Subgroups — #34182877

Order 20224.

560 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098694	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#11929611	C₂	1	1	yes	maximal, characteristic
3	#23764193	C₂	1	1	yes	maximal, characteristic
4	C₂×#19098292	C₂	1	1	yes	maximal, characteristic
5	#23761234	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉⋊#1273	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×Q₈⋊C₈×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#11929611	C₄	1	1	yes	characteristic
9	C₂×C₄×D₃₁₆	C₂²	1	1	yes	characteristic
10	#19098694	—	2	2	no	—
11	#19098694	—	2	2	no	—
12	C₄×#11929611	—	2	2	no	—
13	C₄×#11929611	—	2	2	no	—
14	C₂×#14579092	C₄	1	1	yes	characteristic
15	C₂×C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
16	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×#14579085	C₄	1	1	yes	characteristic
18	C₂×#14579081	C₄	1	1	yes	characteristic
19	C₂×(C₂×D₇₉)⋊C₈	—	2	1	no	—
20	C₂×(C₂×D₇₉)⋊C₈	—	2	1	no	—
21	C₂×#14579072	—	2	1	no	—
22	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
24	#19098292	—	2	2	no	—
25	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
28	Q₈⋊C₈×C₇₉	—	2	2	no	—
29	C₂²×D₃₁₆	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×D₇₉	—	2	1	no	—
31	C₂×#11929611	—	2	2	no	—
32	C₂×#11929611	—	2	2	no	—
33	C₂×#11929611	—	2	2	no	—
34	C₂²×C₇₉⋊C₈	—	2	1	no	—
35	C₂²×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₇₉⋊C₈	D₄	1	1	yes	characteristic
38	C₂²×C₇₉⋊C₈	D₄	1	1	yes	characteristic
39	C₄×D₃₁₆	—	2	1	no	—
40	C₄×D₃₁₆	—	2	1	no	—
41	C₄×D₃₁₆	—	2	1	no	—
42	C₄×D₃₁₆	—	2	1	no	—
43	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
44	C₂×(C₂×D₇₉)⋊C₄	—	2	1	no	—
45	#14579092	—	2	2	no	—
46	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
47	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
48	C₄⋊(C₇₉⋊C₈)	D₄	1	2	yes	—
49	#14579085	—	2	2	no	—
50	#14579081	—	2	2	no	—
51	(C₂×D₇₉)⋊C₈	—	4	2	no	—
52	(C₂×D₇₉)⋊C₈	—	4	2	no	—
53	#14579072	—	2	4	no	—
54	C₄×C₇₉⋊C₈	—	2	1	no	—
55	C₄×C₇₉⋊C₈	—	2	1	no	—
56	C₄×C₇₉⋊C₈	—	2	1	no	—
57	C₄×C₇₉⋊C₈	—	2	1	no	—
58	C₂²×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₈×C₇₉	—	2	1	no	—
60	C₂²×C₈×C₇₉	—	2	1	no	—
61	C₄×Q₈×C₇₉	—	2	1	no	—
62	C₄×Q₈×C₇₉	—	2	1	no	—
63	C₄×Q₈×C₇₉	D₄	1	2	yes	—
64	C₄×Q₈×C₇₉	D₄	1	2	yes	—
65	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₇₉	—	2	1	no	—
68	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
69	C₄⋊C₈×C₇₉	—	2	1	no	—
70	C₄⋊C₈×C₇₉	—	2	1	no	—
71	C₄×C₈×C₇₉	—	2	1	no	—
72	C₄×C₈×C₇₉	—	2	1	no	—
73	C₂³×D₇₉	—	2	1	no	—
74	C₂×D₃₁₆	—	2	1	no	—
75	C₂×D₃₁₆	—	2	1	no	—
76	C₂×D₃₁₆	—	2	1	no	—
77	C₂×D₃₁₆	—	2	1	no	—
78	C₂×D₃₁₆	—	2	1	no	—
79	C₂×D₃₁₆	M₁₆	1	2	yes	—
80	C₂²×Dic₇₉	—	2	1	no	—
81	C₂×C₄×D₇₉	—	4	1	no	—
82	C₂×C₄×D₇₉	—	4	1	no	—
83	C₂×C₄×D₇₉	—	4	1	no	—
84	C₂×C₄×D₇₉	—	4	1	no	—
85	C₂×C₄×D₇₉	—	4	1	no	—
86	C₂×C₄×D₇₉	—	4	1	no	—
87	#11929611	—	2	8	no	—
88	C₂×C₇₉⋊C₈	—	2	1	no	—
89	C₂×C₇₉⋊C₈	—	2	1	no	—
90	C₂×C₇₉⋊C₈	—	2	1	no	—
91	C₂×C₇₉⋊C₈	—	2	1	no	—
92	C₂×C₇₉⋊C₈	—	2	2	no	—
93	C₂×C₇₉⋊C₈	—	2	1	no	—
94	C₂×C₇₉⋊C₈	—	2	1	no	—
95	C₂×C₇₉⋊C₈	—	2	1	no	—
96	C₂×C₇₉⋊C₈	—	2	1	no	—
97	C₂×C₇₉⋊C₈	—	2	1	no	—
98	C₂×C₇₉⋊C₈	—	2	1	no	—
99	C₂×C₇₉⋊C₈	—	4	1	no	—
100	C₂×C₇₉⋊C₈	—	4	1	no	—
101	C₂×C₇₉⋊C₈	M₁₆	1	2	yes	—
102	C₂×C₇₉⋊C₈	SD₁₆	1	2	yes	complemented
103	C₄⋊Dic₇₉	—	2	1	no	—
104	C₄⋊Dic₇₉	—	2	1	no	—
105	(C₂×D₇₉)⋊C₄	—	4	1	no	—
106	(C₂×D₇₉)⋊C₄	—	4	1	no	—
107	C₂×Q₈×C₇₉	—	2	1	no	—
108	C₂×Q₈×C₇₉	—	2	1	no	—
109	C₂×Q₈×C₇₉	—	2	1	no	—
110	C₂×Q₈×C₇₉	—	2	1	no	—
111	C₂×Q₈×C₇₉	—	2	1	no	—
112	C₂×Q₈×C₇₉	C₂²⋊C₄	1	2	yes	—
113	C₂²×C₄×C₇₉	—	2	1	no	—
114	C₂²×C₄×C₇₉	—	2	1	no	—
115	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
118	C₂×C₈×C₇₉	—	2	2	no	—
119	C₂×C₈×C₇₉	—	4	1	no	—
120	C₂×C₈×C₇₉	—	4	1	no	—
121	C₂×C₈×C₇₉	—	4	1	no	—
122	C₂×C₈×C₇₉	—	4	1	no	—
123	C₂×C₈×C₇₉	—	4	1	no	—
124	C₄⋊C₄×C₇₉	—	2	1	no	—
125	C₄⋊C₄×C₇₉	—	2	2	no	—
126	C₄⋊C₄×C₇₉	—	2	2	no	—
127	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
128	C₄²×C₇₉	—	2	2	no	—
129	C₄²×C₇₉	—	2	2	no	—
130	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₇₉	#41	1	1	yes	characteristic
134	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
135	C₂²×D₇₉	—	2	2	no	—
136	C₂²×D₇₉	—	4	1	no	—
137	C₂²×D₇₉	—	4	1	no	—
138	C₂²×D₇₉	—	4	1	no	—
139	C₂²×D₇₉	—	4	1	no	—
140	C₂²×D₇₉	—	4	1	no	—
141	C₂²×D₇₉	—	4	1	no	—
142	Q₈×C₇₉	—	2	2	no	—
143	Q₈×C₇₉	—	2	2	no	—
144	Q₈×C₇₉	—	4	1	no	—
145	Q₈×C₇₉	—	4	1	no	—
146	C₂×C₄×C₇₉	—	2	1	no	—
147	C₂×C₄×C₇₉	—	2	1	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	1	no	—
152	C₂×C₄×C₇₉	—	4	1	no	—
153	C₂×C₄×C₇₉	—	4	1	no	—
154	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
157	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
158	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
159	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
160	C₂×C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
161	C₂×C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
162	C₂×C₄×C₇₉	#131	1	1	yes	characteristic
163	C₂×C₄×C₇₉	#131	1	1	yes	characteristic
164	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
165	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
166	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
167	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
168	C₂×Dic₇₉	—	4	1	no	—
169	C₂×Dic₇₉	—	4	1	no	—
170	C₂×Dic₇₉	—	4	1	no	—
171	D₃₁₆	—	2	2	no	—
172	D₃₁₆	—	2	2	no	—
173	D₃₁₆	—	4	1	no	—
174	D₃₁₆	—	4	1	no	—
175	C₄×D₇₉	—	8	1	no	—
176	C₄×D₇₉	—	8	1	no	—
177	C₄×D₇₉	—	8	1	no	—
178	C₄×D₇₉	—	8	1	no	—
179	C₈×C₇₉	—	4	2	no	—
180	C₈×C₇₉	—	8	1	no	—
181	C₇₉⋊C₈	—	2	2	no	—
182	C₇₉⋊C₈	—	2	2	no	—
183	C₇₉⋊C₈	—	4	1	no	—
184	C₇₉⋊C₈	—	4	1	no	—
185	C₇₉⋊C₈	—	4	2	no	—
186	C₂²×C₇₉	#386	1	1	yes	characteristic
187	C₂²×C₇₉	#435	1	1	yes	characteristic
188	C₂²×C₇₉	#436	1	1	yes	characteristic
189	C₂²×C₇₉	C₄×SD₁₆	1	1	yes	characteristic
190	C₂²×C₇₉	#440	1	1	yes	characteristic
191	C₂²×C₇₉	#443	1	1	yes	characteristic
192	C₂²×C₇₉	#444	1	1	yes	characteristic
193	C₂×D₇₉	—	4	2	no	—
194	C₂×D₇₉	—	4	2	no	—
195	C₂×D₇₉	—	4	2	no	—
196	C₂×D₇₉	—	8	1	no	—
197	C₂×D₇₉	—	8	1	no	—
198	C₂×D₇₉	—	8	1	no	—
199	C₂×D₇₉	—	8	1	no	—
200	C₄×C₇₉	—	2	1	no	—
201	C₄×C₇₉	—	2	1	no	—
202	C₄×C₇₉	—	4	2	no	—
203	C₄×C₇₉	—	4	2	no	—
204	C₄×C₇₉	#407	1	1	yes	characteristic
205	C₄×C₇₉	#408	1	1	yes	characteristic
206	C₄×C₇₉	#435	1	1	yes	characteristic
207	C₄×C₇₉	#436	1	1	yes	characteristic
208	C₄×C₇₉	#448	1	1	yes	characteristic
209	C₄×C₇₉	#449	1	1	yes	characteristic
210	C₄×C₇₉	#460	1	1	yes	characteristic
211	C₄×C₇₉	#464	1	1	yes	characteristic
212	Dic₇₉	—	8	1	no	—
213	#8952	—	79	1	no	maximal, Sylow
214	C₂×C₇₉	#1582	1	1	yes	characteristic
215	C₂×C₇₉	#1585	1	1	yes	characteristic
216	C₂×C₇₉	#1590	1	1	yes	characteristic
217	C₂×C₇₉	#1592	1	1	yes	characteristic
218	C₂×C₇₉	#1870	1	1	yes	characteristic
219	C₂×C₇₉	#1876	1	1	yes	characteristic
220	C₂×C₇₉	#1880	1	1	yes	characteristic
221	D₇₉	—	8	2	no	—
222	C₂×#446	—	79	1	no	—
223	C₂×C₄×SD₁₆	—	79	1	no	—
224	#1954	—	79	1	no	—
225	C₂×Q₈⋊C₈	D₇₉	1	1	yes	characteristic, complemented
226	C₂×D₄⋊C₈	—	79	1	no	—
227	#1277	—	79	1	no	—
228	#1273	—	79	1	no	—
229	C₇₉	#8952	1	1	yes	characteristic, complemented, Sylow
230	C₂²×SD₁₆	—	79	1	no	—
231	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
232	C₂×C₄×D₄	—	79	1	no	—
233	#446	—	158	2	no	—
234	#446	—	158	2	no	—
235	C₄×SD₁₆	—	158	2	no	—
236	C₄×SD₁₆	—	158	2	no	—
237	C₂×#106	—	79	1	no	—
238	C₂×C₄⋊C₈	—	79	1	no	—
239	C₂×C₄⋊C₈	—	158	1	no	—
240	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
241	C₂×#103	—	79	1	no	—
242	C₂×#102	—	79	1	no	—
243	C₂×C₂²⋊C₈	—	158	1	no	—
244	C₂×C₂²⋊C₈	—	158	1	no	—
245	C₂×#97	—	158	1	no	—
246	C₂×C₄×C₈	—	79	1	no	—
247	C₂×C₄×C₈	—	79	1	no	—
248	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
249	Q₈⋊C₈	—	2	2	no	—
250	D₄⋊C₈	—	158	2	no	—
251	C₂²×Q₈	C₄×D₇₉	1	1	yes	characteristic
252	C₂²×D₄	—	79	1	no	—
253	C₂³×C₄	—	158	1	no	—
254	C₂×SD₁₆	—	158	2	no	—
255	C₂×SD₁₆	—	158	2	no	—
256	C₂×SD₁₆	—	158	2	no	—
257	C₂²×C₈	—	2	1	no	—
258	C₂²×C₈	—	2	1	no	—
259	C₂²×C₈	—	79	1	no	—
260	C₂²×C₈	—	79	1	no	—
261	C₂²×C₈	—	79	1	no	—
262	C₂²×C₈	—	79	1	no	—
263	C₂²×C₈	—	158	1	no	—
264	C₄×Q₈	—	2	1	no	—
265	C₄×Q₈	—	2	1	no	—
266	C₄×Q₈	D₃₁₆	1	2	yes	—
267	C₄×Q₈	C₂²⋊D₇₉	1	2	yes	—
268	C₄×D₄	—	158	1	no	—
269	C₄×D₄	—	158	1	no	—
270	C₄×D₄	—	158	1	no	—
271	C₄×D₄	—	158	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	79	1	no	—
274	C₂×C₄⋊C₄	C₄×D₇₉	1	1	yes	characteristic
275	C₂×C₂²⋊C₄	—	158	1	no	—
276	C₂×C₄²	—	2	1	no	—
277	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
278	#106	—	158	2	no	—
279	C₄⋊C₈	—	2	1	no	—
280	C₄⋊C₈	—	2	1	no	—
281	C₄⋊C₈	—	79	2	no	—
282	C₄⋊C₈	—	158	4	no	—
283	C₄⋊C₈	—	158	1	no	—
284	#103	—	158	2	no	—
285	#102	—	158	2	no	—
286	C₂²⋊C₈	—	316	2	no	—
287	C₂²⋊C₈	—	316	2	no	—
288	#97	—	158	4	no	—
289	C₄×C₈	—	2	1	no	—
290	C₄×C₈	—	2	1	no	—
291	C₄×C₈	—	158	1	no	—
292	C₄×C₈	—	158	1	no	—
293	C₄×C₈	—	158	1	no	—
294	C₄×C₈	—	158	1	no	—
295	C₂⁴	—	158	1	no	—
296	C₂×Q₈	—	2	1	no	—
297	C₂×Q₈	—	2	1	no	—
298	C₂×Q₈	—	2	1	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×Q₈	—	2	1	no	—
301	C₂×Q₈	(C₂×D₇₉)⋊C₄	1	2	yes	—
302	C₂×D₄	—	79	2	no	—
303	C₂×D₄	—	158	1	no	—
304	C₂×D₄	—	158	1	no	—
305	C₂×D₄	—	158	1	no	—
306	C₂×D₄	—	158	1	no	—
307	C₂×D₄	—	158	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	316	1	no	—
311	C₂²×C₄	—	316	1	no	—
312	C₂²×C₄	—	316	1	no	—
313	C₂²×C₄	—	316	1	no	—
314	C₂²×C₄	—	316	1	no	—
315	C₂²×C₄	—	316	1	no	—
316	C₂²×C₄	—	158	1	no	—
317	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
318	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
319	C₂²×C₄	#11929623	1	1	yes	characteristic
320	SD₁₆	—	158	8	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	4	1	no	—
323	C₂×C₈	—	4	1	no	—
324	C₂×C₈	—	4	1	no	—
325	C₂×C₈	—	4	1	no	—
326	C₂×C₈	—	4	1	no	—
327	C₂×C₈	—	316	1	no	—
328	C₂×C₈	—	316	1	no	—
329	C₂×C₈	—	79	2	no	—
330	C₂×C₈	—	79	2	no	—
331	C₂×C₈	—	158	1	no	—
332	C₂×C₈	—	158	1	no	—
333	C₂×C₈	—	158	2	no	—
334	C₂×C₈	—	158	1	no	—
335	C₂×C₈	—	158	1	no	—
336	C₂×C₈	—	158	1	no	—
337	C₂×C₈	—	158	1	no	—
338	C₂×C₈	—	158	1	no	—
339	C₂×C₈	—	158	1	no	—
340	C₂×C₈	—	158	1	no	—
341	C₂×C₈	—	158	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	158	1	no	—
346	C₄⋊C₄	—	158	1	no	—
347	C₄⋊C₄	(C₂×D₇₉)⋊C₄	1	2	yes	—
348	C₂²⋊C₄	—	316	1	no	—
349	C₂²⋊C₄	—	316	1	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	2	2	no	—
352	C₄²	D₄×D₇₉	1	1	yes	characteristic
353	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
354	C₄²	C₂×D₃₁₆	1	1	yes	characteristic
355	C₄²	#11929623	1	1	yes	characteristic
356	C₂³	—	316	1	no	—
357	C₂³	—	316	1	no	—
358	C₂³	—	316	1	no	—
359	C₂³	—	316	1	no	—
360	C₂³	—	316	1	no	—
361	C₂³	—	316	1	no	—
362	C₂³	—	158	2	no	—
363	C₂³	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
364	Q₈	—	2	2	no	—
365	Q₈	—	2	2	no	—
366	Q₈	—	4	1	no	—
367	Q₈	—	4	1	no	—
368	D₄	—	316	1	no	—
369	D₄	—	316	1	no	—
370	D₄	—	158	2	no	—
371	D₄	—	158	2	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	316	1	no	—
381	C₂×C₄	—	316	1	no	—
382	C₂×C₄	—	316	1	no	—
383	C₂×C₄	—	632	1	no	—
384	C₂×C₄	—	632	1	no	—
385	C₂×C₄	—	632	1	no	—
386	C₂×C₄	—	632	1	no	—
387	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
388	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
389	C₂×C₄	#14579131	1	1	yes	characteristic
390	C₂×C₄	#14579133	1	1	yes	characteristic
391	C₂×C₄	#14579133	1	1	yes	characteristic
392	C₂×C₄	#14579145	1	1	yes	characteristic
393	C₂×C₄	M₁₆×D₇₉	1	1	yes	characteristic
394	C₂×C₄	M₁₆×D₇₉	1	1	yes	characteristic
395	C₂×C₄	#14579167	1	1	yes	characteristic
396	C₂×C₄	#14579167	1	1	yes	characteristic
397	C₂×C₄	SD₁₆×D₇₉	1	1	yes	characteristic
398	C₂×C₄	#14579184	1	1	yes	characteristic
399	C₂×C₄	#14579188	1	1	yes	characteristic
400	C₂×C₄	#14579193	1	1	yes	characteristic
401	C₈	—	4	2	no	—
402	C₈	—	8	1	no	—
403	C₈	—	316	2	no	—
404	C₈	—	316	1	no	—
405	C₈	—	316	1	no	—
406	C₈	—	158	2	no	—
407	C₈	—	158	2	no	—
408	C₂²	—	316	2	no	—
409	C₂²	—	316	2	no	—
410	C₂²	—	316	2	no	—
411	C₂²	—	632	1	no	—
412	C₂²	—	632	1	no	—
413	C₂²	—	632	1	no	—
414	C₂²	—	632	1	no	—
415	C₂²	#19098440	1	1	yes	characteristic
416	C₂²	#19098637	1	1	yes	characteristic
417	C₂²	#19098638	1	1	yes	characteristic
418	C₂²	#19098648	1	1	yes	characteristic
419	C₂²	#19098666	1	1	yes	characteristic
420	C₂²	#19098677	1	1	yes	characteristic
421	C₂²	#19098682	1	1	yes	characteristic
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	632	1	no	—
427	C₄	#19098526	1	1	yes	characteristic
428	C₄	#19098529	1	1	yes	characteristic
429	C₄	#19098637	1	1	yes	characteristic
430	C₄	#19098638	1	1	yes	characteristic
431	C₄	#19098703	1	1	yes	characteristic
432	C₄	#19098711	1	1	yes	characteristic
433	C₄	#19098761	1	1	yes	characteristic
434	C₄	#19098787	1	1	yes	characteristic
435	C₂	—	632	2	no	—
436	C₂	#23762239	1	1	yes	characteristic
437	C₂	#23762260	1	1	yes	characteristic
438	C₂	#23762287	1	1	yes	characteristic
439	C₂	#23762305	1	1	yes	characteristic
440	C₂	#23763695	1	1	yes	characteristic
441	C₂	#23763725	1	1	yes	characteristic
442	C₂	#23763753	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₇₉
commutator	C₂²×C₄×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₂×Q₈⋊C₈×C₇₉	C₂
socle	C₂³×C₇₉	C₄×D₄
prime radical	C₂²×D₃₁₆	C₂×C₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	C₂×Q₈⋊C₈	D₇₉
hypocenter	C₇₉	#8952
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#19098694	C₂	semidirect
5. #23761234	C₂	semidirect
6. C₇₉⋊#1273	C₂	semidirect
7. C₂×Q₈⋊C₈×C₇₉	C₂	semidirect
102. C₂×C₇₉⋊C₈	SD₁₆	semidirect
225. C₂×Q₈⋊C₈	D₇₉	semidirect
229. C₇₉	#8952	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098694	2
C₂×C₄×#11929611	2
#23764193	2
C₂×#19098292	2
#23761234	2
C₇₉⋊#1273	2
C₂×Q₈⋊C₈×C₇₉	2
#8952	79