Subgroups — C₇₉×#10231 #34121920

Order 20224.

728 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#474×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#461×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#2537	C₂	1	1	yes	maximal, characteristic
4	C₇₉×#1990	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄⋊C₈×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄⋊C₈×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×SD₁₆×C₇₉	—	2	1	no	—
9	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
10	C₂×#121×C₇₉	—	2	1	no	—
11	C₂×#121×C₇₉	—	2	1	no	—
12	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
14	#474×C₇₉	—	2	2	no	—
15	#474×C₇₉	—	2	2	no	—
16	#461×C₇₉	—	2	2	no	—
17	#461×C₇₉	—	2	2	no	—
18	C₂×#107×C₇₉	—	2	1	no	—
19	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×#103×C₇₉	—	2	1	no	—
22	C₂×#102×C₇₉	—	2	1	no	—
23	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
24	#394×C₇₉	—	2	2	no	—
25	#384×C₇₉	C₂²	1	1	yes	characteristic
26	#380×C₇₉	—	2	1	no	—
27	#380×C₇₉	—	2	1	no	—
28	#340×C₇₉	—	2	2	no	—
29	D₄⋊C₈×C₇₉	—	2	2	no	—
30	D₄⋊C₈×C₇₉	—	2	2	no	—
31	C₂²×Q₈×C₇₉	—	2	1	no	—
32	C₂²×D₄×C₇₉	—	2	2	no	—
33	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
34	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₇₉	—	2	1	no	—
36	C₂³×C₄×C₇₉	—	2	1	no	—
37	C₂×SD₁₆×C₇₉	—	2	4	no	—
38	C₂×SD₁₆×C₇₉	—	4	2	no	—
39	C₂×SD₁₆×C₇₉	—	4	2	no	—
40	C₂²×C₈×C₇₉	—	2	1	no	—
41	C₂²×C₈×C₇₉	—	2	1	no	—
42	C₂²×C₈×C₇₉	—	2	1	no	—
43	C₄⋊Q₈×C₇₉	—	2	1	no	—
44	C₄⋊Q₈×C₇₉	—	2	1	no	—
45	C₄⋊Q₈×C₇₉	—	2	1	no	—
46	C₄⋊Q₈×C₇₉	D₄	1	2	yes	complemented
47	#121×C₇₉	—	4	2	no	—
48	#121×C₇₉	—	4	2	no	—
49	#121×C₇₉	—	4	2	no	—
50	#121×C₇₉	—	4	2	no	—
51	C₄×D₄×C₇₉	—	2	1	no	—
52	C₄×D₄×C₇₉	—	2	1	no	—
53	C₄×D₄×C₇₉	—	2	1	no	—
54	C₄×D₄×C₇₉	—	2	1	no	—
55	C₄×D₄×C₇₉	—	2	1	no	—
56	C₄×D₄×C₇₉	—	2	1	no	—
57	C₄×D₄×C₇₉	—	2	1	no	—
58	C₄×D₄×C₇₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₇₉	D₄	1	2	yes	—
66	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
70	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
71	#107×C₇₉	—	2	4	no	—
72	C₄⋊C₈×C₇₉	—	2	1	no	—
73	C₄⋊C₈×C₇₉	—	2	1	no	—
74	C₄⋊C₈×C₇₉	D₄	1	2	yes	complemented
75	C₄⋊C₈×C₇₉	D₄	1	2	yes	complemented
76	#103×C₇₉	—	2	4	no	—
77	#102×C₇₉	—	2	4	no	—
78	C₄×C₈×C₇₉	—	2	1	no	—
79	C₄×C₈×C₇₉	—	2	1	no	—
80	#95×C₇₉	—	2	2	no	—
81	C₂⁴×C₇₉	—	2	1	no	—
82	C₂⁴×C₇₉	—	2	1	no	—
83	C₂×Q₈×C₇₉	—	2	2	no	—
84	C₂×Q₈×C₇₉	—	4	1	no	—
85	C₂×Q₈×C₇₉	—	4	1	no	—
86	C₂×Q₈×C₇₉	—	4	1	no	—
87	C₂×Q₈×C₇₉	—	4	1	no	—
88	C₂×Q₈×C₇₉	—	4	1	no	—
89	C₂×D₄×C₇₉	—	2	1	no	—
90	C₂×D₄×C₇₉	—	2	1	no	—
91	C₂×D₄×C₇₉	—	2	1	no	—
92	C₂×D₄×C₇₉	—	2	1	no	—
93	C₂×D₄×C₇₉	—	2	1	no	—
94	C₂×D₄×C₇₉	—	2	1	no	—
95	C₂×D₄×C₇₉	—	2	1	no	—
96	C₂×D₄×C₇₉	—	2	1	no	—
97	C₂×D₄×C₇₉	—	2	1	no	—
98	C₂×D₄×C₇₉	—	2	1	no	—
99	C₂×D₄×C₇₉	—	4	4	no	—
100	C₂×D₄×C₇₉	—	4	4	no	—
101	C₂×D₄×C₇₉	—	8	2	no	—
102	C₂×D₄×C₇₉	D₈	1	2	yes	—
103	C₂×D₄×C₇₉	SD₁₆	1	2	yes	complemented
104	C₂²×C₄×C₇₉	—	2	1	no	—
105	C₂²×C₄×C₇₉	—	2	1	no	—
106	C₂²×C₄×C₇₉	—	2	2	no	—
107	C₂²×C₄×C₇₉	—	4	1	no	—
108	C₂²×C₄×C₇₉	—	4	1	no	—
109	C₂²×C₄×C₇₉	—	4	1	no	—
110	C₂²×C₄×C₇₉	—	4	1	no	—
111	C₂²×C₄×C₇₉	—	4	1	no	—
112	C₂²×C₄×C₇₉	—	4	1	no	—
113	C₂²×C₄×C₇₉	—	4	1	no	—
114	C₂²×C₄×C₇₉	—	4	1	no	—
115	C₂²×C₄×C₇₉	—	4	1	no	—
116	C₂²×C₄×C₇₉	—	4	1	no	—
117	C₂²×C₄×C₇₉	—	4	1	no	—
118	C₂²×C₄×C₇₉	—	4	1	no	—
119	C₂²×C₄×C₇₉	—	4	1	no	—
120	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
123	SD₁₆×C₇₉	—	4	8	no	—
124	C₂×C₈×C₇₉	—	2	2	no	—
125	C₂×C₈×C₇₉	—	2	2	no	—
126	C₂×C₈×C₇₉	—	2	2	no	—
127	C₂×C₈×C₇₉	—	4	1	no	—
128	C₂×C₈×C₇₉	—	4	1	no	—
129	C₂×C₈×C₇₉	—	4	1	no	—
130	C₂×C₈×C₇₉	—	4	1	no	—
131	C₂×C₈×C₇₉	—	4	1	no	—
132	C₂×C₈×C₇₉	—	4	1	no	—
133	C₄⋊C₄×C₇₉	—	2	2	no	—
134	C₄⋊C₄×C₇₉	—	2	1	no	—
135	C₄⋊C₄×C₇₉	—	2	1	no	—
136	C₄⋊C₄×C₇₉	—	2	2	no	—
137	C₄⋊C₄×C₇₉	—	2	1	no	—
138	C₄⋊C₄×C₇₉	—	2	1	no	—
139	C₄⋊C₄×C₇₉	—	4	2	no	—
140	C₄⋊C₄×C₇₉	—	4	1	no	—
141	C₄⋊C₄×C₇₉	—	4	1	no	—
142	C₄⋊C₄×C₇₉	—	4	1	no	—
143	C₄⋊C₄×C₇₉	—	4	1	no	—
144	C₄⋊C₄×C₇₉	—	4	1	no	—
145	C₄⋊C₄×C₇₉	—	4	1	no	—
146	C₂²⋊C₄×C₇₉	—	4	4	no	—
147	C₂²⋊C₄×C₇₉	—	4	4	no	—
148	C₂²⋊C₄×C₇₉	—	4	1	no	—
149	C₂²⋊C₄×C₇₉	—	4	1	no	—
150	C₂²⋊C₄×C₇₉	—	4	1	no	—
151	C₂²⋊C₄×C₇₉	—	4	1	no	—
152	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₇₉	#41	1	1	yes	characteristic
156	C₂³×C₇₉	—	2	2	no	—
157	C₂³×C₇₉	—	2	2	no	—
158	C₂³×C₇₉	—	4	1	no	—
159	C₂³×C₇₉	—	4	1	no	—
160	C₂³×C₇₉	—	4	1	no	—
161	C₂³×C₇₉	—	4	1	no	—
162	C₂³×C₇₉	—	4	1	no	—
163	C₂³×C₇₉	—	4	1	no	—
164	C₂³×C₇₉	—	4	1	no	—
165	C₂³×C₇₉	—	4	1	no	—
166	C₂³×C₇₉	—	4	1	no	—
167	C₂³×C₇₉	—	4	1	no	—
168	C₂³×C₇₉	—	4	1	no	—
169	C₂³×C₇₉	—	4	1	no	—
170	C₂³×C₇₉	#120	1	1	yes	characteristic
171	Q₈×C₇₉	—	4	2	no	—
172	Q₈×C₇₉	—	4	2	no	—
173	Q₈×C₇₉	—	8	1	no	—
174	Q₈×C₇₉	—	8	1	no	—
175	D₄×C₇₉	—	2	2	no	—
176	D₄×C₇₉	—	2	2	no	—
177	D₄×C₇₉	—	2	2	no	—
178	D₄×C₇₉	—	2	2	no	—
179	D₄×C₇₉	—	4	1	no	—
180	D₄×C₇₉	—	4	1	no	—
181	D₄×C₇₉	—	4	1	no	—
182	D₄×C₇₉	—	4	1	no	—
183	D₄×C₇₉	—	8	8	no	—
184	C₂×C₄×C₇₉	—	2	1	no	—
185	C₂×C₄×C₇₉	—	2	1	no	—
186	C₂×C₄×C₇₉	—	4	1	no	—
187	C₂×C₄×C₇₉	—	4	1	no	—
188	C₂×C₄×C₇₉	—	4	2	no	—
189	C₂×C₄×C₇₉	—	4	1	no	—
190	C₂×C₄×C₇₉	—	4	2	no	—
191	C₂×C₄×C₇₉	—	4	1	no	—
192	C₂×C₄×C₇₉	—	4	1	no	—
193	C₂×C₄×C₇₉	—	4	2	no	—
194	C₂×C₄×C₇₉	—	4	1	no	—
195	C₂×C₄×C₇₉	—	4	2	no	—
196	C₂×C₄×C₇₉	—	8	1	no	—
197	C₂×C₄×C₇₉	—	8	1	no	—
198	C₂×C₄×C₇₉	—	8	1	no	—
199	C₂×C₄×C₇₉	—	8	1	no	—
200	C₂×C₄×C₇₉	—	8	1	no	—
201	C₂×C₄×C₇₉	—	8	1	no	—
202	C₂×C₄×C₇₉	—	8	1	no	—
203	C₂×C₄×C₇₉	—	8	1	no	—
204	C₂×C₄×C₇₉	—	8	1	no	—
205	C₂×C₄×C₇₉	—	8	1	no	—
206	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
207	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
208	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
209	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
210	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
211	C₂×C₄×C₇₉	#127	1	1	yes	characteristic
212	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
213	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
214	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
215	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
216	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
217	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
218	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
219	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
220	C₈×C₇₉	—	4	2	no	—
221	C₈×C₇₉	—	4	2	no	—
222	C₈×C₇₉	—	4	2	no	—
223	C₂²×C₇₉	—	4	2	no	—
224	C₂²×C₇₉	—	4	2	no	—
225	C₂²×C₇₉	—	4	2	no	—
226	C₂²×C₇₉	—	4	2	no	—
227	C₂²×C₇₉	—	4	2	no	—
228	C₂²×C₇₉	—	4	2	no	—
229	C₂²×C₇₉	—	8	1	no	—
230	C₂²×C₇₉	—	8	1	no	—
231	C₂²×C₇₉	—	8	1	no	—
232	C₂²×C₇₉	—	8	1	no	—
233	C₂²×C₇₉	—	8	1	no	—
234	C₂²×C₇₉	—	8	1	no	—
235	C₂²×C₇₉	—	8	1	no	—
236	C₂²×C₇₉	—	8	1	no	—
237	C₂²×C₇₉	#392	1	1	yes	characteristic
238	C₂²×C₇₉	#447	1	1	yes	characteristic
239	C₂²×C₇₉	#449	1	1	yes	characteristic
240	C₂²×C₇₉	#450	1	1	yes	characteristic
241	C₂²×C₇₉	#452	1	1	yes	characteristic
242	C₂²×C₇₉	#455	1	1	yes	characteristic
243	C₂²×C₇₉	#456	1	1	yes	characteristic
244	C₄×C₇₉	—	2	1	no	—
245	C₄×C₇₉	—	2	1	no	—
246	C₄×C₇₉	—	8	2	no	—
247	C₄×C₇₉	—	8	1	no	—
248	C₄×C₇₉	—	8	2	no	—
249	C₄×C₇₉	—	8	1	no	—
250	C₄×C₇₉	#447	1	1	yes	characteristic
251	C₄×C₇₉	#448	1	1	yes	characteristic
252	C₄×C₇₉	#449	1	1	yes	characteristic
253	C₄×C₇₉	#449	1	1	yes	characteristic
254	C₄×C₇₉	#465	1	1	yes	characteristic
255	C₄×C₇₉	#466	1	1	yes	characteristic
256	C₄×C₇₉	#468	1	1	yes	characteristic
257	C₄×C₇₉	#469	1	1	yes	characteristic
258	#10231	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
259	C₂×C₇₉	—	8	2	no	—
260	C₂×C₇₉	—	8	2	no	—
261	C₂×C₇₉	#1639	1	1	yes	characteristic
262	C₂×C₇₉	#1646	1	1	yes	characteristic
263	C₂×C₇₉	#1647	1	1	yes	characteristic
264	C₂×C₇₉	#1654	1	1	yes	characteristic
265	C₂×C₇₉	#1999	1	1	yes	characteristic
266	C₂×C₇₉	#2000	1	1	yes	characteristic
267	C₂×C₇₉	#2007	1	1	yes	characteristic
268	C₂×#474	C₂×C₇₉	1	1	yes	characteristic, complemented
269	C₂×#461	C₂×C₇₉	1	1	yes	characteristic, complemented
270	#2537	C₂×C₇₉	1	1	yes	characteristic
271	#1990	C₂×C₇₉	1	1	yes	characteristic, complemented
272	C₂×D₄⋊C₈	C₂×C₇₉	1	1	yes	characteristic, complemented
273	C₂×D₄⋊C₈	C₂×C₇₉	1	1	yes	characteristic, complemented
274	#1296	C₂×C₇₉	1	1	yes	characteristic, complemented
275	C₇₉	#10231	1	1	yes	characteristic, direct product factor, Sylow
276	C₂²×SD₁₆	—	2	1	no	—
277	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
278	C₂×#121	—	2	1	no	—
279	C₂×#121	—	2	1	no	—
280	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
281	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
282	#474	—	2	2	no	—
283	#474	—	2	2	no	—
284	#461	—	2	2	no	—
285	#461	—	2	2	no	—
286	C₂×#107	—	2	1	no	—
287	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
288	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
289	C₂×#103	—	2	1	no	—
290	C₂×#102	—	2	1	no	—
291	C₂×C₄×C₈	C₂²×C₇₉	1	1	yes	characteristic
292	#394	—	2	2	no	—
293	#384	C₂²×C₇₉	1	1	yes	characteristic
294	#380	—	2	1	no	—
295	#380	—	2	1	no	—
296	#340	—	2	2	no	—
297	D₄⋊C₈	—	2	2	no	—
298	D₄⋊C₈	—	2	2	no	—
299	C₂²×Q₈	—	2	1	no	—
300	C₂²×D₄	—	2	2	no	—
301	C₂²×D₄	D₄×C₇₉	1	1	yes	characteristic
302	C₂²×D₄	D₄×C₇₉	1	1	yes	characteristic
303	C₂³×C₄	—	2	1	no	—
304	C₂³×C₄	—	2	1	no	—
305	C₂×SD₁₆	—	2	4	no	—
306	C₂×SD₁₆	—	4	2	no	—
307	C₂×SD₁₆	—	4	2	no	—
308	C₂²×C₈	—	2	1	no	—
309	C₂²×C₈	—	2	1	no	—
310	C₂²×C₈	—	2	1	no	—
311	C₄⋊Q₈	—	2	1	no	—
312	C₄⋊Q₈	—	2	1	no	—
313	C₄⋊Q₈	—	2	1	no	—
314	C₄⋊Q₈	D₄×C₇₉	1	2	yes	complemented
315	#121	—	4	2	no	—
316	#121	—	4	2	no	—
317	#121	—	4	2	no	—
318	#121	—	4	2	no	—
319	C₄×D₄	—	2	1	no	—
320	C₄×D₄	—	2	1	no	—
321	C₄×D₄	—	2	1	no	—
322	C₄×D₄	—	2	1	no	—
323	C₄×D₄	—	2	1	no	—
324	C₄×D₄	—	2	1	no	—
325	C₄×D₄	—	2	1	no	—
326	C₄×D₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
332	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
333	C₂×C₄⋊C₄	D₄×C₇₉	1	2	yes	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₂²⋊C₄	—	2	1	no	—
337	C₂×C₂²⋊C₄	—	2	1	no	—
338	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
339	#107	—	2	4	no	—
340	C₄⋊C₈	—	2	1	no	—
341	C₄⋊C₈	—	2	1	no	—
342	C₄⋊C₈	D₄×C₇₉	1	2	yes	complemented
343	C₄⋊C₈	D₄×C₇₉	1	2	yes	complemented
344	#103	—	2	4	no	—
345	#102	—	2	4	no	—
346	C₄×C₈	—	2	1	no	—
347	C₄×C₈	—	2	1	no	—
348	#95	—	2	2	no	—
349	C₂⁴	—	2	1	no	—
350	C₂⁴	—	2	1	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	4	1	no	—
353	C₂×Q₈	—	4	1	no	—
354	C₂×Q₈	—	4	1	no	—
355	C₂×Q₈	—	4	1	no	—
356	C₂×Q₈	—	4	1	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	4	4	no	—
368	C₂×D₄	—	4	4	no	—
369	C₂×D₄	—	8	2	no	—
370	C₂×D₄	D₈×C₇₉	1	2	yes	—
371	C₂×D₄	SD₁₆×C₇₉	1	2	yes	complemented
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	4	1	no	—
376	C₂²×C₄	—	4	1	no	—
377	C₂²×C₄	—	4	1	no	—
378	C₂²×C₄	—	4	1	no	—
379	C₂²×C₄	—	4	1	no	—
380	C₂²×C₄	—	4	1	no	—
381	C₂²×C₄	—	4	1	no	—
382	C₂²×C₄	—	4	1	no	—
383	C₂²×C₄	—	4	1	no	—
384	C₂²×C₄	—	4	1	no	—
385	C₂²×C₄	—	4	1	no	—
386	C₂²×C₄	—	4	1	no	—
387	C₂²×C₄	—	4	1	no	—
388	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
391	SD₁₆	—	4	8	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	4	1	no	—
396	C₂×C₈	—	4	1	no	—
397	C₂×C₈	—	4	1	no	—
398	C₂×C₈	—	4	1	no	—
399	C₂×C₈	—	4	1	no	—
400	C₂×C₈	—	4	1	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	4	2	no	—
408	C₄⋊C₄	—	4	1	no	—
409	C₄⋊C₄	—	4	1	no	—
410	C₄⋊C₄	—	4	1	no	—
411	C₄⋊C₄	—	4	1	no	—
412	C₄⋊C₄	—	4	1	no	—
413	C₄⋊C₄	—	4	1	no	—
414	C₂²⋊C₄	—	4	4	no	—
415	C₂²⋊C₄	—	4	4	no	—
416	C₂²⋊C₄	—	4	1	no	—
417	C₂²⋊C₄	—	4	1	no	—
418	C₂²⋊C₄	—	4	1	no	—
419	C₂²⋊C₄	—	4	1	no	—
420	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
421	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
422	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
423	C₄²	#41×C₇₉	1	1	yes	characteristic
424	C₂³	—	2	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	4	1	no	—
427	C₂³	—	4	1	no	—
428	C₂³	—	4	1	no	—
429	C₂³	—	4	1	no	—
430	C₂³	—	4	1	no	—
431	C₂³	—	4	1	no	—
432	C₂³	—	4	1	no	—
433	C₂³	—	4	1	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	4	1	no	—
436	C₂³	—	4	1	no	—
437	C₂³	—	4	1	no	—
438	C₂³	#120×C₇₉	1	1	yes	characteristic
439	Q₈	—	4	2	no	—
440	Q₈	—	4	2	no	—
441	Q₈	—	8	1	no	—
442	Q₈	—	8	1	no	—
443	D₄	—	2	2	no	—
444	D₄	—	2	2	no	—
445	D₄	—	2	2	no	—
446	D₄	—	2	2	no	—
447	D₄	—	4	1	no	—
448	D₄	—	4	1	no	—
449	D₄	—	4	1	no	—
450	D₄	—	4	1	no	—
451	D₄	—	8	8	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	8	1	no	—
465	C₂×C₄	—	8	1	no	—
466	C₂×C₄	—	8	1	no	—
467	C₂×C₄	—	8	1	no	—
468	C₂×C₄	—	8	1	no	—
469	C₂×C₄	—	8	1	no	—
470	C₂×C₄	—	8	1	no	—
471	C₂×C₄	—	8	1	no	—
472	C₂×C₄	—	8	1	no	—
473	C₂×C₄	—	8	1	no	—
474	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
475	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
476	C₂×C₄	#121×C₇₉	1	1	yes	characteristic
477	C₂×C₄	#121×C₇₉	1	1	yes	characteristic
478	C₂×C₄	#121×C₇₉	1	1	yes	characteristic
479	C₂×C₄	#127×C₇₉	1	1	yes	characteristic
480	C₂×C₄	C₂×D₈×C₇₉	1	1	yes	characteristic
481	C₂×C₄	C₂×SD₁₆×C₇₉	1	1	yes	characteristic
482	C₂×C₄	#135×C₇₉	1	1	yes	characteristic
483	C₂×C₄	#135×C₇₉	1	1	yes	characteristic
484	C₂×C₄	AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
485	C₂×C₄	AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
486	C₂×C₄	AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
487	C₂×C₄	#137×C₇₉	1	1	yes	characteristic
488	C₈	—	4	2	no	—
489	C₈	—	4	2	no	—
490	C₈	—	4	2	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	4	2	no	—
497	C₂²	—	8	1	no	—
498	C₂²	—	8	1	no	—
499	C₂²	—	8	1	no	—
500	C₂²	—	8	1	no	—
501	C₂²	—	8	1	no	—
502	C₂²	—	8	1	no	—
503	C₂²	—	8	1	no	—
504	C₂²	—	8	1	no	—
505	C₂²	#392×C₇₉	1	1	yes	characteristic
506	C₂²	#447×C₇₉	1	1	yes	characteristic
507	C₂²	#449×C₇₉	1	1	yes	characteristic
508	C₂²	#450×C₇₉	1	1	yes	characteristic
509	C₂²	#452×C₇₉	1	1	yes	characteristic
510	C₂²	#455×C₇₉	1	1	yes	characteristic
511	C₂²	#456×C₇₉	1	1	yes	characteristic
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	8	1	no	—
515	C₄	—	8	2	no	—
516	C₄	—	8	1	no	—
517	C₄	—	8	2	no	—
518	C₄	#447×C₇₉	1	1	yes	characteristic
519	C₄	#448×C₇₉	1	1	yes	characteristic
520	C₄	#449×C₇₉	1	1	yes	characteristic
521	C₄	#449×C₇₉	1	1	yes	characteristic
522	C₄	#465×C₇₉	1	1	yes	characteristic
523	C₄	#466×C₇₉	1	1	yes	characteristic
524	C₄	#468×C₇₉	1	1	yes	characteristic
525	C₄	#469×C₇₉	1	1	yes	characteristic
526	C₂	—	8	2	no	—
527	C₂	—	8	2	no	—
528	C₂	C₇₉×#1639	1	1	yes	characteristic
529	C₂	C₇₉×#1646	1	1	yes	characteristic
530	C₂	C₇₉×#1647	1	1	yes	characteristic
531	C₂	C₇₉×#1654	1	1	yes	characteristic
532	C₂	C₇₉×#1999	1	1	yes	characteristic
533	C₂	C₇₉×#2000	1	1	yes	characteristic
534	C₂	C₇₉×#2007	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₉	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₇₉
prime radical	C₇₉×#2537	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₂×C₄²×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#474×C₇₉	C₂	semidirect
2. C₂×#461×C₇₉	C₂	semidirect
4. C₇₉×#1990	C₂	semidirect
5. C₂×D₄⋊C₈×C₇₉	C₂	semidirect
6. C₂×D₄⋊C₈×C₇₉	C₂	semidirect
7. C₇₉×#1296	C₂	semidirect
46. C₄⋊Q₈×C₇₉	D₄	semidirect
74. C₄⋊C₈×C₇₉	D₄	semidirect
75. C₄⋊C₈×C₇₉	D₄	semidirect
103. C₂×D₄×C₇₉	SD₁₆	semidirect
258. #10231	C₇₉	direct (N × H)
268. C₂×#474	C₂×C₇₉	semidirect
269. C₂×#461	C₂×C₇₉	semidirect
271. #1990	C₂×C₇₉	semidirect
272. C₂×D₄⋊C₈	C₂×C₇₉	semidirect
273. C₂×D₄⋊C₈	C₂×C₇₉	semidirect
274. #1296	C₂×C₇₉	semidirect
275. C₇₉	#10231	direct (N × H)
314. C₄⋊Q₈	D₄×C₇₉	semidirect
342. C₄⋊C₈	D₄×C₇₉	semidirect
343. C₄⋊C₈	D₄×C₇₉	semidirect
371. C₂×D₄	SD₁₆×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#474×C₇₉	2
C₂×#461×C₇₉	2
C₇₉×#2537	2
C₇₉×#1990	2
C₂×D₄⋊C₈×C₇₉	2
C₇₉×#1296	2
#10231	79

Subgroups — C79×#10231 #34121920

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#10231 #34121920