Subgroups — C₂×#23761286 #34178389

Order 20224.

1226 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098527	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₂²⋊Dic₇₉	C₂	1	1	yes	maximal, characteristic
3	#23761286	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄×C₂²⋊C₄×C₇₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×#11929608	C₄	1	2	yes	complemented
6	C₂²×C₂²⋊Dic₇₉	—	2	1	no	—
7	C₂²×C₄×Dic₇₉	—	2	1	no	—
8	#19098527	—	2	1	no	—
9	#19098527	—	2	1	no	—
10	#19098527	C₄	1	2	yes	complemented
11	#19098527	C₂²	1	2	yes	—
12	C₂×C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
13	C₂×C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
14	C₄×C₂²⋊Dic₇₉	—	2	1	no	—
15	C₄×C₂²⋊Dic₇₉	—	2	1	no	—
16	C₄×C₂²⋊Dic₇₉	C₄	1	2	yes	complemented
17	C₄×C₂²⋊Dic₇₉	C₂²	1	2	yes	—
18	C₂×C₇₉⋊#95	C₄	1	2	yes	complemented
19	C₂⁴×C₄×C₇₉	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊C₄×C₇₉	—	2	1	no	—
21	C₂²×C₄²×C₇₉	—	2	1	no	—
22	C₄×C₂²⋊C₄×C₇₉	—	2	1	no	—
23	C₄×C₂²⋊C₄×C₇₉	—	2	1	no	—
24	C₄×C₂²⋊C₄×C₇₉	C₄	1	2	yes	complemented
25	C₄×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
26	C₂×#95×C₇₉	C₄	1	2	yes	complemented
27	C₂³×Dic₇₉	—	2	2	no	—
28	C₂×#11929608	—	2	2	no	—
29	C₂×#11929608	—	4	4	no	—
30	C₂×#11929608	C₂×C₄	1	4	yes	complemented
31	C₂²×C₇₉⋊C₈	—	2	2	no	—
32	C₂×C₂²⋊Dic₇₉	—	2	8	no	—
33	C₂×C₂²⋊Dic₇₉	—	2	2	no	—
34	C₂×C₂²⋊Dic₇₉	—	2	2	no	—
35	C₂×C₄×Dic₇₉	—	2	2	no	—
36	C₂×C₄×Dic₇₉	—	2	2	no	—
37	C₂×C₄×Dic₇₉	—	4	4	no	—
38	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
39	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
40	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
41	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
42	C₇₉⋊#95	—	2	2	no	—
43	C₇₉⋊#95	C₂×C₄	1	4	yes	complemented
44	C₂⁵×C₇₉	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₇₉	—	2	2	no	—
46	C₂³×C₄×C₇₉	—	4	4	no	—
47	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
53	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
58	C₂³×C₄×C₇₉	Q₈	1	1	yes	characteristic
59	C₂³×C₄×C₇₉	Q₈	1	1	yes	characteristic
60	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
61	C₂×C₂²⋊C₄×C₇₉	—	2	8	no	—
62	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
64	C₂×C₄²×C₇₉	—	2	2	no	—
65	C₂×C₄²×C₇₉	—	2	2	no	—
66	C₂×C₄²×C₇₉	—	4	4	no	—
67	#95×C₇₉	—	2	2	no	—
68	#95×C₇₉	C₂×C₄	1	4	yes	complemented
69	C₂²×Dic₇₉	—	2	8	no	—
70	C₂²×Dic₇₉	—	2	4	no	—
71	C₂²×Dic₇₉	—	4	4	no	—
72	C₂²×Dic₇₉	—	4	4	no	—
73	#11929608	—	4	4	no	—
74	#11929608	—	4	4	no	—
75	C₂×C₇₉⋊C₈	—	2	4	no	—
76	C₂×C₇₉⋊C₈	—	4	4	no	—
77	C₂²⋊Dic₇₉	—	2	8	no	—
78	C₂²⋊Dic₇₉	—	2	8	no	—
79	C₄×Dic₇₉	—	4	4	no	—
80	C₄×Dic₇₉	—	4	4	no	—
81	C₂⁴×C₇₉	—	2	4	no	—
82	C₂⁴×C₇₉	—	2	4	no	—
83	C₂⁴×C₇₉	—	4	2	no	—
84	C₂⁴×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
85	C₂⁴×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
86	C₂⁴×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
87	C₂⁴×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
88	C₂⁴×C₇₉	C₄⋊C₄	1	1	yes	characteristic
89	C₂⁴×C₇₉	C₄⋊C₄	1	1	yes	characteristic
90	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₇₉	—	2	4	no	—
92	C₂²×C₄×C₇₉	—	2	4	no	—
93	C₂²×C₄×C₇₉	—	2	4	no	—
94	C₂²×C₄×C₇₉	—	2	8	no	—
95	C₂²×C₄×C₇₉	—	2	4	no	—
96	C₂²×C₄×C₇₉	—	4	2	no	—
97	C₂²×C₄×C₇₉	—	4	2	no	—
98	C₂²×C₄×C₇₉	—	4	2	no	—
99	C₂²×C₄×C₇₉	—	4	2	no	—
100	C₂²×C₄×C₇₉	—	4	2	no	—
101	C₂²×C₄×C₇₉	—	4	2	no	—
102	C₂²×C₄×C₇₉	—	4	2	no	—
103	C₂²×C₄×C₇₉	—	4	2	no	—
104	C₂²×C₄×C₇₉	—	4	2	no	—
105	C₂²×C₄×C₇₉	—	4	2	no	—
106	C₂²×C₄×C₇₉	—	4	2	no	—
107	C₂²×C₄×C₇₉	—	4	4	no	—
108	C₂²×C₄×C₇₉	—	4	4	no	—
109	C₂²×C₄×C₇₉	C₄²	1	1	yes	characteristic
110	C₂²×C₄×C₇₉	C₄²	1	1	yes	characteristic
111	C₂²×C₄×C₇₉	C₄²	1	1	yes	characteristic
112	C₂²×C₄×C₇₉	C₄²	1	1	yes	characteristic
113	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
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	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
122	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
123	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
124	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
125	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
126	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
127	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
128	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
129	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
130	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
131	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
137	C₂²⋊C₄×C₇₉	—	2	8	no	—
138	C₂²⋊C₄×C₇₉	—	2	8	no	—
139	C₄²×C₇₉	—	4	4	no	—
140	C₄²×C₇₉	—	4	4	no	—
141	C₂³×C₇₉	—	2	2	no	—
142	C₂³×C₇₉	—	2	2	no	—
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	—	2	2	no	—
150	C₂³×C₇₉	—	2	2	no	—
151	C₂³×C₇₉	—	2	2	no	—
152	C₂³×C₇₉	—	2	2	no	—
153	C₂³×C₇₉	—	2	2	no	—
154	C₂³×C₇₉	—	2	2	no	—
155	C₂³×C₇₉	—	2	2	no	—
156	C₂³×C₇₉	—	4	1	no	—
157	C₂³×C₇₉	—	4	1	no	—
158	C₂³×C₇₉	—	4	1	no	—
159	C₂³×C₇₉	—	4	1	no	—
160	C₂³×C₇₉	—	4	16	no	—
161	C₂³×C₇₉	#95	1	1	yes	characteristic
162	C₂³×C₇₉	#95	1	1	yes	characteristic
163	C₂³×C₇₉	#95	1	1	yes	characteristic
164	C₂³×C₇₉	#95	1	1	yes	characteristic
165	C₂³×C₇₉	#104	1	4	yes	—
166	C₂³×C₇₉	#104	1	4	yes	—
167	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂³×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₇₉	—	2	2	no	—
171	C₂×C₄×C₇₉	—	2	2	no	—
172	C₂×C₄×C₇₉	—	2	2	no	—
173	C₂×C₄×C₇₉	—	2	2	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	—	2	2	no	—
178	C₂×C₄×C₇₉	—	2	2	no	—
179	C₂×C₄×C₇₉	—	2	2	no	—
180	C₂×C₄×C₇₉	—	2	2	no	—
181	C₂×C₄×C₇₉	—	2	2	no	—
182	C₂×C₄×C₇₉	—	2	2	no	—
183	C₂×C₄×C₇₉	—	2	2	no	—
184	C₂×C₄×C₇₉	—	2	2	no	—
185	C₂×C₄×C₇₉	—	2	8	no	—
186	C₂×C₄×C₇₉	—	4	1	no	—
187	C₂×C₄×C₇₉	—	4	1	no	—
188	C₂×C₄×C₇₉	—	4	1	no	—
189	C₂×C₄×C₇₉	—	4	1	no	—
190	C₂×C₄×C₇₉	—	4	1	no	—
191	C₂×C₄×C₇₉	—	4	1	no	—
192	C₂×C₄×C₇₉	—	4	1	no	—
193	C₂×C₄×C₇₉	—	4	1	no	—
194	C₂×C₄×C₇₉	—	4	1	no	—
195	C₂×C₄×C₇₉	—	4	1	no	—
196	C₂×C₄×C₇₉	—	4	1	no	—
197	C₂×C₄×C₇₉	—	4	1	no	—
198	C₂×C₄×C₇₉	—	4	4	no	—
199	C₂×C₄×C₇₉	—	4	16	no	—
200	C₂×C₄×C₇₉	—	4	4	no	—
201	C₂×C₄×C₇₉	#95	1	1	yes	characteristic
202	C₂×C₄×C₇₉	#95	1	1	yes	characteristic
203	C₂×C₄×C₇₉	#95	1	1	yes	characteristic
204	C₂×C₄×C₇₉	#95	1	1	yes	characteristic
205	C₂×C₄×C₇₉	#99	1	4	yes	—
206	C₂×C₄×C₇₉	C₂×C₄²	1	1	yes	characteristic
207	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
210	C₂×Dic₇₉	—	2	8	no	—
211	C₂×Dic₇₉	—	4	4	no	—
212	C₂×Dic₇₉	—	4	16	no	—
213	C₂×Dic₇₉	—	4	4	no	—
214	C₇₉⋊C₈	—	4	4	no	—
215	C₂²×C₇₉	—	2	8	no	—
216	C₂²×C₇₉	—	2	8	no	—
217	C₂²×C₇₉	—	2	1	no	—
218	C₂²×C₇₉	—	2	1	no	—
219	C₂²×C₇₉	—	2	1	no	—
220	C₂²×C₇₉	—	2	1	no	—
221	C₂²×C₇₉	—	2	1	no	—
222	C₂²×C₇₉	—	2	1	no	—
223	C₂²×C₇₉	—	2	1	no	—
224	C₂²×C₇₉	—	2	1	no	—
225	C₂²×C₇₉	—	2	1	no	—
226	C₂²×C₇₉	—	2	1	no	—
227	C₂²×C₇₉	—	2	1	no	—
228	C₂²×C₇₉	—	2	1	no	—
229	C₂²×C₇₉	—	2	1	no	—
230	C₂²×C₇₉	—	2	1	no	—
231	C₂²×C₇₉	—	4	4	no	—
232	C₂²×C₇₉	—	4	4	no	—
233	C₂²×C₇₉	—	4	4	no	—
234	C₂²×C₇₉	—	4	4	no	—
235	C₂²×C₇₉	—	4	4	no	—
236	C₂²×C₇₉	#339	1	2	yes	—
237	C₂²×C₇₉	#339	1	2	yes	—
238	C₂²×C₇₉	#339	1	2	yes	—
239	C₂²×C₇₉	#339	1	2	yes	—
240	C₂²×C₇₉	#342	1	2	yes	—
241	C₂²×C₇₉	C₂×#95	1	1	yes	characteristic
242	C₂²×C₇₉	C₂×#104	1	2	yes	—
243	C₂²×C₇₉	C₂×#104	1	2	yes	—
244	C₄×C₇₉	—	2	1	no	—
245	C₄×C₇₉	—	2	1	no	—
246	C₄×C₇₉	—	2	1	no	—
247	C₄×C₇₉	—	2	1	no	—
248	C₄×C₇₉	—	2	1	no	—
249	C₄×C₇₉	—	2	1	no	—
250	C₄×C₇₉	—	4	8	no	—
251	C₄×C₇₉	#342	1	2	yes	—
252	C₄×C₇₉	C₂×#99	1	2	yes	—
253	Dic₇₉	—	4	8	no	—
254	C₂×#1297	—	79	1	no	maximal, Sylow
255	C₂×C₇₉	—	2	2	no	—
256	C₂×C₇₉	—	2	2	no	—
257	C₂×C₇₉	—	2	2	no	—
258	C₂×C₇₉	—	2	2	no	—
259	C₂×C₇₉	—	4	1	no	—
260	C₂×C₇₉	—	4	1	no	—
261	C₂×C₇₉	#1297	1	4	yes	complemented
262	C₂×C₇₉	C₂×#339	1	1	yes	characteristic
263	C₂×C₇₉	C₂×#339	1	1	yes	characteristic
264	C₂×C₇₉	C₂×#342	1	1	yes	characteristic
265	C₂×#407	—	79	1	no	—
266	C₂×C₄×C₂²⋊C₄	—	79	1	no	—
267	C₂×C₄×C₂²⋊C₄	D₇₉	1	1	yes	characteristic
268	#1297	—	79	4	no	—
269	C₇₉	C₂×#1297	1	1	yes	characteristic, complemented, Sylow
270	C₂⁴×C₄	C₂×D₇₉	1	1	yes	characteristic
271	C₂²×M₁₆	—	79	2	no	—
272	C₂²×C₂²⋊C₄	—	2	1	no	—
273	C₂²×C₂²⋊C₄	—	158	1	no	—
274	C₂²×C₄²	—	2	1	no	—
275	C₂²×C₄²	—	158	1	no	—
276	#407	—	79	2	no	—
277	#407	—	79	2	no	—
278	#407	—	158	1	no	—
279	#407	—	158	1	no	—
280	C₂×C₂²⋊C₈	—	158	1	no	—
281	C₂×C₂²⋊C₈	—	158	1	no	—
282	C₄×C₂²⋊C₄	—	2	1	no	—
283	C₄×C₂²⋊C₄	—	2	1	no	—
284	C₄×C₂²⋊C₄	—	79	2	no	—
285	C₄×C₂²⋊C₄	—	79	2	no	—
286	C₄×C₂²⋊C₄	—	158	1	no	—
287	C₄×C₂²⋊C₄	—	158	1	no	—
288	C₄×C₂²⋊C₄	Dic₇₉	1	2	yes	complemented
289	C₄×C₂²⋊C₄	C₂×D₇₉	1	2	yes	—
290	C₂×#95	—	79	2	no	—
291	C₂×#95	Dic₇₉	1	2	yes	complemented
292	C₂⁵	C₂²⋊D₇₉	1	1	yes	characteristic
293	C₂³×C₄	—	2	2	no	—
294	C₂³×C₄	—	4	4	no	—
295	C₂³×C₄	—	158	2	no	—
296	C₂³×C₄	Dic₁₅₈	1	1	yes	characteristic
297	C₂³×C₄	Dic₁₅₈	1	1	yes	characteristic
298	C₂³×C₄	C₄×D₇₉	1	1	yes	characteristic
299	C₂³×C₄	C₄×D₇₉	1	1	yes	characteristic
300	C₂³×C₄	C₄×D₇₉	1	1	yes	characteristic
301	C₂³×C₄	C₄×D₇₉	1	1	yes	characteristic
302	C₂³×C₄	D₃₁₆	1	1	yes	characteristic
303	C₂³×C₄	D₃₁₆	1	1	yes	characteristic
304	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
305	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
306	C₂³×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
307	C₂³×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
308	C₂³×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
309	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
310	C₂×M₁₆	—	316	4	no	—
311	C₂×M₁₆	—	79	4	no	—
312	C₂×M₁₆	—	158	2	no	—
313	C₂²×C₈	—	158	2	no	—
314	C₂×C₂²⋊C₄	—	2	8	no	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	—	158	8	no	—
318	C₂×C₂²⋊C₄	—	158	2	no	—
319	C₂×C₂²⋊C₄	—	158	2	no	—
320	C₂×C₄²	—	2	2	no	—
321	C₂×C₄²	—	2	2	no	—
322	C₂×C₄²	—	4	4	no	—
323	C₂×C₄²	—	316	4	no	—
324	C₂×C₄²	—	158	2	no	—
325	C₂×C₄²	—	158	2	no	—
326	C₂²⋊C₈	—	158	2	no	—
327	C₂²⋊C₈	—	158	2	no	—
328	C₂²⋊C₈	—	158	2	no	—
329	C₂²⋊C₈	—	158	2	no	—
330	#95	—	2	2	no	—
331	#95	—	79	4	no	—
332	#95	—	158	2	no	—
333	#95	C₂×Dic₇₉	1	4	yes	complemented
334	C₂⁴	—	2	4	no	—
335	C₂⁴	—	2	4	no	—
336	C₂⁴	—	4	2	no	—
337	C₂⁴	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
338	C₂⁴	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
339	C₂⁴	C₂²⋊Dic₇₉	1	1	yes	characteristic
340	C₂⁴	C₂²⋊Dic₇₉	1	1	yes	characteristic
341	C₂⁴	Dic₇₉⋊C₄	1	1	yes	characteristic
342	C₂⁴	Dic₇₉⋊C₄	1	1	yes	characteristic
343	C₂⁴	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	8	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	—	4	2	no	—
351	C₂²×C₄	—	4	2	no	—
352	C₂²×C₄	—	4	2	no	—
353	C₂²×C₄	—	4	2	no	—
354	C₂²×C₄	—	4	2	no	—
355	C₂²×C₄	—	4	2	no	—
356	C₂²×C₄	—	4	2	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	—	4	2	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	—	4	4	no	—
361	C₂²×C₄	—	4	4	no	—
362	C₂²×C₄	—	316	4	no	—
363	C₂²×C₄	—	316	4	no	—
364	C₂²×C₄	—	158	8	no	—
365	C₂²×C₄	—	158	4	no	—
366	C₂²×C₄	C₄×Dic₇₉	1	1	yes	characteristic
367	C₂²×C₄	C₄×Dic₇₉	1	1	yes	characteristic
368	C₂²×C₄	C₄×Dic₇₉	1	1	yes	characteristic
369	C₂²×C₄	C₄×Dic₇₉	1	1	yes	characteristic
370	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
371	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
372	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
373	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
374	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
375	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
376	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
377	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
378	C₂²×C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
379	C₂²×C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
380	C₂²×C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
381	C₂²×C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
382	C₂²×C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
383	C₂²×C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
384	C₂²×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
385	C₂²×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
386	C₂²×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
387	C₂²×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
388	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
390	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
391	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
393	C₂²×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
394	M₁₆	—	316	4	no	—
395	M₁₆	—	316	4	no	—
396	C₂×C₈	—	316	4	no	—
397	C₂×C₈	—	158	4	no	—
398	C₂²⋊C₄	—	2	8	no	—
399	C₂²⋊C₄	—	2	8	no	—
400	C₂²⋊C₄	—	158	8	no	—
401	C₂²⋊C₄	—	158	8	no	—
402	C₄²	—	4	4	no	—
403	C₄²	—	4	4	no	—
404	C₄²	—	316	4	no	—
405	C₄²	—	316	4	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	2	2	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	2	2	no	—
418	C₂³	—	2	2	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	4	1	no	—
422	C₂³	—	4	1	no	—
423	C₂³	—	4	1	no	—
424	C₂³	—	4	1	no	—
425	C₂³	—	4	16	no	—
426	C₂³	C₇₉⋊#95	1	1	yes	characteristic
427	C₂³	C₇₉⋊#95	1	1	yes	characteristic
428	C₂³	C₇₉⋊#95	1	1	yes	characteristic
429	C₂³	C₇₉⋊#95	1	1	yes	characteristic
430	C₂³	#14579088	1	4	yes	—
431	C₂³	#14579089	1	4	yes	—
432	C₂³	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
433	C₂³	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
434	C₂³	C₂×Dic₇₉⋊C₄	1	1	yes	characteristic
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	8	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	4	16	no	—
465	C₂×C₄	—	4	4	no	—
466	C₂×C₄	—	316	4	no	—
467	C₂×C₄	—	316	16	no	—
468	C₂×C₄	—	316	4	no	—
469	C₂×C₄	—	158	8	no	—
470	C₂×C₄	C₇₉⋊#95	1	1	yes	characteristic
471	C₂×C₄	C₇₉⋊#95	1	1	yes	characteristic
472	C₂×C₄	C₇₉⋊#95	1	1	yes	characteristic
473	C₂×C₄	C₇₉⋊#95	1	1	yes	characteristic
474	C₂×C₄	#14579075	1	4	yes	—
475	C₂×C₄	C₂×C₄×Dic₇₉	1	1	yes	characteristic
476	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
477	C₂×C₄	C₂×Dic₇₉⋊C₄	1	1	yes	characteristic
478	C₂×C₄	C₂×C₄⋊Dic₇₉	1	1	yes	characteristic
479	C₈	—	316	4	no	—
480	C₂²	—	2	8	no	—
481	C₂²	—	2	8	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	2	1	no	—
488	C₂²	—	2	1	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	2	1	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	4	4	no	—
497	C₂²	—	4	4	no	—
498	C₂²	—	4	4	no	—
499	C₂²	—	4	4	no	—
500	C₂²	—	4	4	no	—
501	C₂²	#19098322	1	2	yes	—
502	C₂²	#19098322	1	2	yes	—
503	C₂²	#19098323	1	2	yes	—
504	C₂²	#19098323	1	2	yes	—
505	C₂²	#19098329	1	2	yes	—
506	C₂²	C₂×C₇₉⋊#95	1	1	yes	characteristic
507	C₂²	C₂×#14579088	1	2	yes	—
508	C₂²	C₂×#14579089	1	2	yes	—
509	C₄	—	2	1	no	—
510	C₄	—	2	1	no	—
511	C₄	—	2	1	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	2	1	no	—
515	C₄	—	4	8	no	—
516	C₄	—	316	8	no	—
517	C₄	#19098329	1	2	yes	—
518	C₄	C₂×#14579075	1	2	yes	—
519	C₂	—	2	2	no	—
520	C₂	—	2	2	no	—
521	C₂	—	2	2	no	—
522	C₂	—	2	2	no	—
523	C₂	—	4	1	no	—
524	C₂	—	4	1	no	—
525	C₂	#23761286	1	4	yes	direct product factor
526	C₂	C₂×#19098322	1	1	yes	characteristic
527	C₂	C₂×#19098323	1	1	yes	characteristic
528	C₂	C₂×#19098329	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	(C₂×D₇₉)⋊C₄
commutator	C₂×C₄×C₇₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₇₉
Fitting	C₂×C₄×C₂²⋊C₄×C₇₉	C₂
socle	C₂³×C₇₉	#95
prime radical	C₂⁵×C₇₉	D₄
cosocle	C₂³×C₄×C₇₉	C₂³
hypercenter	C₂×C₄×C₂²⋊C₄	D₇₉
hypocenter	C₇₉	C₂×#1297
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂⁴×C₄ ◁ C₂×C₄×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
3. #23761286	C₂	direct (N × H)
5. C₂²×#11929608	C₄	semidirect
10. #19098527	C₄	semidirect
16. C₄×C₂²⋊Dic₇₉	C₄	semidirect
18. C₂×C₇₉⋊#95	C₄	semidirect
24. C₄×C₂²⋊C₄×C₇₉	C₄	semidirect
26. C₂×#95×C₇₉	C₄	semidirect
30. C₂×#11929608	C₂×C₄	semidirect
43. C₇₉⋊#95	C₂×C₄	semidirect
68. #95×C₇₉	C₂×C₄	semidirect
261. C₂×C₇₉	#1297	semidirect
269. C₇₉	C₂×#1297	semidirect
288. C₄×C₂²⋊C₄	Dic₇₉	semidirect
291. C₂×#95	Dic₇₉	semidirect
333. #95	C₂×Dic₇₉	semidirect
525. C₂	#23761286	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#19098527	2
C₂×C₄×C₂²⋊Dic₇₉	2
#23761286	2
C₂×C₄×C₂²⋊C₄×C₇₉	2
C₂×#1297	79

Subgroups — C2×#23761286 #34178389

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23761286 #34178389