Subgroups — #34295927

Order 20224.

868 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098848	C₂	1	1	yes	maximal, characteristic
2	C₄×#14579161	C₂	1	1	yes	maximal, characteristic
3	#23764352	C₂	1	1	yes	maximal, characteristic
4	#23764158	C₂	1	1	yes	maximal, characteristic
5	#23763985	C₂	1	2	yes	maximal
6	#23763654	C₂	1	2	yes	maximal
7	#23763405	C₂	1	1	yes	maximal, characteristic
8	#23763298	C₂	1	2	yes	maximal
9	#23763253	C₂	1	1	yes	maximal, characteristic
10	#23763230	C₂	1	2	yes	maximal
11	C₄²×Q₈×C₇₉	C₂	1	1	yes	maximal, characteristic
12	C₂×#14579161	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₁₅₈	—	2	1	no	—
14	#19098848	C₄	1	8	yes	complemented
15	C₂×#14579094	C₂²	1	2	yes	—
16	C₂×#14579092	C₂²	1	2	yes	—
17	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×#14579085	C₂²	1	2	yes	—
20	C₂×#14579085	C₂²	1	2	yes	—
21	C₂×#14579072	C₂²	1	2	yes	—
22	#19098469	—	2	1	no	—
23	#19098461	—	2	1	no	—
24	#19098461	C₂²	1	2	yes	—
25	#19098433	C₂²	1	1	yes	characteristic
26	C₄×C₄⋊Dic₇₉	—	2	1	no	—
27	C₄×C₄⋊Dic₇₉	C₂²	1	2	yes	—
28	#19098325	C₂²	1	2	yes	—
29	#19098325	C₂²	1	2	yes	—
30	#19098325	C₂²	1	2	yes	—
31	#19098325	C₂²	1	2	yes	—
32	#19098318	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₇₉	—	2	1	no	—
37	C₄×C₄⋊C₄×C₇₉	—	2	1	no	—
38	C₄×C₄⋊C₄×C₇₉	—	2	1	no	—
39	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
42	C₄³×C₇₉	—	2	1	no	—
43	C₄³×C₇₉	C₂²	1	1	yes	characteristic
44	C₂²×Dic₁₅₈	—	2	1	no	—
45	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
46	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
47	#14579161	—	2	2	no	—
48	#14579161	C₂×C₄	1	4	yes	—
49	C₄×Dic₁₅₈	—	4	4	no	—
50	C₂×C₄⋊Dic₇₉	—	2	1	no	—
51	C₂×C₄⋊Dic₇₉	—	2	1	no	—
52	C₂×C₄⋊Dic₇₉	—	2	1	no	—
53	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
54	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
55	C₂×Dic₇₉⋊C₄	—	2	2	no	—
56	C₂×C₄×Dic₇₉	—	2	2	no	—
57	#14579094	—	2	4	no	—
58	#14579092	C₂×C₄	1	8	yes	—
59	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
60	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	4	yes	—
61	#14579085	—	2	4	no	—
62	#14579085	C₂×C₄	1	8	yes	—
63	#14579072	—	2	4	no	—
64	C₇₉⋊#95	—	2	2	no	—
65	C₇₉⋊#95	—	2	2	no	—
66	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
67	C₄×Q₈×C₇₉	—	2	2	no	—
68	C₄×Q₈×C₇₉	—	2	2	no	—
69	C₄×Q₈×C₇₉	—	2	2	no	—
70	C₄×Q₈×C₇₉	—	2	2	no	—
71	C₄×Q₈×C₇₉	C₂×C₄	1	4	yes	—
72	C₄×Q₈×C₇₉	Q₈	1	4	yes	complemented
73	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₇₉	—	2	1	no	—
80	C₂×C₄²×C₇₉	—	2	1	no	—
81	C₂×C₄²×C₇₉	—	2	1	no	—
82	C₂×C₄²×C₇₉	—	2	1	no	—
83	C₂×C₄²×C₇₉	—	2	1	no	—
84	C₂×C₄²×C₇₉	—	2	1	no	—
85	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
92	#95×C₇₉	—	2	1	no	—
93	#95×C₇₉	—	2	1	no	—
94	#95×C₇₉	—	2	1	no	—
95	C₂×Dic₁₅₈	—	2	4	no	—
96	C₂×Dic₁₅₈	—	4	2	no	—
97	C₂×Dic₁₅₈	—	4	2	no	—
98	C₂²×Dic₇₉	—	2	2	no	—
99	C₂²×Dic₇₉	—	2	2	no	—
100	C₂×C₇₉⋊C₈	—	2	2	no	—
101	C₂×C₇₉⋊C₈	—	2	2	no	—
102	C₂×C₇₉⋊C₈	—	2	2	no	—
103	C₂×C₇₉⋊C₈	—	2	2	no	—
104	C₂×C₇₉⋊C₈	—	2	2	no	—
105	C₂×C₇₉⋊C₈	C₂²×C₄	1	4	yes	—
106	C₄⋊Dic₇₉	—	2	4	no	—
107	C₄⋊Dic₇₉	—	2	2	no	—
108	C₄⋊Dic₇₉	—	2	2	no	—
109	C₄⋊Dic₇₉	—	2	2	no	—
110	C₄⋊Dic₇₉	—	4	2	no	—
111	C₄⋊Dic₇₉	—	4	2	no	—
112	C₄⋊Dic₇₉	C₂²×C₄	1	4	yes	—
113	Dic₇₉⋊C₄	—	4	4	no	—
114	C₄×Dic₇₉	—	4	4	no	—
115	C₂×Q₈×C₇₉	—	2	1	no	—
116	C₂×Q₈×C₇₉	—	2	1	no	—
117	C₂×Q₈×C₇₉	—	2	1	no	—
118	C₂×Q₈×C₇₉	C₂²×C₄	1	2	yes	—
119	C₂×Q₈×C₇₉	C₂×Q₈	1	2	yes	—
120	C₂×Q₈×C₇₉	#41	1	2	yes	—
121	C₂²×C₄×C₇₉	—	2	1	no	—
122	C₂²×C₄×C₇₉	—	2	1	no	—
123	C₂²×C₄×C₇₉	—	2	1	no	—
124	C₂²×C₄×C₇₉	—	2	1	no	—
125	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
132	C₄⋊C₄×C₇₉	—	2	4	no	—
133	C₄⋊C₄×C₇₉	—	2	4	no	—
134	C₄⋊C₄×C₇₉	—	2	4	no	—
135	C₄⋊C₄×C₇₉	—	2	1	no	—
136	C₄⋊C₄×C₇₉	—	2	1	no	—
137	C₄⋊C₄×C₇₉	—	2	1	no	—
138	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
139	C₄⋊C₄×C₇₉	C₂×Q₈	1	2	yes	—
140	C₄⋊C₄×C₇₉	#41	1	2	yes	—
141	C₄²×C₇₉	—	2	4	no	—
142	C₄²×C₇₉	—	2	4	no	—
143	C₄²×C₇₉	—	2	4	no	—
144	C₄²×C₇₉	—	2	2	no	—
145	C₄²×C₇₉	—	2	2	no	—
146	C₄²×C₇₉	—	2	2	no	—
147	C₄²×C₇₉	—	2	1	no	—
148	C₄²×C₇₉	—	2	1	no	—
149	C₄²×C₇₉	—	4	1	no	—
150	C₄²×C₇₉	—	4	2	no	—
151	C₄²×C₇₉	—	4	2	no	—
152	C₄²×C₇₉	—	4	2	no	—
153	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
154	C₄²×C₇₉	C₂×Q₈	1	2	yes	—
155	C₄²×C₇₉	#41	1	2	yes	—
156	C₄²×C₇₉	#41	1	2	yes	—
157	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
158	Q₈×C₇₉	—	2	2	no	—
159	Q₈×C₇₉	—	2	2	no	—
160	Q₈×C₇₉	—	2	2	no	—
161	Q₈×C₇₉	C₄×Q₈	1	4	yes	complemented
162	C₂×C₄×C₇₉	—	2	2	no	—
163	C₂×C₄×C₇₉	—	2	2	no	—
164	C₂×C₄×C₇₉	—	2	1	no	—
165	C₂×C₄×C₇₉	—	2	2	no	—
166	C₂×C₄×C₇₉	—	2	1	no	—
167	C₂×C₄×C₇₉	—	2	1	no	—
168	C₂×C₄×C₇₉	—	2	1	no	—
169	C₂×C₄×C₇₉	—	2	1	no	—
170	C₂×C₄×C₇₉	—	2	1	no	—
171	C₂×C₄×C₇₉	—	2	1	no	—
172	C₂×C₄×C₇₉	—	2	1	no	—
173	C₂×C₄×C₇₉	—	2	2	no	—
174	C₂×C₄×C₇₉	—	2	2	no	—
175	C₂×C₄×C₇₉	—	2	1	no	—
176	C₂×C₄×C₇₉	—	2	2	no	—
177	C₂×C₄×C₇₉	—	2	1	no	—
178	C₂×C₄×C₇₉	—	2	1	no	—
179	C₂×C₄×C₇₉	—	4	1	no	—
180	C₂×C₄×C₇₉	—	4	1	no	—
181	C₂×C₄×C₇₉	—	4	1	no	—
182	C₂×C₄×C₇₉	—	4	1	no	—
183	C₂×C₄×C₇₉	—	4	1	no	—
184	C₂×C₄×C₇₉	—	4	1	no	—
185	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
186	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
187	C₂×C₄×C₇₉	C₂²⋊Q₈	1	2	yes	—
188	C₂×C₄×C₇₉	C₂²⋊Q₈	1	2	yes	—
189	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
190	C₂×C₄×C₇₉	#137	1	2	yes	—
191	C₂×C₄×C₇₉	#137	1	2	yes	—
192	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
193	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
194	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
198	C₂×Dic₇₉	—	2	4	no	—
199	C₂×Dic₇₉	—	4	2	no	—
200	C₂×Dic₇₉	—	4	2	no	—
201	C₂×Dic₇₉	—	4	2	no	—
202	C₂×Dic₇₉	—	4	2	no	—
203	C₂×Dic₇₉	—	4	2	no	—
204	Dic₁₅₈	—	4	8	no	—
205	C₇₉⋊C₈	—	2	4	no	—
206	C₇₉⋊C₈	—	4	2	no	—
207	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
208	C₂²×C₇₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
209	C₂²×C₇₉	#525	1	1	yes	characteristic
210	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
211	C₂²×C₇₉	C₂×#137	1	1	yes	characteristic
212	C₂²×C₇₉	C₂×#137	1	1	yes	characteristic
213	C₂²×C₇₉	#575	1	1	yes	characteristic
214	C₄×C₇₉	—	2	2	no	—
215	C₄×C₇₉	—	2	2	no	—
216	C₄×C₇₉	—	2	2	no	—
217	C₄×C₇₉	—	2	2	no	—
218	C₄×C₇₉	—	2	4	no	—
219	C₄×C₇₉	—	4	2	no	—
220	C₄×C₇₉	—	4	1	no	—
221	C₄×C₇₉	—	4	2	no	—
222	C₄×C₇₉	—	4	2	no	—
223	C₄×C₇₉	#440	1	4	yes	—
224	C₄×C₇₉	C₂×C₄×Q₈	1	1	yes	characteristic
225	C₄×C₇₉	C₄×#41	1	1	yes	characteristic
226	C₄×C₇₉	#529	1	1	yes	characteristic
227	C₄×C₇₉	#533	1	1	yes	characteristic
228	Dic₇₉	—	4	4	no	—
229	Dic₇₉	—	8	2	no	—
230	#21615	—	79	1	no	maximal, Sylow
231	C₂×C₇₉	C₄×C₂²⋊Q₈	1	1	yes	characteristic
232	C₂×C₇₉	C₂×#440	1	1	yes	characteristic
233	C₂×C₇₉	C₄×#137	1	1	yes	characteristic
234	C₂×C₇₉	#3078	1	1	yes	characteristic
235	C₂×C₇₉	#3079	1	1	yes	characteristic
236	C₂×C₇₉	#3113	1	1	yes	characteristic
237	C₂×C₇₉	#3115	1	1	yes	characteristic
238	C₂×#475	—	79	1	no	—
239	C₄×C₄⋊Q₈	—	79	1	no	—
240	C₄²×Q₈	D₇₉	1	1	yes	characteristic
241	#1988	—	79	1	no	—
242	#1947	—	79	1	no	—
243	#1920	—	79	2	no	—
244	#1863	—	79	2	no	—
245	#1803	—	79	1	no	—
246	#1776	—	79	2	no	—
247	#1767	—	79	1	no	—
248	#1763	—	79	2	no	—
249	C₇₉	#21615	1	1	yes	characteristic, complemented, Sylow
250	C₂×C₄⋊Q₈	—	79	1	no	—
251	C₂×C₄×Q₈	—	158	1	no	—
252	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
253	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
254	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
255	#475	—	79	8	no	—
256	C₂×#107	—	79	2	no	—
257	C₂×#106	—	79	2	no	—
258	C₂×C₄⋊C₈	—	79	1	no	—
259	C₂×C₄⋊C₈	—	79	1	no	—
260	C₂×#103	—	79	2	no	—
261	C₂×#103	—	79	2	no	—
262	C₂×#97	—	79	2	no	—
263	#391	—	158	1	no	—
264	#389	—	79	2	no	—
265	#389	—	158	1	no	—
266	#384	—	79	1	no	—
267	C₄×C₄⋊C₄	—	2	1	no	—
268	C₄×C₄⋊C₄	—	2	1	no	—
269	C₄×C₄⋊C₄	—	2	1	no	—
270	C₄×C₄⋊C₄	—	79	2	no	—
271	C₄×C₄⋊C₄	—	158	1	no	—
272	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
273	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
274	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
275	C₄³	—	2	1	no	—
276	C₄³	C₂×D₇₉	1	1	yes	characteristic
277	#340	—	79	2	no	—
278	#340	—	79	2	no	—
279	#340	—	79	2	no	—
280	#340	—	79	2	no	—
281	#336	—	79	2	no	—
282	C₂²×Q₈	—	158	1	no	—
283	C₂²×Q₈	C₂²×D₇₉	1	1	yes	characteristic
284	C₂²×C₈	—	79	2	no	—
285	C₂²×C₈	—	79	2	no	—
286	C₄⋊Q₈	—	79	4	no	—
287	C₄⋊Q₈	—	158	2	no	—
288	C₄×Q₈	—	2	2	no	—
289	C₄×Q₈	—	2	2	no	—
290	C₄×Q₈	—	2	2	no	—
291	C₄×Q₈	—	2	2	no	—
292	C₄×Q₈	—	316	4	no	—
293	C₄×Q₈	Dic₁₅₈	1	4	yes	complemented
294	C₄×Q₈	C₄×D₇₉	1	4	yes	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	79	2	no	—
299	C₂×C₄⋊C₄	—	79	2	no	—
300	C₂×C₄⋊C₄	—	158	1	no	—
301	C₂×C₄⋊C₄	—	158	2	no	—
302	C₂×C₄⋊C₄	—	158	1	no	—
303	C₂×C₄⋊C₄	—	158	1	no	—
304	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
307	C₂×C₄²	—	2	1	no	—
308	C₂×C₄²	—	2	1	no	—
309	C₂×C₄²	—	2	1	no	—
310	C₂×C₄²	—	2	1	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	—	2	1	no	—
313	C₂×C₄²	—	158	2	no	—
314	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
315	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
316	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
317	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
318	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
319	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
320	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
321	#107	—	158	4	no	—
322	#106	—	79	8	no	—
323	C₄⋊C₈	—	79	4	no	—
324	C₄⋊C₈	—	158	2	no	—
325	#103	—	79	8	no	—
326	#103	—	158	4	no	—
327	#97	—	158	4	no	—
328	#95	—	2	1	no	—
329	#95	—	2	1	no	—
330	#95	—	2	1	no	—
331	#95	—	158	2	no	—
332	#95	—	158	2	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	—	316	2	no	—
337	C₂×Q₈	—	316	2	no	—
338	C₂×Q₈	—	158	4	no	—
339	C₂×Q₈	C₂×C₄×D₇₉	1	2	yes	—
340	C₂×Q₈	C₂×Dic₁₅₈	1	2	yes	—
341	C₂×Q₈	#11929624	1	2	yes	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	158	2	no	—
347	C₂²×C₄	—	158	2	no	—
348	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
349	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
350	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
353	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
354	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
355	C₂×C₈	—	79	4	no	—
356	C₂×C₈	—	158	2	no	—
357	C₂×C₈	—	158	2	no	—
358	C₂×C₈	—	158	2	no	—
359	C₂×C₈	—	158	2	no	—
360	C₂×C₈	—	158	2	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	316	4	no	—
368	C₄⋊C₄	—	316	2	no	—
369	C₄⋊C₄	—	316	2	no	—
370	C₄⋊C₄	—	79	4	no	—
371	C₄⋊C₄	—	158	2	no	—
372	C₄⋊C₄	—	158	2	no	—
373	C₄⋊C₄	—	158	2	no	—
374	C₄⋊C₄	—	158	4	no	—
375	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
376	C₄⋊C₄	C₂×Dic₁₅₈	1	2	yes	—
377	C₄⋊C₄	#11929624	1	2	yes	—
378	C₄²	—	2	4	no	—
379	C₄²	—	2	1	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	2	4	no	—
382	C₄²	—	2	4	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	4	1	no	—
387	C₄²	—	4	2	no	—
388	C₄²	—	4	2	no	—
389	C₄²	—	4	2	no	—
390	C₄²	—	316	4	no	—
391	C₄²	C₂×C₄×D₇₉	1	2	yes	—
392	C₄²	C₂×Dic₁₅₈	1	2	yes	—
393	C₄²	#11929624	1	2	yes	—
394	C₄²	#11929624	1	2	yes	—
395	C₂³	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
396	Q₈	—	2	2	no	—
397	Q₈	—	2	2	no	—
398	Q₈	—	2	2	no	—
399	Q₈	—	316	8	no	—
400	Q₈	C₄×Dic₁₅₈	1	4	yes	complemented
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	316	2	no	—
425	C₂×C₄	—	316	2	no	—
426	C₂×C₄	—	316	2	no	—
427	C₂×C₄	—	316	2	no	—
428	C₂×C₄	—	316	2	no	—
429	C₂×C₄	—	158	4	no	—
430	C₂×C₄	C₄×C₂²⋊D₇₉	1	2	yes	—
431	C₂×C₄	C₄×C₂²⋊D₇₉	1	2	yes	—
432	C₂×C₄	#14579140	1	2	yes	—
433	C₂×C₄	#14579140	1	2	yes	—
434	C₂×C₄	#14579186	1	2	yes	—
435	C₂×C₄	#14579191	1	2	yes	—
436	C₂×C₄	#14579192	1	2	yes	—
437	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
438	C₂×C₄	C₂²×Dic₁₅₈	1	1	yes	characteristic
439	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
440	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
441	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
442	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
443	C₈	—	316	2	no	—
444	C₈	—	158	4	no	—
445	C₂²	C₂×C₄×C₂²⋊D₇₉	1	1	yes	characteristic
446	C₂²	C₂×#14579140	1	1	yes	characteristic
447	C₂²	#19099074	1	1	yes	characteristic
448	C₂²	C₂×#14579186	1	1	yes	characteristic
449	C₂²	C₂×#14579191	1	1	yes	characteristic
450	C₂²	C₂×#14579192	1	1	yes	characteristic
451	C₂²	#19099361	1	1	yes	characteristic
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	2	4	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	1	no	—
460	C₄	—	4	2	no	—
461	C₄	—	316	4	no	—
462	C₄	—	632	2	no	—
463	C₄	#19098661	1	4	yes	—
464	C₄	C₂×C₄×Dic₁₅₈	1	1	yes	characteristic
465	C₄	C₄×#11929624	1	1	yes	characteristic
466	C₄	#19099097	1	1	yes	characteristic
467	C₄	#19099120	1	1	yes	characteristic
468	C₂	C₄×#14579140	1	1	yes	characteristic
469	C₂	C₂×#19098661	1	1	yes	characteristic
470	C₂	C₄×#14579191	1	1	yes	characteristic
471	C₂	#23773205	1	1	yes	characteristic
472	C₂	#23773215	1	1	yes	characteristic
473	C₂	#23773530	1	1	yes	characteristic
474	C₂	#23773551	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₄²×Q₈×C₇₉	C₂
socle, prime radical	C₂³×C₇₉	C₂²×D₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₄²×Q₈	D₇₉
hypocenter	C₇₉	#21615
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ C₄²×Q₈

Complements

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

N	H ≅ G/N	type
14. #19098848	C₄	semidirect
72. C₄×Q₈×C₇₉	Q₈	semidirect
161. Q₈×C₇₉	C₄×Q₈	semidirect
249. C₇₉	#21615	semidirect
293. C₄×Q₈	Dic₁₅₈	semidirect
400. Q₈	C₄×Dic₁₅₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098848	2
C₄×#14579161	2
#23764352	2
#23764158	2
#23763985	2
#23763654	2
#23763405	2
#23763298	2
#23763253	2
#23763230	2
C₄²×Q₈×C₇₉	2
#21615	79