Subgroups — #34314686

Order 20224.

700 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14579140	C₂	1	1	yes	maximal, characteristic
2	#23764338	C₂	1	1	yes	maximal, characteristic, complemented
3	#23764334	C₂	1	1	yes	maximal, characteristic, complemented
4	#23764122	C₂	1	1	yes	maximal, characteristic, complemented
5	#23764117	C₂	1	1	yes	maximal, characteristic, complemented
6	#23764016	C₂	1	1	yes	maximal, characteristic
7	#23764010	C₂	1	1	yes	maximal, characteristic
8	#23764009	C₂	1	1	yes	maximal, characteristic
9	#23764003	C₂	1	1	yes	maximal, characteristic
10	#23763967	C₂	1	1	yes	maximal, characteristic, complemented
11	#23763965	C₂	1	1	yes	maximal, characteristic, complemented
12	#23763960	C₂	1	1	yes	maximal, characteristic, complemented
13	#23763958	C₂	1	1	yes	maximal, characteristic, complemented
14	#23763380	C₂	1	1	yes	maximal, characteristic
15	C₇₉×#1817	C₂	1	1	yes	maximal, characteristic
16	C₂×#14579140	C₄	1	1	yes	characteristic
17	C₂×C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
26	C₂×#14579071	C₂²	1	1	yes	characteristic
27	C₂×#14579071	C₂²	1	1	yes	characteristic
28	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
30	#19098469	C₄	1	1	yes	characteristic
31	#19098461	C₄	1	1	yes	characteristic
32	#19098447	C₄	1	1	yes	characteristic
33	#19098447	C₄	1	1	yes	characteristic
34	#19098436	C₄	1	1	yes	characteristic
35	#19098436	C₄	1	1	yes	characteristic
36	#19098423	C₄	1	1	yes	characteristic
37	C₄×Dic₇₉⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×Dic₇₉⋊C₄	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊Dic₇₉	C₂²	1	1	yes	characteristic
41	C₄×C₂²⋊Dic₇₉	C₂²	1	1	yes	characteristic
42	#19098318	C₂²	1	1	yes	characteristic
43	#19098318	C₂²	1	1	yes	characteristic
44	#19098317	C₂²	1	1	yes	characteristic
45	#19098317	C₂²	1	1	yes	characteristic
46	#19098317	C₂²	1	1	yes	characteristic
47	#19098317	C₂²	1	1	yes	characteristic
48	#19098317	C₂²	1	1	yes	characteristic
49	#19098317	C₂²	1	1	yes	characteristic
50	#19098317	C₂²	1	1	yes	characteristic
51	#19098317	C₂²	1	1	yes	characteristic
52	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
54	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
55	#336×C₇₉	C₂²	1	1	yes	characteristic
56	#336×C₇₉	C₂²	1	1	yes	characteristic
57	#336×C₇₉	C₂²	1	1	yes	characteristic
58	#336×C₇₉	C₂²	1	1	yes	characteristic
59	C₂²×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
62	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
64	#14579140	—	2	4	no	—
65	C₄×Dic₁₅₈	—	4	1	no	—
66	C₄×Dic₁₅₈	—	4	1	no	—
67	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
70	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
77	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
78	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
79	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
81	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
82	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
83	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
84	C₄⋊(C₇₉⋊C₈)	—	4	1	no	—
85	C₄⋊(C₇₉⋊C₈)	—	4	1	no	—
86	Dic₇₉⋊C₈	—	4	1	no	—
87	Dic₇₉⋊C₈	—	4	1	no	—
88	Dic₇₉⋊C₈	—	4	1	no	—
89	Dic₇₉⋊C₈	—	4	1	no	—
90	C₂²⋊(C₇₉⋊C₈)	—	4	1	no	—
91	C₂²⋊(C₇₉⋊C₈)	—	4	1	no	—
92	#14579071	—	4	1	no	—
93	#14579071	—	4	1	no	—
94	C₈×Dic₇₉	—	4	1	no	—
95	C₈×Dic₇₉	—	4	1	no	—
96	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
97	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
98	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
99	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
100	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
101	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
102	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
103	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
104	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
105	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
106	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
107	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
108	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₇₉	—	4	1	no	—
114	C₂×C₄²×C₇₉	—	4	1	no	—
115	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
116	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
117	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
119	C₂²⋊C₈×C₇₉	—	4	1	no	—
120	C₂²⋊C₈×C₇₉	—	4	1	no	—
121	C₂×Dic₁₅₈	—	2	2	no	—
122	C₂×Dic₁₅₈	—	2	2	no	—
123	C₂×Dic₁₅₈	—	4	1	no	—
124	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
125	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
126	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
127	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
128	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
129	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
130	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
131	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₇₉⋊C₈	—	2	1	no	—
133	C₂×C₇₉⋊C₈	—	2	1	no	—
134	C₂×C₇₉⋊C₈	—	2	1	no	—
135	C₂×C₇₉⋊C₈	—	2	1	no	—
136	C₂×C₇₉⋊C₈	—	2	1	no	—
137	C₂×C₇₉⋊C₈	—	2	1	no	—
138	C₂×C₇₉⋊C₈	—	2	1	no	—
139	C₂×C₇₉⋊C₈	—	2	1	no	—
140	C₂×C₇₉⋊C₈	—	2	1	no	—
141	C₂×C₇₉⋊C₈	—	2	1	no	—
142	C₂×C₇₉⋊C₈	—	2	1	no	—
143	C₂×C₇₉⋊C₈	—	2	1	no	—
144	C₄⋊Dic₇₉	—	2	2	no	—
145	C₄⋊Dic₇₉	—	2	2	no	—
146	C₄⋊Dic₇₉	—	4	1	no	—
147	Dic₇₉⋊C₄	—	2	2	no	—
148	Dic₇₉⋊C₄	—	2	2	no	—
149	Dic₇₉⋊C₄	—	2	2	no	—
150	Dic₇₉⋊C₄	—	2	2	no	—
151	Dic₇₉⋊C₄	—	4	1	no	—
152	Dic₇₉⋊C₄	—	4	1	no	—
153	C₂²⋊Dic₇₉	—	2	2	no	—
154	C₂²⋊Dic₇₉	—	4	1	no	—
155	C₂²⋊Dic₇₉	—	4	1	no	—
156	C₂²⋊Dic₇₉	M₁₆	1	4	yes	—
157	C₄×Dic₇₉	—	2	1	no	—
158	C₄×Dic₇₉	—	2	1	no	—
159	C₄×Dic₇₉	—	2	1	no	—
160	C₄×Dic₇₉	—	2	1	no	—
161	C₄×Dic₇₉	—	2	1	no	—
162	C₄×Dic₇₉	—	2	1	no	—
163	C₄×Dic₇₉	—	2	1	no	—
164	C₄×Dic₇₉	—	2	1	no	—
165	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₇₉	—	2	2	no	—
167	C₂²×C₄×C₇₉	—	2	2	no	—
168	C₂²×C₄×C₇₉	—	2	2	no	—
169	C₂²×C₄×C₇₉	—	2	1	no	—
170	C₂²×C₄×C₇₉	—	2	1	no	—
171	C₂²×C₄×C₇₉	—	2	1	no	—
172	C₂²×C₄×C₇₉	—	2	1	no	—
173	C₂²×C₄×C₇₉	—	2	1	no	—
174	C₂²×C₄×C₇₉	—	2	1	no	—
175	C₂²×C₄×C₇₉	—	4	1	no	—
176	C₂²×C₄×C₇₉	—	4	1	no	—
177	C₂²×C₄×C₇₉	—	4	1	no	—
178	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
183	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
184	C₂×C₈×C₇₉	—	2	1	no	—
185	C₂×C₈×C₇₉	—	2	1	no	—
186	C₂×C₈×C₇₉	—	2	1	no	—
187	C₂×C₈×C₇₉	—	2	1	no	—
188	C₂×C₈×C₇₉	—	2	1	no	—
189	C₂×C₈×C₇₉	—	2	1	no	—
190	C₂×C₈×C₇₉	—	2	1	no	—
191	C₂×C₈×C₇₉	—	2	1	no	—
192	C₂×C₈×C₇₉	—	2	1	no	—
193	C₂×C₈×C₇₉	—	2	1	no	—
194	C₂×C₈×C₇₉	—	2	1	no	—
195	C₂×C₈×C₇₉	—	2	1	no	—
196	C₄²×C₇₉	—	2	1	no	—
197	C₄²×C₇₉	—	2	1	no	—
198	C₄²×C₇₉	—	2	1	no	—
199	C₄²×C₇₉	—	2	1	no	—
200	C₄²×C₇₉	—	4	1	no	—
201	C₄²×C₇₉	—	4	1	no	—
202	C₂³×C₇₉	—	2	1	no	—
203	C₂³×C₇₉	—	2	1	no	—
204	C₂³×C₇₉	—	2	1	no	—
205	C₂³×C₇₉	—	2	1	no	—
206	C₂³×C₇₉	—	2	1	no	—
207	C₂³×C₇₉	—	2	1	no	—
208	C₂³×C₇₉	C₂×M₁₆	1	2	yes	—
209	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
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	—	4	4	no	—
224	C₂×C₄×C₇₉	—	4	4	no	—
225	C₂×C₄×C₇₉	—	4	1	no	—
226	C₂×C₄×C₇₉	—	4	1	no	—
227	C₂×C₄×C₇₉	—	4	1	no	—
228	C₂×C₄×C₇₉	—	4	1	no	—
229	C₂×C₄×C₇₉	#131	1	2	yes	—
230	C₂×C₄×C₇₉	#131	1	2	yes	—
231	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
232	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
233	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
234	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
235	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
236	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
237	C₂×Dic₇₉	—	2	1	no	—
238	C₂×Dic₇₉	—	2	1	no	—
239	C₂×Dic₇₉	—	2	1	no	—
240	C₂×Dic₇₉	—	2	1	no	—
241	C₂×Dic₇₉	—	2	1	no	—
242	C₂×Dic₇₉	—	2	1	no	—
243	C₂×Dic₇₉	—	2	1	no	—
244	C₂×Dic₇₉	—	2	1	no	—
245	C₂×Dic₇₉	—	2	1	no	—
246	C₂×Dic₇₉	—	2	1	no	—
247	C₂×Dic₇₉	—	2	1	no	—
248	C₂×Dic₇₉	—	2	1	no	—
249	C₂×Dic₇₉	—	2	1	no	—
250	C₂×Dic₇₉	—	2	1	no	—
251	C₂×Dic₇₉	—	2	1	no	—
252	C₂×Dic₇₉	—	2	1	no	—
253	C₂×Dic₇₉	—	2	1	no	—
254	C₂×Dic₇₉	—	2	1	no	—
255	C₂×Dic₇₉	—	2	1	no	—
256	C₂×Dic₇₉	—	2	1	no	—
257	C₂×Dic₇₉	—	2	1	no	—
258	C₂×Dic₇₉	—	2	1	no	—
259	C₂×Dic₇₉	C₂×M₁₆	1	2	yes	—
260	C₂×Dic₇₉	C₂×M₁₆	1	2	yes	—
261	Dic₁₅₈	—	4	4	no	—
262	C₈×C₇₉	—	4	1	no	—
263	C₈×C₇₉	—	4	1	no	—
264	C₈×C₇₉	—	4	1	no	—
265	C₈×C₇₉	—	4	1	no	—
266	C₇₉⋊C₈	—	4	1	no	—
267	C₇₉⋊C₈	—	4	1	no	—
268	C₇₉⋊C₈	—	4	1	no	—
269	C₇₉⋊C₈	—	4	1	no	—
270	C₂²×C₇₉	—	2	2	no	—
271	C₂²×C₇₉	—	2	2	no	—
272	C₂²×C₇₉	—	2	2	no	—
273	C₂²×C₇₉	—	4	1	no	—
274	C₂²×C₇₉	—	4	1	no	—
275	C₂²×C₇₉	—	4	1	no	—
276	C₂²×C₇₉	—	4	1	no	—
277	C₂²×C₇₉	#518	1	1	yes	characteristic
278	C₂²×C₇₉	#519	1	1	yes	characteristic
279	C₂²×C₇₉	#520	1	1	yes	characteristic
280	C₂²×C₇₉	C₂²×M₁₆	1	1	yes	characteristic
281	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
282	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
283	C₂²×C₇₉	#568	1	1	yes	characteristic
284	C₄×C₇₉	—	2	2	no	—
285	C₄×C₇₉	—	2	2	no	—
286	C₄×C₇₉	—	4	1	no	—
287	C₄×C₇₉	—	4	1	no	—
288	C₄×C₇₉	—	4	1	no	—
289	C₄×C₇₉	#562	1	1	yes	characteristic
290	C₄×C₇₉	#562	1	1	yes	characteristic
291	C₄×C₇₉	#563	1	1	yes	characteristic
292	C₄×C₇₉	#563	1	1	yes	characteristic
293	Dic₇₉	—	2	2	no	—
294	Dic₇₉	—	2	2	no	—
295	Dic₇₉	—	4	1	no	—
296	Dic₇₉	—	4	1	no	—
297	Dic₇₉	—	4	1	no	—
298	Dic₇₉	—	4	1	no	—
299	Dic₇₉	—	4	1	no	—
300	Dic₇₉	—	4	1	no	—
301	#23341	—	79	1	no	maximal, Sylow
302	C₂×C₇₉	—	4	2	no	—
303	C₂×C₇₉	#2378	1	1	yes	characteristic
304	C₂×C₇₉	#2974	1	1	yes	characteristic
305	C₂×C₇₉	#2976	1	1	yes	characteristic
306	C₂×C₇₉	#2983	1	1	yes	characteristic
307	C₂×C₇₉	#2986	1	1	yes	characteristic
308	C₂×C₇₉	#2990	1	1	yes	characteristic
309	C₂×C₇₉	#2993	1	1	yes	characteristic
310	C₄×C₂²⋊Q₈	—	79	1	no	—
311	#1985	—	79	1	no	—
312	#1984	—	79	1	no	—
313	#1940	—	79	1	no	—
314	#1939	—	79	1	no	—
315	#1924	—	79	1	no	—
316	#1924	—	79	1	no	—
317	#1923	—	79	1	no	—
318	#1923	—	79	1	no	—
319	#1917	—	79	1	no	—
320	#1917	—	79	1	no	—
321	#1916	—	79	1	no	—
322	#1916	—	79	1	no	—
323	#1817	D₇₉	1	1	yes	characteristic
324	#1797	—	79	1	no	—
325	C₇₉	#23341	1	1	yes	characteristic, complemented, Sylow
326	C₂×C₂²⋊Q₈	—	79	1	no	—
327	C₂×C₄×Q₈	—	79	1	no	—
328	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
329	C₂×C₄⋊C₈	—	79	1	no	—
330	C₂×C₄⋊C₈	—	79	1	no	—
331	C₂×C₄⋊C₈	—	79	1	no	—
332	C₂×C₄⋊C₈	—	79	1	no	—
333	C₂×C₄⋊C₈	—	79	1	no	—
334	C₂×C₄⋊C₈	—	79	1	no	—
335	C₂×C₂²⋊C₈	—	79	1	no	—
336	C₂×C₂²⋊C₈	—	79	1	no	—
337	C₂×C₂²⋊C₈	C₂×D₇₉	1	1	yes	characteristic
338	C₂×C₂²⋊C₈	C₂×D₇₉	1	1	yes	characteristic
339	C₂×#97	—	79	1	no	—
340	C₂×#97	—	79	1	no	—
341	C₂×C₄×C₈	—	79	1	no	—
342	C₂×C₄×C₈	—	79	1	no	—
343	#391	—	79	1	no	—
344	#389	—	79	1	no	—
345	#387	—	79	1	no	—
346	#387	—	79	1	no	—
347	#385	—	79	1	no	—
348	#385	—	79	1	no	—
349	#380	—	79	1	no	—
350	C₄×C₄⋊C₄	—	79	1	no	—
351	C₄×C₄⋊C₄	—	79	1	no	—
352	C₄×C₄⋊C₄	—	79	1	no	—
353	C₄×C₂²⋊C₄	—	79	1	no	—
354	C₄×C₂²⋊C₄	—	79	1	no	—
355	#336	—	79	1	no	—
356	#336	—	79	1	no	—
357	#336	—	79	1	no	—
358	#336	—	79	1	no	—
359	#336	—	79	1	no	—
360	#336	—	79	1	no	—
361	#336	—	79	1	no	—
362	#336	—	79	1	no	—
363	#336	—	79	1	no	—
364	#336	—	79	1	no	—
365	#336	C₂×D₇₉	1	1	yes	characteristic
366	#336	C₂×D₇₉	1	1	yes	characteristic
367	#336	C₂×D₇₉	1	1	yes	characteristic
368	#336	C₂×D₇₉	1	1	yes	characteristic
369	C₂²×Q₈	—	79	1	no	—
370	C₂³×C₄	C₄×D₇₉	1	1	yes	characteristic
371	C₂³×C₄	C₄×D₇₉	1	1	yes	characteristic
372	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
373	C₂²×C₈	—	79	1	no	—
374	C₂²×C₈	—	79	1	no	—
375	C₂²×C₈	—	79	1	no	—
376	C₂²×C₈	—	79	1	no	—
377	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
378	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
379	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
380	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
381	C₂²⋊Q₈	—	158	4	no	—
382	C₄×Q₈	—	316	1	no	—
383	C₄×Q₈	—	316	1	no	—
384	C₂×C₄⋊C₄	—	79	1	no	—
385	C₂×C₄⋊C₄	—	79	1	no	—
386	C₂×C₄⋊C₄	—	79	1	no	—
387	C₂×C₄⋊C₄	—	79	1	no	—
388	C₂×C₄⋊C₄	—	79	1	no	—
389	C₂×C₄⋊C₄	—	79	1	no	—
390	C₂×C₄⋊C₄	—	79	1	no	—
391	C₂×C₄⋊C₄	—	79	1	no	—
392	C₂×C₄⋊C₄	—	79	1	no	—
393	C₂×C₂²⋊C₄	—	79	1	no	—
394	C₂×C₂²⋊C₄	—	79	1	no	—
395	C₂×C₂²⋊C₄	—	79	1	no	—
396	C₂×C₂²⋊C₄	—	79	1	no	—
397	C₂×C₄²	—	4	1	no	—
398	C₂×C₄²	—	4	1	no	—
399	C₂×C₄²	—	79	1	no	—
400	C₂×C₄²	—	79	1	no	—
401	C₂×C₄²	—	79	1	no	—
402	C₂×C₄²	—	79	1	no	—
403	C₂×C₄²	C₄×D₇₉	1	1	yes	characteristic
404	C₂×C₄²	C₄×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	1	no	—
408	C₄⋊C₈	—	316	1	no	—
409	C₄⋊C₈	—	316	1	no	—
410	C₄⋊C₈	—	316	1	no	—
411	C₄⋊C₈	—	316	1	no	—
412	C₄⋊C₈	—	316	1	no	—
413	C₂²⋊C₈	—	4	1	no	—
414	C₂²⋊C₈	—	4	1	no	—
415	C₂²⋊C₈	—	316	1	no	—
416	C₂²⋊C₈	—	316	1	no	—
417	#97	—	316	1	no	—
418	#97	—	316	1	no	—
419	C₄×C₈	—	316	1	no	—
420	C₄×C₈	—	316	1	no	—
421	#95	—	79	1	no	—
422	#95	—	79	1	no	—
423	#95	—	79	1	no	—
424	#95	—	79	1	no	—
425	#95	—	79	1	no	—
426	#95	—	79	1	no	—
427	#95	—	79	1	no	—
428	#95	—	79	1	no	—
429	#95	—	79	1	no	—
430	#95	—	79	1	no	—
431	C₂⁴	C₂×C₄×D₇₉	1	1	yes	characteristic
432	C₂×Q₈	—	316	1	no	—
433	C₂×Q₈	—	158	2	no	—
434	C₂×Q₈	—	158	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	4	1	no	—
445	C₂²×C₄	—	4	1	no	—
446	C₂²×C₄	—	4	1	no	—
447	C₂²×C₄	—	79	1	no	—
448	C₂²×C₄	—	79	1	no	—
449	C₂²×C₄	—	79	1	no	—
450	C₂²×C₄	—	79	1	no	—
451	C₂²×C₄	—	79	1	no	—
452	C₂²×C₄	—	79	1	no	—
453	C₂²×C₄	—	79	1	no	—
454	C₂²×C₄	—	79	1	no	—
455	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
456	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
457	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
458	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
459	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
460	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	158	1	no	—
474	C₂×C₈	—	158	1	no	—
475	C₂×C₈	—	158	1	no	—
476	C₂×C₈	—	158	1	no	—
477	C₂×C₈	—	158	1	no	—
478	C₂×C₈	—	158	1	no	—
479	C₂×C₈	—	158	1	no	—
480	C₂×C₈	—	158	1	no	—
481	C₂×C₈	—	158	1	no	—
482	C₂×C₈	—	158	1	no	—
483	C₂×C₈	—	158	1	no	—
484	C₂×C₈	—	158	1	no	—
485	C₄⋊C₄	—	316	1	no	—
486	C₄⋊C₄	—	316	1	no	—
487	C₄⋊C₄	—	316	1	no	—
488	C₄⋊C₄	—	158	2	no	—
489	C₄⋊C₄	—	158	2	no	—
490	C₄⋊C₄	—	158	2	no	—
491	C₄⋊C₄	—	158	2	no	—
492	C₄⋊C₄	—	158	2	no	—
493	C₄⋊C₄	—	158	2	no	—
494	C₂²⋊C₄	—	316	1	no	—
495	C₂²⋊C₄	—	316	1	no	—
496	C₂²⋊C₄	—	79	4	no	—
497	C₂²⋊C₄	—	158	2	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	4	1	no	—
503	C₄²	—	4	1	no	—
504	C₄²	—	158	1	no	—
505	C₄²	—	158	1	no	—
506	C₄²	—	158	1	no	—
507	C₄²	—	158	1	no	—
508	C₄²	—	158	1	no	—
509	C₄²	—	158	1	no	—
510	C₄²	—	158	1	no	—
511	C₄²	—	158	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	—	2	1	no	—
518	C₂³	M₁₆×D₇₉	1	2	yes	—
519	C₂³	C₂²×C₄×D₇₉	1	1	yes	characteristic
520	Q₈	—	316	4	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	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	—	4	4	no	—
535	C₂×C₄	—	4	4	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	79	2	no	—
541	C₂×C₄	—	79	2	no	—
542	C₂×C₄	—	158	1	no	—
543	C₂×C₄	—	158	1	no	—
544	C₂×C₄	—	158	1	no	—
545	C₂×C₄	—	158	1	no	—
546	C₂×C₄	—	158	1	no	—
547	C₂×C₄	—	158	1	no	—
548	C₂×C₄	—	158	1	no	—
549	C₂×C₄	—	158	1	no	—
550	C₂×C₄	—	158	1	no	—
551	C₂×C₄	—	158	1	no	—
552	C₂×C₄	—	158	1	no	—
553	C₂×C₄	—	158	1	no	—
554	C₂×C₄	—	158	1	no	—
555	C₂×C₄	—	158	1	no	—
556	C₂×C₄	—	158	1	no	—
557	C₂×C₄	—	158	1	no	—
558	C₂×C₄	—	158	1	no	—
559	C₂×C₄	—	158	1	no	—
560	C₂×C₄	—	158	1	no	—
561	C₂×C₄	—	158	1	no	—
562	C₂×C₄	—	158	1	no	—
563	C₂×C₄	—	158	1	no	—
564	C₂×C₄	#14579167	1	2	yes	—
565	C₂×C₄	#14579169	1	2	yes	—
566	C₂×C₄	#14579206	1	1	yes	characteristic
567	C₂×C₄	#14579206	1	1	yes	characteristic
568	C₂×C₄	#14579207	1	1	yes	characteristic
569	C₂×C₄	#14579208	1	1	yes	characteristic
570	C₂×C₄	#14579208	1	1	yes	characteristic
571	C₂×C₄	#14579208	1	1	yes	characteristic
572	C₈	—	4	1	no	—
573	C₈	—	4	1	no	—
574	C₈	—	4	1	no	—
575	C₈	—	4	1	no	—
576	C₈	—	316	1	no	—
577	C₈	—	316	1	no	—
578	C₈	—	316	1	no	—
579	C₈	—	316	1	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	#19099036	1	1	yes	characteristic
588	C₂²	#19099040	1	1	yes	characteristic
589	C₂²	#19099043	1	1	yes	characteristic
590	C₂²	C₂×M₁₆×D₇₉	1	1	yes	characteristic
591	C₂²	C₂×#14579167	1	1	yes	characteristic
592	C₂²	C₂×#14579169	1	1	yes	characteristic
593	C₂²	#19099329	1	1	yes	characteristic
594	C₄	—	2	2	no	—
595	C₄	—	2	2	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	1	no	—
599	C₄	—	316	1	no	—
600	C₄	—	316	1	no	—
601	C₄	—	316	1	no	—
602	C₄	—	316	1	no	—
603	C₄	—	316	1	no	—
604	C₄	—	316	1	no	—
605	C₄	—	158	2	no	—
606	C₄	—	158	2	no	—
607	C₄	#19099310	1	1	yes	characteristic
608	C₄	#19099310	1	1	yes	characteristic
609	C₄	#19099316	1	1	yes	characteristic
610	C₄	#19099316	1	1	yes	characteristic
611	C₂	—	4	2	no	—
612	C₂	#23766568	1	1	yes	characteristic
613	C₂	#23772431	1	1	yes	characteristic
614	C₂	#23772450	1	1	yes	characteristic
615	C₂	#23772484	1	1	yes	characteristic
616	C₂	#23772501	1	1	yes	characteristic
617	C₂	#23772527	1	1	yes	characteristic
618	C₂	#23772551	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator, socle	C₂³×C₇₉	C₂³×C₄
Fitting	C₇₉×#1817	C₂
prime radical	C₂⁴×C₇₉	C₂²×C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#1817	D₇₉
hypocenter	C₇₉	#23341
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ #1817

Complements

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

N	H ≅ G/N	type
2. #23764338	C₂	semidirect
3. #23764334	C₂	semidirect
4. #23764122	C₂	semidirect
5. #23764117	C₂	semidirect
10. #23763967	C₂	semidirect
11. #23763965	C₂	semidirect
12. #23763960	C₂	semidirect
13. #23763958	C₂	semidirect
325. C₇₉	#23341	semidirect

Maximal subgroups

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

subgroup	index
C₄×#14579140	2
#23764338	2
#23764334	2
#23764122	2
#23764117	2
#23764016	2
#23764010	2
#23764009	2
#23764003	2
#23763967	2
#23763965	2
#23763960	2
#23763958	2
#23763380	2
C₇₉×#1817	2
#23341	79