Subgroups — #34306315

Order 20224.

1116 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098635	C₂	1	2	yes	maximal
2	C₂×#19098587	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄⋊(C₇₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	#23764124	C₂	1	2	yes	maximal, complemented
5	#23763585	C₂	1	2	yes	maximal, complemented
6	#23763580	C₂	1	2	yes	maximal, complemented
7	#23763552	C₂	1	1	yes	maximal, characteristic, complemented
8	#23763380	C₂	1	1	yes	maximal, characteristic, complemented
9	#23763380	C₂	1	1	yes	maximal, characteristic, complemented
10	#23763253	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄²×D₄×C₇₉	C₂	1	1	yes	maximal, characteristic
12	C₂²×#11929608	C₂²	1	2	yes	—
13	C₂³×C₇₉⋊C₈	C₂²	1	2	yes	—
14	#19098635	—	2	8	no	—
15	#19098587	—	2	4	no	—
16	C₂×C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
17	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
19	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
21	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
23	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
24	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
26	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
27	C₂×#14579072	C₂²	1	2	yes	—
28	#19098318	C₂²	1	2	yes	—
29	#19098318	C₂²	1	2	yes	—
30	#19098318	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₇₉	C₄	1	1	yes	characteristic
32	C₂×C₄×D₄×C₇₉	C₄	1	1	yes	characteristic
33	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₇₉	C₄	1	1	yes	characteristic
37	C₄×C₄⋊C₄×C₇₉	C₄	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
39	C₄×C₂²⋊C₄×C₇₉	C₄	1	1	yes	characteristic
40	C₄×C₂²⋊C₄×C₇₉	C₄	1	1	yes	characteristic
41	C₄×C₂²⋊C₄×C₇₉	C₄	1	1	yes	characteristic
42	C₄×C₂²⋊C₄×C₇₉	C₄	1	1	yes	characteristic
43	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
44	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
45	C₄³×C₇₉	C₂²	1	1	yes	characteristic
46	C₂×#11929608	—	2	4	no	—
47	C₂×#11929608	—	2	4	no	—
48	C₂×#11929608	—	4	2	no	—
49	C₂²×C₇₉⋊C₈	—	2	4	no	—
50	C₂²×C₇₉⋊C₈	—	2	4	no	—
51	C₂²×C₇₉⋊C₈	—	4	2	no	—
52	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
53	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
54	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
55	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
56	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
57	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
58	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
59	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
60	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
61	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
62	C₄⋊(C₇₉⋊C₈)	—	4	2	no	—
63	C₄⋊(C₇₉⋊C₈)	D₄	1	4	yes	complemented
64	C₂²⋊(C₇₉⋊C₈)	—	2	4	no	—
65	C₂²⋊(C₇₉⋊C₈)	—	2	4	no	—
66	#14579072	—	2	4	no	—
67	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
68	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
69	C₂³×C₄×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	1	yes	characteristic
73	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
74	C₄×D₄×C₇₉	—	2	4	no	—
75	C₄×D₄×C₇₉	—	2	4	no	—
76	C₄×D₄×C₇₉	D₄	1	4	yes	—
77	C₄×D₄×C₇₉	Q₈	1	4	yes	—
78	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
83	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
85	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
86	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄²×C₇₉	—	2	2	no	—
88	C₂×C₄²×C₇₉	—	2	2	no	—
89	C₂×C₄²×C₇₉	—	2	2	no	—
90	C₂×C₄²×C₇₉	—	2	2	no	—
91	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
104	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
105	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
106	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
107	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
108	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
109	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
110	#11929608	—	4	8	no	—
111	C₂×C₇₉⋊C₈	—	2	2	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	—	2	2	no	—
116	C₂×C₇₉⋊C₈	—	2	2	no	—
117	C₂×C₇₉⋊C₈	—	2	2	no	—
118	C₂×C₇₉⋊C₈	—	2	2	no	—
119	C₂×C₇₉⋊C₈	—	2	2	no	—
120	C₂×C₇₉⋊C₈	—	2	2	no	—
121	C₂×C₇₉⋊C₈	—	2	2	no	—
122	C₂×C₇₉⋊C₈	—	4	8	no	—
123	C₂×C₇₉⋊C₈	C₂×D₄	1	4	yes	—
124	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
125	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
126	C₂×D₄×C₇₉	—	2	2	no	—
127	C₂×D₄×C₇₉	—	2	2	no	—
128	C₂×D₄×C₇₉	C₄⋊C₄	1	4	yes	—
129	C₂²×C₄×C₇₉	—	2	2	no	—
130	C₂²×C₄×C₇₉	—	2	2	no	—
131	C₂²×C₄×C₇₉	—	2	1	no	—
132	C₂²×C₄×C₇₉	—	2	1	no	—
133	C₂²×C₄×C₇₉	—	2	1	no	—
134	C₂²×C₄×C₇₉	—	2	1	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	—	2	2	no	—
146	C₂²×C₄×C₇₉	—	4	1	no	—
147	C₂²×C₄×C₇₉	—	4	1	no	—
148	C₂²×C₄×C₇₉	M₁₆	1	4	yes	complemented
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	1	yes	characteristic
152	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
163	C₂²×C₄×C₇₉	C₂×Q₈	1	2	yes	—
164	C₂²×C₄×C₇₉	C₂×Q₈	1	2	yes	—
165	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
166	C₄⋊C₄×C₇₉	—	2	2	no	—
167	C₄⋊C₄×C₇₉	—	2	2	no	—
168	C₄⋊C₄×C₇₉	C₄⋊C₄	1	4	yes	—
169	C₂²⋊C₄×C₇₉	—	2	2	no	—
170	C₂²⋊C₄×C₇₉	—	2	2	no	—
171	C₂²⋊C₄×C₇₉	—	2	2	no	—
172	C₂²⋊C₄×C₇₉	C₄⋊C₄	1	4	yes	—
173	C₂²⋊C₄×C₇₉	C₄⋊C₄	1	4	yes	—
174	C₂²⋊C₄×C₇₉	M₁₆	1	4	yes	complemented
175	C₄²×C₇₉	—	2	2	no	—
176	C₄²×C₇₉	—	2	2	no	—
177	C₄²×C₇₉	—	2	2	no	—
178	C₄²×C₇₉	—	2	2	no	—
179	C₄²×C₇₉	—	2	2	no	—
180	C₄²×C₇₉	—	2	2	no	—
181	C₄²×C₇₉	—	2	2	no	—
182	C₄²×C₇₉	—	2	1	no	—
183	C₄²×C₇₉	—	2	1	no	—
184	C₄²×C₇₉	—	2	1	no	—
185	C₄²×C₇₉	—	2	1	no	—
186	C₄²×C₇₉	—	2	1	no	—
187	C₄²×C₇₉	—	2	1	no	—
188	C₄²×C₇₉	—	4	1	no	—
189	C₄²×C₇₉	C₂×D₄	1	2	yes	—
190	C₄²×C₇₉	C₂×D₄	1	2	yes	—
191	C₄²×C₇₉	C₂×Q₈	1	2	yes	—
192	C₄²×C₇₉	#41	1	2	yes	—
193	C₂³×C₇₉	—	2	1	no	—
194	C₂³×C₇₉	—	2	1	no	—
195	C₂³×C₇₉	—	2	1	no	—
196	C₂³×C₇₉	—	2	1	no	—
197	C₂³×C₇₉	—	2	1	no	—
198	C₂³×C₇₉	—	2	1	no	—
199	C₂³×C₇₉	—	2	1	no	—
200	C₂³×C₇₉	—	2	1	no	—
201	C₂³×C₇₉	—	2	1	no	—
202	C₂³×C₇₉	—	2	1	no	—
203	C₂³×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
204	C₂³×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
205	C₂³×C₇₉	C₂×M₁₆	1	2	yes	—
206	C₂³×C₇₉	C₂×M₁₆	1	2	yes	—
207	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
208	D₄×C₇₉	—	2	8	no	—
209	C₂×C₄×C₇₉	—	2	1	no	—
210	C₂×C₄×C₇₉	—	2	1	no	—
211	C₂×C₄×C₇₉	—	2	1	no	—
212	C₂×C₄×C₇₉	—	2	1	no	—
213	C₂×C₄×C₇₉	—	2	1	no	—
214	C₂×C₄×C₇₉	—	2	1	no	—
215	C₂×C₄×C₇₉	—	2	1	no	—
216	C₂×C₄×C₇₉	—	2	1	no	—
217	C₂×C₄×C₇₉	—	2	1	no	—
218	C₂×C₄×C₇₉	—	2	1	no	—
219	C₂×C₄×C₇₉	—	2	1	no	—
220	C₂×C₄×C₇₉	—	2	1	no	—
221	C₂×C₄×C₇₉	—	2	1	no	—
222	C₂×C₄×C₇₉	—	2	1	no	—
223	C₂×C₄×C₇₉	—	2	1	no	—
224	C₂×C₄×C₇₉	—	2	1	no	—
225	C₂×C₄×C₇₉	—	2	2	no	—
226	C₂×C₄×C₇₉	—	2	2	no	—
227	C₂×C₄×C₇₉	—	2	2	no	—
228	C₂×C₄×C₇₉	—	2	2	no	—
229	C₂×C₄×C₇₉	—	2	2	no	—
230	C₂×C₄×C₇₉	—	2	2	no	—
231	C₂×C₄×C₇₉	—	2	2	no	—
232	C₂×C₄×C₇₉	—	2	2	no	—
233	C₂×C₄×C₇₉	—	2	8	no	—
234	C₂×C₄×C₇₉	—	2	1	no	—
235	C₂×C₄×C₇₉	—	2	1	no	—
236	C₂×C₄×C₇₉	—	2	1	no	—
237	C₂×C₄×C₇₉	—	2	1	no	—
238	C₂×C₄×C₇₉	—	2	1	no	—
239	C₂×C₄×C₇₉	—	2	1	no	—
240	C₂×C₄×C₇₉	—	2	1	no	—
241	C₂×C₄×C₇₉	—	2	1	no	—
242	C₂×C₄×C₇₉	—	2	1	no	—
243	C₂×C₄×C₇₉	—	4	4	no	—
244	C₂×C₄×C₇₉	—	4	4	no	—
245	C₂×C₄×C₇₉	—	4	4	no	—
246	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
247	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
248	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
249	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
250	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
251	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
252	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
253	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
254	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
255	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
256	C₂×C₄×C₇₉	#131	1	2	yes	—
257	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
260	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
261	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
262	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
263	C₇₉⋊C₈	—	2	4	no	—
264	C₇₉⋊C₈	—	4	2	no	—
265	C₇₉⋊C₈	—	4	2	no	—
266	C₇₉⋊C₈	—	4	2	no	—
267	C₂²×C₇₉	—	2	2	no	—
268	C₂²×C₇₉	—	2	2	no	—
269	C₂²×C₇₉	—	2	2	no	—
270	C₂²×C₇₉	—	2	2	no	—
271	C₂²×C₇₉	—	2	2	no	—
272	C₂²×C₇₉	—	2	2	no	—
273	C₂²×C₇₉	—	2	2	no	—
274	C₂²×C₇₉	—	2	2	no	—
275	C₂²×C₇₉	—	2	2	no	—
276	C₂²×C₇₉	—	4	1	no	—
277	C₂²×C₇₉	—	4	1	no	—
278	C₂²×C₇₉	—	4	1	no	—
279	C₂²×C₇₉	—	4	1	no	—
280	C₂²×C₇₉	#423	1	4	yes	complemented
281	C₂²×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
282	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
283	C₂²×C₇₉	#520	1	1	yes	characteristic
284	C₂²×C₇₉	C₂²×M₁₆	1	1	yes	characteristic
285	C₂²×C₇₉	C₂²×M₁₆	1	1	yes	characteristic
286	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
287	C₂²×C₇₉	#568	1	1	yes	characteristic
288	C₄×C₇₉	—	2	2	no	—
289	C₄×C₇₉	—	2	2	no	—
290	C₄×C₇₉	—	2	2	no	—
291	C₄×C₇₉	—	2	2	no	—
292	C₄×C₇₉	—	2	2	no	—
293	C₄×C₇₉	—	2	2	no	—
294	C₄×C₇₉	—	2	2	no	—
295	C₄×C₇₉	—	2	2	no	—
296	C₄×C₇₉	—	4	1	no	—
297	C₄×C₇₉	—	4	1	no	—
298	C₄×C₇₉	—	4	1	no	—
299	C₄×C₇₉	#435	1	4	yes	complemented
300	C₄×C₇₉	D₄²	1	1	yes	characteristic
301	C₄×C₇₉	#547	1	1	yes	characteristic
302	C₄×C₇₉	D₄×Q₈	1	1	yes	characteristic
303	C₄×C₇₉	#554	1	1	yes	characteristic
304	#22648	—	79	1	no	maximal, Sylow
305	C₂×C₇₉	—	2	4	no	—
306	C₂×C₇₉	—	4	2	no	—
307	C₂×C₇₉	D₄×C₄⋊C₄	1	1	yes	characteristic
308	C₂×C₇₉	C₂×#423	1	1	yes	characteristic
309	C₂×C₇₉	#2906	1	1	yes	characteristic
310	C₂×C₇₉	C₂×#435	1	1	yes	characteristic
311	C₂×C₇₉	D₄×M₁₆	1	1	yes	characteristic
312	C₂×C₇₉	#2989	1	1	yes	characteristic
313	C₂×C₇₉	#2990	1	1	yes	characteristic
314	C₂×#435	—	79	2	no	—
315	C₂×#423	—	79	1	no	—
316	C₂²×C₄⋊C₈	—	79	1	no	—
317	C₄²×D₄	D₇₉	1	1	yes	characteristic
318	#1940	—	79	2	no	—
319	#1851	—	79	2	no	—
320	#1850	—	79	2	no	—
321	#1842	—	79	1	no	—
322	#1797	—	79	1	no	—
323	#1797	—	79	1	no	—
324	#1767	—	79	1	no	—
325	C₇₉	#22648	1	1	yes	characteristic, complemented, Sylow
326	C₂²×M₁₆	—	79	2	no	—
327	C₂³×C₈	—	79	2	no	—
328	C₂×C₄×D₄	Dic₇₉	1	1	yes	characteristic
329	C₂×C₄×D₄	Dic₇₉	1	1	yes	characteristic
330	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
331	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
332	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
333	#435	—	158	8	no	—
334	#423	—	158	4	no	—
335	C₂×C₄⋊C₈	—	79	2	no	—
336	C₂×C₄⋊C₈	—	79	1	no	—
337	C₂×C₄⋊C₈	—	79	1	no	—
338	C₂×C₄⋊C₈	—	79	1	no	—
339	C₂×C₄⋊C₈	—	79	1	no	—
340	C₂×C₄⋊C₈	—	79	2	no	—
341	C₂×C₄⋊C₈	—	79	2	no	—
342	C₂×C₄⋊C₈	—	79	2	no	—
343	C₂×C₄⋊C₈	—	158	4	no	—
344	C₂×C₂²⋊C₈	—	79	2	no	—
345	C₂×C₂²⋊C₈	—	79	2	no	—
346	C₂×#97	—	79	2	no	—
347	C₄×C₄⋊C₄	Dic₇₉	1	1	yes	characteristic
348	C₄×C₄⋊C₄	Dic₇₉	1	1	yes	characteristic
349	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
350	C₄×C₂²⋊C₄	Dic₇₉	1	1	yes	characteristic
351	C₄×C₂²⋊C₄	Dic₇₉	1	1	yes	characteristic
352	C₄×C₂²⋊C₄	Dic₇₉	1	1	yes	characteristic
353	C₄×C₂²⋊C₄	Dic₇₉	1	1	yes	characteristic
354	C₄×C₂²⋊C₄	C₂×D₇₉	1	1	yes	characteristic
355	C₄×C₂²⋊C₄	C₂×D₇₉	1	1	yes	characteristic
356	C₄³	C₂×D₇₉	1	1	yes	characteristic
357	#336	—	79	2	no	—
358	#336	—	79	2	no	—
359	#336	—	79	2	no	—
360	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
361	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
362	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
363	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
364	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
365	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
366	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
367	C₂×M₁₆	—	316	2	no	—
368	C₂×M₁₆	—	158	4	no	—
369	C₂×M₁₆	—	158	4	no	—
370	C₂²×C₈	—	316	2	no	—
371	C₂²×C₈	—	79	2	no	—
372	C₂²×C₈	—	79	2	no	—
373	C₂²×C₈	—	79	2	no	—
374	C₂²×C₈	—	79	2	no	—
375	C₂²×C₈	—	158	4	no	—
376	C₂²×C₈	—	158	4	no	—
377	C₄×D₄	—	2	4	no	—
378	C₄×D₄	—	2	4	no	—
379	C₄×D₄	Dic₁₅₈	1	4	yes	—
380	C₄×D₄	D₃₁₆	1	4	yes	—
381	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
384	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
385	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
386	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
387	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
388	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
389	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
390	C₂×C₄²	—	2	2	no	—
391	C₂×C₄²	—	2	2	no	—
392	C₂×C₄²	—	2	2	no	—
393	C₂×C₄²	—	2	2	no	—
394	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
395	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
396	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
397	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
398	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
399	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
400	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
401	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
402	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
403	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
404	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
405	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
406	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
407	C₄⋊C₈	—	316	2	no	—
408	C₄⋊C₈	—	79	4	no	—
409	C₄⋊C₈	—	158	4	no	—
410	C₄⋊C₈	—	158	4	no	—
411	C₄⋊C₈	—	158	2	no	—
412	C₄⋊C₈	—	158	2	no	—
413	C₄⋊C₈	—	158	4	no	—
414	C₄⋊C₈	—	158	2	no	—
415	C₂²⋊C₈	—	158	4	no	—
416	C₂²⋊C₈	—	158	4	no	—
417	#97	—	158	4	no	—
418	#95	C₂×Dic₇₉	1	1	yes	characteristic
419	#95	C₂×Dic₇₉	1	1	yes	characteristic
420	#95	C₂×Dic₇₉	1	1	yes	characteristic
421	#95	C₂×Dic₇₉	1	1	yes	characteristic
422	#95	C₂×Dic₇₉	1	1	yes	characteristic
423	#95	C₂×Dic₇₉	1	1	yes	characteristic
424	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
425	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	C₄⋊Dic₇₉	1	4	yes	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	4	1	no	—
447	C₂²×C₄	—	4	1	no	—
448	C₂²×C₄	#11929608	1	4	yes	complemented
449	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
450	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
451	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
452	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
453	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
454	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
455	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
456	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
457	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
458	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
459	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
460	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₃₁₆	1	2	yes	—
462	C₂²×C₄	C₂×D₃₁₆	1	2	yes	—
463	C₂²×C₄	C₂×Dic₁₅₈	1	2	yes	—
464	C₂²×C₄	C₂×Dic₁₅₈	1	2	yes	—
465	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
466	M₁₆	—	316	8	no	—
467	C₂×C₈	—	316	8	no	—
468	C₂×C₈	—	79	4	no	—
469	C₂×C₈	—	158	2	no	—
470	C₂×C₈	—	158	2	no	—
471	C₂×C₈	—	158	2	no	—
472	C₂×C₈	—	158	2	no	—
473	C₂×C₈	—	158	2	no	—
474	C₂×C₈	—	158	2	no	—
475	C₂×C₈	—	158	2	no	—
476	C₂×C₈	—	158	2	no	—
477	C₂×C₈	—	158	2	no	—
478	C₂×C₈	—	158	2	no	—
479	C₂×C₈	—	158	2	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	C₄⋊Dic₇₉	1	4	yes	—
483	C₂²⋊C₄	—	2	2	no	—
484	C₂²⋊C₄	—	2	2	no	—
485	C₂²⋊C₄	—	2	2	no	—
486	C₂²⋊C₄	C₄⋊Dic₇₉	1	4	yes	—
487	C₂²⋊C₄	C₄⋊Dic₇₉	1	4	yes	—
488	C₂²⋊C₄	#11929608	1	4	yes	complemented
489	C₄²	—	2	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	2	no	—
494	C₄²	—	2	2	no	—
495	C₄²	—	2	2	no	—
496	C₄²	—	2	2	no	—
497	C₄²	—	2	2	no	—
498	C₄²	—	2	2	no	—
499	C₄²	—	2	2	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	4	1	no	—
503	C₄²	D₄×D₇₉	1	2	yes	—
504	C₄²	C₂×D₃₁₆	1	2	yes	—
505	C₄²	C₂×Dic₁₅₈	1	2	yes	—
506	C₄²	#11929623	1	2	yes	—
507	C₂³	—	2	1	no	—
508	C₂³	—	2	1	no	—
509	C₂³	—	2	1	no	—
510	C₂³	—	2	1	no	—
511	C₂³	—	2	1	no	—
512	C₂³	—	2	1	no	—
513	C₂³	—	2	1	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	2	1	no	—
516	C₂³	—	2	1	no	—
517	C₂³	C₂×C₄⋊Dic₇₉	1	2	yes	—
518	C₂³	C₂×C₄⋊Dic₇₉	1	2	yes	—
519	C₂³	C₂×#11929608	1	2	yes	—
520	C₂³	C₂×#11929608	1	2	yes	—
521	C₂³	C₂³×Dic₇₉	1	1	yes	characteristic
522	D₄	—	2	8	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	8	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	4	4	no	—
558	C₂×C₄	—	4	4	no	—
559	C₂×C₄	—	4	4	no	—
560	C₂×C₄	C₂×C₄⋊Dic₇₉	1	2	yes	—
561	C₂×C₄	C₂×C₄⋊Dic₇₉	1	2	yes	—
562	C₂×C₄	C₂×C₄⋊Dic₇₉	1	2	yes	—
563	C₂×C₄	C₂×C₄⋊Dic₇₉	1	2	yes	—
564	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
565	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
566	C₂×C₄	C₂×#11929608	1	2	yes	—
567	C₂×C₄	C₂×#11929608	1	2	yes	—
568	C₂×C₄	C₂×#11929608	1	2	yes	—
569	C₂×C₄	C₂×#11929608	1	2	yes	—
570	C₂×C₄	#14579168	1	2	yes	—
571	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
572	C₂×C₄	C₂²×D₃₁₆	1	1	yes	characteristic
573	C₂×C₄	C₂²×Dic₁₅₈	1	1	yes	characteristic
574	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
575	C₂×C₄	#14579207	1	1	yes	characteristic
576	C₂×C₄	#14579208	1	1	yes	characteristic
577	C₈	—	316	2	no	—
578	C₈	—	316	2	no	—
579	C₈	—	316	2	no	—
580	C₈	—	158	4	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	2	2	no	—
584	C₂²	—	2	2	no	—
585	C₂²	—	2	2	no	—
586	C₂²	—	2	2	no	—
587	C₂²	—	2	2	no	—
588	C₂²	—	2	2	no	—
589	C₂²	—	2	2	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	#19098587	1	4	yes	complemented
595	C₂²	C₂²×C₄⋊Dic₇₉	1	1	yes	characteristic
596	C₂²	C₂×D₄×Dic₇₉	1	1	yes	characteristic
597	C₂²	#19099046	1	1	yes	characteristic
598	C₂²	C₂²×#11929608	1	1	yes	characteristic
599	C₂²	C₂²×#11929608	1	1	yes	characteristic
600	C₂²	C₂×#14579168	1	1	yes	characteristic
601	C₂²	#19099330	1	1	yes	characteristic
602	C₄	—	2	2	no	—
603	C₄	—	2	2	no	—
604	C₄	—	2	2	no	—
605	C₄	—	2	2	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	2	2	no	—
609	C₄	—	2	2	no	—
610	C₄	—	4	1	no	—
611	C₄	—	4	1	no	—
612	C₄	—	4	1	no	—
613	C₄	#19098635	1	4	yes	complemented
614	C₄	D₄×D₃₁₆	1	1	yes	characteristic
615	C₄	#19099217	1	1	yes	characteristic
616	C₄	D₄×Dic₁₅₈	1	1	yes	characteristic
617	C₄	#19099270	1	1	yes	characteristic
618	C₂	—	2	4	no	—
619	C₂	—	4	2	no	—
620	C₂	D₄×C₄⋊Dic₇₉	1	1	yes	characteristic
621	C₂	C₂×#19098587	1	1	yes	characteristic
622	C₂	#23771968	1	1	yes	characteristic
623	C₂	C₂×#19098635	1	1	yes	characteristic
624	C₂	D₄×#11929608	1	1	yes	characteristic
625	C₂	#23772517	1	1	yes	characteristic
626	C₂	#23772525	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator, socle	C₂³×C₇₉	C₂³×C₄
Fitting	C₄²×D₄×C₇₉	C₂
prime radical	C₂²×D₄×C₇₉	C₂×C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₄²×D₄	D₇₉
hypocenter	C₇₉	#22648
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄²×D₄

Complements

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

N	H ≅ G/N	type
2. C₂×#19098587	C₂	semidirect
3. C₂²×C₄⋊(C₇₉⋊C₈)	C₂	semidirect
4. #23764124	C₂	semidirect
5. #23763585	C₂	semidirect
6. #23763580	C₂	semidirect
7. #23763552	C₂	semidirect
8. #23763380	C₂	semidirect
9. #23763380	C₂	semidirect
10. #23763253	C₂	semidirect
63. C₄⋊(C₇₉⋊C₈)	D₄	semidirect
148. C₂²×C₄×C₇₉	M₁₆	semidirect
174. C₂²⋊C₄×C₇₉	M₁₆	semidirect
280. C₂²×C₇₉	#423	semidirect
299. C₄×C₇₉	#435	semidirect
325. C₇₉	#22648	semidirect
448. C₂²×C₄	#11929608	semidirect
488. C₂²⋊C₄	#11929608	semidirect
594. C₂²	#19098587	semidirect
613. C₄	#19098635	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098635	2
C₂×#19098587	2
C₂²×C₄⋊(C₇₉⋊C₈)	2
#23764124	2
#23763585	2
#23763580	2
#23763552	2
#23763380	2
#23763253	2
C₄²×D₄×C₇₉	2
#22648	79