Subgroups — #34257941

Order 20224.

726 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23772441	C₂	1	1	yes	maximal, characteristic, complemented
2	#23772424	C₂	1	1	yes	maximal, characteristic, complemented
3	#23762265	C₂	1	4	yes	maximal, complemented
4	#23762230	C₂	1	4	yes	maximal, complemented
5	#23762148	C₂	1	1	yes	maximal, characteristic, complemented
6	#23761791	C₂	1	1	yes	maximal, characteristic, complemented
7	#23761791	C₂	1	1	yes	maximal, characteristic, complemented
8	#23761692	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×D₈×C₇₉	C₂	1	1	yes	maximal, characteristic
10	#19098641	—	2	2	no	—
11	#19098641	C₂²	1	4	yes	complemented
12	D₄×C₇₉⋊C₈	—	2	2	no	—
13	D₄×C₇₉⋊C₈	C₂²	1	4	yes	complemented
14	#19098616	C₂²	1	1	yes	characteristic
15	#19098616	C₂²	1	1	yes	characteristic
16	#19098616	C₂²	1	1	yes	characteristic
17	#19098616	C₂²	1	1	yes	characteristic
18	#19098527	—	2	2	no	—
19	C₂×C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
20	#19098316	C₂²	1	2	yes	complemented
21	#19098314	C₂²	1	2	yes	complemented
22	D₄⋊(C₇₉⋊C₈)	C₂²	1	4	yes	complemented
23	D₄⋊(C₇₉⋊C₈)	C₂²	1	4	yes	complemented
24	#19098285	C₂²	1	2	yes	complemented
25	#19098285	C₂²	1	2	yes	complemented
26	C₂²×D₈×C₇₉	C₄	1	1	yes	characteristic
27	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
29	C₄×D₈×C₇₉	C₄	1	2	yes	—
30	C₄×D₈×C₇₉	C₄	1	2	yes	—
31	C₄×D₈×C₇₉	C₂²	1	2	yes	—
32	C₄×D₈×C₇₉	C₂²	1	2	yes	—
33	C₂×#107×C₇₉	C₄	1	1	yes	characteristic
34	C₂×#102×C₇₉	C₄	1	1	yes	characteristic
35	C₂×#102×C₇₉	C₄	1	1	yes	characteristic
36	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
37	C₂×#11929608	—	2	4	no	—
38	C₂²×C₇₉⋊C₈	—	2	4	no	—
39	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
40	C₄⋊(C₇₉⋊C₈)	D₄	1	2	yes	—
41	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
42	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
43	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
44	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
45	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
46	C₂²⋊(C₇₉⋊C₈)	—	2	4	no	—
47	C₂²⋊(C₇₉⋊C₈)	—	2	4	no	—
48	C₂²⋊(C₇₉⋊C₈)	D₄	1	2	yes	—
49	C₄×C₇₉⋊C₈	—	2	1	no	—
50	C₄×C₇₉⋊C₈	—	2	1	no	—
51	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
52	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
53	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
54	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
55	C₂³×C₄×C₇₉	—	2	1	no	—
56	C₂³×C₄×C₇₉	—	2	1	no	—
57	C₂×D₈×C₇₉	—	2	4	no	—
58	C₂×D₈×C₇₉	C₂×C₄	1	2	yes	—
59	C₂×D₈×C₇₉	C₂×C₄	1	2	yes	—
60	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
62	C₄×D₄×C₇₉	—	2	1	no	—
63	C₄×D₄×C₇₉	—	2	1	no	—
64	C₄×D₄×C₇₉	—	2	1	no	—
65	C₄×D₄×C₇₉	—	2	1	no	—
66	C₄×D₄×C₇₉	C₂×C₄	1	2	yes	—
67	C₄×D₄×C₇₉	C₂×C₄	1	2	yes	—
68	C₄×D₄×C₇₉	C₂³	1	2	yes	—
69	C₄×D₄×C₇₉	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
74	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
75	#107×C₇₉	C₂×C₄	1	2	yes	—
76	#107×C₇₉	C₂×C₄	1	2	yes	—
77	#102×C₇₉	C₂×C₄	1	2	yes	—
78	#102×C₇₉	C₂×C₄	1	2	yes	—
79	#102×C₇₉	C₂×C₄	1	2	yes	—
80	#102×C₇₉	C₂×C₄	1	2	yes	—
81	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
82	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
83	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
84	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
85	#11929608	—	8	4	no	—
86	C₂×C₇₉⋊C₈	—	2	2	no	—
87	C₂×C₇₉⋊C₈	—	2	2	no	—
88	C₂×C₇₉⋊C₈	—	2	2	no	—
89	C₂×C₇₉⋊C₈	—	8	4	no	—
90	C₂×C₇₉⋊C₈	C₂×D₄	1	4	yes	—
91	C₂⁴×C₇₉	—	2	1	no	—
92	C₂⁴×C₇₉	—	2	1	no	—
93	C₂×D₄×C₇₉	—	2	1	no	—
94	C₂×D₄×C₇₉	—	2	1	no	—
95	C₂×D₄×C₇₉	—	2	2	no	—
96	C₂×D₄×C₇₉	—	2	2	no	—
97	C₂×D₄×C₇₉	—	2	2	no	—
98	C₂×D₄×C₇₉	M₁₆	1	4	yes	complemented
99	C₂×D₄×C₇₉	C₂²×C₄	1	2	yes	—
100	C₂×D₄×C₇₉	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₇₉	—	2	1	no	—
102	C₂²×C₄×C₇₉	—	2	1	no	—
103	C₂²×C₄×C₇₉	—	2	2	no	—
104	C₂²×C₄×C₇₉	—	2	2	no	—
105	C₂²×C₄×C₇₉	—	2	2	no	—
106	C₂²×C₄×C₇₉	—	2	2	no	—
107	C₂²×C₄×C₇₉	—	8	2	no	—
108	C₂²×C₄×C₇₉	—	8	2	no	—
109	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
112	D₈×C₇₉	—	2	4	no	—
113	D₈×C₇₉	—	2	4	no	—
114	C₂×C₈×C₇₉	—	2	2	no	—
115	C₂×C₈×C₇₉	—	2	2	no	—
116	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
120	C₄⋊C₄×C₇₉	—	2	1	no	—
121	C₄⋊C₄×C₇₉	—	2	1	no	—
122	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
123	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
124	C₂²⋊C₄×C₇₉	—	2	2	no	—
125	C₂²⋊C₄×C₇₉	—	2	2	no	—
126	C₂²⋊C₄×C₇₉	—	2	2	no	—
127	C₂²⋊C₄×C₇₉	—	2	2	no	—
128	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₇₉	#41	1	1	yes	characteristic
131	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
132	C₂³×C₇₉	—	2	2	no	—
133	C₂³×C₇₉	—	2	4	no	—
134	C₂³×C₇₉	—	2	2	no	—
135	C₂³×C₇₉	—	4	2	no	—
136	C₂³×C₇₉	—	8	1	no	—
137	C₂³×C₇₉	—	8	1	no	—
138	C₂³×C₇₉	—	8	1	no	—
139	C₂³×C₇₉	—	8	1	no	—
140	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
141	D₄×C₇₉	—	2	2	no	—
142	D₄×C₇₉	—	2	2	no	—
143	D₄×C₇₉	—	2	2	no	—
144	D₄×C₇₉	—	2	4	no	—
145	D₄×C₇₉	—	4	2	no	—
146	D₄×C₇₉	C₂×M₁₆	1	4	yes	—
147	C₂×C₄×C₇₉	—	2	2	no	—
148	C₂×C₄×C₇₉	—	2	2	no	—
149	C₂×C₄×C₇₉	—	2	2	no	—
150	C₂×C₄×C₇₉	—	4	1	no	—
151	C₂×C₄×C₇₉	—	4	4	no	—
152	C₂×C₄×C₇₉	—	4	4	no	—
153	C₂×C₄×C₇₉	—	8	2	no	—
154	C₂×C₄×C₇₉	—	8	2	no	—
155	C₂×C₄×C₇₉	—	8	1	no	—
156	C₂×C₄×C₇₉	—	8	1	no	—
157	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
161	C₂×C₄×C₇₉	#131	1	2	yes	—
162	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
163	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
165	C₈×C₇₉	—	2	1	no	—
166	C₈×C₇₉	—	2	1	no	—
167	C₈×C₇₉	—	2	1	no	—
168	C₈×C₇₉	—	2	1	no	—
169	C₇₉⋊C₈	—	2	4	no	—
170	C₇₉⋊C₈	—	4	2	no	—
171	C₇₉⋊C₈	—	4	2	no	—
172	C₇₉⋊C₈	—	4	2	no	—
173	C₂²×C₇₉	—	2	1	no	—
174	C₂²×C₇₉	—	2	1	no	—
175	C₂²×C₇₉	—	2	4	no	—
176	C₂²×C₇₉	—	4	2	no	—
177	C₂²×C₇₉	—	4	2	no	—
178	C₂²×C₇₉	—	4	2	no	—
179	C₂²×C₇₉	—	4	2	no	—
180	C₂²×C₇₉	—	4	2	no	—
181	C₂²×C₇₉	—	8	4	no	—
182	C₂²×C₇₉	—	8	4	no	—
183	C₂²×C₇₉	#435	1	2	yes	—
184	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
185	C₄×C₇₉	—	2	1	no	—
186	C₄×C₇₉	—	2	1	no	—
187	C₄×C₇₉	—	2	1	no	—
188	C₄×C₇₉	—	4	2	no	—
189	C₄×C₇₉	—	4	2	no	—
190	C₄×C₇₉	#435	1	2	yes	—
191	C₄×C₇₉	C₂²×M₁₆	1	1	yes	characteristic
192	C₄×C₇₉	C₂×#131	1	1	yes	characteristic
193	C₄×C₇₉	#576	1	2	yes	—
194	#17877	—	79	1	no	maximal, Sylow
195	C₂×C₇₉	—	2	2	no	—
196	C₂×C₇₉	—	4	4	no	—
197	C₂×C₇₉	—	8	2	no	—
198	C₂×C₇₉	C₂×#435	1	1	yes	characteristic
199	C₂×C₇₉	#2948	1	1	yes	characteristic
200	C₂×C₇₉	#2957	1	1	yes	characteristic
201	#2975	—	79	1	no	—
202	#2972	—	79	1	no	—
203	C₂×C₄×D₈	D₇₉	1	1	yes	characteristic
204	#1586	—	79	4	no	—
205	#1581	—	79	4	no	—
206	#1564	—	79	1	no	—
207	#1478	—	79	1	no	—
208	#1478	—	79	1	no	—
209	#1452	—	79	1	no	—
210	C₇₉	#17877	1	1	yes	characteristic, complemented, Sylow
211	C₂²×D₈	Dic₇₉	1	1	yes	characteristic
212	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
213	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
214	C₄×D₈	Dic₇₉	1	2	yes	—
215	C₄×D₈	Dic₇₉	1	2	yes	—
216	C₄×D₈	C₂×D₇₉	1	2	yes	—
217	C₄×D₈	C₂×D₇₉	1	2	yes	—
218	#436	—	79	4	no	—
219	#436	—	158	2	no	—
220	C₈×D₄	—	79	4	no	—
221	C₈×D₄	—	158	2	no	—
222	#431	—	79	1	no	—
223	#431	—	79	1	no	—
224	#431	—	79	1	no	—
225	#431	—	79	1	no	—
226	C₂×#107	Dic₇₉	1	1	yes	characteristic
227	C₂×#102	Dic₇₉	1	1	yes	characteristic
228	C₂×#102	Dic₇₉	1	1	yes	characteristic
229	#407	—	158	2	no	—
230	C₂×C₂²⋊C₈	—	158	2	no	—
231	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
232	#335	—	79	2	no	—
233	#334	—	79	2	no	—
234	D₄⋊C₈	—	79	4	no	—
235	D₄⋊C₈	—	79	4	no	—
236	#322	—	79	2	no	—
237	#322	—	79	2	no	—
238	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
239	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
240	C₂³×C₄	—	2	1	no	—
241	C₂³×C₄	—	2	1	no	—
242	C₂×D₈	—	2	4	no	—
243	C₂×D₈	C₂×Dic₇₉	1	2	yes	—
244	C₂×D₈	C₂×Dic₇₉	1	2	yes	—
245	C₂×M₁₆	—	158	4	no	—
246	C₂²×C₈	—	158	4	no	—
247	C₂²×C₈	C₂×Dic₇₉	1	1	yes	characteristic
248	C₂²×C₈	C₂×Dic₇₉	1	1	yes	characteristic
249	C₄×D₄	—	2	1	no	—
250	C₄×D₄	—	2	1	no	—
251	C₄×D₄	—	2	1	no	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	C₂×Dic₇₉	1	2	yes	—
254	C₄×D₄	C₂×Dic₇₉	1	2	yes	—
255	C₄×D₄	C₂²×D₇₉	1	2	yes	—
256	C₄×D₄	C₂²×D₇₉	1	2	yes	—
257	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	—	2	1	no	—
260	C₂×C₂²⋊C₄	—	2	1	no	—
261	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
262	#107	C₂×Dic₇₉	1	2	yes	—
263	#107	C₂×Dic₇₉	1	2	yes	—
264	C₄⋊C₈	—	79	2	no	—
265	C₄⋊C₈	—	79	2	no	—
266	C₄⋊C₈	—	79	2	no	—
267	C₄⋊C₈	—	158	1	no	—
268	#102	C₂×Dic₇₉	1	2	yes	—
269	#102	C₂×Dic₇₉	1	2	yes	—
270	#102	C₂×Dic₇₉	1	2	yes	—
271	#102	C₂×Dic₇₉	1	2	yes	—
272	C₂²⋊C₈	—	79	2	no	—
273	C₂²⋊C₈	—	158	4	no	—
274	C₂²⋊C₈	—	158	4	no	—
275	C₂²⋊C₈	—	158	1	no	—
276	C₂²⋊C₈	—	158	1	no	—
277	C₂²⋊C₈	—	158	1	no	—
278	C₄×C₈	—	79	2	no	—
279	C₄×C₈	—	79	2	no	—
280	C₄×C₈	—	158	1	no	—
281	C₄×C₈	—	158	1	no	—
282	C₄×C₈	C₂×Dic₇₉	1	1	yes	characteristic
283	C₄×C₈	C₂×Dic₇₉	1	1	yes	characteristic
284	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
285	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
286	C₂⁴	—	2	1	no	—
287	C₂⁴	—	2	1	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	#11929608	1	4	yes	complemented
294	C₂×D₄	C₂²×Dic₇₉	1	2	yes	—
295	C₂×D₄	C₂²×Dic₇₉	1	2	yes	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	8	2	no	—
303	C₂²×C₄	—	8	2	no	—
304	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
305	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
306	C₂²×C₄	#11929623	1	1	yes	characteristic
307	D₈	—	2	4	no	—
308	D₈	—	2	4	no	—
309	M₁₆	—	632	4	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	79	4	no	—
313	C₂×C₈	—	632	4	no	—
314	C₂×C₈	—	158	2	no	—
315	C₂×C₈	—	158	2	no	—
316	C₂×C₈	—	158	2	no	—
317	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
318	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
319	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
320	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	C₂²×Dic₇₉	1	2	yes	—
324	C₄⋊C₄	C₂²×Dic₇₉	1	2	yes	—
325	C₂²⋊C₄	—	2	2	no	—
326	C₂²⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	2	2	no	—
328	C₂²⋊C₄	—	2	2	no	—
329	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
330	C₄²	D₄×D₇₉	1	1	yes	characteristic
331	C₄²	#11929623	1	1	yes	characteristic
332	C₄²	C₂³×D₇₉	1	1	yes	characteristic
333	C₂³	—	2	2	no	—
334	C₂³	—	2	4	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	4	2	no	—
337	C₂³	—	8	1	no	—
338	C₂³	—	8	1	no	—
339	C₂³	—	8	1	no	—
340	C₂³	—	8	1	no	—
341	C₂³	D₄×Dic₇₉	1	1	yes	characteristic
342	D₄	—	2	4	no	—
343	D₄	—	2	2	no	—
344	D₄	—	2	2	no	—
345	D₄	—	2	2	no	—
346	D₄	—	4	2	no	—
347	D₄	C₂×#11929608	1	4	yes	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	8	2	no	—
355	C₂×C₄	—	8	2	no	—
356	C₂×C₄	—	8	1	no	—
357	C₂×C₄	—	8	1	no	—
358	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
359	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
360	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
361	C₂×C₄	C₂×#11929608	1	2	yes	—
362	C₂×C₄	#14579168	1	2	yes	—
363	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
364	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
365	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
366	C₈	—	2	1	no	—
367	C₈	—	2	1	no	—
368	C₈	—	2	1	no	—
369	C₈	—	2	1	no	—
370	C₈	—	316	2	no	—
371	C₈	—	316	2	no	—
372	C₈	—	316	2	no	—
373	C₈	—	158	4	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	4	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	8	4	no	—
383	C₂²	—	8	4	no	—
384	C₂²	#19098635	1	2	yes	—
385	C₂²	C₂×D₄×Dic₇₉	1	1	yes	characteristic
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	4	2	no	—
390	C₄	—	4	2	no	—
391	C₄	#19098635	1	2	yes	—
392	C₄	C₂²×#11929608	1	1	yes	characteristic
393	C₄	C₂×#14579168	1	1	yes	characteristic
394	C₄	#19099364	1	2	yes	—
395	C₂	—	2	2	no	—
396	C₂	—	4	4	no	—
397	C₂	—	8	2	no	—
398	C₂	C₂×#19098635	1	1	yes	characteristic
399	C₂	#23772252	1	1	yes	characteristic
400	C₂	#23772317	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₄²	C₂³×D₇₉
Fitting	C₂×C₄×D₈×C₇₉	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	C₂²×D₈×C₇₉	C₄
cosocle	C₄²×C₇₉	C₂⁴
hypercenter	C₂×C₄×D₈	D₇₉
hypocenter	C₇₉	#17877
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×D₈

Complements

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

N	H ≅ G/N	type
1. #23772441	C₂	semidirect
2. #23772424	C₂	semidirect
3. #23762265	C₂	semidirect
4. #23762230	C₂	semidirect
5. #23762148	C₂	semidirect
6. #23761791	C₂	semidirect
7. #23761791	C₂	semidirect
8. #23761692	C₂	semidirect
11. #19098641	C₂²	semidirect
13. D₄×C₇₉⋊C₈	C₂²	semidirect
20. #19098316	C₂²	semidirect
21. #19098314	C₂²	semidirect
22. D₄⋊(C₇₉⋊C₈)	C₂²	semidirect
23. D₄⋊(C₇₉⋊C₈)	C₂²	semidirect
24. #19098285	C₂²	semidirect
25. #19098285	C₂²	semidirect
98. C₂×D₄×C₇₉	M₁₆	semidirect
210. C₇₉	#17877	semidirect
293. C₂×D₄	#11929608	semidirect

Maximal subgroups

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

subgroup	index
#23772441	2
#23772424	2
#23762265	2
#23762230	2
#23762148	2
#23761791	2
#23761692	2
C₂×C₄×D₈×C₇₉	2
#17877	79