Subgroups — C₇₉×#23511 #34135200

Order 20224.

1606 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#535×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#417×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#418×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#416×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#102×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉×#2316	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#2042	C₂	1	4	yes	maximal, complemented
8	C₇₉×#2041	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×D₄×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	#535×C₇₉	—	2	4	no	—
15	#535×C₇₉	—	2	4	no	—
16	C₂×#127×C₇₉	C₂²	1	2	yes	—
17	C₂×#124×C₇₉	C₂²	1	2	yes	—
18	C₂×#121×C₇₉	—	2	2	no	—
19	C₂×#120×C₇₉	—	2	2	no	—
20	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
23	#418×C₇₉	—	2	4	no	—
24	#417×C₇₉	—	2	4	no	—
25	#416×C₇₉	—	2	4	no	—
26	C₂×#103×C₇₉	C₂²	1	2	yes	complemented
27	C₂×#103×C₇₉	C₂²	1	2	yes	complemented
28	C₂×#102×C₇₉	—	2	4	no	—
29	C₂×#102×C₇₉	C₂²	1	4	yes	—
30	C₂×#102×C₇₉	C₂²	1	4	yes	—
31	C₂×#102×C₇₉	C₂²	1	2	yes	complemented
32	C₂×#102×C₇₉	C₂²	1	2	yes	complemented
33	#389×C₇₉	—	2	2	no	—
34	#389×C₇₉	C₂²	1	4	yes	complemented
35	#380×C₇₉	—	2	2	no	—
36	#336×C₇₉	C₂²	1	4	yes	complemented
37	C₂⁵×C₇₉	—	2	1	no	—
38	C₂×#41×C₇₉	—	2	2	no	—
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	D₄	1	4	yes	—
44	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₇₉	—	2	1	no	—
46	C₂²×D₄×C₇₉	—	2	2	no	—
47	C₂²×D₄×C₇₉	—	2	1	no	—
48	C₂²×D₄×C₇₉	—	2	2	no	—
49	C₂²×D₄×C₇₉	—	2	4	no	—
50	C₂²×D₄×C₇₉	—	2	2	no	—
51	C₂²×D₄×C₇₉	—	2	2	no	—
52	C₂²×D₄×C₇₉	—	2	2	no	—
53	C₂²×D₄×C₇₉	D₄	1	4	yes	—
54	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
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	C₂³	1	1	yes	characteristic
59	C₂×M₁₆×C₇₉	—	2	2	no	—
60	C₂×M₁₆×C₇₉	—	2	2	no	—
61	C₂×M₁₆×C₇₉	—	2	2	no	—
62	C₂²×C₈×C₇₉	—	2	2	no	—
63	C₂²×C₈×C₇₉	—	2	2	no	—
64	C₂²×C₈×C₇₉	—	2	2	no	—
65	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
66	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
67	#127×C₇₉	—	2	4	no	—
68	#127×C₇₉	—	2	4	no	—
69	#124×C₇₉	—	2	4	no	—
70	#124×C₇₉	—	2	4	no	—
71	#121×C₇₉	—	2	16	no	—
72	#120×C₇₉	—	2	16	no	—
73	#117×C₇₉	—	2	2	no	—
74	#117×C₇₉	—	2	2	no	—
75	#117×C₇₉	—	2	2	no	—
76	#117×C₇₉	—	2	2	no	—
77	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
79	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
80	C₂×C₄⋊C₄×C₇₉	D₄	1	2	yes	—
81	C₂×C₄⋊C₄×C₇₉	D₄	1	4	yes	complemented
82	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
84	C₂×C₂²⋊C₄×C₇₉	—	2	4	no	—
85	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₇₉	D₄	1	2	yes	—
87	C₂×C₄²×C₇₉	—	2	1	no	—
88	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
89	#103×C₇₉	—	2	4	no	—
90	#103×C₇₉	—	2	4	no	—
91	#102×C₇₉	—	2	8	no	—
92	#102×C₇₉	—	2	4	no	—
93	#102×C₇₉	—	2	4	no	—
94	#102×C₇₉	—	2	8	no	—
95	#95×C₇₉	—	2	4	no	—
96	C₂⁴×C₇₉	—	2	2	no	—
97	C₂⁴×C₇₉	—	2	1	no	—
98	C₂⁴×C₇₉	—	2	4	no	—
99	C₂⁴×C₇₉	—	4	2	no	—
100	C₂⁴×C₇₉	—	4	2	no	—
101	C₂⁴×C₇₉	—	8	2	no	—
102	C₂⁴×C₇₉	—	8	2	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	1	no	—
109	C₂×Q₈×C₇₉	—	2	1	no	—
110	C₂×Q₈×C₇₉	—	2	1	no	—
111	C₂×Q₈×C₇₉	—	2	1	no	—
112	C₂×Q₈×C₇₉	—	2	1	no	—
113	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
114	C₂×D₄×C₇₉	—	2	4	no	—
115	C₂×D₄×C₇₉	—	2	16	no	—
116	C₂×D₄×C₇₉	—	2	4	no	—
117	C₂×D₄×C₇₉	—	2	8	no	—
118	C₂×D₄×C₇₉	—	2	8	no	—
119	C₂×D₄×C₇₉	—	2	2	no	—
120	C₂×D₄×C₇₉	—	2	1	no	—
121	C₂×D₄×C₇₉	—	2	2	no	—
122	C₂×D₄×C₇₉	—	2	1	no	—
123	C₂×D₄×C₇₉	—	2	2	no	—
124	C₂×D₄×C₇₉	—	2	2	no	—
125	C₂×D₄×C₇₉	—	2	2	no	—
126	C₂×D₄×C₇₉	—	2	1	no	—
127	C₂×D₄×C₇₉	—	2	1	no	—
128	C₂×D₄×C₇₉	—	2	1	no	—
129	C₂×D₄×C₇₉	—	4	2	no	—
130	C₂×D₄×C₇₉	—	4	2	no	—
131	C₂×D₄×C₇₉	—	4	4	no	—
132	C₂×D₄×C₇₉	—	4	2	no	—
133	C₂×D₄×C₇₉	—	4	4	no	—
134	C₂×D₄×C₇₉	—	4	2	no	—
135	C₂×D₄×C₇₉	—	8	4	no	—
136	C₂×D₄×C₇₉	—	8	4	no	—
137	C₂×D₄×C₇₉	C₂×D₄	1	4	yes	—
138	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₇₉	—	2	2	no	—
140	C₂²×C₄×C₇₉	—	2	1	no	—
141	C₂²×C₄×C₇₉	—	2	4	no	—
142	C₂²×C₄×C₇₉	—	2	4	no	—
143	C₂²×C₄×C₇₉	—	2	2	no	—
144	C₂²×C₄×C₇₉	—	4	2	no	—
145	C₂²×C₄×C₇₉	—	4	2	no	—
146	C₂²×C₄×C₇₉	—	8	2	no	—
147	C₂²×C₄×C₇₉	C₂×D₄	1	4	yes	—
148	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₇₉	#41	1	2	yes	—
153	C₂²×C₄×C₇₉	#41	1	2	yes	—
154	C₂²×C₄×C₇₉	#41	1	2	yes	—
155	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
156	M₁₆×C₇₉	—	4	4	no	—
157	C₂×C₈×C₇₉	—	2	2	no	—
158	C₂×C₈×C₇₉	—	2	2	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	—	4	4	no	—
164	C₄⋊C₄×C₇₉	—	2	4	no	—
165	C₄⋊C₄×C₇₉	—	2	4	no	—
166	C₄⋊C₄×C₇₉	—	2	2	no	—
167	C₄⋊C₄×C₇₉	—	2	2	no	—
168	C₄⋊C₄×C₇₉	—	2	2	no	—
169	C₄⋊C₄×C₇₉	—	8	4	no	—
170	C₄⋊C₄×C₇₉	C₂×D₄	1	4	yes	—
171	C₂²⋊C₄×C₇₉	—	2	16	no	—
172	C₂²⋊C₄×C₇₉	—	2	4	no	—
173	C₂²⋊C₄×C₇₉	—	4	2	no	—
174	C₄²×C₇₉	—	2	2	no	—
175	C₄²×C₇₉	—	2	2	no	—
176	C₄²×C₇₉	—	4	2	no	—
177	C₂³×C₇₉	—	2	2	no	—
178	C₂³×C₇₉	—	2	2	no	—
179	C₂³×C₇₉	—	2	4	no	—
180	C₂³×C₇₉	—	2	2	no	—
181	C₂³×C₇₉	—	4	1	no	—
182	C₂³×C₇₉	—	4	2	no	—
183	C₂³×C₇₉	—	4	1	no	—
184	C₂³×C₇₉	—	4	2	no	—
185	C₂³×C₇₉	—	4	2	no	—
186	C₂³×C₇₉	—	4	4	no	—
187	C₂³×C₇₉	—	4	2	no	—
188	C₂³×C₇₉	—	4	4	no	—
189	C₂³×C₇₉	—	4	8	no	—
190	C₂³×C₇₉	—	8	8	no	—
191	C₂³×C₇₉	—	8	8	no	—
192	C₂³×C₇₉	—	8	4	no	—
193	C₂³×C₇₉	—	8	4	no	—
194	C₂³×C₇₉	#120	1	2	yes	—
195	C₂³×C₇₉	#121	1	2	yes	—
196	C₂³×C₇₉	#124	1	2	yes	—
197	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
198	Q₈×C₇₉	—	2	2	no	—
199	Q₈×C₇₉	—	2	2	no	—
200	Q₈×C₇₉	—	4	1	no	—
201	Q₈×C₇₉	—	4	1	no	—
202	D₄×C₇₉	—	2	4	no	—
203	D₄×C₇₉	—	2	2	no	—
204	D₄×C₇₉	—	2	4	no	—
205	D₄×C₇₉	—	2	2	no	—
206	D₄×C₇₉	—	4	8	no	—
207	D₄×C₇₉	—	4	2	no	—
208	D₄×C₇₉	—	4	1	no	—
209	D₄×C₇₉	—	4	2	no	—
210	D₄×C₇₉	—	4	1	no	—
211	D₄×C₇₉	—	4	8	no	—
212	D₄×C₇₉	—	8	16	no	—
213	C₂×C₄×C₇₉	—	2	4	no	—
214	C₂×C₄×C₇₉	—	2	2	no	—
215	C₂×C₄×C₇₉	—	2	4	no	—
216	C₂×C₄×C₇₉	—	2	4	no	—
217	C₂×C₄×C₇₉	—	2	4	no	—
218	C₂×C₄×C₇₉	—	4	1	no	—
219	C₂×C₄×C₇₉	—	4	1	no	—
220	C₂×C₄×C₇₉	—	4	4	no	—
221	C₂×C₄×C₇₉	—	4	8	no	—
222	C₂×C₄×C₇₉	—	4	2	no	—
223	C₂×C₄×C₇₉	—	4	2	no	—
224	C₂×C₄×C₇₉	—	4	2	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	4	no	—
243	C₂²×C₇₉	—	2	2	no	—
244	C₂²×C₇₉	—	2	2	no	—
245	C₂²×C₇₉	—	4	2	no	—
246	C₂²×C₇₉	—	4	4	no	—
247	C₂²×C₇₉	—	4	4	no	—
248	C₂²×C₇₉	—	4	8	no	—
249	C₂²×C₇₉	—	8	16	no	—
250	C₂²×C₇₉	—	8	2	no	—
251	C₂²×C₇₉	—	8	4	no	—
252	C₂²×C₇₉	—	8	1	no	—
253	C₂²×C₇₉	—	8	2	no	—
254	C₂²×C₇₉	—	8	1	no	—
255	C₂²×C₇₉	—	8	2	no	—
256	C₂²×C₇₉	#394	1	4	yes	—
257	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
258	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
259	C₂²×C₇₉	C₂×#124	1	1	yes	characteristic
260	C₂²×C₇₉	#576	1	2	yes	—
261	C₂²×C₇₉	#577	1	2	yes	—
262	C₄×C₇₉	—	4	2	no	—
263	C₄×C₇₉	—	4	4	no	—
264	C₄×C₇₉	—	4	4	no	—
265	C₄×C₇₉	—	8	2	no	—
266	C₄×C₇₉	#394	1	4	yes	—
267	C₄×C₇₉	C₂×#121	1	1	yes	characteristic
268	C₄×C₇₉	C₂×#121	1	1	yes	characteristic
269	C₄×C₇₉	C₂×#123	1	1	yes	characteristic
270	C₄×C₇₉	C₂×#123	1	1	yes	characteristic
271	#23511	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
272	C₂×C₇₉	—	2	4	no	—
273	C₂×C₇₉	—	8	2	no	—
274	C₂×C₇₉	—	8	4	no	—
275	C₂×C₇₉	C₂×#394	1	1	yes	characteristic
276	C₂×C₇₉	#3012	1	2	yes	—
277	C₂×C₇₉	#3041	1	1	yes	characteristic
278	C₂×C₇₉	#3043	1	1	yes	characteristic
279	C₂×C₇₉	#3136	1	2	yes	—
280	C₂×#535	C₂×C₇₉	1	1	yes	characteristic
281	C₂×#417	C₂×C₇₉	1	1	yes	characteristic, complemented
282	C₂×#418	C₂×C₇₉	1	1	yes	characteristic, complemented
283	C₂×#416	C₂×C₇₉	1	1	yes	characteristic, complemented
284	C₂²×#102	C₂×C₇₉	1	1	yes	characteristic, complemented
285	#2316	C₂×C₇₉	1	1	yes	characteristic, complemented
286	#2042	C₂×C₇₉	1	4	yes	complemented
287	#2041	C₂×C₇₉	1	4	yes	complemented
288	#1729	C₂×C₇₉	1	1	yes	characteristic, complemented
289	C₇₉	#23511	1	1	yes	characteristic, direct product factor, Sylow
290	C₂²×#41	C₂²×C₇₉	1	1	yes	characteristic
291	C₂³×D₄	C₂²×C₇₉	1	1	yes	characteristic
292	C₂²×M₁₆	C₂²×C₇₉	1	1	yes	characteristic
293	C₂³×C₈	C₂²×C₇₉	1	1	yes	characteristic
294	#535	—	2	4	no	—
295	#535	—	2	4	no	—
296	C₂×#127	C₂²×C₇₉	1	2	yes	—
297	C₂×#124	C₂²×C₇₉	1	2	yes	—
298	C₂×#121	—	2	2	no	—
299	C₂×#120	—	2	2	no	—
300	C₂×#117	C₂²×C₇₉	1	1	yes	characteristic
301	C₂×#117	C₂²×C₇₉	1	1	yes	characteristic
302	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
303	#418	—	2	4	no	—
304	#417	—	2	4	no	—
305	#416	—	2	4	no	—
306	C₂×#103	C₂²×C₇₉	1	2	yes	complemented
307	C₂×#103	C₂²×C₇₉	1	2	yes	complemented
308	C₂×#102	—	2	4	no	—
309	C₂×#102	C₂²×C₇₉	1	4	yes	—
310	C₂×#102	C₂²×C₇₉	1	4	yes	—
311	C₂×#102	C₂²×C₇₉	1	2	yes	complemented
312	C₂×#102	C₂²×C₇₉	1	2	yes	complemented
313	#389	—	2	2	no	—
314	#389	C₂²×C₇₉	1	4	yes	complemented
315	#380	—	2	2	no	—
316	#336	C₂²×C₇₉	1	4	yes	complemented
317	C₂⁵	—	2	1	no	—
318	C₂×#41	—	2	2	no	—
319	C₂×#41	—	2	2	no	—
320	C₂×#41	—	2	2	no	—
321	C₂×#41	—	2	2	no	—
322	C₂×#41	—	2	2	no	—
323	C₂×#41	D₄×C₇₉	1	4	yes	—
324	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
325	C₂²×D₄	—	2	1	no	—
326	C₂²×D₄	—	2	2	no	—
327	C₂²×D₄	—	2	1	no	—
328	C₂²×D₄	—	2	2	no	—
329	C₂²×D₄	—	2	4	no	—
330	C₂²×D₄	—	2	2	no	—
331	C₂²×D₄	—	2	2	no	—
332	C₂²×D₄	—	2	2	no	—
333	C₂²×D₄	D₄×C₇₉	1	4	yes	—
334	C₂²×D₄	C₂³×C₇₉	1	2	yes	—
335	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
336	C₂³×C₄	—	2	1	no	—
337	C₂³×C₄	—	2	1	no	—
338	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
339	C₂×M₁₆	—	2	2	no	—
340	C₂×M₁₆	—	2	2	no	—
341	C₂×M₁₆	—	2	2	no	—
342	C₂²×C₈	—	2	2	no	—
343	C₂²×C₈	—	2	2	no	—
344	C₂²×C₈	—	2	2	no	—
345	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
346	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
347	#127	—	2	4	no	—
348	#127	—	2	4	no	—
349	#124	—	2	4	no	—
350	#124	—	2	4	no	—
351	#121	—	2	16	no	—
352	#120	—	2	16	no	—
353	#117	—	2	2	no	—
354	#117	—	2	2	no	—
355	#117	—	2	2	no	—
356	#117	—	2	2	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	2	no	—
359	C₂×C₄⋊C₄	—	2	4	no	—
360	C₂×C₄⋊C₄	D₄×C₇₉	1	2	yes	—
361	C₂×C₄⋊C₄	D₄×C₇₉	1	4	yes	complemented
362	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
363	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
364	C₂×C₂²⋊C₄	—	2	4	no	—
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₂²⋊C₄	D₄×C₇₉	1	2	yes	—
367	C₂×C₄²	—	2	1	no	—
368	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
369	#103	—	2	4	no	—
370	#103	—	2	4	no	—
371	#102	—	2	8	no	—
372	#102	—	2	4	no	—
373	#102	—	2	8	no	—
374	#102	—	2	4	no	—
375	#95	—	2	4	no	—
376	C₂⁴	—	2	2	no	—
377	C₂⁴	—	2	1	no	—
378	C₂⁴	—	2	4	no	—
379	C₂⁴	—	4	2	no	—
380	C₂⁴	—	4	2	no	—
381	C₂⁴	—	8	2	no	—
382	C₂⁴	—	8	2	no	—
383	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
384	#41	—	2	8	no	—
385	#41	—	2	8	no	—
386	#41	—	4	4	no	—
387	#41	—	4	4	no	—
388	C₂×Q₈	—	2	1	no	—
389	C₂×Q₈	—	2	1	no	—
390	C₂×Q₈	—	2	1	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	2	1	no	—
393	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	16	no	—
396	C₂×D₄	—	2	4	no	—
397	C₂×D₄	—	2	8	no	—
398	C₂×D₄	—	2	8	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	1	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	—	4	2	no	—
410	C₂×D₄	—	4	2	no	—
411	C₂×D₄	—	4	4	no	—
412	C₂×D₄	—	4	2	no	—
413	C₂×D₄	—	4	4	no	—
414	C₂×D₄	—	4	2	no	—
415	C₂×D₄	—	8	4	no	—
416	C₂×D₄	—	8	4	no	—
417	C₂×D₄	C₂×D₄×C₇₉	1	4	yes	—
418	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	4	2	no	—
425	C₂²×C₄	—	4	2	no	—
426	C₂²×C₄	—	8	2	no	—
427	C₂²×C₄	C₂×D₄×C₇₉	1	4	yes	—
428	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
430	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
431	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
432	C₂²×C₄	#41×C₇₉	1	2	yes	—
433	C₂²×C₄	#41×C₇₉	1	2	yes	—
434	C₂²×C₄	#41×C₇₉	1	2	yes	—
435	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
436	M₁₆	—	4	4	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	4	4	no	—
444	C₄⋊C₄	—	2	4	no	—
445	C₄⋊C₄	—	2	4	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	8	4	no	—
450	C₄⋊C₄	C₂×D₄×C₇₉	1	4	yes	—
451	C₂²⋊C₄	—	2	16	no	—
452	C₂²⋊C₄	—	2	4	no	—
453	C₂²⋊C₄	—	4	2	no	—
454	C₄²	—	2	2	no	—
455	C₄²	—	2	2	no	—
456	C₄²	—	4	2	no	—
457	C₂³	—	2	2	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	2	4	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	4	1	no	—
462	C₂³	—	4	2	no	—
463	C₂³	—	4	1	no	—
464	C₂³	—	4	2	no	—
465	C₂³	—	4	2	no	—
466	C₂³	—	4	4	no	—
467	C₂³	—	4	2	no	—
468	C₂³	—	4	4	no	—
469	C₂³	—	4	8	no	—
470	C₂³	—	8	8	no	—
471	C₂³	—	8	4	no	—
472	C₂³	—	8	4	no	—
473	C₂³	—	8	8	no	—
474	C₂³	#120×C₇₉	1	2	yes	—
475	C₂³	#121×C₇₉	1	2	yes	—
476	C₂³	#124×C₇₉	1	2	yes	—
477	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
478	Q₈	—	2	2	no	—
479	Q₈	—	2	2	no	—
480	Q₈	—	4	1	no	—
481	Q₈	—	4	1	no	—
482	D₄	—	2	4	no	—
483	D₄	—	2	2	no	—
484	D₄	—	2	4	no	—
485	D₄	—	2	2	no	—
486	D₄	—	4	8	no	—
487	D₄	—	4	2	no	—
488	D₄	—	4	1	no	—
489	D₄	—	4	2	no	—
490	D₄	—	4	1	no	—
491	D₄	—	4	8	no	—
492	D₄	—	8	16	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	4	no	—
501	C₂×C₄	—	4	8	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	8	4	no	—
506	C₂×C₄	#120×C₇₉	1	2	yes	—
507	C₂×C₄	#121×C₇₉	1	4	yes	—
508	C₂×C₄	#121×C₇₉	1	4	yes	—
509	C₂×C₄	#121×C₇₉	1	2	yes	—
510	C₂×C₄	#123×C₇₉	1	4	yes	—
511	C₂×C₄	#123×C₇₉	1	4	yes	—
512	C₂×C₄	#124×C₇₉	1	2	yes	—
513	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
514	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
515	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
516	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
517	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
518	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
519	C₈	—	4	2	no	—
520	C₈	—	4	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	4	no	—
524	C₂²	—	2	4	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	4	no	—
527	C₂²	—	4	4	no	—
528	C₂²	—	4	8	no	—
529	C₂²	—	8	16	no	—
530	C₂²	—	8	2	no	—
531	C₂²	—	8	1	no	—
532	C₂²	—	8	2	no	—
533	C₂²	—	8	1	no	—
534	C₂²	—	8	4	no	—
535	C₂²	—	8	2	no	—
536	C₂²	#394×C₇₉	1	4	yes	—
537	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
538	C₂²	C₂×#121×C₇₉	1	1	yes	characteristic
539	C₂²	C₂×#124×C₇₉	1	1	yes	characteristic
540	C₂²	#576×C₇₉	1	2	yes	—
541	C₂²	#577×C₇₉	1	2	yes	—
542	C₄	—	4	4	no	—
543	C₄	—	4	2	no	—
544	C₄	—	4	4	no	—
545	C₄	—	8	2	no	—
546	C₄	#394×C₇₉	1	4	yes	—
547	C₄	C₂×#121×C₇₉	1	1	yes	characteristic
548	C₄	C₂×#121×C₇₉	1	1	yes	characteristic
549	C₄	C₂×#123×C₇₉	1	1	yes	characteristic
550	C₄	C₂×#123×C₇₉	1	1	yes	characteristic
551	C₂	—	2	4	no	—
552	C₂	—	8	4	no	—
553	C₂	—	8	2	no	—
554	C₂	C₂×#394×C₇₉	1	1	yes	characteristic
555	C₂	C₇₉×#3012	1	2	yes	—
556	C₂	C₇₉×#3041	1	1	yes	characteristic
557	C₂	C₇₉×#3043	1	1	yes	characteristic
558	C₂	C₇₉×#3136	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₂×#535×C₇₉	C₂
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
2. C₂×#417×C₇₉	C₂	semidirect
3. C₂×#418×C₇₉	C₂	semidirect
4. C₂×#416×C₇₉	C₂	semidirect
5. C₂²×#102×C₇₉	C₂	semidirect
6. C₇₉×#2316	C₂	semidirect
7. C₇₉×#2042	C₂	semidirect
8. C₇₉×#2041	C₂	semidirect
9. C₇₉×#1729	C₂	semidirect
26. C₂×#103×C₇₉	C₂²	semidirect
27. C₂×#103×C₇₉	C₂²	semidirect
31. C₂×#102×C₇₉	C₂²	semidirect
32. C₂×#102×C₇₉	C₂²	semidirect
34. #389×C₇₉	C₂²	semidirect
36. #336×C₇₉	C₂²	semidirect
81. C₂×C₄⋊C₄×C₇₉	D₄	semidirect
271. #23511	C₇₉	direct (N × H)
281. C₂×#417	C₂×C₇₉	semidirect
282. C₂×#418	C₂×C₇₉	semidirect
283. C₂×#416	C₂×C₇₉	semidirect
284. C₂²×#102	C₂×C₇₉	semidirect
285. #2316	C₂×C₇₉	semidirect
286. #2042	C₂×C₇₉	semidirect
287. #2041	C₂×C₇₉	semidirect
288. #1729	C₂×C₇₉	semidirect
289. C₇₉	#23511	direct (N × H)
306. C₂×#103	C₂²×C₇₉	semidirect
307. C₂×#103	C₂²×C₇₉	semidirect
311. C₂×#102	C₂²×C₇₉	semidirect
312. C₂×#102	C₂²×C₇₉	semidirect
314. #389	C₂²×C₇₉	semidirect
316. #336	C₂²×C₇₉	semidirect
361. C₂×C₄⋊C₄	D₄×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#535×C₇₉	2
C₂×#417×C₇₉	2
C₂×#418×C₇₉	2
C₂×#416×C₇₉	2
C₂²×#102×C₇₉	2
C₇₉×#2316	2
C₇₉×#2042	2
C₇₉×#2041	2
C₇₉×#1729	2
#23511	79

Subgroups — C79×#23511 #34135200

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#23511 #34135200