Subgroups — #34310377

Order 20224.

1168 conjugacy classes of subgroups.

The subgroup lattice has 552 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	1	yes	maximal, characteristic, complemented
2	C₂×D₄×C₇₉⋊C₈	C₂	1	2	yes	maximal, 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	#23763580	C₂	1	2	yes	maximal, complemented
9	C₄⋊C₄×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₂²⋊(C₇₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#121×C₇₉	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₇₉⋊C₈	C₂²	1	2	yes	—
13	C₂³×C₇₉⋊C₈	C₂²	1	2	yes	—
14	D₄×C₇₉⋊C₈	—	2	4	no	—
15	D₄×C₇₉⋊C₈	—	2	8	no	—
16	C₂×C₄⋊(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	2	yes	—
20	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
24	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
25	C₂×C₂²⋊(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	#19098318	C₂²	1	1	yes	characteristic
30	#19098318	C₂²	1	2	yes	—
31	#19098318	C₂²	1	2	yes	—
32	#19098318	C₂²	1	1	yes	characteristic
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	4	no	—
45	C₂²×C₇₉⋊C₈	—	2	4	no	—
46	C₂²×C₇₉⋊C₈	—	2	4	no	—
47	C₂²×C₇₉⋊C₈	—	2	4	no	—
48	C₂²×C₇₉⋊C₈	—	4	2	no	—
49	C₂²×C₇₉⋊C₈	—	4	2	no	—
50	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
51	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
52	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
53	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
54	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
55	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
56	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
57	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
58	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
59	C₄⋊(C₇₉⋊C₈)	D₄	1	4	yes	complemented
60	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
61	C₂²⋊(C₇₉⋊C₈)	—	2	4	no	—
62	C₂²⋊(C₇₉⋊C₈)	—	2	4	no	—
63	C₂²⋊(C₇₉⋊C₈)	—	4	2	no	—
64	C₂²⋊(C₇₉⋊C₈)	D₄	1	4	yes	complemented
65	C₄×C₇₉⋊C₈	—	2	2	no	—
66	C₄×C₇₉⋊C₈	—	2	2	no	—
67	C₄×C₇₉⋊C₈	—	2	4	no	—
68	C₂²×D₄×C₇₉	C₂×C₄	1	2	yes	—
69	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
70	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
71	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
72	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
73	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
74	#121×C₇₉	C₈	1	8	yes	complemented
75	C₄×D₄×C₇₉	—	2	4	no	—
76	C₄×D₄×C₇₉	—	2	4	no	—
77	C₄×D₄×C₇₉	—	2	2	no	—
78	C₄×D₄×C₇₉	—	2	2	no	—
79	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
81	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
83	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
84	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
85	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
86	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
87	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
88	C₂×C₄²×C₇₉	—	2	2	no	—
89	C₂×C₄²×C₇₉	—	2	2	no	—
90	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
94	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
95	#95×C₇₉	C₂×C₄	1	2	yes	—
96	#95×C₇₉	C₂×C₄	1	2	yes	—
97	#95×C₇₉	C₂×C₄	1	2	yes	—
98	C₂×C₇₉⋊C₈	—	2	2	no	—
99	C₂×C₇₉⋊C₈	—	2	1	no	—
100	C₂×C₇₉⋊C₈	—	2	1	no	—
101	C₂×C₇₉⋊C₈	—	2	2	no	—
102	C₂×C₇₉⋊C₈	—	2	2	no	—
103	C₂×C₇₉⋊C₈	—	2	1	no	—
104	C₂×C₇₉⋊C₈	—	2	1	no	—
105	C₂×C₇₉⋊C₈	—	2	1	no	—
106	C₂×C₇₉⋊C₈	—	2	1	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	—	4	8	no	—
114	C₂×C₇₉⋊C₈	—	4	8	no	—
115	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
116	C₂×C₇₉⋊C₈	C₂×D₄	1	4	yes	—
117	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
118	C₂⁴×C₇₉	C₂²×C₄	1	2	yes	—
119	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
120	C₂×D₄×C₇₉	—	2	4	no	—
121	C₂×D₄×C₇₉	—	2	4	no	—
122	C₂×D₄×C₇₉	—	2	2	no	—
123	C₂×D₄×C₇₉	—	2	2	no	—
124	C₂×D₄×C₇₉	C₂×C₈	1	8	yes	complemented
125	C₂×D₄×C₇₉	C₂×C₈	1	4	yes	complemented
126	C₂²×C₄×C₇₉	—	2	2	no	—
127	C₂²×C₄×C₇₉	—	2	2	no	—
128	C₂²×C₄×C₇₉	—	2	1	no	—
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	2	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	—	2	2	no	—
139	C₂²×C₄×C₇₉	—	2	2	no	—
140	C₂²×C₄×C₇₉	—	4	1	no	—
141	C₂²×C₄×C₇₉	C₂×C₈	1	4	yes	complemented
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	C₂²×C₄	1	2	yes	—
149	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₇₉	#41	1	2	yes	—
152	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
153	C₄⋊C₄×C₇₉	—	2	4	no	—
154	C₄⋊C₄×C₇₉	—	2	2	no	—
155	C₄⋊C₄×C₇₉	—	2	2	no	—
156	C₄⋊C₄×C₇₉	C₂×C₈	1	4	yes	complemented
157	C₂²⋊C₄×C₇₉	—	2	4	no	—
158	C₂²⋊C₄×C₇₉	—	2	4	no	—
159	C₂²⋊C₄×C₇₉	—	2	4	no	—
160	C₂²⋊C₄×C₇₉	—	4	2	no	—
161	C₂²⋊C₄×C₇₉	C₂×C₈	1	8	yes	complemented
162	C₄²×C₇₉	—	2	2	no	—
163	C₄²×C₇₉	—	2	2	no	—
164	C₄²×C₇₉	—	2	1	no	—
165	C₄²×C₇₉	—	2	2	no	—
166	C₄²×C₇₉	—	2	1	no	—
167	C₄²×C₇₉	—	2	2	no	—
168	C₄²×C₇₉	C₂×D₄	1	2	yes	—
169	C₄²×C₇₉	#41	1	2	yes	—
170	C₂³×C₇₉	—	2	1	no	—
171	C₂³×C₇₉	—	2	1	no	—
172	C₂³×C₇₉	—	2	1	no	—
173	C₂³×C₇₉	—	2	1	no	—
174	C₂³×C₇₉	—	2	2	no	—
175	C₂³×C₇₉	—	2	2	no	—
176	C₂³×C₇₉	—	2	2	no	—
177	C₂³×C₇₉	—	2	2	no	—
178	C₂³×C₇₉	—	2	2	no	—
179	C₂³×C₇₉	—	2	2	no	—
180	C₂³×C₇₉	C₄×D₄	1	2	yes	—
181	C₂³×C₇₉	C₂²×C₈	1	4	yes	—
182	C₂³×C₇₉	C₂²×C₈	1	2	yes	—
183	C₂³×C₇₉	#131	1	2	yes	—
184	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
185	D₄×C₇₉	—	2	16	no	—
186	D₄×C₇₉	—	2	8	no	—
187	C₂×C₄×C₇₉	—	2	1	no	—
188	C₂×C₄×C₇₉	—	2	1	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	1	no	—
193	C₂×C₄×C₇₉	—	2	2	no	—
194	C₂×C₄×C₇₉	—	2	1	no	—
195	C₂×C₄×C₇₉	—	2	2	no	—
196	C₂×C₄×C₇₉	—	2	2	no	—
197	C₂×C₄×C₇₉	—	2	2	no	—
198	C₂×C₄×C₇₉	—	2	2	no	—
199	C₂×C₄×C₇₉	—	2	8	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	1	no	—
207	C₂×C₄×C₇₉	—	2	1	no	—
208	C₂×C₄×C₇₉	—	2	2	no	—
209	C₂×C₄×C₇₉	—	4	4	no	—
210	C₂×C₄×C₇₉	—	4	2	no	—
211	C₂×C₄×C₇₉	—	4	2	no	—
212	C₂×C₄×C₇₉	—	4	2	no	—
213	C₂×C₄×C₇₉	—	4	2	no	—
214	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
215	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
216	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
217	C₂×C₄×C₇₉	C₂²×C₈	1	2	yes	—
218	C₂×C₄×C₇₉	C₂²×C₈	1	4	yes	—
219	C₂×C₄×C₇₉	C₂²×C₈	1	2	yes	—
220	C₂×C₄×C₇₉	#131	1	2	yes	—
221	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
226	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
227	C₇₉⋊C₈	—	2	4	no	—
228	C₇₉⋊C₈	—	2	2	no	—
229	C₇₉⋊C₈	—	2	2	no	—
230	C₇₉⋊C₈	—	4	2	no	—
231	C₇₉⋊C₈	—	4	1	no	—
232	C₇₉⋊C₈	—	4	1	no	—
233	C₂²×C₇₉	—	2	2	no	—
234	C₂²×C₇₉	—	2	2	no	—
235	C₂²×C₇₉	—	2	2	no	—
236	C₂²×C₇₉	—	2	2	no	—
237	C₂²×C₇₉	—	2	2	no	—
238	C₂²×C₇₉	—	2	2	no	—
239	C₂²×C₇₉	—	2	4	no	—
240	C₂²×C₇₉	—	2	4	no	—
241	C₂²×C₇₉	—	2	4	no	—
242	C₂²×C₇₉	—	4	2	no	—
243	C₂²×C₇₉	—	4	2	no	—
244	C₂²×C₇₉	—	4	2	no	—
245	C₂²×C₇₉	—	4	2	no	—
246	C₂²×C₇₉	C₈×D₄	1	4	yes	complemented
247	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
248	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
249	C₂²×C₇₉	#520	1	1	yes	characteristic
250	C₂²×C₇₉	C₂³×C₈	1	1	yes	characteristic
251	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
252	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
253	C₂²×C₇₉	#568	1	1	yes	characteristic
254	C₄×C₇₉	—	2	2	no	—
255	C₄×C₇₉	—	2	2	no	—
256	C₄×C₇₉	—	2	4	no	—
257	C₄×C₇₉	—	2	2	no	—
258	C₄×C₇₉	—	4	2	no	—
259	C₄×C₇₉	—	4	1	no	—
260	C₄×C₇₉	—	4	2	no	—
261	C₄×C₇₉	C₈×D₄	1	4	yes	complemented
262	C₄×C₇₉	D₄²	1	1	yes	characteristic
263	C₄×C₇₉	#547	1	1	yes	characteristic
264	C₄×C₇₉	#548	1	1	yes	characteristic
265	C₄×C₇₉	#553	1	1	yes	characteristic
266	#22985	—	79	1	no	maximal, Sylow
267	C₂×C₇₉	—	2	4	no	—
268	C₂×C₇₉	—	4	4	no	—
269	C₂×C₇₉	#2361	1	1	yes	characteristic
270	C₂×C₇₉	C₂×C₈×D₄	1	1	yes	characteristic
271	C₂×C₇₉	C₂×C₈×D₄	1	1	yes	characteristic
272	C₂×C₇₉	#2933	1	1	yes	characteristic
273	C₂×C₇₉	#2935	1	1	yes	characteristic
274	C₂×C₇₉	#2988	1	1	yes	characteristic
275	C₂×C₇₉	#2994	1	1	yes	characteristic
276	C₂×C₈×D₄	—	79	2	no	—
277	C₂×C₈×D₄	—	79	1	no	—
278	C₂²×C₄⋊C₈	—	79	1	no	—
279	C₄×#121	D₇₉	1	1	yes	characteristic
280	#1954	—	79	1	no	—
281	#1939	—	79	1	no	—
282	#1923	—	79	2	no	—
283	#1869	—	79	2	no	—
284	#1850	—	79	2	no	—
285	C₈×C₄⋊C₄	—	79	1	no	—
286	C₄×C₂²⋊C₈	—	79	1	no	—
287	C₇₉	#22985	1	1	yes	characteristic, complemented, Sylow
288	C₂³×C₈	—	79	2	no	—
289	C₂³×C₈	—	79	2	no	—
290	C₂×#121	Dic₇₉	1	1	yes	characteristic
291	C₂×C₄×D₄	C₂×D₇₉	1	2	yes	—
292	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
293	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
294	C₈×D₄	—	158	8	no	—
295	C₈×D₄	—	158	4	no	—
296	C₂×C₄⋊C₈	—	79	1	no	—
297	C₂×C₄⋊C₈	—	79	2	no	—
298	C₂×C₄⋊C₈	—	79	2	no	—
299	C₂×C₄⋊C₈	—	79	1	no	—
300	C₂×C₄⋊C₈	—	158	4	no	—
301	C₂×C₂²⋊C₈	—	79	2	no	—
302	C₂×C₂²⋊C₈	—	79	1	no	—
303	C₂×C₂²⋊C₈	—	79	1	no	—
304	C₂×C₂²⋊C₈	—	79	2	no	—
305	C₂×C₂²⋊C₈	—	79	2	no	—
306	C₂×C₄×C₈	—	79	2	no	—
307	C₂×C₄×C₈	—	79	1	no	—
308	C₂×C₄×C₈	—	79	1	no	—
309	#390	Dic₇₉	1	1	yes	characteristic
310	#389	Dic₇₉	1	1	yes	characteristic
311	#388	Dic₇₉	1	2	yes	—
312	#386	Dic₇₉	1	2	yes	—
313	#380	Dic₇₉	1	1	yes	characteristic
314	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
315	C₄×C₂²⋊C₄	C₂×D₇₉	1	2	yes	—
316	#336	—	79	1	no	—
317	#336	—	79	2	no	—
318	#336	—	79	2	no	—
319	#336	—	79	1	no	—
320	C₂²×D₄	C₂×Dic₇₉	1	2	yes	—
321	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
322	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
323	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
324	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
325	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
326	C₂²×C₈	—	316	2	no	—
327	C₂²×C₈	—	316	2	no	—
328	C₂²×C₈	—	79	1	no	—
329	C₂²×C₈	—	79	2	no	—
330	C₂²×C₈	—	79	1	no	—
331	C₂²×C₈	—	79	2	no	—
332	C₂²×C₈	—	79	1	no	—
333	C₂²×C₈	—	79	1	no	—
334	C₂²×C₈	—	158	4	no	—
335	C₂²×C₈	—	158	4	no	—
336	C₂²×C₈	—	158	4	no	—
337	C₂²×C₈	—	158	4	no	—
338	#121	C₇₉⋊C₈	1	8	yes	complemented
339	C₄×D₄	—	2	4	no	—
340	C₄×D₄	—	2	4	no	—
341	C₄×D₄	—	2	2	no	—
342	C₄×D₄	—	2	2	no	—
343	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
345	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
346	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
347	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
348	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
349	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
350	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
351	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
352	C₂×C₄²	—	2	2	no	—
353	C₂×C₄²	—	2	2	no	—
354	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
355	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
356	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
357	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
358	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
359	C₄⋊C₈	—	79	4	no	—
360	C₄⋊C₈	—	158	4	no	—
361	C₄⋊C₈	—	158	4	no	—
362	C₄⋊C₈	—	158	2	no	—
363	C₂²⋊C₈	—	316	2	no	—
364	C₂²⋊C₈	—	79	4	no	—
365	C₂²⋊C₈	—	158	4	no	—
366	C₂²⋊C₈	—	158	4	no	—
367	C₂²⋊C₈	—	158	2	no	—
368	C₄×C₈	—	158	4	no	—
369	C₄×C₈	—	158	2	no	—
370	C₄×C₈	—	158	2	no	—
371	#95	C₂×Dic₇₉	1	2	yes	—
372	#95	C₂×Dic₇₉	1	2	yes	—
373	#95	C₂×Dic₇₉	1	2	yes	—
374	C₂⁴	C₂²×Dic₇₉	1	2	yes	—
375	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
376	C₂×D₄	—	2	4	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	C₂×C₇₉⋊C₈	1	8	yes	complemented
381	C₂×D₄	C₂×C₇₉⋊C₈	1	4	yes	complemented
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	4	1	no	—
397	C₂²×C₄	C₂×C₇₉⋊C₈	1	4	yes	complemented
398	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
399	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
400	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
401	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
402	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
403	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
404	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
405	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
406	C₂²×C₄	D₄×D₇₉	1	2	yes	—
407	C₂²×C₄	#11929623	1	2	yes	—
408	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
409	C₂×C₈	—	316	8	no	—
410	C₂×C₈	—	316	8	no	—
411	C₂×C₈	—	79	2	no	—
412	C₂×C₈	—	79	2	no	—
413	C₂×C₈	—	79	4	no	—
414	C₂×C₈	—	158	1	no	—
415	C₂×C₈	—	158	1	no	—
416	C₂×C₈	—	158	1	no	—
417	C₂×C₈	—	158	1	no	—
418	C₂×C₈	—	158	2	no	—
419	C₂×C₈	—	158	1	no	—
420	C₂×C₈	—	158	1	no	—
421	C₂×C₈	—	158	2	no	—
422	C₂×C₈	—	158	2	no	—
423	C₂×C₈	—	158	1	no	—
424	C₂×C₈	—	158	2	no	—
425	C₂×C₈	—	158	1	no	—
426	C₂×C₈	—	158	1	no	—
427	C₂×C₈	—	158	2	no	—
428	C₂×C₈	—	158	1	no	—
429	C₄⋊C₄	—	2	4	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	C₂×C₇₉⋊C₈	1	4	yes	complemented
433	C₂²⋊C₄	—	2	4	no	—
434	C₂²⋊C₄	—	2	4	no	—
435	C₂²⋊C₄	—	2	4	no	—
436	C₂²⋊C₄	—	4	2	no	—
437	C₂²⋊C₄	C₂×C₇₉⋊C₈	1	8	yes	complemented
438	C₄²	—	2	1	no	—
439	C₄²	—	2	2	no	—
440	C₄²	—	2	2	no	—
441	C₄²	—	2	2	no	—
442	C₄²	—	2	2	no	—
443	C₄²	—	2	1	no	—
444	C₄²	D₄×D₇₉	1	2	yes	—
445	C₄²	#11929623	1	2	yes	—
446	C₂³	—	2	1	no	—
447	C₂³	—	2	1	no	—
448	C₂³	—	2	1	no	—
449	C₂³	—	2	1	no	—
450	C₂³	—	2	2	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	2	no	—
455	C₂³	—	2	2	no	—
456	C₂³	D₄×Dic₇₉	1	2	yes	—
457	C₂³	C₂²×C₇₉⋊C₈	1	4	yes	—
458	C₂³	C₂²×C₇₉⋊C₈	1	2	yes	—
459	C₂³	#14579168	1	2	yes	—
460	C₂³	C₂³×Dic₇₉	1	1	yes	characteristic
461	D₄	—	2	16	no	—
462	D₄	—	2	8	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	8	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	4	4	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
491	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
492	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
493	C₂×C₄	C₂²×C₇₉⋊C₈	1	2	yes	—
494	C₂×C₄	C₂²×C₇₉⋊C₈	1	4	yes	—
495	C₂×C₄	C₂²×C₇₉⋊C₈	1	2	yes	—
496	C₂×C₄	#14579168	1	2	yes	—
497	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
498	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
499	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
500	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
501	C₂×C₄	#14579207	1	1	yes	characteristic
502	C₂×C₄	#14579208	1	1	yes	characteristic
503	C₈	—	316	2	no	—
504	C₈	—	316	1	no	—
505	C₈	—	316	1	no	—
506	C₈	—	158	4	no	—
507	C₈	—	158	2	no	—
508	C₈	—	158	2	no	—
509	C₂²	—	2	2	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	2	2	no	—
513	C₂²	—	2	2	no	—
514	C₂²	—	2	2	no	—
515	C₂²	—	2	4	no	—
516	C₂²	—	2	4	no	—
517	C₂²	—	2	4	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	D₄×C₇₉⋊C₈	1	4	yes	complemented
523	C₂²	C₂×D₄×Dic₇₉	1	1	yes	characteristic
524	C₂²	C₂×D₄×Dic₇₉	1	1	yes	characteristic
525	C₂²	#19099046	1	1	yes	characteristic
526	C₂²	C₂³×C₇₉⋊C₈	1	1	yes	characteristic
527	C₂²	C₂×#14579168	1	1	yes	characteristic
528	C₂²	C₂×#14579168	1	1	yes	characteristic
529	C₂²	#19099330	1	1	yes	characteristic
530	C₄	—	2	2	no	—
531	C₄	—	2	2	no	—
532	C₄	—	2	4	no	—
533	C₄	—	2	2	no	—
534	C₄	—	4	2	no	—
535	C₄	—	4	1	no	—
536	C₄	—	4	2	no	—
537	C₄	D₄×C₇₉⋊C₈	1	4	yes	complemented
538	C₄	#19099197	1	1	yes	characteristic
539	C₄	#19099213	1	1	yes	characteristic
540	C₄	#19099219	1	1	yes	characteristic
541	C₄	#19099265	1	1	yes	characteristic
542	C₂	—	2	4	no	—
543	C₂	—	4	4	no	—
544	C₂	#23766420	1	1	yes	characteristic
545	C₂	C₂×D₄×C₇₉⋊C₈	1	1	yes	characteristic
546	C₂	C₂×D₄×C₇₉⋊C₈	1	1	yes	characteristic
547	C₂	#23772127	1	1	yes	characteristic
548	C₂	#23772144	1	1	yes	characteristic
549	C₂	#23772511	1	1	yes	characteristic
550	C₂	#23772560	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	#22985
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. #23763580	C₂	semidirect
9. C₄⋊C₄×C₇₉⋊C₈	C₂	semidirect
10. C₄×C₂²⋊(C₇₉⋊C₈)	C₂	semidirect
59. C₄⋊(C₇₉⋊C₈)	D₄	semidirect
64. C₂²⋊(C₇₉⋊C₈)	D₄	semidirect
74. #121×C₇₉	C₈	semidirect
124. C₂×D₄×C₇₉	C₂×C₈	semidirect
125. C₂×D₄×C₇₉	C₂×C₈	semidirect
141. C₂²×C₄×C₇₉	C₂×C₈	semidirect
156. C₄⋊C₄×C₇₉	C₂×C₈	semidirect
161. C₂²⋊C₄×C₇₉	C₂×C₈	semidirect
246. C₂²×C₇₉	C₈×D₄	semidirect
261. C₄×C₇₉	C₈×D₄	semidirect
287. C₇₉	#22985	semidirect
338. #121	C₇₉⋊C₈	semidirect
380. C₂×D₄	C₂×C₇₉⋊C₈	semidirect
381. C₂×D₄	C₂×C₇₉⋊C₈	semidirect
397. C₂²×C₄	C₂×C₇₉⋊C₈	semidirect
432. C₄⋊C₄	C₂×C₇₉⋊C₈	semidirect
437. C₂²⋊C₄	C₂×C₇₉⋊C₈	semidirect
522. C₂²	D₄×C₇₉⋊C₈	semidirect
537. 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
#23763580	2
C₄⋊C₄×C₇₉⋊C₈	2
C₄×C₂²⋊(C₇₉⋊C₈)	2
C₄×#121×C₇₉	2
#22985	79