Subgroups — #34297668

Order 20224.

1352 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23772033	C₂	1	1	yes	maximal, characteristic, complemented
2	#23765798	C₂	1	1	yes	maximal, characteristic, complemented
3	#23764320	C₂	1	4	yes	maximal, complemented
4	#23764233	C₂	1	4	yes	maximal, complemented
5	#23763344	C₂	1	4	yes	maximal, complemented
6	C₂×#532×C₇₉	C₂	1	1	yes	maximal, characteristic
7	#19098620	—	2	1	no	—
8	#19098620	—	2	1	no	—
9	#19098616	—	2	1	no	—
10	#19098616	—	2	1	no	—
11	#19098587	C₂²	1	2	yes	complemented
12	C₂×#14579088	C₂²	1	16	yes	complemented
13	#19098527	C₂²	1	2	yes	—
14	C₄×#11929608	C₂²	1	2	yes	complemented
15	#19098431	—	2	1	no	—
16	#19098429	—	2	1	no	—
17	#19098426	—	2	1	no	—
18	#19098423	—	2	1	no	—
19	C₄×C₄⋊Dic₇₉	C₂²	1	2	yes	complemented
20	C₄×C₂²⋊Dic₇₉	C₂²	1	2	yes	—
21	#19098409	C₂²	1	2	yes	complemented
22	C₂²×#41×C₇₉	C₂²	1	2	yes	—
23	#532×C₇₉	—	2	1	no	—
24	#532×C₇₉	—	2	1	no	—
25	#532×C₇₉	—	2	1	no	—
26	#532×C₇₉	—	2	1	no	—
27	#532×C₇₉	C₄	1	2	yes	complemented
28	#532×C₇₉	C₄	1	2	yes	complemented
29	#532×C₇₉	C₂²	1	2	yes	—
30	#532×C₇₉	C₂²	1	2	yes	—
31	C₂×C₄⋊Q₈×C₇₉	C₄	1	1	yes	characteristic, complemented
32	C₂×#127×C₇₉	C₄	1	1	yes	characteristic, complemented
33	C₂×#124×C₇₉	C₄	1	2	yes	complemented
34	C₂×#121×C₇₉	—	2	1	no	—
35	C₂×#121×C₇₉	—	2	1	no	—
36	C₂×C₄×D₄×C₇₉	—	2	1	no	—
37	C₂×C₄×D₄×C₇₉	—	2	1	no	—
38	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
39	C₂×#11929608	C₂³	1	4	yes	—
40	C₂×C₄⋊Dic₇₉	—	2	2	no	—
41	C₂×C₂²⋊Dic₇₉	—	2	2	no	—
42	C₂×C₄×Dic₇₉	C₂³	1	4	yes	—
43	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
44	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
45	#14579088	—	4	16	no	—
46	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
47	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
48	#14579072	—	2	2	no	—
49	C₄×C₇₉⋊C₈	—	2	2	no	—
50	C₇₉⋊#95	—	2	2	no	—
51	C₇₉⋊#95	—	2	2	no	—
52	C₇₉⋊#95	—	2	2	no	—
53	C₇₉⋊#95	—	2	2	no	—
54	C₂×#41×C₇₉	—	2	2	no	—
55	C₂×#41×C₇₉	—	2	2	no	—
56	C₂×#41×C₇₉	—	4	8	no	—
57	C₂×#41×C₇₉	C₂×C₄	1	4	yes	—
58	C₂×#41×C₇₉	C₂³	1	4	yes	—
59	C₂²×Q₈×C₇₉	C₂×C₄	1	2	yes	—
60	C₂²×D₄×C₇₉	—	2	2	no	—
61	C₂²×D₄×C₇₉	—	2	1	no	—
62	C₂²×D₄×C₇₉	—	2	1	no	—
63	C₂²×D₄×C₇₉	C₂×C₄	1	2	yes	—
64	C₂³×C₄×C₇₉	—	2	2	no	—
65	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
66	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
67	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
68	C₄⋊Q₈×C₇₉	—	2	1	no	—
69	C₄⋊Q₈×C₇₉	—	2	1	no	—
70	C₄⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
71	C₄⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
72	#127×C₇₉	—	2	1	no	—
73	#127×C₇₉	—	2	1	no	—
74	#127×C₇₉	C₂×C₄	1	2	yes	—
75	#127×C₇₉	C₂×C₄	1	2	yes	—
76	#124×C₇₉	—	2	2	no	—
77	#124×C₇₉	—	2	2	no	—
78	#124×C₇₉	C₂×C₄	1	4	yes	—
79	#124×C₇₉	C₂×C₄	1	4	yes	—
80	#121×C₇₉	—	2	2	no	—
81	#121×C₇₉	—	2	2	no	—
82	#121×C₇₉	—	2	2	no	—
83	#121×C₇₉	—	2	2	no	—
84	#121×C₇₉	—	2	2	no	—
85	#121×C₇₉	—	2	2	no	—
86	#121×C₇₉	—	2	2	no	—
87	#121×C₇₉	—	2	2	no	—
88	C₄×D₄×C₇₉	—	2	2	no	—
89	C₄×D₄×C₇₉	—	2	2	no	—
90	C₄×D₄×C₇₉	—	2	2	no	—
91	C₄×D₄×C₇₉	—	2	2	no	—
92	C₄×D₄×C₇₉	—	2	2	no	—
93	C₄×D₄×C₇₉	—	2	2	no	—
94	C₄×D₄×C₇₉	—	2	2	no	—
95	C₄×D₄×C₇₉	—	2	2	no	—
96	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
97	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
99	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
100	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
101	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
102	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
104	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
106	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
107	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
108	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
110	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
112	C₂²×Dic₇₉	—	2	4	no	—
113	#11929608	—	2	8	no	—
114	C₂×C₇₉⋊C₈	—	2	4	no	—
115	C₄⋊Dic₇₉	—	4	4	no	—
116	C₂²⋊Dic₇₉	—	4	4	no	—
117	C₄×Dic₇₉	—	2	8	no	—
118	C₂⁴×C₇₉	—	2	2	no	—
119	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
120	#41×C₇₉	—	2	16	no	—
121	#41×C₇₉	—	4	8	no	—
122	#41×C₇₉	—	4	8	no	—
123	#41×C₇₉	—	4	8	no	—
124	C₂×Q₈×C₇₉	—	2	2	no	—
125	C₂×Q₈×C₇₉	—	4	4	no	—
126	C₂×Q₈×C₇₉	C₂²×C₄	1	4	yes	—
127	C₂×D₄×C₇₉	—	2	4	no	—
128	C₂×D₄×C₇₉	—	2	4	no	—
129	C₂×D₄×C₇₉	—	2	2	no	—
130	C₂×D₄×C₇₉	—	2	2	no	—
131	C₂×D₄×C₇₉	—	2	2	no	—
132	C₂×D₄×C₇₉	—	2	2	no	—
133	C₂×D₄×C₇₉	—	2	2	no	—
134	C₂×D₄×C₇₉	—	4	4	no	—
135	C₂×D₄×C₇₉	—	4	4	no	—
136	C₂×D₄×C₇₉	—	4	4	no	—
137	C₂×D₄×C₇₉	—	4	8	no	—
138	C₂×D₄×C₇₉	C₂²×C₄	1	4	yes	—
139	C₂²×C₄×C₇₉	—	2	4	no	—
140	C₂²×C₄×C₇₉	—	2	2	no	—
141	C₂²×C₄×C₇₉	—	2	4	no	—
142	C₂²×C₄×C₇₉	—	2	4	no	—
143	C₂²×C₄×C₇₉	—	4	2	no	—
144	C₂²×C₄×C₇₉	—	4	2	no	—
145	C₂²×C₄×C₇₉	—	4	8	no	—
146	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
147	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
148	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
164	C₄⋊C₄×C₇₉	—	2	2	no	—
165	C₄⋊C₄×C₇₉	—	2	2	no	—
166	C₄⋊C₄×C₇₉	—	2	2	no	—
167	C₄⋊C₄×C₇₉	—	2	2	no	—
168	C₂²⋊C₄×C₇₉	—	2	4	no	—
169	C₂²⋊C₄×C₇₉	—	2	4	no	—
170	C₂²⋊C₄×C₇₉	—	2	4	no	—
171	C₂²⋊C₄×C₇₉	—	2	4	no	—
172	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
173	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
174	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
175	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
176	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
177	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
178	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
179	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
180	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
181	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
182	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
183	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
184	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
186	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
188	C₂³×C₇₉	—	2	2	no	—
189	C₂³×C₇₉	—	2	2	no	—
190	C₂³×C₇₉	—	2	4	no	—
191	C₂³×C₇₉	—	4	1	no	—
192	C₂³×C₇₉	—	4	4	no	—
193	C₂³×C₇₉	—	4	4	no	—
194	C₂³×C₇₉	—	4	4	no	—
195	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
197	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
198	Q₈×C₇₉	—	2	8	no	—
199	Q₈×C₇₉	—	4	4	no	—
200	D₄×C₇₉	—	2	8	no	—
201	D₄×C₇₉	—	4	4	no	—
202	D₄×C₇₉	—	4	4	no	—
203	D₄×C₇₉	—	4	4	no	—
204	D₄×C₇₉	—	4	4	no	—
205	D₄×C₇₉	—	4	8	no	—
206	D₄×C₇₉	—	4	8	no	—
207	D₄×C₇₉	—	4	4	no	—
208	C₂×C₄×C₇₉	—	2	2	no	—
209	C₂×C₄×C₇₉	—	2	2	no	—
210	C₂×C₄×C₇₉	—	2	2	no	—
211	C₂×C₄×C₇₉	—	2	2	no	—
212	C₂×C₄×C₇₉	—	2	2	no	—
213	C₂×C₄×C₇₉	—	2	2	no	—
214	C₂×C₄×C₇₉	—	2	2	no	—
215	C₂×C₄×C₇₉	—	2	2	no	—
216	C₂×C₄×C₇₉	—	2	2	no	—
217	C₂×C₄×C₇₉	—	2	2	no	—
218	C₂×C₄×C₇₉	—	2	4	no	—
219	C₂×C₄×C₇₉	—	4	1	no	—
220	C₂×C₄×C₇₉	—	4	1	no	—
221	C₂×C₄×C₇₉	—	4	1	no	—
222	C₂×C₄×C₇₉	—	4	1	no	—
223	C₂×C₄×C₇₉	—	4	1	no	—
224	C₂×C₄×C₇₉	—	4	1	no	—
225	C₂×C₄×C₇₉	—	4	1	no	—
226	C₂×C₄×C₇₉	—	4	8	no	—
227	C₂×C₄×C₇₉	—	4	4	no	—
228	C₂×C₄×C₇₉	—	4	8	no	—
229	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
232	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
233	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
237	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
240	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₇₉	H(5,𝔽₂)	1	4	yes	—
242	C₂×Dic₇₉	—	4	4	no	—
243	C₂×Dic₇₉	—	4	4	no	—
244	C₂×Dic₇₉	—	4	4	no	—
245	C₇₉⋊C₈	—	4	4	no	—
246	C₂²×C₇₉	—	2	1	no	—
247	C₂²×C₇₉	—	2	1	no	—
248	C₂²×C₇₉	—	2	1	no	—
249	C₂²×C₇₉	—	2	1	no	—
250	C₂²×C₇₉	—	2	1	no	—
251	C₂²×C₇₉	—	2	1	no	—
252	C₂²×C₇₉	—	2	1	no	—
253	C₂²×C₇₉	—	4	4	no	—
254	C₂²×C₇₉	—	4	4	no	—
255	C₂²×C₇₉	—	4	4	no	—
256	C₂²×C₇₉	—	4	4	no	—
257	C₂²×C₇₉	—	8	8	no	—
258	C₂²×C₇₉	#421	1	2	yes	—
259	C₂²×C₇₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
260	C₂²×C₇₉	#535	1	2	yes	—
261	C₄×C₇₉	—	2	1	no	—
262	C₄×C₇₉	—	2	1	no	—
263	C₄×C₇₉	—	2	1	no	—
264	C₄×C₇₉	—	2	1	no	—
265	C₄×C₇₉	—	2	1	no	—
266	C₄×C₇₉	—	2	1	no	—
267	C₄×C₇₉	—	2	1	no	—
268	C₄×C₇₉	—	2	1	no	—
269	C₄×C₇₉	—	2	1	no	—
270	C₄×C₇₉	—	4	4	no	—
271	C₄×C₇₉	#421	1	2	yes	—
272	C₄×C₇₉	#518	1	2	yes	—
273	C₄×C₇₉	#535	1	2	yes	—
274	Dic₇₉	—	8	4	no	—
275	#21816	—	79	1	no	maximal, Sylow
276	C₂×C₇₉	—	2	2	no	—
277	C₂×C₇₉	—	2	2	no	—
278	C₂×C₇₉	—	4	1	no	—
279	C₂×C₇₉	—	8	4	no	—
280	C₂×C₇₉	#2309	1	1	yes	characteristic
281	C₂×C₇₉	C₂×#421	1	1	yes	characteristic
282	C₂×C₇₉	C₂×#421	1	1	yes	characteristic
283	C₂×#532	D₇₉	1	1	yes	characteristic
284	#2920	—	79	1	no	—
285	#2283	—	79	1	no	—
286	#1980	—	79	4	no	—
287	#1963	—	79	4	no	—
288	#1789	—	79	4	no	—
289	C₇₉	#21816	1	1	yes	characteristic, complemented, Sylow
290	C₂²×#41	C₂×D₇₉	1	2	yes	—
291	#532	—	2	1	no	—
292	#532	—	2	1	no	—
293	#532	—	2	1	no	—
294	#532	—	2	1	no	—
295	#532	Dic₇₉	1	2	yes	complemented
296	#532	Dic₇₉	1	2	yes	complemented
297	#532	C₂×D₇₉	1	2	yes	—
298	#532	C₂×D₇₉	1	2	yes	—
299	C₂×C₄⋊Q₈	Dic₇₉	1	1	yes	characteristic, complemented
300	C₂×#127	Dic₇₉	1	1	yes	characteristic, complemented
301	C₂×#124	Dic₇₉	1	2	yes	complemented
302	C₂×#121	—	2	1	no	—
303	C₂×#121	—	2	1	no	—
304	C₂×C₄×D₄	—	2	1	no	—
305	C₂×C₄×D₄	—	2	1	no	—
306	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
307	#432	—	158	1	no	—
308	#432	—	158	1	no	—
309	#431	—	158	1	no	—
310	#431	—	158	1	no	—
311	#423	—	79	2	no	—
312	C₂×#104	—	79	16	no	—
313	#407	—	79	2	no	—
314	C₄×M₁₆	—	79	2	no	—
315	#383	—	158	1	no	—
316	#382	—	158	1	no	—
317	#381	—	158	1	no	—
318	#380	—	158	1	no	—
319	C₄×C₄⋊C₄	—	79	2	no	—
320	C₄×C₂²⋊C₄	—	79	2	no	—
321	#376	—	79	2	no	—
322	C₂×#41	—	2	2	no	—
323	C₂×#41	—	2	2	no	—
324	C₂×#41	—	4	8	no	—
325	C₂×#41	C₂×Dic₇₉	1	4	yes	—
326	C₂×#41	C₂²×D₇₉	1	4	yes	—
327	C₂²×Q₈	C₂×Dic₇₉	1	2	yes	—
328	C₂²×D₄	—	2	2	no	—
329	C₂²×D₄	—	2	1	no	—
330	C₂²×D₄	—	2	1	no	—
331	C₂²×D₄	C₂×Dic₇₉	1	2	yes	—
332	C₂³×C₄	—	2	2	no	—
333	C₂³×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
334	C₂³×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
335	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
336	C₂×M₁₆	—	79	4	no	—
337	C₄⋊Q₈	—	2	1	no	—
338	C₄⋊Q₈	—	2	1	no	—
339	C₄⋊Q₈	C₂×Dic₇₉	1	2	yes	—
340	C₄⋊Q₈	C₂×Dic₇₉	1	2	yes	—
341	#127	—	2	1	no	—
342	#127	—	2	1	no	—
343	#127	C₂×Dic₇₉	1	2	yes	—
344	#127	C₂×Dic₇₉	1	2	yes	—
345	#124	—	2	2	no	—
346	#124	—	2	2	no	—
347	#124	C₂×Dic₇₉	1	4	yes	—
348	#124	C₂×Dic₇₉	1	4	yes	—
349	#121	—	2	2	no	—
350	#121	—	2	2	no	—
351	#121	—	2	2	no	—
352	#121	—	2	2	no	—
353	#121	—	2	2	no	—
354	#121	—	2	2	no	—
355	#121	—	2	2	no	—
356	#121	—	2	2	no	—
357	C₄×D₄	—	2	2	no	—
358	C₄×D₄	—	2	2	no	—
359	C₄×D₄	—	2	2	no	—
360	C₄×D₄	—	2	2	no	—
361	C₄×D₄	—	2	2	no	—
362	C₄×D₄	—	2	2	no	—
363	C₄×D₄	—	2	2	no	—
364	C₄×D₄	—	2	2	no	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	—	2	1	no	—
367	C₂×C₄⋊C₄	—	158	2	no	—
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₂²⋊C₄	—	2	2	no	—
370	C₂×C₂²⋊C₄	—	158	2	no	—
371	C₂×C₄²	—	79	4	no	—
372	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
373	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
374	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
375	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
376	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
377	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
378	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
379	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
380	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
381	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
382	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
383	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
384	C₄⋊C₈	—	158	2	no	—
385	C₄⋊C₈	—	158	2	no	—
386	#104	—	316	16	no	—
387	C₂²⋊C₈	—	158	2	no	—
388	C₂²⋊C₈	—	158	2	no	—
389	#97	—	158	2	no	—
390	C₄×C₈	—	158	2	no	—
391	#95	—	158	2	no	—
392	#95	—	158	2	no	—
393	#95	—	158	2	no	—
394	#95	—	158	2	no	—
395	C₂⁴	—	2	2	no	—
396	C₂⁴	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
397	#41	—	2	16	no	—
398	#41	—	4	8	no	—
399	#41	—	4	8	no	—
400	#41	—	4	8	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	—	4	4	no	—
403	C₂×Q₈	C₂²×Dic₇₉	1	4	yes	—
404	C₂×D₄	—	2	4	no	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	4	4	no	—
412	C₂×D₄	—	4	4	no	—
413	C₂×D₄	—	4	4	no	—
414	C₂×D₄	—	4	8	no	—
415	C₂×D₄	C₂²×Dic₇₉	1	4	yes	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	4	2	no	—
421	C₂²×C₄	—	4	2	no	—
422	C₂²×C₄	—	4	8	no	—
423	C₂²×C₄	—	158	4	no	—
424	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
425	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
426	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
427	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
428	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
429	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
430	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
431	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
432	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
433	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
434	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
435	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
436	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
437	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
438	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
439	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
440	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
441	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
442	M₁₆	—	158	8	no	—
443	C₂×C₈	—	158	4	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	316	4	no	—
449	C₂²⋊C₄	—	2	4	no	—
450	C₂²⋊C₄	—	2	4	no	—
451	C₂²⋊C₄	—	2	4	no	—
452	C₂²⋊C₄	—	2	4	no	—
453	C₂²⋊C₄	—	316	4	no	—
454	C₄²	—	158	8	no	—
455	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
456	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
457	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
458	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
459	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
460	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
461	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
462	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
463	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
464	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
465	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
466	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
467	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
468	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
469	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
470	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
471	C₂³	—	2	2	no	—
472	C₂³	—	2	2	no	—
473	C₂³	—	2	4	no	—
474	C₂³	—	4	1	no	—
475	C₂³	—	4	4	no	—
476	C₂³	—	4	4	no	—
477	C₂³	—	4	4	no	—
478	C₂³	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
479	C₂³	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
480	C₂³	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
481	Q₈	—	2	8	no	—
482	Q₈	—	4	4	no	—
483	D₄	—	2	8	no	—
484	D₄	—	4	4	no	—
485	D₄	—	4	4	no	—
486	D₄	—	4	4	no	—
487	D₄	—	4	4	no	—
488	D₄	—	4	8	no	—
489	D₄	—	4	8	no	—
490	D₄	—	4	4	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	8	no	—
510	C₂×C₄	—	4	4	no	—
511	C₂×C₄	—	4	8	no	—
512	C₂×C₄	—	316	4	no	—
513	C₂×C₄	—	316	4	no	—
514	C₂×C₄	—	316	4	no	—
515	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
516	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
517	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
518	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
519	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
520	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
521	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
522	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
523	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
524	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
525	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
526	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
527	C₂×C₄	#14579206	1	4	yes	—
528	C₈	—	316	4	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	1	no	—
533	C₂²	—	2	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	4	4	no	—
537	C₂²	—	4	4	no	—
538	C₂²	—	4	4	no	—
539	C₂²	—	4	4	no	—
540	C₂²	—	8	8	no	—
541	C₂²	#19098580	1	2	yes	—
542	C₂²	C₂²×C₂²⋊Dic₇₉	1	1	yes	characteristic
543	C₂²	#19099130	1	2	yes	—
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	2	1	no	—
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	4	4	no	—
554	C₄	—	632	4	no	—
555	C₄	#19098580	1	2	yes	—
556	C₄	#19099038	1	2	yes	—
557	C₄	#19099130	1	2	yes	—
558	C₂	—	2	2	no	—
559	C₂	—	2	2	no	—
560	C₂	—	4	1	no	—
561	C₂	—	8	4	no	—
562	C₂	#23765982	1	1	yes	characteristic
563	C₂	C₂×#19098580	1	1	yes	characteristic
564	C₂	C₂×#19098580	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting, prime radical	C₂×#532×C₇₉	C₂
socle	C₂²×C₇₉	C₂²×C₂²⋊C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₂×#532	D₇₉
hypocenter	C₇₉	#21816
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. #23772033	C₂	semidirect
2. #23765798	C₂	semidirect
3. #23764320	C₂	semidirect
4. #23764233	C₂	semidirect
5. #23763344	C₂	semidirect
11. #19098587	C₂²	semidirect
12. C₂×#14579088	C₂²	semidirect
14. C₄×#11929608	C₂²	semidirect
19. C₄×C₄⋊Dic₇₉	C₂²	semidirect
21. #19098409	C₂²	semidirect
27. #532×C₇₉	C₄	semidirect
28. #532×C₇₉	C₄	semidirect
31. C₂×C₄⋊Q₈×C₇₉	C₄	semidirect
32. C₂×#127×C₇₉	C₄	semidirect
33. C₂×#124×C₇₉	C₄	semidirect
289. C₇₉	#21816	semidirect
295. #532	Dic₇₉	semidirect
296. #532	Dic₇₉	semidirect
299. C₂×C₄⋊Q₈	Dic₇₉	semidirect
300. C₂×#127	Dic₇₉	semidirect
301. C₂×#124	Dic₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23772033	2
#23765798	2
#23764320	2
#23764233	2
#23763344	2
C₂×#532×C₇₉	2
#21816	79