Subgroups — #34306359

Order 20224.

964 conjugacy classes of subgroups.

The subgroup lattice has 458 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×#19098590	C₂	1	2	yes	maximal, complemented
3	#23764124	C₂	1	2	yes	maximal, complemented
4	#23763585	C₂	1	2	yes	maximal, complemented
5	#23763580	C₂	1	2	yes	maximal, complemented
6	#23763552	C₂	1	1	yes	maximal, characteristic, complemented
7	#23763384	C₂	1	2	yes	maximal, complemented
8	#23763253	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#2293	C₂	1	1	yes	maximal, characteristic
10	C₂²×#11929608	C₂²	1	2	yes	—
11	C₂³×C₇₉⋊C₈	C₂²	1	2	yes	—
12	#19098635	—	2	8	no	—
13	#19098590	—	2	8	no	—
14	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
16	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
17	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
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	1	yes	characteristic
21	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
23	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
24	C₂×#14579072	C₂²	1	2	yes	—
25	#19098318	C₂²	1	2	yes	—
26	#19098318	C₂²	1	2	yes	—
27	#19098318	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
29	C₂×#117×C₇₉	C₂²	1	2	yes	—
30	#390×C₇₉	C₄	1	1	yes	characteristic
31	#390×C₇₉	C₄	1	1	yes	characteristic
32	#389×C₇₉	C₄	1	1	yes	characteristic
33	#389×C₇₉	C₄	1	1	yes	characteristic
34	#388×C₇₉	C₄	1	2	yes	—
35	#388×C₇₉	C₄	1	2	yes	—
36	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
37	C₄×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
38	C₄³×C₇₉	C₂²	1	1	yes	characteristic
39	C₂×#11929608	—	2	4	no	—
40	C₂×#11929608	—	2	4	no	—
41	C₂×#11929608	—	4	2	no	—
42	C₂²×C₇₉⋊C₈	—	2	4	no	—
43	C₂²×C₇₉⋊C₈	—	2	4	no	—
44	C₂²×C₇₉⋊C₈	—	4	2	no	—
45	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
46	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
47	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
48	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
49	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
50	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
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)	—	4	1	no	—
55	C₄⋊(C₇₉⋊C₈)	—	4	1	no	—
56	C₄⋊(C₇₉⋊C₈)	D₄	1	4	yes	complemented
57	C₂²⋊(C₇₉⋊C₈)	—	2	4	no	—
58	C₂²⋊(C₇₉⋊C₈)	—	2	4	no	—
59	#14579072	—	2	4	no	—
60	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
62	C₄×D₄×C₇₉	D₄	1	4	yes	—
63	C₄×D₄×C₇₉	Q₈	1	4	yes	—
64	#117×C₇₉	—	2	4	no	—
65	#117×C₇₉	—	2	4	no	—
66	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
67	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
68	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
72	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
73	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
74	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
75	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
76	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
81	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
84	#95×C₇₉	C₂×C₄	1	2	yes	—
85	#95×C₇₉	C₂×C₄	1	2	yes	—
86	#95×C₇₉	C₂×C₄	1	2	yes	—
87	#11929608	—	4	8	no	—
88	C₂×C₇₉⋊C₈	—	2	2	no	—
89	C₂×C₇₉⋊C₈	—	2	2	no	—
90	C₂×C₇₉⋊C₈	—	2	2	no	—
91	C₂×C₇₉⋊C₈	—	2	2	no	—
92	C₂×C₇₉⋊C₈	—	2	2	no	—
93	C₂×C₇₉⋊C₈	—	2	2	no	—
94	C₂×C₇₉⋊C₈	—	2	2	no	—
95	C₂×C₇₉⋊C₈	—	2	2	no	—
96	C₂×C₇₉⋊C₈	—	2	2	no	—
97	C₂×C₇₉⋊C₈	—	2	2	no	—
98	C₂×C₇₉⋊C₈	—	2	2	no	—
99	C₂×C₇₉⋊C₈	—	4	8	no	—
100	C₂×C₇₉⋊C₈	C₂×D₄	1	4	yes	—
101	C₂⁴×C₇₉	C₂²×C₄	1	2	yes	—
102	C₂×D₄×C₇₉	—	4	1	no	—
103	C₂×D₄×C₇₉	—	4	1	no	—
104	C₂×D₄×C₇₉	C₄⋊C₄	1	4	yes	—
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	2	no	—
109	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₇₉	C₂×D₄	1	4	yes	—
119	C₂²×C₄×C₇₉	C₂×Q₈	1	4	yes	—
120	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
121	C₄⋊C₄×C₇₉	—	2	4	no	—
122	C₄⋊C₄×C₇₉	—	2	4	no	—
123	C₄⋊C₄×C₇₉	—	4	1	no	—
124	C₄⋊C₄×C₇₉	—	4	1	no	—
125	C₄⋊C₄×C₇₉	C₄⋊C₄	1	4	yes	—
126	C₂²⋊C₄×C₇₉	—	2	4	no	—
127	C₂²⋊C₄×C₇₉	—	2	4	no	—
128	C₂²⋊C₄×C₇₉	—	2	4	no	—
129	C₂²⋊C₄×C₇₉	—	4	2	no	—
130	C₂²⋊C₄×C₇₉	C₄⋊C₄	1	8	yes	—
131	C₄²×C₇₉	—	2	2	no	—
132	C₄²×C₇₉	—	2	2	no	—
133	C₄²×C₇₉	—	2	2	no	—
134	C₄²×C₇₉	—	2	1	no	—
135	C₄²×C₇₉	—	2	1	no	—
136	C₄²×C₇₉	—	4	1	no	—
137	C₄²×C₇₉	—	4	1	no	—
138	C₄²×C₇₉	—	4	1	no	—
139	C₄²×C₇₉	C₂×D₄	1	2	yes	—
140	C₄²×C₇₉	C₂×D₄	1	2	yes	—
141	C₄²×C₇₉	C₂×Q₈	1	2	yes	—
142	C₄²×C₇₉	#41	1	2	yes	—
143	C₂³×C₇₉	—	2	2	no	—
144	C₂³×C₇₉	—	2	2	no	—
145	C₂³×C₇₉	—	2	2	no	—
146	C₂³×C₇₉	—	2	2	no	—
147	C₂³×C₇₉	—	2	2	no	—
148	C₂³×C₇₉	—	2	2	no	—
149	C₂³×C₇₉	C₂×C₄⋊C₄	1	4	yes	—
150	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
151	D₄×C₇₉	—	4	4	no	—
152	C₂×C₄×C₇₉	—	2	2	no	—
153	C₂×C₄×C₇₉	—	2	1	no	—
154	C₂×C₄×C₇₉	—	2	2	no	—
155	C₂×C₄×C₇₉	—	2	1	no	—
156	C₂×C₄×C₇₉	—	2	1	no	—
157	C₂×C₄×C₇₉	—	2	1	no	—
158	C₂×C₄×C₇₉	—	2	1	no	—
159	C₂×C₄×C₇₉	—	2	1	no	—
160	C₂×C₄×C₇₉	—	2	1	no	—
161	C₂×C₄×C₇₉	—	2	1	no	—
162	C₂×C₄×C₇₉	—	2	1	no	—
163	C₂×C₄×C₇₉	—	2	1	no	—
164	C₂×C₄×C₇₉	—	2	4	no	—
165	C₂×C₄×C₇₉	—	2	4	no	—
166	C₂×C₄×C₇₉	—	2	4	no	—
167	C₂×C₄×C₇₉	—	2	4	no	—
168	C₂×C₄×C₇₉	—	2	2	no	—
169	C₂×C₄×C₇₉	—	2	2	no	—
170	C₂×C₄×C₇₉	—	2	1	no	—
171	C₂×C₄×C₇₉	—	2	2	no	—
172	C₂×C₄×C₇₉	—	2	1	no	—
173	C₂×C₄×C₇₉	—	2	1	no	—
174	C₂×C₄×C₇₉	—	2	2	no	—
175	C₂×C₄×C₇₉	—	2	2	no	—
176	C₂×C₄×C₇₉	—	2	2	no	—
177	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
178	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
179	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	4	yes	—
180	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
181	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
182	C₂×C₄×C₇₉	#131	1	2	yes	—
183	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
186	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
189	C₇₉⋊C₈	—	2	4	no	—
190	C₇₉⋊C₈	—	4	2	no	—
191	C₇₉⋊C₈	—	4	2	no	—
192	C₇₉⋊C₈	—	4	2	no	—
193	C₂²×C₇₉	—	2	4	no	—
194	C₂²×C₇₉	—	2	4	no	—
195	C₂²×C₇₉	—	2	4	no	—
196	C₂²×C₇₉	—	4	2	no	—
197	C₂²×C₇₉	—	4	2	no	—
198	C₂²×C₇₉	—	4	2	no	—
199	C₂²×C₇₉	—	4	2	no	—
200	C₂²×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
201	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
202	C₂²×C₇₉	#520	1	1	yes	characteristic
203	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
204	C₂²×C₇₉	#568	1	1	yes	characteristic
205	C₂²×C₇₉	#568	1	1	yes	characteristic
206	C₂²×C₇₉	#568	1	1	yes	characteristic
207	C₄×C₇₉	—	2	4	no	—
208	C₄×C₇₉	—	2	2	no	—
209	C₄×C₇₉	—	2	2	no	—
210	C₄×C₇₉	—	2	2	no	—
211	C₄×C₇₉	—	2	2	no	—
212	C₄×C₇₉	—	2	2	no	—
213	C₄×C₇₉	—	4	2	no	—
214	C₄×C₇₉	—	4	2	no	—
215	C₄×C₇₉	—	4	1	no	—
216	C₄×C₇₉	D₄²	1	1	yes	characteristic
217	C₄×C₇₉	#547	1	1	yes	characteristic
218	C₄×C₇₉	D₄×Q₈	1	1	yes	characteristic
219	C₄×C₇₉	#554	1	1	yes	characteristic
220	#22652	—	79	1	no	maximal, Sylow
221	C₂×C₇₉	—	4	4	no	—
222	C₂×C₇₉	D₄×C₄⋊C₄	1	1	yes	characteristic
223	C₂×C₇₉	#2905	1	1	yes	characteristic
224	C₂×C₇₉	#2906	1	1	yes	characteristic
225	C₂×C₇₉	#2932	1	1	yes	characteristic
226	C₂×C₇₉	#2935	1	1	yes	characteristic
227	C₂×C₇₉	#2992	1	1	yes	characteristic
228	C₂×C₇₉	#2995	1	1	yes	characteristic
229	C₂×#435	—	79	2	no	—
230	C₂×#424	—	79	2	no	—
231	#2293	D₇₉	1	1	yes	characteristic
232	#1940	—	79	2	no	—
233	#1851	—	79	2	no	—
234	#1850	—	79	2	no	—
235	#1842	—	79	1	no	—
236	#1798	—	79	2	no	—
237	#1767	—	79	1	no	—
238	C₇₉	#22652	1	1	yes	characteristic, complemented, Sylow
239	C₂²×M₁₆	—	79	2	no	—
240	C₂³×C₈	—	79	2	no	—
241	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
242	C₂×#117	C₂×D₇₉	1	2	yes	—
243	#435	—	158	8	no	—
244	#424	—	158	8	no	—
245	C₂×C₄⋊C₈	—	79	1	no	—
246	C₂×C₄⋊C₈	—	79	1	no	—
247	C₂×C₄⋊C₈	—	79	1	no	—
248	C₂×C₄⋊C₈	—	79	1	no	—
249	C₂×C₄⋊C₈	—	79	2	no	—
250	C₂×C₄⋊C₈	—	79	2	no	—
251	C₂×C₄⋊C₈	—	79	2	no	—
252	C₂×C₄⋊C₈	—	79	2	no	—
253	C₂×C₂²⋊C₈	—	79	2	no	—
254	C₂×C₂²⋊C₈	—	79	2	no	—
255	C₂×#97	—	79	2	no	—
256	#390	Dic₇₉	1	1	yes	characteristic
257	#390	Dic₇₉	1	1	yes	characteristic
258	#389	Dic₇₉	1	1	yes	characteristic
259	#389	Dic₇₉	1	1	yes	characteristic
260	#388	Dic₇₉	1	2	yes	—
261	#388	Dic₇₉	1	2	yes	—
262	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
263	C₄×C₂²⋊C₄	C₂×D₇₉	1	2	yes	—
264	C₄³	C₂×D₇₉	1	1	yes	characteristic
265	#336	—	79	2	no	—
266	#336	—	79	2	no	—
267	#336	—	79	2	no	—
268	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
269	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
270	C₂×M₁₆	—	316	2	no	—
271	C₂×M₁₆	—	158	4	no	—
272	C₂×M₁₆	—	158	4	no	—
273	C₂²×C₈	—	316	2	no	—
274	C₂²×C₈	—	79	2	no	—
275	C₂²×C₈	—	79	2	no	—
276	C₂²×C₈	—	79	2	no	—
277	C₂²×C₈	—	79	2	no	—
278	C₂²×C₈	—	158	4	no	—
279	C₂²×C₈	—	158	4	no	—
280	C₄×D₄	Dic₁₅₈	1	4	yes	—
281	C₄×D₄	D₃₁₆	1	4	yes	—
282	#117	—	2	4	no	—
283	#117	—	2	4	no	—
284	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
285	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
286	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
289	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
290	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
291	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
292	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
293	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
294	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
295	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
296	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
297	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
298	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
299	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
300	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
301	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
302	C₄⋊C₈	—	316	1	no	—
303	C₄⋊C₈	—	316	1	no	—
304	C₄⋊C₈	—	79	4	no	—
305	C₄⋊C₈	—	158	4	no	—
306	C₄⋊C₈	—	158	4	no	—
307	C₄⋊C₈	—	158	4	no	—
308	C₄⋊C₈	—	158	4	no	—
309	C₄⋊C₈	—	158	2	no	—
310	C₂²⋊C₈	—	158	4	no	—
311	C₂²⋊C₈	—	158	4	no	—
312	#97	—	158	4	no	—
313	#95	C₂×Dic₇₉	1	2	yes	—
314	#95	C₂×Dic₇₉	1	2	yes	—
315	#95	C₂×Dic₇₉	1	2	yes	—
316	C₂⁴	C₂²×Dic₇₉	1	2	yes	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂×D₄	C₄⋊Dic₇₉	1	4	yes	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
325	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
326	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
327	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
328	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
329	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
330	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
331	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
332	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₃₁₆	1	4	yes	—
334	C₂²×C₄	C₂×Dic₁₅₈	1	4	yes	—
335	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
336	M₁₆	—	316	8	no	—
337	C₂×C₈	—	316	8	no	—
338	C₂×C₈	—	79	4	no	—
339	C₂×C₈	—	158	2	no	—
340	C₂×C₈	—	158	2	no	—
341	C₂×C₈	—	158	2	no	—
342	C₂×C₈	—	158	2	no	—
343	C₂×C₈	—	158	2	no	—
344	C₂×C₈	—	158	2	no	—
345	C₂×C₈	—	158	2	no	—
346	C₂×C₈	—	158	2	no	—
347	C₂×C₈	—	158	2	no	—
348	C₂×C₈	—	158	2	no	—
349	C₂×C₈	—	158	2	no	—
350	C₄⋊C₄	—	2	4	no	—
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	—	4	1	no	—
354	C₄⋊C₄	C₄⋊Dic₇₉	1	4	yes	—
355	C₂²⋊C₄	—	2	4	no	—
356	C₂²⋊C₄	—	2	4	no	—
357	C₂²⋊C₄	—	2	4	no	—
358	C₂²⋊C₄	—	4	2	no	—
359	C₂²⋊C₄	C₄⋊Dic₇₉	1	8	yes	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	1	no	—
362	C₄²	—	2	1	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	4	1	no	—
366	C₄²	—	4	1	no	—
367	C₄²	—	4	1	no	—
368	C₄²	D₄×D₇₉	1	2	yes	—
369	C₄²	C₂×D₃₁₆	1	2	yes	—
370	C₄²	C₂×Dic₁₅₈	1	2	yes	—
371	C₄²	#11929623	1	2	yes	—
372	C₂³	—	2	2	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	2	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	2	no	—
378	C₂³	C₂×C₄⋊Dic₇₉	1	4	yes	—
379	C₂³	C₂³×Dic₇₉	1	1	yes	characteristic
380	D₄	—	4	4	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	C₂×C₄⋊Dic₇₉	1	2	yes	—
407	C₂×C₄	C₂×C₄⋊Dic₇₉	1	2	yes	—
408	C₂×C₄	C₂×C₄⋊Dic₇₉	1	4	yes	—
409	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
410	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
411	C₂×C₄	#14579168	1	2	yes	—
412	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
413	C₂×C₄	C₂²×D₃₁₆	1	1	yes	characteristic
414	C₂×C₄	C₂²×Dic₁₅₈	1	1	yes	characteristic
415	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
416	C₂×C₄	#14579207	1	1	yes	characteristic
417	C₂×C₄	#14579208	1	1	yes	characteristic
418	C₈	—	316	2	no	—
419	C₈	—	316	2	no	—
420	C₈	—	316	2	no	—
421	C₈	—	158	4	no	—
422	C₂²	—	2	4	no	—
423	C₂²	—	2	4	no	—
424	C₂²	—	2	4	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	C₂²×C₄⋊Dic₇₉	1	1	yes	characteristic
430	C₂²	C₂×D₄×Dic₇₉	1	1	yes	characteristic
431	C₂²	#19099046	1	1	yes	characteristic
432	C₂²	C₂×#14579168	1	1	yes	characteristic
433	C₂²	#19099330	1	1	yes	characteristic
434	C₂²	#19099330	1	1	yes	characteristic
435	C₂²	#19099330	1	1	yes	characteristic
436	C₄	—	2	4	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	2	no	—
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	2	no	—
442	C₄	—	4	1	no	—
443	C₄	—	4	2	no	—
444	C₄	—	4	2	no	—
445	C₄	D₄×D₃₁₆	1	1	yes	characteristic
446	C₄	#19099217	1	1	yes	characteristic
447	C₄	D₄×Dic₁₅₈	1	1	yes	characteristic
448	C₄	#19099270	1	1	yes	characteristic
449	C₂	—	4	4	no	—
450	C₂	D₄×C₄⋊Dic₇₉	1	1	yes	characteristic
451	C₂	#23771964	1	1	yes	characteristic
452	C₂	#23771968	1	1	yes	characteristic
453	C₂	#23772118	1	1	yes	characteristic
454	C₂	#23772144	1	1	yes	characteristic
455	C₂	#23772539	1	1	yes	characteristic
456	C₂	#23772570	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator, socle	C₂³×C₇₉	C₂³×C₄
Fitting	C₇₉×#2293	C₂
prime radical	C₂²×D₄×C₇₉	C₂×C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#2293	D₇₉
hypocenter	C₇₉	#22652
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ #2293

Complements

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

N	H ≅ G/N	type
2. C₂×#19098590	C₂	semidirect
3. #23764124	C₂	semidirect
4. #23763585	C₂	semidirect
5. #23763580	C₂	semidirect
6. #23763552	C₂	semidirect
7. #23763384	C₂	semidirect
8. #23763253	C₂	semidirect
56. C₄⋊(C₇₉⋊C₈)	D₄	semidirect
238. C₇₉	#22652	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×#19098590	2
#23764124	2
#23763585	2
#23763580	2
#23763552	2
#23763384	2
#23763253	2
C₇₉×#2293	2
#22652	79