Subgroups — #34293298

Order 20224.

1256 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#11929608	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#14579120	C₂	1	1	yes	maximal, characteristic, complemented
3	#23764345	C₂	1	2	yes	maximal, complemented
4	#23764320	C₂	1	2	yes	maximal, complemented
5	#23763703	C₂	1	4	yes	maximal, complemented
6	C₄×#14579088	C₂	1	4	yes	maximal, complemented
7	C₇₉×#3444	C₂	1	1	yes	maximal, characteristic
8	C₂²×#11929608	C₂²	1	2	yes	—
9	C₂×#14579120	—	2	1	no	—
10	C₂×#14579088	C₂²	1	8	yes	—
11	C₄×#11929608	—	2	1	no	—
12	C₄×#11929608	—	2	1	no	—
13	C₄×#11929608	C₂²	1	2	yes	—
14	C₄×#11929608	C₂²	1	2	yes	—
15	C₂×#14579072	—	2	1	no	—
16	C₂×C₄×C₇₉⋊C₈	—	2	1	no	—
17	C₄×C₄⋊Dic₇₉	—	2	1	no	—
18	C₄×C₄⋊Dic₇₉	C₂²	1	2	yes	—
19	C₄×C₂²⋊Dic₇₉	—	2	1	no	—
20	C₄×C₂²⋊Dic₇₉	C₂²	1	2	yes	—
21	#19098409	—	2	1	no	—
22	C₄²×Dic₇₉	C₂²	1	2	yes	—
23	#19098322	C₂²	1	8	yes	—
24	#533×C₇₉	C₄	1	1	yes	characteristic, complemented
25	#533×C₇₉	C₄	1	1	yes	characteristic, complemented
26	#533×C₇₉	C₂²	1	1	yes	characteristic
27	#532×C₇₉	C₄	1	1	yes	characteristic, complemented
28	#532×C₇₉	C₄	1	1	yes	characteristic, complemented
29	#532×C₇₉	C₂²	1	1	yes	characteristic
30	#529×C₇₉	—	2	1	no	—
31	#529×C₇₉	—	2	1	no	—
32	#529×C₇₉	—	2	1	no	—
33	#529×C₇₉	—	2	1	no	—
34	#529×C₇₉	C₄	1	2	yes	complemented
35	#529×C₇₉	C₄	1	2	yes	complemented
36	#525×C₇₉	—	2	1	no	—
37	#525×C₇₉	—	2	1	no	—
38	#525×C₇₉	C₂²	1	2	yes	—
39	C₄×#41×C₇₉	—	2	1	no	—
40	C₄×#41×C₇₉	—	2	1	no	—
41	C₄×#41×C₇₉	C₂²	1	2	yes	—
42	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
43	C₂×#11929608	—	2	2	no	—
44	C₂×#11929608	—	2	8	no	—
45	C₂×#11929608	C₂³	1	4	yes	—
46	C₂²×C₇₉⋊C₈	—	2	2	no	—
47	#14579120	—	2	8	no	—
48	C₂×C₄⋊Dic₇₉	—	2	2	no	—
49	C₂×C₂²⋊Dic₇₉	—	2	2	no	—
50	C₂×C₄×Dic₇₉	—	2	2	no	—
51	C₂×C₄×Dic₇₉	—	2	2	no	—
52	C₂×C₄×Dic₇₉	C₂³	1	4	yes	—
53	#14579088	—	2	16	no	—
54	#14579072	—	2	2	no	—
55	#14579072	—	2	2	no	—
56	C₄×C₇₉⋊C₈	—	2	2	no	—
57	C₄×C₇₉⋊C₈	—	2	2	no	—
58	C₇₉⋊#95	—	2	2	no	—
59	C₇₉⋊#95	—	2	2	no	—
60	C₂×#41×C₇₉	—	2	1	no	—
61	C₂×#41×C₇₉	—	2	1	no	—
62	C₂×#41×C₇₉	C₂³	1	2	yes	—
63	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
66	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
67	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
68	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
69	#127×C₇₉	C₂×C₄	1	1	yes	characteristic
70	#126×C₇₉	—	2	2	no	—
71	#126×C₇₉	—	2	2	no	—
72	#125×C₇₉	—	2	1	no	—
73	#125×C₇₉	—	2	1	no	—
74	#125×C₇₉	C₂×C₄	1	2	yes	—
75	#124×C₇₉	—	2	1	no	—
76	#124×C₇₉	—	2	1	no	—
77	#124×C₇₉	C₂×C₄	1	2	yes	—
78	#123×C₇₉	—	2	2	no	—
79	#123×C₇₉	—	2	2	no	—
80	#123×C₇₉	—	2	2	no	—
81	C₂²⋊Q₈×C₇₉	—	2	1	no	—
82	C₂²⋊Q₈×C₇₉	—	2	1	no	—
83	C₂²⋊Q₈×C₇₉	—	2	1	no	—
84	C₂²⋊Q₈×C₇₉	—	2	1	no	—
85	C₂²⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
86	C₂²⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
87	#121×C₇₉	—	2	1	no	—
88	#121×C₇₉	—	2	1	no	—
89	#121×C₇₉	—	2	1	no	—
90	#121×C₇₉	—	2	1	no	—
91	#121×C₇₉	C₂×C₄	1	2	yes	—
92	#121×C₇₉	C₂×C₄	1	2	yes	—
93	#120×C₇₉	—	2	2	no	—
94	C₄×Q₈×C₇₉	—	2	1	no	—
95	C₄×Q₈×C₇₉	—	2	1	no	—
96	C₄×Q₈×C₇₉	—	2	1	no	—
97	C₄×Q₈×C₇₉	—	2	1	no	—
98	C₄×Q₈×C₇₉	C₂×C₄	1	2	yes	—
99	C₄×Q₈×C₇₉	C₂×C₄	1	2	yes	—
100	C₄×D₄×C₇₉	—	2	2	no	—
101	C₄×D₄×C₇₉	—	2	2	no	—
102	C₄×D₄×C₇₉	—	2	2	no	—
103	C₄×D₄×C₇₉	—	2	2	no	—
104	C₄×D₄×C₇₉	—	2	2	no	—
105	C₄×D₄×C₇₉	—	2	2	no	—
106	C₄×D₄×C₇₉	—	2	1	no	—
107	C₄×D₄×C₇₉	—	2	1	no	—
108	C₄×D₄×C₇₉	—	2	1	no	—
109	C₄×D₄×C₇₉	—	2	1	no	—
110	C₄×D₄×C₇₉	C₂×C₄	1	2	yes	—
111	C₄×D₄×C₇₉	C₂×C₄	1	2	yes	—
112	#117×C₇₉	—	2	1	no	—
113	#117×C₇₉	—	2	1	no	—
114	#117×C₇₉	—	2	2	no	—
115	#117×C₇₉	—	2	2	no	—
116	#117×C₇₉	—	2	2	no	—
117	#117×C₇₉	C₂³	1	2	yes	—
118	C₂×C₄²×C₇₉	—	2	2	no	—
119	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
120	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
121	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
122	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
123	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
124	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
125	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
126	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
127	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
128	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
129	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
131	C₂²×Dic₇₉	—	2	4	no	—
132	#11929608	—	2	8	no	—
133	#11929608	—	2	4	no	—
134	#11929608	#41	1	8	yes	complemented
135	C₂×C₇₉⋊C₈	—	2	8	no	—
136	C₂×C₇₉⋊C₈	—	2	4	no	—
137	C₄⋊Dic₇₉	—	2	8	no	—
138	C₂²⋊Dic₇₉	—	2	8	no	—
139	C₄×Dic₇₉	—	2	8	no	—
140	C₄×Dic₇₉	—	2	8	no	—
141	C₄×Dic₇₉	—	4	4	no	—
142	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
143	#41×C₇₉	—	2	8	no	—
144	#41×C₇₉	—	4	4	no	—
145	#41×C₇₉	—	4	4	no	—
146	C₂×Q₈×C₇₉	—	2	1	no	—
147	C₂×Q₈×C₇₉	—	2	1	no	—
148	C₂×Q₈×C₇₉	C₂²×C₄	1	2	yes	—
149	C₂×D₄×C₇₉	—	2	2	no	—
150	C₂×D₄×C₇₉	—	2	2	no	—
151	C₂×D₄×C₇₉	—	2	2	no	—
152	C₂×D₄×C₇₉	—	2	1	no	—
153	C₂×D₄×C₇₉	—	2	1	no	—
154	C₂×D₄×C₇₉	C₂²×C₄	1	2	yes	—
155	C₂²×C₄×C₇₉	—	2	4	no	—
156	C₂²×C₄×C₇₉	—	2	4	no	—
157	C₂²×C₄×C₇₉	—	2	2	no	—
158	C₂²×C₄×C₇₉	—	2	2	no	—
159	C₂²×C₄×C₇₉	—	2	2	no	—
160	C₂²×C₄×C₇₉	—	4	2	no	—
161	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
162	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
163	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
164	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
165	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
166	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
167	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
168	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
169	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
179	C₄⋊C₄×C₇₉	—	2	1	no	—
180	C₄⋊C₄×C₇₉	—	2	1	no	—
181	C₄⋊C₄×C₇₉	—	2	1	no	—
182	C₄⋊C₄×C₇₉	—	2	1	no	—
183	C₄⋊C₄×C₇₉	—	2	2	no	—
184	C₄⋊C₄×C₇₉	—	2	2	no	—
185	C₄⋊C₄×C₇₉	—	2	2	no	—
186	C₄⋊C₄×C₇₉	—	2	2	no	—
187	C₄⋊C₄×C₇₉	—	2	2	no	—
188	C₄⋊C₄×C₇₉	—	2	2	no	—
189	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
190	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
191	C₂²⋊C₄×C₇₉	—	2	2	no	—
192	C₂²⋊C₄×C₇₉	—	2	2	no	—
193	C₂²⋊C₄×C₇₉	—	2	2	no	—
194	C₂²⋊C₄×C₇₉	—	2	2	no	—
195	C₂²⋊C₄×C₇₉	—	2	2	no	—
196	C₂²⋊C₄×C₇₉	—	2	2	no	—
197	C₂²⋊C₄×C₇₉	—	2	2	no	—
198	C₂²⋊C₄×C₇₉	—	2	2	no	—
199	C₂²⋊C₄×C₇₉	—	2	2	no	—
200	C₄²×C₇₉	—	2	2	no	—
201	C₄²×C₇₉	—	2	2	no	—
202	C₄²×C₇₉	—	2	2	no	—
203	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
204	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
205	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
206	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
207	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
208	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
209	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
210	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
211	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
212	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
213	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
214	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
215	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
216	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
217	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
218	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
219	C₂³×C₇₉	—	2	2	no	—
220	C₂³×C₇₉	—	2	2	no	—
221	C₂³×C₇₉	—	2	2	no	—
222	C₂³×C₇₉	—	4	1	no	—
223	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
226	Q₈×C₇₉	—	2	4	no	—
227	Q₈×C₇₉	—	4	2	no	—
228	Q₈×C₇₉	—	4	2	no	—
229	D₄×C₇₉	—	2	4	no	—
230	D₄×C₇₉	—	4	2	no	—
231	D₄×C₇₉	—	4	4	no	—
232	D₄×C₇₉	—	4	4	no	—
233	D₄×C₇₉	—	4	4	no	—
234	D₄×C₇₉	—	4	2	no	—
235	C₂×C₄×C₇₉	—	2	2	no	—
236	C₂×C₄×C₇₉	—	2	2	no	—
237	C₂×C₄×C₇₉	—	2	2	no	—
238	C₂×C₄×C₇₉	—	2	2	no	—
239	C₂×C₄×C₇₉	—	2	2	no	—
240	C₂×C₄×C₇₉	—	2	2	no	—
241	C₂×C₄×C₇₉	—	2	2	no	—
242	C₂×C₄×C₇₉	—	2	2	no	—
243	C₂×C₄×C₇₉	—	2	2	no	—
244	C₂×C₄×C₇₉	—	2	2	no	—
245	C₂×C₄×C₇₉	—	2	2	no	—
246	C₂×C₄×C₇₉	—	2	2	no	—
247	C₂×C₄×C₇₉	—	2	2	no	—
248	C₂×C₄×C₇₉	—	2	2	no	—
249	C₂×C₄×C₇₉	—	2	2	no	—
250	C₂×C₄×C₇₉	—	2	2	no	—
251	C₂×C₄×C₇₉	—	4	1	no	—
252	C₂×C₄×C₇₉	—	4	1	no	—
253	C₂×C₄×C₇₉	—	4	1	no	—
254	C₂×C₄×C₇₉	—	4	4	no	—
255	C₂×C₄×C₇₉	—	4	4	no	—
256	C₂×C₄×C₇₉	—	4	4	no	—
257	C₂×C₄×C₇₉	#104	1	4	yes	complemented
258	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
269	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₇₉	C₂×#41	1	4	yes	—
271	C₂×Dic₇₉	—	2	8	no	—
272	C₂×Dic₇₉	—	4	4	no	—
273	C₂×Dic₇₉	—	4	4	no	—
274	C₇₉⋊C₈	—	2	8	no	—
275	C₂²×C₇₉	—	2	1	no	—
276	C₂²×C₇₉	—	2	1	no	—
277	C₂²×C₇₉	—	2	1	no	—
278	C₂²×C₇₉	—	2	1	no	—
279	C₂²×C₇₉	—	2	1	no	—
280	C₂²×C₇₉	—	2	1	no	—
281	C₂²×C₇₉	—	2	1	no	—
282	C₂²×C₇₉	—	4	4	no	—
283	C₂²×C₇₉	—	4	2	no	—
284	C₂²×C₇₉	—	4	2	no	—
285	C₂²×C₇₉	—	4	2	no	—
286	C₂²×C₇₉	C₂×#104	1	2	yes	—
287	C₂²×C₇₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
288	C₂²×C₇₉	#532	1	2	yes	—
289	C₄×C₇₉	—	2	1	no	—
290	C₄×C₇₉	—	2	1	no	—
291	C₄×C₇₉	—	2	1	no	—
292	C₄×C₇₉	—	2	1	no	—
293	C₄×C₇₉	—	2	1	no	—
294	C₄×C₇₉	—	2	1	no	—
295	C₄×C₇₉	—	2	1	no	—
296	C₄×C₇₉	—	4	2	no	—
297	C₄×C₇₉	—	4	2	no	—
298	C₄×C₇₉	—	4	2	no	—
299	C₄×C₇₉	C₂×#104	1	2	yes	—
300	C₄×C₇₉	C₂×#104	1	2	yes	—
301	C₄×C₇₉	#421	1	2	yes	—
302	C₄×C₇₉	C₄×#41	1	2	yes	—
303	C₄×C₇₉	#525	1	2	yes	—
304	Dic₇₉	—	4	8	no	—
305	#21382	—	79	1	no	maximal, Sylow
306	C₂×C₇₉	—	2	2	no	—
307	C₂×C₇₉	—	2	2	no	—
308	C₂×C₇₉	—	4	1	no	—
309	C₂×C₇₉	—	8	2	no	—
310	C₂×C₇₉	#2297	1	1	yes	characteristic
311	C₂×C₇₉	C₂²×#104	1	1	yes	characteristic
312	C₂×C₇₉	C₂×#421	1	1	yes	characteristic
313	#3444	D₇₉	1	1	yes	characteristic
314	C₂×C₄×M₁₆	—	79	1	no	—
315	C₄×#117	—	79	1	no	—
316	#1986	—	79	2	no	—
317	#1980	—	79	2	no	—
318	#1871	—	79	4	no	—
319	C₄×#104	—	79	4	no	—
320	C₇₉	#21382	1	1	yes	characteristic, complemented, Sylow
321	C₂²×M₁₆	—	79	2	no	—
322	#533	Dic₇₉	1	1	yes	characteristic, complemented
323	#533	Dic₇₉	1	1	yes	characteristic, complemented
324	#533	C₂×D₇₉	1	1	yes	characteristic
325	#532	Dic₇₉	1	1	yes	characteristic, complemented
326	#532	Dic₇₉	1	1	yes	characteristic, complemented
327	#532	C₂×D₇₉	1	1	yes	characteristic
328	#529	—	2	1	no	—
329	#529	—	2	1	no	—
330	#529	—	2	1	no	—
331	#529	—	2	1	no	—
332	#529	Dic₇₉	1	2	yes	complemented
333	#529	Dic₇₉	1	2	yes	complemented
334	#525	—	2	1	no	—
335	#525	—	2	1	no	—
336	#525	C₂×D₇₉	1	2	yes	—
337	C₄×#41	—	2	1	no	—
338	C₄×#41	—	2	1	no	—
339	C₄×#41	C₂×D₇₉	1	2	yes	—
340	C₂×#117	—	158	1	no	—
341	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
342	C₂×#104	—	79	8	no	—
343	C₄×M₁₆	—	79	2	no	—
344	C₄×M₁₆	—	79	2	no	—
345	C₄×M₁₆	—	158	1	no	—
346	C₄×M₁₆	—	158	1	no	—
347	C₂×#97	—	158	1	no	—
348	C₂×C₄×C₈	—	158	1	no	—
349	C₄×C₄⋊C₄	—	79	2	no	—
350	C₄×C₄⋊C₄	—	158	1	no	—
351	C₄×C₂²⋊C₄	—	79	2	no	—
352	C₄×C₂²⋊C₄	—	158	1	no	—
353	#376	—	158	1	no	—
354	C₄³	—	79	2	no	—
355	#339	—	79	8	no	—
356	C₂×#41	—	2	1	no	—
357	C₂×#41	—	2	1	no	—
358	C₂×#41	C₂²×D₇₉	1	2	yes	—
359	C₂³×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
360	C₂³×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
361	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
362	C₂×M₁₆	—	79	4	no	—
363	C₂×M₁₆	—	158	8	no	—
364	C₂×M₁₆	—	158	2	no	—
365	C₂²×C₈	—	158	2	no	—
366	C₄⋊Q₈	C₂×Dic₇₉	1	1	yes	characteristic
367	C₄⋊Q₈	C₂×Dic₇₉	1	1	yes	characteristic
368	C₄⋊Q₈	C₂×Dic₇₉	1	1	yes	characteristic
369	#127	C₂×Dic₇₉	1	1	yes	characteristic
370	#126	—	2	2	no	—
371	#126	—	2	2	no	—
372	#125	—	2	1	no	—
373	#125	—	2	1	no	—
374	#125	C₂×Dic₇₉	1	2	yes	—
375	#124	—	2	1	no	—
376	#124	—	2	1	no	—
377	#124	C₂×Dic₇₉	1	2	yes	—
378	#123	—	2	2	no	—
379	#123	—	2	2	no	—
380	#123	—	2	2	no	—
381	C₂²⋊Q₈	—	2	1	no	—
382	C₂²⋊Q₈	—	2	1	no	—
383	C₂²⋊Q₈	—	2	1	no	—
384	C₂²⋊Q₈	—	2	1	no	—
385	C₂²⋊Q₈	C₂×Dic₇₉	1	2	yes	—
386	C₂²⋊Q₈	C₂×Dic₇₉	1	2	yes	—
387	#121	—	2	1	no	—
388	#121	—	2	1	no	—
389	#121	—	2	1	no	—
390	#121	—	2	1	no	—
391	#121	C₂×Dic₇₉	1	2	yes	—
392	#121	C₂×Dic₇₉	1	2	yes	—
393	#120	—	2	2	no	—
394	C₄×Q₈	—	2	1	no	—
395	C₄×Q₈	—	2	1	no	—
396	C₄×Q₈	—	2	1	no	—
397	C₄×Q₈	—	2	1	no	—
398	C₄×Q₈	C₂×Dic₇₉	1	2	yes	—
399	C₄×Q₈	C₂×Dic₇₉	1	2	yes	—
400	C₄×D₄	—	2	2	no	—
401	C₄×D₄	—	2	2	no	—
402	C₄×D₄	—	2	2	no	—
403	C₄×D₄	—	2	2	no	—
404	C₄×D₄	—	2	2	no	—
405	C₄×D₄	—	2	2	no	—
406	C₄×D₄	—	2	1	no	—
407	C₄×D₄	—	2	1	no	—
408	C₄×D₄	—	2	1	no	—
409	C₄×D₄	—	2	1	no	—
410	C₄×D₄	C₂×Dic₇₉	1	2	yes	—
411	C₄×D₄	C₂×Dic₇₉	1	2	yes	—
412	#117	—	2	1	no	—
413	#117	—	2	1	no	—
414	#117	—	2	2	no	—
415	#117	—	2	2	no	—
416	#117	—	2	2	no	—
417	#117	—	158	8	no	—
418	#117	C₂²×D₇₉	1	2	yes	—
419	C₂×C₄⋊C₄	—	158	2	no	—
420	C₂×C₂²⋊C₄	—	158	2	no	—
421	C₂×C₄²	—	2	2	no	—
422	C₂×C₄²	—	79	4	no	—
423	C₂×C₄²	—	158	2	no	—
424	C₂×C₄²	—	158	2	no	—
425	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
426	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
427	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
428	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
429	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
430	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
431	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
432	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
433	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
434	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
435	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
436	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
437	#104	—	158	16	no	—
438	#97	—	158	2	no	—
439	#97	—	158	2	no	—
440	C₄×C₈	—	158	2	no	—
441	C₄×C₈	—	158	2	no	—
442	#95	—	158	2	no	—
443	#95	—	158	2	no	—
444	C₂⁴	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
445	#41	—	2	8	no	—
446	#41	—	4	4	no	—
447	#41	—	4	4	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	C₂²×Dic₇₉	1	2	yes	—
451	C₂×D₄	—	2	2	no	—
452	C₂×D₄	—	2	2	no	—
453	C₂×D₄	—	2	2	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	C₂²×Dic₇₉	1	2	yes	—
457	C₂²×C₄	—	2	4	no	—
458	C₂²×C₄	—	2	4	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	4	2	no	—
463	C₂²×C₄	—	158	4	no	—
464	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
465	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
466	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
467	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
468	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
469	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
470	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
471	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
472	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
473	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
474	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
475	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
476	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
477	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
478	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
479	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
480	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
481	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
482	M₁₆	—	79	8	no	—
483	M₁₆	—	158	8	no	—
484	M₁₆	—	158	4	no	—
485	C₂×C₈	—	158	8	no	—
486	C₂×C₈	—	158	4	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	158	8	no	—
498	C₄⋊C₄	C₂²×Dic₇₉	1	2	yes	—
499	C₄⋊C₄	C₂²×Dic₇₉	1	2	yes	—
500	C₂²⋊C₄	—	2	2	no	—
501	C₂²⋊C₄	—	2	2	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	158	8	no	—
510	C₄²	—	2	2	no	—
511	C₄²	—	2	2	no	—
512	C₄²	—	2	2	no	—
513	C₄²	—	316	4	no	—
514	C₄²	—	158	8	no	—
515	C₄²	—	158	8	no	—
516	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
517	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
518	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
519	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
520	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
521	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
522	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
523	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
524	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
525	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
526	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
527	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
528	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
529	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
530	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
531	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
532	C₂³	—	2	2	no	—
533	C₂³	—	2	2	no	—
534	C₂³	—	2	2	no	—
535	C₂³	—	4	1	no	—
536	C₂³	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
537	C₂³	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
538	C₂³	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
539	Q₈	—	2	4	no	—
540	Q₈	—	4	2	no	—
541	Q₈	—	4	2	no	—
542	D₄	—	2	4	no	—
543	D₄	—	4	2	no	—
544	D₄	—	4	4	no	—
545	D₄	—	4	4	no	—
546	D₄	—	4	4	no	—
547	D₄	—	4	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	4	no	—
568	C₂×C₄	—	4	4	no	—
569	C₂×C₄	—	4	4	no	—
570	C₂×C₄	—	316	4	no	—
571	C₂×C₄	—	316	4	no	—
572	C₂×C₄	—	158	8	no	—
573	C₂×C₄	#14579088	1	4	yes	complemented
574	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
575	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
576	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
577	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
578	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
579	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
580	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
581	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
582	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
583	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
584	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
585	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
586	C₂×C₄	#41×D₇₉	1	4	yes	—
587	C₈	—	158	8	no	—
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	4	4	no	—
596	C₂²	—	4	2	no	—
597	C₂²	—	4	2	no	—
598	C₂²	—	4	2	no	—
599	C₂²	C₂×#14579088	1	2	yes	—
600	C₂²	C₂²×C₂²⋊Dic₇₉	1	1	yes	characteristic
601	C₂²	#19099109	1	2	yes	—
602	C₄	—	2	1	no	—
603	C₄	—	2	1	no	—
604	C₄	—	2	1	no	—
605	C₄	—	2	1	no	—
606	C₄	—	2	1	no	—
607	C₄	—	2	1	no	—
608	C₄	—	2	1	no	—
609	C₄	—	4	2	no	—
610	C₄	—	4	2	no	—
611	C₄	—	4	2	no	—
612	C₄	—	316	8	no	—
613	C₄	C₂×#14579088	1	2	yes	—
614	C₄	C₂×#14579088	1	2	yes	—
615	C₄	#19098580	1	2	yes	—
616	C₄	#41×Dic₇₉	1	2	yes	—
617	C₄	#19099070	1	2	yes	—
618	C₂	—	2	2	no	—
619	C₂	—	2	2	no	—
620	C₂	—	4	1	no	—
621	C₂	—	8	2	no	—
622	C₂	#23765891	1	1	yes	characteristic
623	C₂	C₂²×#14579088	1	1	yes	characteristic
624	C₂	C₂×#19098580	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×C₂²⋊D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting, prime radical	C₇₉×#3444	C₂
socle	C₂²×C₇₉	C₂²×C₂²⋊C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#3444	D₇₉
hypocenter	C₇₉	#21382
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₄² ◁ C₂²×C₄² ◁ #3444

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×#11929608	C₂	semidirect
2. C₄×#14579120	C₂	semidirect
3. #23764345	C₂	semidirect
4. #23764320	C₂	semidirect
5. #23763703	C₂	semidirect
6. C₄×#14579088	C₂	semidirect
24. #533×C₇₉	C₄	semidirect
25. #533×C₇₉	C₄	semidirect
27. #532×C₇₉	C₄	semidirect
28. #532×C₇₉	C₄	semidirect
34. #529×C₇₉	C₄	semidirect
35. #529×C₇₉	C₄	semidirect
134. #11929608	#41	semidirect
257. C₂×C₄×C₇₉	#104	semidirect
320. C₇₉	#21382	semidirect
322. #533	Dic₇₉	semidirect
323. #533	Dic₇₉	semidirect
325. #532	Dic₇₉	semidirect
326. #532	Dic₇₉	semidirect
332. #529	Dic₇₉	semidirect
333. #529	Dic₇₉	semidirect
573. C₂×C₄	#14579088	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#11929608	2
C₄×#14579120	2
#23764345	2
#23764320	2
#23763703	2
C₄×#14579088	2
C₇₉×#3444	2
#21382	79