	2	no	—
137	C₂²×C₄×C₇₉	—	2	2	no	—
138	C₂²×C₄×C₇₉	—	4	1	no	—
139	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
144	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
145	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₇₉	C₂×Q₈	1	2	yes	—
149	C₂²×C₄×C₇₉	#41	1	2	yes	—
150	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
151	C₄⋊C₄×C₇₉	—	2	4	no	—
152	C₄⋊C₄×C₇₉	—	2	4	no	—
153	C₄⋊C₄×C₇₉	—	2	4	no	—
154	C₄⋊C₄×C₇₉	—	2	4	no	—
155	C₄⋊C₄×C₇₉	—	2	4	no	—
156	C₄⋊C₄×C₇₉	—	2	4	no	—
157	C₄⋊C₄×C₇₉	—	2	2	no	—
158	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	8	yes	—
159	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	4	yes	—
160	C₂²⋊C₄×C₇₉	—	2	4	no	—
161	C₂²⋊C₄×C₇₉	—	2	4	no	—
162	C₄²×C₇₉	—	2	2	no	—
163	C₄²×C₇₉	—	2	2	no	—
164	C₄²×C₇₉	—	2	1	no	—
165	C₄²×C₇₉	—	2	1	no	—
166	C₄²×C₇₉	—	2	2	no	—
167	C₄²×C₇₉	—	2	2	no	—
168	C₄²×C₇₉	C₂×D₄	1	2	yes	—
169	C₄²×C₇₉	C₂×D₄	1	2	yes	—
170	C₄²×C₇₉	C₂×D₄	1	4	yes	—
171	C₄²×C₇₉	C₂×D₄	1	4	yes	—
172	C₂³×C₇₉	—	2	1	no	—
173	C₂³×C₇₉	—	2	1	no	—
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	C₄×Q₈	1	2	yes	—
179	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
180	Q₈×C₇₉	—	2	8	no	—
181	Q₈×C₇₉	—	4	8	no	—
182	Q₈×C₇₉	—	4	4	no	—
183	C₂×C₄×C₇₉	—	2	1	no	—
184	C₂×C₄×C₇₉	—	2	1	no	—
185	C₂×C₄×C₇₉	—	2	1	no	—
186	C₂×C₄×C₇₉	—	2	1	no	—
187	C₂×C₄×C₇₉	—	2	2	no	—
188	C₂×C₄×C₇₉	—	2	2	no	—
189	C₂×C₄×C₇₉	—	2	2	no	—
190	C₂×C₄×C₇₉	—	2	1	no	—
191	C₂×C₄×C₇₉	—	2	1	no	—
192	C₂×C₄×C₇₉	—	2	2	no	—
193	C₂×C₄×C₇₉	—	2	2	no	—
194	C₂×C₄×C₇₉	—	2	2	no	—
195	C₂×C₄×C₇₉	—	2	2	no	—
196	C₂×C₄×C₇₉	—	2	2	no	—
197	C₂×C₄×C₇₉	—	2	1	no	—
198	C₂×C₄×C₇₉	—	2	2	no	—
199	C₂×C₄×C₇₉	—	2	2	no	—
200	C₂×C₄×C₇₉	—	2	1	no	—
201	C₂×C₄×C₇₉	—	2	1	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	—	4	4	no	—
207	C₂×C₄×C₇₉	—	4	4	no	—
208	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
209	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	4	yes	—
210	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	4	yes	—
211	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
212	C₂×C₄×C₇₉	C₄×Q₈	1	2	yes	—
213	C₂×C₄×C₇₉	#131	1	2	yes	—
214	C₂×C₄×C₇₉	#131	1	2	yes	—
215	C₂×C₄×C₇₉	#131	1	2	yes	—
216	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
219	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
221	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
222	C₇₉⋊C₈	—	2	2	no	—
223	C₇₉⋊C₈	—	2	2	no	—
224	C₇₉⋊C₈	—	4	1	no	—
225	C₇₉⋊C₈	—	4	2	no	—
226	C₇₉⋊C₈	—	4	1	no	—
227	C₇₉⋊C₈	—	4	2	no	—
228	C₂²×C₇₉	—	2	2	no	—
229	C₂²×C₇₉	—	2	2	no	—
230	C₂²×C₇₉	—	2	2	no	—
231	C₂²×C₇₉	—	4	1	no	—
232	C₂²×C₇₉	—	4	1	no	—
233	C₂²×C₇₉	—	4	1	no	—
234	C₂²×C₇₉	—	4	1	no	—
235	C₂²×C₇₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
236	C₂²×C₇₉	C₂×C₄×Q₈	1	1	yes	characteristic
237	C₂²×C₇₉	#519	1	1	yes	characteristic
238	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
239	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
240	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
241	C₂²×C₇₉	#568	1	1	yes	characteristic
242	C₄×C₇₉	—	2	2	no	—
243	C₄×C₇₉	—	2	4	no	—
244	C₄×C₇₉	—	2	2	no	—
245	C₄×C₇₉	—	2	2	no	—
246	C₄×C₇₉	—	2	4	no	—
247	C₄×C₇₉	—	4	1	no	—
248	C₄×C₇₉	—	4	2	no	—
249	C₄×C₇₉	—	4	2	no	—
250	C₄×C₇₉	#408	1	4	yes	—
251	C₄×C₇₉	#548	1	1	yes	characteristic
252	C₄×C₇₉	#548	1	1	yes	characteristic
253	C₄×C₇₉	D₄×Q₈	1	1	yes	characteristic
254	C₄×C₇₉	D₄×Q₈	1	1	yes	characteristic
255	#22509	—	79	1	no	maximal, Sylow
256	C₂×C₇₉	—	4	2	no	—
257	C₂×C₇₉	Q₈×C₂²⋊C₄	1	1	yes	characteristic
258	C₂×C₇₉	C₂×#408	1	1	yes	characteristic
259	C₂×C₇₉	#2880	1	1	yes	characteristic
260	C₂×C₇₉	#2960	1	1	yes	characteristic
261	C₂×C₇₉	#2962	1	1	yes	characteristic
262	C₂×C₇₉	#2985	1	1	yes	characteristic
263	C₂×C₇₉	#2986	1	1	yes	characteristic
264	C₂×#533	D₇₉	1	1	yes	characteristic
265	C₂×#446	—	79	1	no	—
266	C₂×C₈×Q₈	—	79	1	no	—
267	#1985	—	79	2	no	—
268	#1984	—	79	1	no	—
269	#1984	—	79	1	no	—
270	#1984	—	79	2	no	—
271	#1798	—	79	2	no	—
272	#1797	—	79	1	no	—
273	#1750	—	79	2	no	—
274	C₄×C₂²⋊C₈	—	79	1	no	—
275	C₇₉	#22509	1	1	yes	characteristic, complemented, Sylow
276	#533	—	2	4	no	—
277	#533	—	2	4	no	—
278	C₂×C₄⋊Q₈	Dic₇₉	1	1	yes	characteristic
279	C₂×C₄⋊Q₈	Dic₇₉	1	1	yes	characteristic
280	C₂×#125	Dic₇₉	1	2	yes	—
281	C₂×C₂²⋊Q₈	Dic₇₉	1	1	yes	characteristic
282	C₂×C₂²⋊Q₈	Dic₇₉	1	1	yes	characteristic
283	C₂×C₂²⋊Q₈	Dic₇₉	1	2	yes	—
284	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
285	C₂×C₄×Q₈	C₂×D₇₉	1	2	yes	—
286	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
287	C₂×#117	C₂×D₇₉	1	2	yes	—
288	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
289	#446	—	158	4	no	—
290	C₈×Q₈	—	158	4	no	—
291	C₂×C₄⋊C₈	—	79	1	no	—
292	C₂×C₄⋊C₈	—	79	1	no	—
293	C₂×C₄⋊C₈	—	79	2	no	—
294	C₂×C₄⋊C₈	—	79	2	no	—
295	C₂×C₂²⋊C₈	—	79	1	no	—
296	C₂×C₂²⋊C₈	—	79	2	no	—
297	C₂×C₂²⋊C₈	—	79	1	no	—
298	C₂×#97	—	79	2	no	—
299	C₂×C₄×C₈	—	79	1	no	—
300	C₂×C₄×C₈	—	79	2	no	—
301	C₂×C₄×C₈	—	79	1	no	—
302	#336	—	79	2	no	—
303	#336	—	79	2	no	—
304	#336	—	79	2	no	—
305	#336	—	79	1	no	—
306	#336	—	79	2	no	—
307	#336	—	79	2	no	—
308	#336	—	79	1	no	—
309	C₂²×Q₈	C₂×Dic₇₉	1	1	yes	characteristic
310	C₂²×Q₈	C₂×Dic₇₉	1	2	yes	—
311	C₂²×Q₈	C₂×Dic₇₉	1	1	yes	characteristic
312	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
313	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
314	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
315	C₂²×C₈	—	79	1	no	—
316	C₂²×C₈	—	79	1	no	—
317	C₂²×C₈	—	79	2	no	—
318	C₂²×C₈	—	79	1	no	—
319	C₂²×C₈	—	79	1	no	—
320	C₂²×C₈	—	79	2	no	—
321	C₄⋊Q₈	—	2	4	no	—
322	C₄⋊Q₈	—	2	4	no	—
323	#125	—	2	8	no	—
324	C₂²⋊Q₈	—	2	4	no	—
325	C₂²⋊Q₈	—	2	4	no	—
326	C₂²⋊Q₈	—	2	8	no	—
327	C₄×Q₈	—	2	4	no	—
328	C₄×Q₈	—	2	4	no	—
329	C₄×Q₈	—	2	2	no	—
330	C₄×Q₈	—	2	2	no	—
331	C₄×Q₈	C₂²⋊D₇₉	1	4	yes	—
332	C₄×Q₈	C₂²⋊D₇₉	1	4	yes	—
333	#117	—	2	4	no	—
334	#117	—	2	4	no	—
335	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
336	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
337	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
338	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
339	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
340	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
342	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
343	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
344	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
345	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
346	C₂×C₄²	—	2	2	no	—
347	C₂×C₄²	—	2	2	no	—
348	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
349	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
350	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
351	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
352	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
353	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
354	C₄⋊C₈	—	158	2	no	—
355	C₄⋊C₈	—	158	4	no	—
356	C₄⋊C₈	—	158	2	no	—
357	C₄⋊C₈	—	158	4	no	—
358	C₂²⋊C₈	—	79	4	no	—
359	C₂²⋊C₈	—	158	4	no	—
360	C₂²⋊C₈	—	158	2	no	—
361	#97	—	158	4	no	—
362	C₄×C₈	—	158	2	no	—
363	C₄×C₈	—	158	4	no	—
364	C₄×C₈	—	158	2	no	—
365	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
366	C₂×Q₈	—	2	4	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	4	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	4	2	no	—
374	C₂×Q₈	C₂²⋊Dic₇₉	1	4	yes	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	4	1	no	—
385	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
386	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
387	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
388	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
389	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
390	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
391	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
392	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
393	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
394	C₂²×C₄	Q₈×D₇₉	1	2	yes	—
395	C₂²×C₄	#11929625	1	2	yes	—
396	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
397	C₂×C₈	—	79	2	no	—
398	C₂×C₈	—	79	2	no	—
399	C₂×C₈	—	158	2	no	—
400	C₂×C₈	—	158	1	no	—
401	C₂×C₈	—	158	1	no	—
402	C₂×C₈	—	158	2	no	—
403	C₂×C₈	—	158	2	no	—
404	C₂×C₈	—	158	1	no	—
405	C₂×C₈	—	158	1	no	—
406	C₂×C₈	—	158	2	no	—
407	C₂×C₈	—	158	1	no	—
408	C₂×C₈	—	158	2	no	—
409	C₂×C₈	—	158	1	no	—
410	C₂×C₈	—	158	2	no	—
411	C₂×C₈	—	158	1	no	—
412	C₂×C₈	—	158	1	no	—
413	C₂×C₈	—	158	1	no	—
414	C₂×C₈	—	158	1	no	—
415	C₄⋊C₄	—	2	4	no	—
416	C₄⋊C₄	—	2	4	no	—
417	C₄⋊C₄	—	2	4	no	—
418	C₄⋊C₄	—	2	4	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	C₂²⋊Dic₇₉	1	8	yes	—
423	C₄⋊C₄	C₂²⋊Dic₇₉	1	4	yes	—
424	C₂²⋊C₄	—	2	4	no	—
425	C₂²⋊C₄	—	2	4	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	2	no	—
428	C₄²	—	2	1	no	—
429	C₄²	—	2	1	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	2	2	no	—
432	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
433	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
434	C₄²	C₂×C₂²⋊D₇₉	1	4	yes	—
435	C₄²	C₂×C₂²⋊D₇₉	1	4	yes	—
436	C₂³	—	2	1	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	2	1	no	—
439	C₂³	—	2	1	no	—
440	C₂³	—	2	1	no	—
441	C₂³	—	2	1	no	—
442	C₂³	Q₈×Dic₇₉	1	2	yes	—
443	C₂³	C₂³×Dic₇₉	1	1	yes	characteristic
444	Q₈	—	2	8	no	—
445	Q₈	—	4	8	no	—
446	Q₈	—	4	4	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	4	4	no	—
471	C₂×C₄	—	4	4	no	—
472	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	2	yes	—
473	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	4	yes	—
474	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	4	yes	—
475	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	2	yes	—
476	C₂×C₄	Q₈×Dic₇₉	1	2	yes	—
477	C₂×C₄	#14579168	1	2	yes	—
478	C₂×C₄	#14579168	1	2	yes	—
479	C₂×C₄	#14579168	1	2	yes	—
480	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
481	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
482	C₂×C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
483	C₂×C₄	C₂×#11929625	1	1	yes	characteristic
484	C₂×C₄	#14579209	1	1	yes	characteristic
485	C₂×C₄	#14579209	1	1	yes	characteristic
486	C₈	—	316	2	no	—
487	C₈	—	316	1	no	—
488	C₈	—	316	1	no	—
489	C₈	—	316	2	no	—
490	C₈	—	158	2	no	—
491	C₈	—	158	2	no	—
492	C₂²	—	2	2	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	4	1	no	—
496	C₂²	—	4	1	no	—
497	C₂²	—	4	1	no	—
498	C₂²	—	4	1	no	—
499	C₂²	C₂²×C₂²⋊Dic₇₉	1	1	yes	characteristic
500	C₂²	C₂×Q₈×Dic₇₉	1	1	yes	characteristic
501	C₂²	#19099041	1	1	yes	characteristic
502	C₂²	C₂×#14579168	1	1	yes	characteristic
503	C₂²	C₂×#14579168	1	1	yes	characteristic
504	C₂²	C₂×#14579168	1	1	yes	characteristic
505	C₂²	#19099330	1	1	yes	characteristic
506	C₄	—	2	4	no	—
507	C₄	—	2	2	no	—
508	C₄	—	2	2	no	—
509	C₄	—	2	4	no	—
510	C₄	—	2	2	no	—
511	C₄	—	4	1	no	—
512	C₄	—	4	2	no	—
513	C₄	—	4	2	no	—
514	C₄	#19098530	1	4	yes	—
515	C₄	#19099224	1	1	yes	characteristic
516	C₄	#19099224	1	1	yes	characteristic
517	C₄	Q₈×C₂²⋊D₇₉	1	1	yes	characteristic
518	C₄	Q₈×C₂²⋊D₇₉	1	1	yes	characteristic
519	C₂	—	4	2	no	—
520	C₂	Q₈×C₂²⋊Dic₇₉	1	1	yes	characteristic
521	C₂	C₂×#19098530	1	1	yes	characteristic
522	C₂	#23771849	1	1	yes	characteristic
523	C₂	#23772335	1	1	yes	characteristic
524	C₂	#23772349	1	1	yes	characteristic
525	C₂	#23772495	1	1	yes	characteristic
526	C₂	#23772502	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator, socle	C₂³×C₇₉	C₂³×C₄
Fitting	C₂×#533×C₇₉	C₂
prime radical	C₂⁴×C₇₉	C₂²×C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₂×#533	D₇₉
hypocenter	C₇₉	#22509
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#533

Complements

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

N	H ≅ G/N	type
1. C₂×#19098694	C₂	semidirect
2. C₂×Q₈×C₇₉⋊C₈	C₂	semidirect
3. #23764341	C₂	semidirect
4. #23764337	C₂	semidirect
5. #23764337	C₂	semidirect
6. #23764337	C₂	semidirect
57. C₂²⋊(C₇₉⋊C₈)	Q₈	semidirect
275. C₇₉	#22509	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098694	2
C₂×Q₈×C₇₉⋊C₈	2
#23764341	2
#23764337	2
#23763384	2
#23763380	2
#23763166	2
C₄×C₂²⋊(C₇₉⋊C₈)	2
C₂×#533×C₇₉	2
#22509	79