Subgroups — C₇₉×#23510 #34135199

Order 20224.

1414 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#536×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#417×C₇₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#419×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#416×C₇₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×#103×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉×#2317	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#2043	C₂	1	4	yes	maximal, complemented
8	C₇₉×#2042	C₂	1	4	yes	maximal, complemented
9	C₇₉×#1729	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₇₉	C₂²	1	1	yes	characteristic
11	C₂³×Q₈×C₇₉	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₇₉	C₂²	1	1	yes	characteristic
14	#536×C₇₉	—	2	4	no	—
15	#536×C₇₉	—	2	4	no	—
16	C₂×C₄⋊Q₈×C₇₉	C₂²	1	2	yes	—
17	C₂×#124×C₇₉	C₂²	1	2	yes	—
18	C₂×#123×C₇₉	—	2	2	no	—
19	C₂×C₂²⋊Q₈×C₇₉	—	2	1	no	—
20	C₂×C₂²⋊Q₈×C₇₉	—	2	1	no	—
21	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
22	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
24	#419×C₇₉	—	2	4	no	—
25	#417×C₇₉	—	2	4	no	—
26	#416×C₇₉	—	2	4	no	—
27	C₂×#103×C₇₉	—	2	4	no	—
28	C₂×#103×C₇₉	C₂²	1	4	yes	—
29	C₂×#103×C₇₉	C₂²	1	4	yes	—
30	C₂×#103×C₇₉	C₂²	1	2	yes	—
31	C₂×#103×C₇₉	C₂²	1	2	yes	—
32	C₂×#102×C₇₉	C₂²	1	2	yes	—
33	C₂×#102×C₇₉	C₂²	1	2	yes	—
34	#389×C₇₉	C₂²	1	4	yes	—
35	#385×C₇₉	—	2	2	no	—
36	#384×C₇₉	—	2	1	no	—
37	#382×C₇₉	—	2	1	no	—
38	#336×C₇₉	C₂²	1	4	yes	—
39	C₂×#41×C₇₉	—	2	2	no	—
40	C₂×#41×C₇₉	—	2	2	no	—
41	C₂×#41×C₇₉	—	2	2	no	—
42	C₂×#41×C₇₉	—	2	2	no	—
43	C₂×#41×C₇₉	—	2	2	no	—
44	C₂×#41×C₇₉	D₄	1	4	yes	—
45	C₂²×Q₈×C₇₉	—	2	1	no	—
46	C₂²×Q₈×C₇₉	—	2	2	no	—
47	C₂²×Q₈×C₇₉	—	2	2	no	—
48	C₂²×Q₈×C₇₉	—	2	2	no	—
49	C₂²×Q₈×C₇₉	—	2	2	no	—
50	C₂²×Q₈×C₇₉	—	2	2	no	—
51	C₂²×Q₈×C₇₉	D₄	1	4	yes	—
52	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
53	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
54	C₂²×D₄×C₇₉	—	2	1	no	—
55	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₇₉	—	2	1	no	—
57	C₂³×C₄×C₇₉	—	2	1	no	—
58	C₂³×C₄×C₇₉	—	2	1	no	—
59	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
60	C₂×M₁₆×C₇₉	—	2	2	no	—
61	C₂×M₁₆×C₇₉	—	2	2	no	—
62	C₂×M₁₆×C₇₉	—	2	2	no	—
63	C₂²×C₈×C₇₉	—	2	2	no	—
64	C₂²×C₈×C₇₉	—	2	2	no	—
65	C₂²×C₈×C₇₉	—	2	2	no	—
66	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
67	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
68	C₄⋊Q₈×C₇₉	—	2	4	no	—
69	C₄⋊Q₈×C₇₉	—	2	4	no	—
70	#124×C₇₉	—	2	4	no	—
71	#124×C₇₉	—	2	4	no	—
72	#123×C₇₉	—	2	16	no	—
73	C₂²⋊Q₈×C₇₉	—	2	8	no	—
74	C₂²⋊Q₈×C₇₉	—	2	8	no	—
75	#117×C₇₉	—	2	2	no	—
76	#117×C₇₉	—	2	2	no	—
77	#117×C₇₉	—	2	2	no	—
78	#117×C₇₉	D₄	1	4	yes	—
79	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
80	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
81	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
82	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
83	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
85	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
89	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₇₉	D₄	1	2	yes	—
93	C₂×C₄²×C₇₉	—	2	1	no	—
94	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
95	#103×C₇₉	—	2	4	no	—
96	#103×C₇₉	—	2	8	no	—
97	#103×C₇₉	—	2	8	no	—
98	#103×C₇₉	—	2	4	no	—
99	#102×C₇₉	—	2	4	no	—
100	#102×C₇₉	—	2	4	no	—
101	#95×C₇₉	—	2	4	no	—
102	C₂⁴×C₇₉	—	2	1	no	—
103	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
104	#41×C₇₉	—	2	8	no	—
105	#41×C₇₉	—	2	8	no	—
106	#41×C₇₉	—	4	4	no	—
107	#41×C₇₉	—	4	4	no	—
108	C₂×Q₈×C₇₉	—	2	4	no	—
109	C₂×Q₈×C₇₉	—	2	2	no	—
110	C₂×Q₈×C₇₉	—	2	1	no	—
111	C₂×Q₈×C₇₉	—	2	8	no	—
112	C₂×Q₈×C₇₉	—	2	8	no	—
113	C₂×Q₈×C₇₉	—	2	2	no	—
114	C₂×Q₈×C₇₉	—	2	1	no	—
115	C₂×Q₈×C₇₉	—	2	2	no	—
116	C₂×Q₈×C₇₉	—	2	2	no	—
117	C₂×Q₈×C₇₉	—	2	2	no	—
118	C₂×Q₈×C₇₉	—	2	1	no	—
119	C₂×Q₈×C₇₉	—	2	1	no	—
120	C₂×Q₈×C₇₉	—	2	1	no	—
121	C₂×Q₈×C₇₉	—	4	2	no	—
122	C₂×Q₈×C₇₉	—	4	4	no	—
123	C₂×Q₈×C₇₉	—	4	4	no	—
124	C₂×Q₈×C₇₉	—	4	2	no	—
125	C₂×Q₈×C₇₉	C₂×D₄	1	4	yes	—
126	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
127	C₂×D₄×C₇₉	—	2	4	no	—
128	C₂×D₄×C₇₉	—	2	1	no	—
129	C₂×D₄×C₇₉	—	2	1	no	—
130	C₂×D₄×C₇₉	—	2	1	no	—
131	C₂×D₄×C₇₉	—	2	1	no	—
132	C₂×D₄×C₇₉	—	2	1	no	—
133	C₂×D₄×C₇₉	—	4	2	no	—
134	C₂×D₄×C₇₉	—	4	2	no	—
135	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₇₉	—	2	4	no	—
137	C₂²×C₄×C₇₉	—	2	2	no	—
138	C₂²×C₄×C₇₉	—	2	2	no	—
139	C₂²×C₄×C₇₉	—	2	1	no	—
140	C₂²×C₄×C₇₉	—	2	4	no	—
141	C₂²×C₄×C₇₉	—	2	2	no	—
142	C₂²×C₄×C₇₉	—	4	2	no	—
143	C₂²×C₄×C₇₉	—	4	2	no	—
144	C₂²×C₄×C₇₉	—	4	2	no	—
145	C₂²×C₄×C₇₉	—	4	2	no	—
146	C₂²×C₄×C₇₉	—	4	2	no	—
147	C₂²×C₄×C₇₉	—	8	2	no	—
148	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₇₉	#41	1	2	yes	—
155	C₂²×C₄×C₇₉	#41	1	2	yes	—
156	C₂²×C₄×C₇₉	#41	1	2	yes	—
157	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
158	M₁₆×C₇₉	—	4	4	no	—
159	C₂×C₈×C₇₉	—	2	2	no	—
160	C₂×C₈×C₇₉	—	2	2	no	—
161	C₂×C₈×C₇₉	—	2	2	no	—
162	C₂×C₈×C₇₉	—	2	2	no	—
163	C₂×C₈×C₇₉	—	2	2	no	—
164	C₂×C₈×C₇₉	—	2	2	no	—
165	C₂×C₈×C₇₉	—	4	4	no	—
166	C₄⋊C₄×C₇₉	—	2	8	no	—
167	C₄⋊C₄×C₇₉	—	2	8	no	—
168	C₄⋊C₄×C₇₉	—	2	2	no	—
169	C₄⋊C₄×C₇₉	—	2	2	no	—
170	C₄⋊C₄×C₇₉	—	2	2	no	—
171	C₄⋊C₄×C₇₉	—	2	2	no	—
172	C₄⋊C₄×C₇₉	—	2	2	no	—
173	C₄⋊C₄×C₇₉	—	4	2	no	—
174	C₄⋊C₄×C₇₉	—	8	4	no	—
175	C₄⋊C₄×C₇₉	C₂×D₄	1	4	yes	—
176	C₂²⋊C₄×C₇₉	—	2	8	no	—
177	C₂²⋊C₄×C₇₉	—	2	8	no	—
178	C₂²⋊C₄×C₇₉	—	2	4	no	—
179	C₂²⋊C₄×C₇₉	—	2	4	no	—
180	C₄²×C₇₉	—	2	4	no	—
181	C₄²×C₇₉	—	2	2	no	—
182	C₄²×C₇₉	—	2	2	no	—
183	C₂³×C₇₉	—	2	2	no	—
184	C₂³×C₇₉	—	2	2	no	—
185	C₂³×C₇₉	—	2	2	no	—
186	C₂³×C₇₉	—	4	1	no	—
187	C₂³×C₇₉	—	4	1	no	—
188	C₂³×C₇₉	—	4	2	no	—
189	C₂³×C₇₉	—	4	2	no	—
190	C₂³×C₇₉	#120	1	2	yes	—
191	C₂³×C₇₉	#121	1	2	yes	—
192	C₂³×C₇₉	#124	1	2	yes	—
193	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
194	Q₈×C₇₉	—	2	4	no	—
195	Q₈×C₇₉	—	2	2	no	—
196	Q₈×C₇₉	—	2	4	no	—
197	Q₈×C₇₉	—	2	2	no	—
198	Q₈×C₇₉	—	4	2	no	—
199	Q₈×C₇₉	—	4	1	no	—
200	Q₈×C₇₉	—	4	2	no	—
201	Q₈×C₇₉	—	4	1	no	—
202	Q₈×C₇₉	—	4	8	no	—
203	D₄×C₇₉	—	2	2	no	—
204	D₄×C₇₉	—	2	2	no	—
205	D₄×C₇₉	—	4	8	no	—
206	D₄×C₇₉	—	4	1	no	—
207	D₄×C₇₉	—	4	1	no	—
208	C₂×C₄×C₇₉	—	2	2	no	—
209	C₂×C₄×C₇₉	—	2	2	no	—
210	C₂×C₄×C₇₉	—	2	4	no	—
211	C₂×C₄×C₇₉	—	2	2	no	—
212	C₂×C₄×C₇₉	—	2	4	no	—
213	C₂×C₄×C₇₉	—	2	4	no	—
214	C₂×C₄×C₇₉	—	2	4	no	—
215	C₂×C₄×C₇₉	—	4	1	no	—
216	C₂×C₄×C₇₉	—	4	2	no	—
217	C₂×C₄×C₇₉	—	4	1	no	—
218	C₂×C₄×C₇₉	—	4	2	no	—
219	C₂×C₄×C₇₉	—	4	2	no	—
220	C₂×C₄×C₇₉	—	4	2	no	—
221	C₂×C₄×C₇₉	—	4	8	no	—
222	C₂×C₄×C₇₉	—	4	8	no	—
223	C₂×C₄×C₇₉	—	4	2	no	—
224	C₂×C₄×C₇₉	—	4	4	no	—
225	C₂×C₄×C₇₉	—	8	4	no	—
226	C₂×C₄×C₇₉	#120	1	2	yes	—
227	C₂×C₄×C₇₉	#121	1	4	yes	—
228	C₂×C₄×C₇₉	#121	1	4	yes	—
229	C₂×C₄×C₇₉	#121	1	2	yes	—
230	C₂×C₄×C₇₉	#123	1	4	yes	—
231	C₂×C₄×C₇₉	#123	1	4	yes	—
232	C₂×C₄×C₇₉	#124	1	2	yes	—
233	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
238	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
239	C₈×C₇₉	—	4	2	no	—
240	C₈×C₇₉	—	4	2	no	—
241	C₂²×C₇₉	—	2	4	no	—
242	C₂²×C₇₉	—	2	2	no	—
243	C₂²×C₇₉	—	2	2	no	—
244	C₂²×C₇₉	—	2	4	no	—
245	C₂²×C₇₉	—	4	2	no	—
246	C₂²×C₇₉	—	4	2	no	—
247	C₂²×C₇₉	—	4	2	no	—
248	C₂²×C₇₉	—	8	2	no	—
249	C₂²×C₇₉	—	8	2	no	—
250	C₂²×C₇₉	#394	1	4	yes	—
251	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
252	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
253	C₂²×C₇₉	C₂×#124	1	1	yes	characteristic
254	C₂²×C₇₉	#577	1	2	yes	—
255	C₂²×C₇₉	#578	1	2	yes	—
256	C₄×C₇₉	—	4	2	no	—
257	C₄×C₇₉	—	4	4	no	—
258	C₄×C₇₉	—	4	2	no	—
259	C₄×C₇₉	—	4	2	no	—
260	C₄×C₇₉	—	4	4	no	—
261	C₄×C₇₉	—	8	2	no	—
262	C₄×C₇₉	#394	1	4	yes	—
263	C₄×C₇₉	C₂×#121	1	1	yes	characteristic
264	C₄×C₇₉	C₂×#121	1	1	yes	characteristic
265	C₄×C₇₉	C₂×#123	1	1	yes	characteristic
266	C₄×C₇₉	C₂×#123	1	1	yes	characteristic
267	#23510	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
268	C₂×C₇₉	—	2	4	no	—
269	C₂×C₇₉	—	8	2	no	—
270	C₂×C₇₉	C₂×#394	1	1	yes	characteristic
271	C₂×C₇₉	#3010	1	1	yes	characteristic
272	C₂×C₇₉	#3011	1	1	yes	characteristic
273	C₂×C₇₉	#3046	1	2	yes	—
274	C₂×C₇₉	#3137	1	2	yes	—
275	C₂×#536	C₂×C₇₉	1	1	yes	characteristic
276	C₂×#417	C₂×C₇₉	1	1	yes	characteristic
277	C₂×#419	C₂×C₇₉	1	1	yes	characteristic, complemented
278	C₂×#416	C₂×C₇₉	1	1	yes	characteristic
279	C₂²×#103	C₂×C₇₉	1	1	yes	characteristic, complemented
280	#2317	C₂×C₇₉	1	1	yes	characteristic, complemented
281	#2043	C₂×C₇₉	1	4	yes	complemented
282	#2042	C₂×C₇₉	1	4	yes	complemented
283	#1729	C₂×C₇₉	1	1	yes	characteristic, complemented
284	C₇₉	#23510	1	1	yes	characteristic, direct product factor, Sylow
285	C₂²×#41	C₂²×C₇₉	1	1	yes	characteristic
286	C₂³×Q₈	C₂²×C₇₉	1	1	yes	characteristic
287	C₂²×M₁₆	C₂²×C₇₉	1	1	yes	characteristic
288	C₂³×C₈	C₂²×C₇₉	1	1	yes	characteristic
289	#536	—	2	4	no	—
290	#536	—	2	4	no	—
291	C₂×C₄⋊Q₈	C₂²×C₇₉	1	2	yes	—
292	C₂×#124	C₂²×C₇₉	1	2	yes	—
293	C₂×#123	—	2	2	no	—
294	C₂×C₂²⋊Q₈	—	2	1	no	—
295	C₂×C₂²⋊Q₈	—	2	1	no	—
296	C₂×#117	C₂²×C₇₉	1	1	yes	characteristic
297	C₂×#117	C₂²×C₇₉	1	1	yes	characteristic
298	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
299	#419	—	2	4	no	—
300	#417	—	2	4	no	—
301	#416	—	2	4	no	—
302	C₂×#103	—	2	4	no	—
303	C₂×#103	C₂²×C₇₉	1	4	yes	—
304	C₂×#103	C₂²×C₇₉	1	2	yes	—
305	C₂×#103	C₂²×C₇₉	1	4	yes	—
306	C₂×#103	C₂²×C₇₉	1	2	yes	—
307	C₂×#102	C₂²×C₇₉	1	2	yes	—
308	C₂×#102	C₂²×C₇₉	1	2	yes	—
309	#389	C₂²×C₇₉	1	4	yes	—
310	#385	—	2	2	no	—
311	#384	—	2	1	no	—
312	#382	—	2	1	no	—
313	#336	C₂²×C₇₉	1	4	yes	—
314	C₂×#41	—	2	2	no	—
315	C₂×#41	—	2	2	no	—
316	C₂×#41	—	2	2	no	—
317	C₂×#41	—	2	2	no	—
318	C₂×#41	—	2	2	no	—
319	C₂×#41	D₄×C₇₉	1	4	yes	—
320	C₂²×Q₈	—	2	1	no	—
321	C₂²×Q₈	—	2	2	no	—
322	C₂²×Q₈	—	2	2	no	—
323	C₂²×Q₈	—	2	2	no	—
324	C₂²×Q₈	—	2	2	no	—
325	C₂²×Q₈	—	2	2	no	—
326	C₂²×Q₈	D₄×C₇₉	1	4	yes	—
327	C₂²×Q₈	C₂³×C₇₉	1	2	yes	—
328	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
329	C₂²×D₄	—	2	1	no	—
330	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
331	C₂³×C₄	—	2	1	no	—
332	C₂³×C₄	—	2	1	no	—
333	C₂³×C₄	—	2	1	no	—
334	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
335	C₂×M₁₆	—	2	2	no	—
336	C₂×M₁₆	—	2	2	no	—
337	C₂×M₁₆	—	2	2	no	—
338	C₂²×C₈	—	2	2	no	—
339	C₂²×C₈	—	2	2	no	—
340	C₂²×C₈	—	2	2	no	—
341	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
342	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
343	C₄⋊Q₈	—	2	4	no	—
344	C₄⋊Q₈	—	2	4	no	—
345	#124	—	2	4	no	—
346	#124	—	2	4	no	—
347	#123	—	2	16	no	—
348	C₂²⋊Q₈	—	2	8	no	—
349	C₂²⋊Q₈	—	2	8	no	—
350	#117	—	2	2	no	—
351	#117	—	2	2	no	—
352	#117	—	2	2	no	—
353	#117	D₄×C₇₉	1	4	yes	—
354	C₂×C₄⋊C₄	—	2	2	no	—
355	C₂×C₄⋊C₄	—	2	2	no	—
356	C₂×C₄⋊C₄	—	2	2	no	—
357	C₂×C₄⋊C₄	—	2	2	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	4	no	—
360	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
361	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
363	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₂²⋊C₄	—	2	2	no	—
366	C₂×C₂²⋊C₄	—	2	2	no	—
367	C₂×C₂²⋊C₄	D₄×C₇₉	1	2	yes	—
368	C₂×C₄²	—	2	1	no	—
369	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
370	#103	—	2	8	no	—
371	#103	—	2	4	no	—
372	#103	—	2	4	no	—
373	#103	—	2	8	no	—
374	#102	—	2	4	no	—
375	#102	—	2	4	no	—
376	#95	—	2	4	no	—
377	C₂⁴	—	2	1	no	—
378	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
379	#41	—	2	8	no	—
380	#41	—	2	8	no	—
381	#41	—	4	4	no	—
382	#41	—	4	4	no	—
383	C₂×Q₈	—	2	4	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	2	1	no	—
386	C₂×Q₈	—	2	8	no	—
387	C₂×Q₈	—	2	8	no	—
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	—	2	1	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	2	no	—
392	C₂×Q₈	—	2	2	no	—
393	C₂×Q₈	—	2	1	no	—
394	C₂×Q₈	—	2	1	no	—
395	C₂×Q₈	—	2	1	no	—
396	C₂×Q₈	—	4	2	no	—
397	C₂×Q₈	—	4	4	no	—
398	C₂×Q₈	—	4	4	no	—
399	C₂×Q₈	—	4	2	no	—
400	C₂×Q₈	C₂×D₄×C₇₉	1	4	yes	—
401	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
402	C₂×D₄	—	2	4	no	—
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	4	2	no	—
409	C₂×D₄	—	4	2	no	—
410	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	4	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	4	2	no	—
418	C₂²×C₄	—	4	2	no	—
419	C₂²×C₄	—	4	2	no	—
420	C₂²×C₄	—	4	2	no	—
421	C₂²×C₄	—	4	2	no	—
422	C₂²×C₄	—	8	2	no	—
423	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
424	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
425	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
426	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
427	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
428	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
429	C₂²×C₄	#41×C₇₉	1	2	yes	—
430	C₂²×C₄	#41×C₇₉	1	2	yes	—
431	C₂²×C₄	#41×C₇₉	1	2	yes	—
432	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
433	M₁₆	—	4	4	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	4	4	no	—
441	C₄⋊C₄	—	2	8	no	—
442	C₄⋊C₄	—	2	8	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	4	2	no	—
449	C₄⋊C₄	—	8	4	no	—
450	C₄⋊C₄	C₂×D₄×C₇₉	1	4	yes	—
451	C₂²⋊C₄	—	2	8	no	—
452	C₂²⋊C₄	—	2	8	no	—
453	C₂²⋊C₄	—	2	4	no	—
454	C₂²⋊C₄	—	2	4	no	—
455	C₄²	—	2	4	no	—
456	C₄²	—	2	2	no	—
457	C₄²	—	2	2	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	4	1	no	—
462	C₂³	—	4	1	no	—
463	C₂³	—	4	2	no	—
464	C₂³	—	4	2	no	—
465	C₂³	#120×C₇₉	1	2	yes	—
466	C₂³	#121×C₇₉	1	2	yes	—
467	C₂³	#124×C₇₉	1	2	yes	—
468	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
469	Q₈	—	2	4	no	—
470	Q₈	—	2	2	no	—
471	Q₈	—	2	4	no	—
472	Q₈	—	2	2	no	—
473	Q₈	—	4	2	no	—
474	Q₈	—	4	1	no	—
475	Q₈	—	4	2	no	—
476	Q₈	—	4	1	no	—
477	Q₈	—	4	8	no	—
478	D₄	—	2	2	no	—
479	D₄	—	2	2	no	—
480	D₄	—	4	8	no	—
481	D₄	—	4	1	no	—
482	D₄	—	4	1	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	8	no	—
497	C₂×C₄	—	4	8	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	4	no	—
500	C₂×C₄	—	8	4	no	—
501	C₂×C₄	#120×C₇₉	1	2	yes	—
502	C₂×C₄	#121×C₇₉	1	4	yes	—
503	C₂×C₄	#121×C₇₉	1	4	yes	—
504	C₂×C₄	#121×C₇₉	1	2	yes	—
505	C₂×C₄	#123×C₇₉	1	4	yes	—
506	C₂×C₄	#123×C₇₉	1	4	yes	—
507	C₂×C₄	#124×C₇₉	1	2	yes	—
508	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
509	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
510	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
511	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
512	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
513	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
514	C₈	—	4	2	no	—
515	C₈	—	4	2	no	—
516	C₂²	—	2	4	no	—
517	C₂²	—	2	4	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	8	2	no	—
524	C₂²	—	8	2	no	—
525	C₂²	#394×C₇₉	1	4	yes	—
526	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
527	C₂²	C₂×#121×C₇₉	1	1	yes	characteristic
528	C₂²	C₂×#124×C₇₉	1	1	yes	characteristic
529	C₂²	#577×C₇₉	1	2	yes	—
530	C₂²	#578×C₇₉	1	2	yes	—
531	C₄	—	4	4	no	—
532	C₄	—	4	2	no	—
533	C₄	—	4	4	no	—
534	C₄	—	4	2	no	—
535	C₄	—	4	2	no	—
536	C₄	—	8	2	no	—
537	C₄	#394×C₇₉	1	4	yes	—
538	C₄	C₂×#121×C₇₉	1	1	yes	characteristic
539	C₄	C₂×#121×C₇₉	1	1	yes	characteristic
540	C₄	C₂×#123×C₇₉	1	1	yes	characteristic
541	C₄	C₂×#123×C₇₉	1	1	yes	characteristic
542	C₂	—	2	4	no	—
543	C₂	—	8	2	no	—
544	C₂	C₂×#394×C₇₉	1	1	yes	characteristic
545	C₂	C₇₉×#3010	1	1	yes	characteristic
546	C₂	C₇₉×#3011	1	1	yes	characteristic
547	C₂	C₇₉×#3046	1	2	yes	—
548	C₂	C₇₉×#3137	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₂²×#41×C₇₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₂×#117×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×#419×C₇₉	C₂	semidirect
5. C₂²×#103×C₇₉	C₂	semidirect
6. C₇₉×#2317	C₂	semidirect
7. C₇₉×#2043	C₂	semidirect
8. C₇₉×#2042	C₂	semidirect
9. C₇₉×#1729	C₂	semidirect
267. #23510	C₇₉	direct (N × H)
277. C₂×#419	C₂×C₇₉	semidirect
279. C₂²×#103	C₂×C₇₉	semidirect
280. #2317	C₂×C₇₉	semidirect
281. #2043	C₂×C₇₉	semidirect
282. #2042	C₂×C₇₉	semidirect
283. #1729	C₂×C₇₉	semidirect
284. C₇₉	#23510	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#536×C₇₉	2
C₂×#417×C₇₉	2
C₂×#419×C₇₉	2
C₂×#416×C₇₉	2
C₂²×#103×C₇₉	2
C₇₉×#2317	2
C₇₉×#2043	2
C₇₉×#2042	2
C₇₉×#1729	2
#23510	79

Subgroups — C79×#23510 #34135199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#23510 #34135199