Subgroups — #34178820

Order 20224.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14579076	C₂	1	1	yes	maximal, characteristic
2	#23763176	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×C₂²⋊Dic₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#23761718	C₂	1	1	yes	maximal, characteristic
5	#23761247	C₂	1	1	yes	maximal, characteristic, complemented
6	#23761247	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#435×C₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂×#14579076	C₄	1	2	yes	—
9	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
10	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×#14579071	—	2	1	no	—
12	C₂×C₈×Dic₇₉	—	2	1	no	—
13	C₄×C₂²⋊Dic₇₉	C₂²	1	1	yes	characteristic
14	C₄×C₂²⋊Dic₇₉	C₂²	1	1	yes	characteristic
15	#19098330	C₄	1	2	yes	—
16	#19098317	—	2	1	no	—
17	#19098317	—	2	1	no	—
18	#19098289	C₄	1	2	yes	complemented
19	#19098287	C₄	1	2	yes	complemented
20	C₂²×M₁₆×C₇₉	C₄	1	1	yes	characteristic, complemented
21	C₂³×C₈×C₇₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
23	#435×C₇₉	—	2	1	no	—
24	#435×C₇₉	—	2	1	no	—
25	#435×C₇₉	—	2	1	no	—
26	#435×C₇₉	—	2	1	no	—
27	C₂×C₄⋊C₈×C₇₉	C₄	1	1	yes	characteristic, complemented
28	C₂×C₂²⋊C₈×C₇₉	C₄	1	1	yes	characteristic, complemented
29	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
30	C₂×#97×C₇₉	C₄	1	1	yes	characteristic, complemented
31	C₂²×C₇₉⋊C₈	—	2	1	no	—
32	C₂²×C₇₉⋊C₈	—	2	1	no	—
33	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	2	yes	—
34	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	2	yes	—
35	C₂×C₄×Dic₇₉	—	2	1	no	—
36	C₂×C₄×Dic₇₉	—	2	1	no	—
37	#14579076	—	2	4	no	—
38	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
39	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
40	C₂²⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	—
41	C₂²⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	—
42	#14579071	—	4	2	no	—
43	C₈×Dic₇₉	—	4	2	no	—
44	C₇₉⋊#95	—	2	1	no	—
45	C₇₉⋊#95	—	2	1	no	—
46	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
49	C₂×M₁₆×C₇₉	—	2	1	no	—
50	C₂×M₁₆×C₇₉	—	2	1	no	—
51	C₂×M₁₆×C₇₉	—	4	2	no	—
52	C₂²×C₈×C₇₉	—	4	2	no	—
53	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
58	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
59	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
60	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
61	C₄×D₄×C₇₉	—	2	1	no	—
62	C₄×D₄×C₇₉	—	2	1	no	—
63	C₄×D₄×C₇₉	—	2	1	no	—
64	C₄×D₄×C₇₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
69	C₄⋊C₈×C₇₉	—	2	1	no	—
70	C₄⋊C₈×C₇₉	—	2	1	no	—
71	C₂²⋊C₈×C₇₉	—	2	1	no	—
72	C₂²⋊C₈×C₇₉	—	2	1	no	—
73	C₂²⋊C₈×C₇₉	—	2	1	no	—
74	C₂²⋊C₈×C₇₉	—	2	1	no	—
75	#97×C₇₉	—	2	1	no	—
76	#97×C₇₉	—	2	1	no	—
77	C₂²×Dic₇₉	—	2	2	no	—
78	C₂²×Dic₇₉	—	2	2	no	—
79	C₂×C₇₉⋊C₈	—	2	2	no	—
80	C₂×C₇₉⋊C₈	—	2	2	no	—
81	C₂×C₇₉⋊C₈	—	4	1	no	—
82	C₂×C₇₉⋊C₈	—	4	1	no	—
83	C₂×C₇₉⋊C₈	—	4	1	no	—
84	C₂×C₇₉⋊C₈	—	4	1	no	—
85	C₂²⋊Dic₇₉	—	2	2	no	—
86	C₂²⋊Dic₇₉	—	2	2	no	—
87	C₂²⋊Dic₇₉	—	2	2	no	—
88	C₂²⋊Dic₇₉	M₁₆	1	4	yes	complemented
89	C₄×Dic₇₉	—	4	1	no	—
90	C₄×Dic₇₉	—	4	1	no	—
91	C₄×Dic₇₉	—	4	1	no	—
92	C₄×Dic₇₉	—	4	1	no	—
93	C₂⁴×C₇₉	C₄²	1	1	yes	characteristic
94	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
95	C₂×D₄×C₇₉	—	2	1	no	—
96	C₂×D₄×C₇₉	—	2	1	no	—
97	C₂×D₄×C₇₉	—	2	2	no	—
98	C₂×D₄×C₇₉	—	2	2	no	—
99	C₂²×C₄×C₇₉	—	2	1	no	—
100	C₂²×C₄×C₇₉	—	2	1	no	—
101	C₂²×C₄×C₇₉	—	4	1	no	—
102	C₂²×C₄×C₇₉	—	4	1	no	—
103	C₂²×C₄×C₇₉	—	4	1	no	—
104	C₂²×C₄×C₇₉	—	4	1	no	—
105	C₂²×C₄×C₇₉	C₄²	1	1	yes	characteristic
106	C₂²×C₄×C₇₉	C₄²	1	1	yes	characteristic
107	C₂²×C₄×C₇₉	C₄²	1	1	yes	characteristic
108	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
113	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
114	M₁₆×C₇₉	—	4	2	no	—
115	M₁₆×C₇₉	—	4	2	no	—
116	C₂×C₈×C₇₉	—	2	2	no	—
117	C₂×C₈×C₇₉	—	2	2	no	—
118	C₂×C₈×C₇₉	—	2	2	no	—
119	C₂×C₈×C₇₉	—	2	1	no	—
120	C₂×C₈×C₇₉	—	2	1	no	—
121	C₂×C₈×C₇₉	—	4	1	no	—
122	C₂×C₈×C₇₉	—	4	1	no	—
123	C₂×C₈×C₇₉	—	4	1	no	—
124	C₂×C₈×C₇₉	—	4	1	no	—
125	C₂×C₈×C₇₉	—	4	1	no	—
126	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
127	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
128	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
129	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
130	C₄⋊C₄×C₇₉	—	2	1	no	—
131	C₄⋊C₄×C₇₉	—	2	1	no	—
132	C₂²⋊C₄×C₇₉	—	2	1	no	—
133	C₂²⋊C₄×C₇₉	—	2	1	no	—
134	C₂²⋊C₄×C₇₉	—	2	1	no	—
135	C₂²⋊C₄×C₇₉	—	2	1	no	—
136	C₄²×C₇₉	—	2	1	no	—
137	C₄²×C₇₉	—	2	1	no	—
138	C₂³×C₇₉	—	2	1	no	—
139	C₂³×C₇₉	—	2	1	no	—
140	C₂³×C₇₉	—	2	1	no	—
141	C₂³×C₇₉	—	4	1	no	—
142	C₂³×C₇₉	—	4	1	no	—
143	C₂³×C₇₉	—	4	1	no	—
144	C₂³×C₇₉	—	4	1	no	—
145	C₂³×C₇₉	C₂×C₄²	1	1	yes	characteristic
146	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
147	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
148	C₂³×C₇₉	C₂×M₁₆	1	2	yes	—
149	C₂³×C₇₉	#131	1	2	yes	—
150	D₄×C₇₉	—	4	2	no	—
151	D₄×C₇₉	—	4	2	no	—
152	C₂×C₄×C₇₉	—	2	1	no	—
153	C₂×C₄×C₇₉	—	2	1	no	—
154	C₂×C₄×C₇₉	—	2	1	no	—
155	C₂×C₄×C₇₉	—	2	1	no	—
156	C₂×C₄×C₇₉	—	2	1	no	—
157	C₂×C₄×C₇₉	—	2	1	no	—
158	C₂×C₄×C₇₉	—	2	1	no	—
159	C₂×C₄×C₇₉	—	2	1	no	—
160	C₂×C₄×C₇₉	—	2	1	no	—
161	C₂×C₄×C₇₉	—	2	1	no	—
162	C₂×C₄×C₇₉	—	2	1	no	—
163	C₂×C₄×C₇₉	—	4	1	no	—
164	C₂×C₄×C₇₉	—	4	1	no	—
165	C₂×C₄×C₇₉	—	4	1	no	—
166	C₂×C₄×C₇₉	—	4	2	no	—
167	C₂×C₄×C₇₉	—	4	1	no	—
168	C₂×C₄×C₇₉	—	4	1	no	—
169	C₂×C₄×C₇₉	—	4	1	no	—
170	C₂×C₄×C₇₉	—	4	1	no	—
171	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₇₉	#117	1	1	yes	characteristic
173	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
175	C₂×Dic₇₉	—	2	4	no	—
176	C₂×Dic₇₉	—	4	2	no	—
177	C₂×Dic₇₉	—	4	2	no	—
178	C₂×Dic₇₉	—	4	2	no	—
179	C₂×Dic₇₉	—	4	2	no	—
180	C₂×Dic₇₉	—	4	2	no	—
181	C₈×C₇₉	—	2	1	no	—
182	C₈×C₇₉	—	2	1	no	—
183	C₈×C₇₉	—	2	1	no	—
184	C₈×C₇₉	—	4	1	no	—
185	C₈×C₇₉	—	4	1	no	—
186	C₈×C₇₉	#99	1	2	yes	complemented
187	C₇₉⋊C₈	—	4	2	no	—
188	C₇₉⋊C₈	—	4	2	no	—
189	C₂²×C₇₉	—	2	1	no	—
190	C₂²×C₇₉	—	2	1	no	—
191	C₂²×C₇₉	—	2	1	no	—
192	C₂²×C₇₉	—	2	1	no	—
193	C₂²×C₇₉	—	2	1	no	—
194	C₂²×C₇₉	—	2	1	no	—
195	C₂²×C₇₉	—	4	2	no	—
196	C₂²×C₇₉	—	4	2	no	—
197	C₂²×C₇₉	—	4	1	no	—
198	C₂²×C₇₉	—	4	1	no	—
199	C₂²×C₇₉	—	4	1	no	—
200	C₂²×C₇₉	—	8	1	no	—
201	C₂²×C₇₉	—	8	1	no	—
202	C₂²×C₇₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
203	C₂²×C₇₉	C₄×M₁₆	1	1	yes	characteristic
204	C₂²×C₇₉	#405	1	1	yes	characteristic
205	C₂²×C₇₉	#435	1	2	yes	—
206	C₂²×C₇₉	#436	1	2	yes	—
207	C₄×C₇₉	—	2	1	no	—
208	C₄×C₇₉	—	2	1	no	—
209	C₄×C₇₉	—	2	1	no	—
210	C₄×C₇₉	—	4	1	no	—
211	C₄×C₇₉	—	4	1	no	—
212	C₄×C₇₉	—	4	1	no	—
213	C₄×C₇₉	C₂×#99	1	1	yes	characteristic
214	C₄×C₇₉	#410	1	1	yes	characteristic
215	Dic₇₉	—	4	4	no	—
216	Dic₇₉	—	8	2	no	—
217	#8161	—	79	1	no	maximal, Sylow
218	C₂×C₇₉	—	2	2	no	—
219	C₂×C₇₉	—	2	2	no	—
220	C₂×C₇₉	—	2	1	no	—
221	C₂×C₇₉	—	2	1	no	—
222	C₂×C₇₉	—	8	1	no	—
223	C₂×C₇₉	#1753	1	1	yes	characteristic
224	C₂×C₇₉	C₄×#99	1	1	yes	characteristic
225	C₂×C₇₉	#1757	1	1	yes	characteristic
226	C₂×#435	D₇₉	1	1	yes	characteristic
227	C₄×#99	—	79	1	no	—
228	#1752	—	79	1	no	—
229	C₈×C₂²⋊C₄	—	79	1	no	—
230	#1459	—	79	1	no	—
231	#1282	—	79	1	no	—
232	#1282	—	79	1	no	—
233	C₇₉	#8161	1	1	yes	characteristic, complemented, Sylow
234	C₂²×M₁₆	Dic₇₉	1	1	yes	characteristic, complemented
235	C₂³×C₈	C₂×D₇₉	1	1	yes	characteristic
236	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
237	#435	—	2	1	no	—
238	#435	—	2	1	no	—
239	#435	—	2	1	no	—
240	#435	—	2	1	no	—
241	C₂×C₄⋊C₈	Dic₇₉	1	1	yes	characteristic, complemented
242	C₂×#99	—	79	2	no	—
243	C₂×C₂²⋊C₈	—	79	1	no	—
244	C₂×C₂²⋊C₈	—	79	1	no	—
245	C₂×C₂²⋊C₈	Dic₇₉	1	1	yes	characteristic, complemented
246	C₂×C₂²⋊C₈	C₂×D₇₉	1	1	yes	characteristic
247	C₂×#97	—	158	1	no	—
248	C₂×#97	Dic₇₉	1	1	yes	characteristic, complemented
249	C₂×C₄×C₈	—	158	1	no	—
250	C₄×C₂²⋊C₄	—	79	1	no	—
251	C₄×C₂²⋊C₄	—	79	1	no	—
252	#342	—	79	2	no	—
253	#336	—	158	1	no	—
254	#336	—	158	1	no	—
255	#324	—	79	2	no	—
256	#323	—	79	2	no	—
257	C₂²×D₄	C₄×D₇₉	1	1	yes	characteristic
258	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
259	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
260	C₂×M₁₆	—	2	1	no	—
261	C₂×M₁₆	—	2	1	no	—
262	C₂×M₁₆	—	4	2	no	—
263	C₂²×C₈	—	4	2	no	—
264	C₂²×C₈	—	158	1	no	—
265	C₂²×C₈	—	158	1	no	—
266	C₂²×C₈	C₂×Dic₇₉	1	1	yes	characteristic
267	C₂²×C₈	C₂×Dic₇₉	1	1	yes	characteristic
268	C₂²×C₈	C₂×Dic₇₉	1	1	yes	characteristic
269	C₂²×C₈	C₂×Dic₇₉	1	1	yes	characteristic
270	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
271	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
272	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
273	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
274	C₄×D₄	—	2	1	no	—
275	C₄×D₄	—	2	1	no	—
276	C₄×D₄	—	2	1	no	—
277	C₄×D₄	—	2	1	no	—
278	C₂×C₄⋊C₄	C₄×D₇₉	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	—	79	2	no	—
280	C₂×C₂²⋊C₄	—	79	2	no	—
281	C₂×C₂²⋊C₄	C₄×D₇₉	1	1	yes	characteristic
282	C₂×C₂²⋊C₄	C₄×D₇₉	1	1	yes	characteristic
283	C₂×C₄²	—	158	1	no	—
284	C₂×C₄²	—	158	1	no	—
285	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
286	C₄⋊C₈	—	2	1	no	—
287	C₄⋊C₈	—	2	1	no	—
288	#99	—	158	4	no	—
289	C₂²⋊C₈	—	2	1	no	—
290	C₂²⋊C₈	—	2	1	no	—
291	C₂²⋊C₈	—	2	1	no	—
292	C₂²⋊C₈	—	2	1	no	—
293	C₂²⋊C₈	—	79	2	no	—
294	C₂²⋊C₈	—	79	2	no	—
295	C₂²⋊C₈	—	158	1	no	—
296	C₂²⋊C₈	—	158	1	no	—
297	#97	—	2	1	no	—
298	#97	—	2	1	no	—
299	#97	—	316	2	no	—
300	C₄×C₈	—	316	2	no	—
301	#95	—	158	1	no	—
302	#95	—	158	1	no	—
303	C₂⁴	C₄×Dic₇₉	1	1	yes	characteristic
304	C₂⁴	C₂×C₄×D₇₉	1	1	yes	characteristic
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	—	4	1	no	—
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	—	4	1	no	—
315	C₂²×C₄	—	158	2	no	—
316	C₂²×C₄	—	158	2	no	—
317	C₂²×C₄	C₄×Dic₇₉	1	1	yes	characteristic
318	C₂²×C₄	C₄×Dic₇₉	1	1	yes	characteristic
319	C₂²×C₄	C₄×Dic₇₉	1	1	yes	characteristic
320	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
321	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
322	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
323	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
324	C₂²×C₄	#11929624	1	1	yes	characteristic
325	C₂²×C₄	#11929624	1	1	yes	characteristic
326	M₁₆	—	4	2	no	—
327	M₁₆	—	4	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	—	4	1	no	—
338	C₂×C₈	—	316	1	no	—
339	C₂×C₈	—	316	1	no	—
340	C₂×C₈	—	316	1	no	—
341	C₂×C₈	—	316	1	no	—
342	C₂×C₈	—	158	2	no	—
343	C₂×C₈	—	158	2	no	—
344	C₂×C₈	C₂²⋊Dic₇₉	1	1	yes	characteristic
345	C₂×C₈	C₂²⋊Dic₇₉	1	1	yes	characteristic
346	C₂×C₈	C₂²⋊Dic₇₉	1	1	yes	characteristic
347	C₂×C₈	C₂²⋊Dic₇₉	1	1	yes	characteristic
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₂²⋊C₄	—	2	1	no	—
351	C₂²⋊C₄	—	2	1	no	—
352	C₂²⋊C₄	—	2	1	no	—
353	C₂²⋊C₄	—	2	1	no	—
354	C₂²⋊C₄	—	79	4	no	—
355	C₂²⋊C₄	—	158	2	no	—
356	C₂²⋊C₄	—	158	2	no	—
357	C₂²⋊C₄	—	158	2	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	316	1	no	—
361	C₄²	—	316	1	no	—
362	C₄²	—	316	1	no	—
363	C₄²	—	316	1	no	—
364	C₂³	—	2	1	no	—
365	C₂³	—	2	1	no	—
366	C₂³	—	2	1	no	—
367	C₂³	—	4	1	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	4	1	no	—
370	C₂³	—	4	1	no	—
371	C₂³	C₂×C₄×Dic₇₉	1	1	yes	characteristic
372	C₂³	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
373	C₂³	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
374	C₂³	M₁₆×D₇₉	1	2	yes	—
375	C₂³	#14579169	1	2	yes	—
376	D₄	—	4	2	no	—
377	D₄	—	4	2	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	316	2	no	—
398	C₂×C₄	—	316	2	no	—
399	C₂×C₄	—	316	2	no	—
400	C₂×C₄	—	316	2	no	—
401	C₂×C₄	—	316	2	no	—
402	C₂×C₄	—	158	4	no	—
403	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
404	C₂×C₄	#14579120	1	1	yes	characteristic
405	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
406	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
407	C₈	—	2	1	no	—
408	C₈	—	2	1	no	—
409	C₈	—	2	1	no	—
410	C₈	—	4	1	no	—
411	C₈	—	4	1	no	—
412	C₈	—	316	2	no	—
413	C₈	—	316	2	no	—
414	C₈	#14579076	1	2	yes	complemented
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	4	1	no	—
425	C₂²	—	4	1	no	—
426	C₂²	—	8	1	no	—
427	C₂²	—	8	1	no	—
428	C₂²	C₄×C₂²⋊Dic₇₉	1	1	yes	characteristic
429	C₂²	M₁₆×Dic₇₉	1	1	yes	characteristic
430	C₂²	#19098521	1	1	yes	characteristic
431	C₂²	#19098632	1	2	yes	—
432	C₂²	#19098639	1	2	yes	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	4	1	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	1	no	—
439	C₄	—	316	4	no	—
440	C₄	—	632	2	no	—
441	C₄	C₂×#14579076	1	1	yes	characteristic
442	C₄	#19098537	1	1	yes	characteristic
443	C₂	—	2	2	no	—
444	C₂	—	2	2	no	—
445	C₂	—	2	1	no	—
446	C₂	—	2	1	no	—
447	C₂	—	8	1	no	—
448	C₂	#23763181	1	1	yes	characteristic
449	C₂	C₄×#14579076	1	1	yes	characteristic
450	C₂	#23763200	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊Dic₇₉
commutator	C₂³×C₇₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₇₉
Fitting	C₂×#435×C₇₉	C₂
socle	C₂²×C₇₉	C₄×C₂²⋊C₄
prime radical	C₂²×D₄×C₇₉	C₂×C₄
cosocle	C₂³×C₄×C₇₉	C₂³
hypercenter	C₂×#435	D₇₉
hypocenter	C₇₉	#8161
LCS	G ▷ C₂³×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₈ ◁ C₂×#435

Complements

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

N	H ≅ G/N	type
2. #23763176	C₂	semidirect
3. C₈×C₂²⋊Dic₇₉	C₂	semidirect
5. #23761247	C₂	semidirect
6. #23761247	C₂	semidirect
18. #19098289	C₄	semidirect
19. #19098287	C₄	semidirect
20. C₂²×M₁₆×C₇₉	C₄	semidirect
27. C₂×C₄⋊C₈×C₇₉	C₄	semidirect
28. C₂×C₂²⋊C₈×C₇₉	C₄	semidirect
30. C₂×#97×C₇₉	C₄	semidirect
88. C₂²⋊Dic₇₉	M₁₆	semidirect
186. C₈×C₇₉	#99	semidirect
233. C₇₉	#8161	semidirect
234. C₂²×M₁₆	Dic₇₉	semidirect
241. C₂×C₄⋊C₈	Dic₇₉	semidirect
245. C₂×C₂²⋊C₈	Dic₇₉	semidirect
248. C₂×#97	Dic₇₉	semidirect
414. C₈	#14579076	semidirect

Maximal subgroups

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

subgroup	index
C₄×#14579076	2
#23763176	2
C₈×C₂²⋊Dic₇₉	2
#23761718	2
#23761247	2
C₂×#435×C₇₉	2
#8161	79