Subgroups — #34178371

Order 20224.

790 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098615	C₂	1	1	yes	maximal, characteristic
2	C₂×#19098585	C₂	1	1	yes	maximal, characteristic
3	#384×D₇₉	C₂	1	1	yes	maximal, characteristic
4	#23761284	C₂	1	1	yes	maximal, characteristic, complemented
5	#23761284	C₂	1	1	yes	maximal, characteristic, complemented
6	#23761283	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#11929607	—	2	1	no	—
9	C₂×C₄⋊C₄×D₇₉	—	2	1	no	—
10	C₂×C₄⋊C₄×D₇₉	—	2	1	no	—
11	C₂×C₄⋊C₄×D₇₉	C₄	1	2	yes	—
12	C₂×C₄²×D₇₉	C₂²	1	1	yes	characteristic
13	#19098615	—	2	2	no	—
14	#19098615	C₄	1	4	yes	complemented
15	#19098585	—	2	2	no	—
16	#19098585	C₄	1	4	yes	complemented
17	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×Dic₇₉⋊C₈	—	2	1	no	—
20	C₂×(C₂×D₇₉)⋊C₈	—	2	1	no	—
21	C₂×C₈×Dic₇₉	—	2	1	no	—
22	#19098433	C₂²	1	1	yes	characteristic
23	#19098432	—	2	1	no	—
24	#19098432	—	2	1	no	—
25	#19098432	C₄	1	2	yes	—
26	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
28	#384×C₇₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₇₉	—	2	2	no	—
30	C₂²×C₄×D₇₉	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₄×D₇₉	D₄	1	1	yes	characteristic
32	C₂²×C₄×D₇₉	D₄	1	1	yes	characteristic
33	C₂×#11929607	—	2	4	no	—
34	C₂×#11929607	—	4	2	no	—
35	C₂×#11929607	—	4	2	no	—
36	C₂²×C₇₉⋊C₈	—	2	1	no	—
37	C₂²×C₇₉⋊C₈	—	2	1	no	—
38	C₂×C₄⋊Dic₇₉	—	2	1	no	—
39	C₂×C₄⋊Dic₇₉	—	2	1	no	—
40	C₂×C₄⋊Dic₇₉	C₂×C₄	1	2	yes	—
41	C₂×Dic₇₉⋊C₄	—	2	2	no	—
42	C₂×Dic₇₉⋊C₄	—	2	2	no	—
43	C₂×Dic₇₉⋊C₄	—	2	2	no	—
44	C₄⋊C₄×D₇₉	—	4	2	no	—
45	C₄⋊C₄×D₇₉	—	4	2	no	—
46	C₄⋊C₄×D₇₉	—	4	2	no	—
47	C₄⋊C₄×D₇₉	—	4	2	no	—
48	C₄⋊C₄×D₇₉	—	4	4	no	—
49	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄×Dic₇₉	D₄	1	1	yes	characteristic
51	C₂×C₄×Dic₇₉	D₄	1	1	yes	characteristic
52	C₄²×D₇₉	C₂×C₄	1	2	yes	—
53	C₄²×D₇₉	C₂×C₄	1	2	yes	—
54	C₄²×D₇₉	D₄	1	2	yes	—
55	C₄²×D₇₉	Q₈	1	2	yes	—
56	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
57	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
58	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	complemented
59	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	complemented
60	Dic₇₉⋊C₈	—	2	4	no	—
61	(C₂×D₇₉)⋊C₈	—	2	4	no	—
62	C₈×Dic₇₉	—	2	4	no	—
63	C₂²×C₈×C₇₉	—	2	1	no	—
64	C₂²×C₈×C₇₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
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	C₂×C₄	1	2	yes	complemented
72	C₄⋊C₈×C₇₉	C₂×C₄	1	2	yes	complemented
73	C₂³×D₇₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×Dic₇₉	—	2	2	no	—
75	C₂²×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
78	C₂×C₄×D₇₉	—	2	2	no	—
79	C₂×C₄×D₇₉	—	2	2	no	—
80	C₂×C₄×D₇₉	—	2	1	no	—
81	C₂×C₄×D₇₉	—	2	1	no	—
82	C₂×C₄×D₇₉	—	2	1	no	—
83	C₂×C₄×D₇₉	—	2	1	no	—
84	C₂×C₄×D₇₉	—	4	4	no	—
85	C₂×C₄×D₇₉	—	4	4	no	—
86	C₂×C₄×D₇₉	—	4	4	no	—
87	C₂×C₄×D₇₉	C₄²	1	2	yes	—
88	C₂×C₄×D₇₉	C₂²⋊C₄	1	2	yes	—
89	C₂×C₄×D₇₉	C₂²⋊C₄	1	2	yes	—
90	C₂×C₄×D₇₉	C₄⋊C₄	1	2	yes	—
91	C₂×C₄×D₇₉	C₄⋊C₄	1	2	yes	—
92	C₂×C₄×D₇₉	C₄⋊C₄	1	2	yes	—
93	C₂×C₄×D₇₉	D₈	1	2	yes	—
94	C₂×C₄×D₇₉	SD₁₆	1	2	yes	—
95	C₂×C₄×D₇₉	SD₁₆	1	2	yes	—
96	C₂×C₄×D₇₉	Q₁₆	1	2	yes	—
97	#11929607	—	4	8	no	—
98	C₂×C₇₉⋊C₈	—	2	2	no	—
99	C₂×C₇₉⋊C₈	—	2	2	no	—
100	C₂×C₇₉⋊C₈	—	4	1	no	—
101	C₂×C₇₉⋊C₈	—	4	1	no	—
102	C₂×C₇₉⋊C₈	—	4	1	no	—
103	C₂×C₇₉⋊C₈	—	4	1	no	—
104	C₄⋊Dic₇₉	—	4	2	no	—
105	C₄⋊Dic₇₉	—	4	1	no	—
106	C₄⋊Dic₇₉	—	4	1	no	—
107	C₄⋊Dic₇₉	—	4	1	no	—
108	C₄⋊Dic₇₉	—	4	1	no	—
109	Dic₇₉⋊C₄	—	4	4	no	—
110	Dic₇₉⋊C₄	—	4	4	no	—
111	Dic₇₉⋊C₄	—	4	4	no	—
112	C₄×Dic₇₉	C₄²	1	2	yes	—
113	C₄×Dic₇₉	C₂²⋊C₄	1	2	yes	—
114	C₄×Dic₇₉	C₂²⋊C₄	1	2	yes	—
115	C₄×Dic₇₉	C₄⋊C₄	1	2	yes	—
116	C₄×Dic₇₉	C₄⋊C₄	1	2	yes	—
117	C₄×Dic₇₉	C₄⋊C₄	1	2	yes	—
118	C₂²×C₄×C₇₉	—	2	2	no	—
119	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₇₉	—	2	2	no	—
123	C₂×C₈×C₇₉	—	2	2	no	—
124	C₂×C₈×C₇₉	—	4	1	no	—
125	C₂×C₈×C₇₉	—	4	1	no	—
126	C₂×C₈×C₇₉	—	4	1	no	—
127	C₂×C₈×C₇₉	—	4	1	no	—
128	C₄⋊C₄×C₇₉	—	4	2	no	—
129	C₄⋊C₄×C₇₉	—	4	1	no	—
130	C₄⋊C₄×C₇₉	—	4	1	no	—
131	C₄⋊C₄×C₇₉	—	4	1	no	—
132	C₄⋊C₄×C₇₉	—	4	1	no	—
133	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
134	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
135	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₇₉	C₂×Q₈	1	1	yes	characteristic
137	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
138	C₂²×D₇₉	—	2	1	no	—
139	C₂²×D₇₉	—	2	1	no	—
140	C₂²×D₇₉	—	2	1	no	—
141	C₂²×D₇₉	—	2	1	no	—
142	C₂²×D₇₉	#95	1	2	yes	—
143	C₂²×D₇₉	#102	1	2	yes	—
144	C₂²×D₇₉	#103	1	2	yes	—
145	C₂×C₄×C₇₉	—	2	1	no	—
146	C₂×C₄×C₇₉	—	2	1	no	—
147	C₂×C₄×C₇₉	—	4	2	no	—
148	C₂×C₄×C₇₉	—	4	2	no	—
149	C₂×C₄×C₇₉	—	4	2	no	—
150	C₂×C₄×C₇₉	C₂×C₄²	1	1	yes	characteristic
151	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
157	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
158	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
159	C₂×C₄×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
160	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
161	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
162	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
163	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
164	C₂×Dic₇₉	—	2	1	no	—
165	C₂×Dic₇₉	—	2	1	no	—
166	C₂×Dic₇₉	—	4	2	no	—
167	C₂×Dic₇₉	—	4	2	no	—
168	C₂×Dic₇₉	—	4	2	no	—
169	C₂×Dic₇₉	#95	1	2	yes	—
170	C₂×Dic₇₉	#95	1	2	yes	—
171	C₂×Dic₇₉	#95	1	2	yes	—
172	C₂×Dic₇₉	#100	1	2	yes	—
173	C₂×Dic₇₉	#101	1	2	yes	—
174	C₂×Dic₇₉	#102	1	2	yes	—
175	C₂×Dic₇₉	#103	1	2	yes	—
176	C₄×D₇₉	—	2	2	no	—
177	C₄×D₇₉	—	2	2	no	—
178	C₄×D₇₉	—	2	2	no	—
179	C₄×D₇₉	—	2	2	no	—
180	C₄×D₇₉	—	2	4	no	—
181	C₄×D₇₉	—	2	4	no	—
182	C₄×D₇₉	—	8	8	no	—
183	C₄×D₇₉	#102	1	4	yes	—
184	C₄×D₇₉	#103	1	4	yes	—
185	C₄×D₇₉	#106	1	4	yes	—
186	C₄×D₇₉	#107	1	4	yes	—
187	C₈×C₇₉	—	4	2	no	—
188	C₈×C₇₉	—	4	2	no	—
189	C₇₉⋊C₈	—	4	2	no	—
190	C₇₉⋊C₈	—	4	2	no	—
191	C₂²×C₇₉	C₂×#95	1	1	yes	characteristic
192	C₂²×C₇₉	C₂×#100	1	1	yes	characteristic
193	C₂²×C₇₉	C₂×#101	1	1	yes	characteristic
194	C₂²×C₇₉	C₂×#102	1	1	yes	characteristic
195	C₂²×C₇₉	C₂×#103	1	1	yes	characteristic
196	C₂²×C₇₉	#418	1	1	yes	characteristic
197	C₂²×C₇₉	#419	1	1	yes	characteristic
198	C₂×D₇₉	—	2	2	no	—
199	C₂×D₇₉	—	2	2	no	—
200	C₂×D₇₉	—	2	2	no	—
201	C₂×D₇₉	—	2	2	no	—
202	C₂×D₇₉	—	2	2	no	—
203	C₂×D₇₉	—	2	2	no	—
204	C₂×D₇₉	#340	1	4	yes	—
205	C₄×C₇₉	—	2	1	no	—
206	C₄×C₇₉	—	2	1	no	—
207	C₄×C₇₉	—	8	2	no	—
208	C₄×C₇₉	C₂×#102	1	1	yes	characteristic
209	C₄×C₇₉	C₂×#103	1	1	yes	characteristic
210	C₄×C₇₉	#417	1	1	yes	characteristic
211	C₄×C₇₉	#417	1	1	yes	characteristic
212	C₄×C₇₉	C₂×#106	1	1	yes	characteristic
213	C₄×C₇₉	C₂×#107	1	1	yes	characteristic
214	C₄×C₇₉	#428	1	1	yes	characteristic
215	C₄×C₇₉	#428	1	1	yes	characteristic
216	Dic₇₉	—	2	2	no	—
217	Dic₇₉	—	8	2	no	—
218	Dic₇₉	#340	1	4	yes	—
219	Dic₇₉	#343	1	4	yes	—
220	#8043	—	79	1	no	maximal, Sylow
221	C₂×C₇₉	#1545	1	1	yes	characteristic
222	C₂×C₇₉	#1546	1	1	yes	characteristic
223	C₂×C₇₉	#1548	1	1	yes	characteristic
224	C₂×C₇₉	#1549	1	1	yes	characteristic
225	C₂×C₇₉	C₂×#340	1	1	yes	characteristic
226	C₂×C₇₉	#1736	1	1	yes	characteristic
227	C₂×C₇₉	C₂×#343	1	1	yes	characteristic
228	D₇₉	—	2	4	no	—
229	C₂×#431	—	79	1	no	—
230	C₂×#423	—	79	1	no	—
231	C₂×#384	—	79	1	no	—
232	#1296	—	79	1	no	—
233	#1296	—	79	1	no	—
234	#1296	—	79	1	no	—
235	#1296	D₇₉	1	1	yes	characteristic, complemented
236	C₇₉	#8043	1	1	yes	characteristic, complemented, Sylow
237	C₂²×M₁₆	—	158	1	no	—
238	C₂²×C₄⋊C₄	—	79	2	no	—
239	C₂²×C₄⋊C₄	—	158	1	no	—
240	C₂²×C₄⋊C₄	—	158	1	no	—
241	C₂²×C₄²	—	79	1	no	—
242	#431	—	79	4	no	—
243	#431	—	158	2	no	—
244	#423	—	79	4	no	—
245	#423	—	158	2	no	—
246	C₂×C₄⋊C₈	—	79	1	no	—
247	C₂×C₄⋊C₈	—	79	1	no	—
248	C₂×C₄⋊C₈	—	158	1	no	—
249	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
250	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
251	C₂×C₂²⋊C₈	—	158	1	no	—
252	C₂×C₄×C₈	—	158	1	no	—
253	#384	—	79	2	no	—
254	#384	—	79	1	no	—
255	#384	—	158	1	no	—
256	#384	—	158	1	no	—
257	#384	C₂×D₇₉	1	1	yes	characteristic
258	C₂³×C₄	—	79	1	no	—
259	C₂³×C₄	—	79	1	no	—
260	C₂³×C₄	—	79	1	no	—
261	C₂³×C₄	—	158	2	no	—
262	C₂×M₁₆	—	316	2	no	—
263	C₂×M₁₆	—	316	2	no	—
264	C₂×M₁₆	—	158	4	no	—
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	—	2	1	no	—
267	C₂²×C₈	—	158	1	no	—
268	C₂²×C₈	—	158	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	316	2	no	—
272	C₂×C₄⋊C₄	—	316	2	no	—
273	C₂×C₄⋊C₄	—	316	2	no	—
274	C₂×C₄⋊C₄	—	316	2	no	—
275	C₂×C₄⋊C₄	—	316	4	no	—
276	C₂×C₄⋊C₄	—	79	2	no	—
277	C₂×C₄⋊C₄	—	158	2	no	—
278	C₂×C₄⋊C₄	—	158	2	no	—
279	C₂×C₄⋊C₄	—	158	2	no	—
280	C₂×C₄⋊C₄	—	158	1	no	—
281	C₂×C₄⋊C₄	—	158	1	no	—
282	C₂×C₄⋊C₄	C₄×D₇₉	1	2	yes	—
283	C₂×C₄²	—	79	1	no	—
284	C₂×C₄²	—	79	1	no	—
285	C₂×C₄²	—	79	1	no	—
286	C₂×C₄²	—	79	2	no	—
287	C₂×C₄²	—	79	2	no	—
288	C₂×C₄²	—	79	2	no	—
289	C₂×C₄²	—	79	2	no	—
290	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	—	2	1	no	—
293	C₄⋊C₈	—	79	2	no	—
294	C₄⋊C₈	—	79	2	no	—
295	C₄⋊C₈	—	158	4	no	—
296	C₄⋊C₈	—	158	1	no	—
297	C₄⋊C₈	—	158	1	no	—
298	C₄⋊C₈	C₄×D₇₉	1	2	yes	complemented
299	C₄⋊C₈	C₄×D₇₉	1	2	yes	complemented
300	C₂²⋊C₈	—	158	4	no	—
301	C₄×C₈	—	158	4	no	—
302	C₂⁴	—	79	1	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	316	4	no	—
305	C₂²×C₄	—	316	4	no	—
306	C₂²×C₄	—	316	4	no	—
307	C₂²×C₄	—	79	1	no	—
308	C₂²×C₄	—	79	1	no	—
309	C₂²×C₄	—	79	2	no	—
310	C₂²×C₄	—	79	2	no	—
311	C₂²×C₄	—	79	2	no	—
312	C₂²×C₄	—	79	2	no	—
313	C₂²×C₄	—	79	2	no	—
314	C₂²×C₄	—	79	2	no	—
315	C₂²×C₄	—	79	1	no	—
316	C₂²×C₄	—	79	2	no	—
317	C₂²×C₄	—	79	2	no	—
318	C₂²×C₄	—	79	2	no	—
319	C₂²×C₄	—	79	2	no	—
320	C₂²×C₄	—	158	2	no	—
321	C₂²×C₄	—	158	2	no	—
322	C₂²×C₄	—	158	2	no	—
323	C₂²×C₄	—	158	1	no	—
324	C₂²×C₄	—	158	1	no	—
325	C₂²×C₄	—	158	1	no	—
326	C₂²×C₄	—	158	1	no	—
327	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
328	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
329	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
330	M₁₆	—	316	8	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	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	—	316	1	no	—
338	C₂×C₈	—	316	1	no	—
339	C₂×C₈	—	316	1	no	—
340	C₂×C₈	—	316	1	no	—
341	C₂×C₈	—	158	2	no	—
342	C₂×C₈	—	158	2	no	—
343	C₄⋊C₄	—	4	2	no	—
344	C₄⋊C₄	—	4	1	no	—
345	C₄⋊C₄	—	4	1	no	—
346	C₄⋊C₄	—	4	1	no	—
347	C₄⋊C₄	—	4	1	no	—
348	C₄⋊C₄	—	316	2	no	—
349	C₄⋊C₄	—	316	4	no	—
350	C₄⋊C₄	—	316	4	no	—
351	C₄⋊C₄	—	316	4	no	—
352	C₄⋊C₄	—	316	1	no	—
353	C₄⋊C₄	—	316	1	no	—
354	C₄⋊C₄	—	316	1	no	—
355	C₄⋊C₄	—	316	1	no	—
356	C₄²	—	79	2	no	—
357	C₄²	—	79	2	no	—
358	C₄²	—	79	2	no	—
359	C₄²	—	79	2	no	—
360	C₄²	—	79	2	no	—
361	C₄²	—	79	2	no	—
362	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
363	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
364	C₄²	D₄×D₇₉	1	1	yes	characteristic
365	C₄²	Q₈×D₇₉	1	1	yes	characteristic
366	C₂³	—	79	2	no	—
367	C₂³	—	79	2	no	—
368	C₂³	—	79	2	no	—
369	C₂³	—	158	1	no	—
370	C₂³	—	158	1	no	—
371	C₂³	—	158	1	no	—
372	C₂³	—	158	1	no	—
373	C₂³	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	316	2	no	—
380	C₂×C₄	—	316	2	no	—
381	C₂×C₄	—	316	2	no	—
382	C₂×C₄	—	79	2	no	—
383	C₂×C₄	—	79	2	no	—
384	C₂×C₄	—	79	2	no	—
385	C₂×C₄	—	79	2	no	—
386	C₂×C₄	—	79	2	no	—
387	C₂×C₄	—	79	2	no	—
388	C₂×C₄	—	79	4	no	—
389	C₂×C₄	—	79	4	no	—
390	C₂×C₄	—	79	4	no	—
391	C₂×C₄	—	79	4	no	—
392	C₂×C₄	—	79	2	no	—
393	C₂×C₄	—	632	8	no	—
394	C₂×C₄	—	158	4	no	—
395	C₂×C₄	—	158	4	no	—
396	C₂×C₄	—	158	1	no	—
397	C₂×C₄	—	158	1	no	—
398	C₂×C₄	—	158	2	no	—
399	C₂×C₄	—	158	2	no	—
400	C₂×C₄	—	158	2	no	—
401	C₂×C₄	—	158	2	no	—
402	C₂×C₄	C₄²×D₇₉	1	1	yes	characteristic
403	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
404	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
405	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
406	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
407	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
408	C₂×C₄	D₈×D₇₉	1	1	yes	characteristic
409	C₂×C₄	SD₁₆×D₇₉	1	1	yes	characteristic
410	C₂×C₄	SD₁₆×D₇₉	1	1	yes	characteristic
411	C₂×C₄	Q₁₆×D₇₉	1	1	yes	characteristic
412	C₂×C₄	#14579185	1	1	yes	characteristic
413	C₂×C₄	#14579188	1	1	yes	characteristic
414	C₂×C₄	#14579190	1	1	yes	characteristic
415	C₂×C₄	#14579193	1	1	yes	characteristic
416	C₈	—	4	2	no	—
417	C₈	—	4	2	no	—
418	C₈	—	316	2	no	—
419	C₈	—	316	2	no	—
420	C₂²	—	79	4	no	—
421	C₂²	—	158	2	no	—
422	C₂²	—	158	2	no	—
423	C₂²	—	158	2	no	—
424	C₂²	—	158	2	no	—
425	C₂²	—	158	2	no	—
426	C₂²	—	158	2	no	—
427	C₂²	#95×D₇₉	1	1	yes	characteristic
428	C₂²	#100×D₇₉	1	1	yes	characteristic
429	C₂²	#101×D₇₉	1	1	yes	characteristic
430	C₂²	#102×D₇₉	1	1	yes	characteristic
431	C₂²	#103×D₇₉	1	1	yes	characteristic
432	C₂²	#19098566	1	1	yes	characteristic
433	C₂²	#19098570	1	1	yes	characteristic
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	8	2	no	—
437	C₄	—	79	4	no	—
438	C₄	—	79	4	no	—
439	C₄	—	632	2	no	—
440	C₄	—	158	2	no	—
441	C₄	#102×D₇₉	1	1	yes	characteristic
442	C₄	#103×D₇₉	1	1	yes	characteristic
443	C₄	#19098561	1	1	yes	characteristic
444	C₄	#19098563	1	1	yes	characteristic
445	C₄	#106×D₇₉	1	1	yes	characteristic
446	C₄	#107×D₇₉	1	1	yes	characteristic
447	C₄	#19098602	1	1	yes	characteristic
448	C₄	#19098604	1	1	yes	characteristic
449	C₂	—	158	4	no	—
450	C₂	#23762066	1	1	yes	characteristic
451	C₂	#23762070	1	1	yes	characteristic
452	C₂	#23762079	1	1	yes	characteristic
453	C₂	#23762083	1	1	yes	characteristic
454	C₂	#340×D₇₉	1	1	yes	characteristic
455	C₂	#23763118	1	1	yes	characteristic
456	C₂	#343×D₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1296	C₂
socle	C₂³×C₇₉	C₂×C₂²⋊C₄
prime radical	C₂³×D₇₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#1296	D₇₉
hypocenter	C₇₉	#8043
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

Complements

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

N	H ≅ G/N	type
4. #23761284	C₂	semidirect
5. #23761284	C₂	semidirect
6. #23761283	C₂	semidirect
7. C₇₉×#1296	C₂	semidirect
14. #19098615	C₄	semidirect
16. #19098585	C₄	semidirect
58. C₄⋊(C₇₉⋊C₈)	C₂×C₄	semidirect
59. C₄⋊(C₇₉⋊C₈)	C₂×C₄	semidirect
71. C₄⋊C₈×C₇₉	C₂×C₄	semidirect
72. C₄⋊C₈×C₇₉	C₂×C₄	semidirect
235. #1296	D₇₉	semidirect
236. C₇₉	#8043	semidirect
298. C₄⋊C₈	C₄×D₇₉	semidirect
299. C₄⋊C₈	C₄×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098615	2
C₂×#19098585	2
#384×D₇₉	2
#23761284	2
#23761283	2
C₇₉×#1296	2
#8043	79