Subgroups — C₇₉×#18573 #34130262

Order 20224.

934 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3522	C₂	1	1	yes	maximal, characteristic
2	C₇₉×#3218	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#3141	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#475×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#1645	C₂	1	2	yes	maximal, complemented
6	C₇₉×#1643	C₂	1	2	yes	maximal, complemented
7	C₇₉×#1642	C₂	1	2	yes	maximal, complemented
8	C₇₉×#1640	C₂	1	2	yes	maximal, complemented
9	C₇₉×#1551	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#1491	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1483	C₂	1	1	yes	maximal, characteristic, complemented
12	#559×C₇₉	—	2	1	no	—
13	#559×C₇₉	C₂²	1	1	yes	characteristic
14	Q₈²×C₇₉	C₂²	1	1	yes	characteristic
15	#554×C₇₉	—	2	1	no	—
16	#554×C₇₉	C₂²	1	1	yes	characteristic
17	#550×C₇₉	C₂²	1	1	yes	characteristic
18	#548×C₇₉	—	2	1	no	—
19	#547×C₇₉	—	2	2	no	—
20	#547×C₇₉	—	2	1	no	—
21	#542×C₇₉	—	2	2	no	—
22	#542×C₇₉	—	2	1	no	—
23	#532×C₇₉	—	2	1	no	—
24	#532×C₇₉	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
26	#529×C₇₉	—	2	1	no	—
27	#529×C₇₉	C₂²	1	1	yes	characteristic
28	#520×C₇₉	—	2	1	no	—
29	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
30	#497×C₇₉	—	2	1	no	—
31	#491×C₇₉	—	2	1	no	—
32	#489×C₇₉	—	2	2	no	—
33	#487×C₇₉	C₂²	1	2	yes	—
34	#486×C₇₉	C₂²	1	2	yes	—
35	#475×C₇₉	—	2	1	no	—
36	#475×C₇₉	—	2	1	no	—
37	#475×C₇₉	C₂²	1	2	yes	—
38	#475×C₇₉	C₂²	1	2	yes	—
39	#462×C₇₉	C₂²	1	2	yes	—
40	#461×C₇₉	C₂²	1	2	yes	—
41	#451×C₇₉	—	2	1	no	—
42	#448×C₇₉	—	2	1	no	—
43	#432×C₇₉	C₂²	1	1	yes	characteristic
44	C₂×#106×C₇₉	—	2	1	no	—
45	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
46	#417×C₇₉	—	2	2	no	—
47	C₂×#103×C₇₉	—	2	1	no	—
48	C₄×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
49	#333×C₇₉	C₂²	1	2	yes	—
50	#331×C₇₉	C₂²	1	2	yes	—
51	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	—
52	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	—
53	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	—
54	D₄⋊C₈×C₇₉	C₂²	1	2	yes	—
55	C₂×#41×C₇₉	—	2	2	no	—
56	C₂×#41×C₇₉	—	2	1	no	—
57	C₂×#41×C₇₉	D₄	1	2	yes	—
58	C₂²×Q₈×C₇₉	—	2	1	no	—
59	C₂²×Q₈×C₇₉	D₄	1	1	yes	characteristic
60	C₂×Q₁₆×C₇₉	—	2	2	no	—
61	C₂×SD₁₆×C₇₉	—	2	2	no	—
62	C₂×M₁₆×C₇₉	—	2	1	no	—
63	C₂²×C₈×C₇₉	—	2	1	no	—
64	C₄⋊Q₈×C₇₉	—	2	2	no	—
65	C₄⋊Q₈×C₇₉	—	2	1	no	—
66	C₄⋊Q₈×C₇₉	—	2	1	no	—
67	C₄⋊Q₈×C₇₉	—	2	1	no	—
68	C₄⋊Q₈×C₇₉	—	2	1	no	—
69	C₄⋊Q₈×C₇₉	—	2	1	no	—
70	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
71	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
72	#127×C₇₉	—	2	1	no	—
73	#127×C₇₉	C₂³	1	1	yes	characteristic
74	#126×C₇₉	—	2	2	no	—
75	#126×C₇₉	—	2	1	no	—
76	#125×C₇₉	—	2	1	no	—
77	#125×C₇₉	D₄	1	1	yes	characteristic
78	#124×C₇₉	—	2	2	no	—
79	#124×C₇₉	—	2	2	no	—
80	#124×C₇₉	—	2	1	no	—
81	#124×C₇₉	—	2	1	no	—
82	#124×C₇₉	D₄	1	2	yes	—
83	#124×C₇₉	D₄	1	1	yes	characteristic
84	#123×C₇₉	—	2	2	no	—
85	#123×C₇₉	—	2	2	no	—
86	#123×C₇₉	—	2	2	no	—
87	#123×C₇₉	—	2	2	no	—
88	#123×C₇₉	—	2	1	no	—
89	C₂²⋊Q₈×C₇₉	—	2	2	no	—
90	C₂²⋊Q₈×C₇₉	—	2	2	no	—
91	C₂²⋊Q₈×C₇₉	—	2	2	no	—
92	C₂²⋊Q₈×C₇₉	—	2	2	no	—
93	C₂²⋊Q₈×C₇₉	—	2	1	no	—
94	C₂²⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
95	#121×C₇₉	—	2	2	no	—
96	#121×C₇₉	—	2	2	no	—
97	#121×C₇₉	—	2	1	no	—
98	#121×C₇₉	—	2	1	no	—
99	#121×C₇₉	—	2	1	no	—
100	#121×C₇₉	D₄	1	1	yes	characteristic
101	C₄×Q₈×C₇₉	—	2	1	no	—
102	C₄×Q₈×C₇₉	—	2	1	no	—
103	C₄×Q₈×C₇₉	—	2	1	no	—
104	C₄×Q₈×C₇₉	—	2	1	no	—
105	C₄×Q₈×C₇₉	D₄	1	1	yes	characteristic
106	C₄×Q₈×C₇₉	D₄	1	1	yes	characteristic
107	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
108	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
109	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
110	C₄×D₄×C₇₉	—	2	2	no	—
111	C₄×D₄×C₇₉	—	2	2	no	—
112	C₄×D₄×C₇₉	—	2	2	no	—
113	C₄×D₄×C₇₉	—	2	1	no	—
114	C₄×D₄×C₇₉	—	2	1	no	—
115	C₄×D₄×C₇₉	—	2	1	no	—
116	C₄×D₄×C₇₉	—	2	1	no	—
117	C₄×D₄×C₇₉	—	2	1	no	—
118	C₄×D₄×C₇₉	—	2	1	no	—
119	C₄×D₄×C₇₉	—	2	1	no	—
120	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
121	#117×C₇₉	—	2	2	no	—
122	#117×C₇₉	—	2	1	no	—
123	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
124	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
125	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
126	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
127	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
128	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
129	C₂×C₄²×C₇₉	—	2	1	no	—
130	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
131	#106×C₇₉	—	2	2	no	—
132	#106×C₇₉	—	2	2	no	—
133	C₄⋊C₈×C₇₉	—	2	1	no	—
134	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
135	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
136	#103×C₇₉	—	2	4	no	—
137	#103×C₇₉	—	2	2	no	—
138	#103×C₇₉	—	2	2	no	—
139	#103×C₇₉	—	2	2	no	—
140	#103×C₇₉	—	2	2	no	—
141	#102×C₇₉	—	2	4	no	—
142	C₂²⋊C₈×C₇₉	—	2	1	no	—
143	#97×C₇₉	—	2	1	no	—
144	#97×C₇₉	—	2	1	no	—
145	C₄×C₈×C₇₉	C₂³	1	2	yes	—
146	#41×C₇₉	—	4	4	no	—
147	#41×C₇₉	—	4	2	no	—
148	#41×C₇₉	—	4	2	no	—
149	#41×C₇₉	—	8	4	no	—
150	C₂×Q₈×C₇₉	—	2	2	no	—
151	C₂×Q₈×C₇₉	—	2	1	no	—
152	C₂×Q₈×C₇₉	—	2	2	no	—
153	C₂×Q₈×C₇₉	—	2	2	no	—
154	C₂×Q₈×C₇₉	—	4	1	no	—
155	C₂×Q₈×C₇₉	—	4	1	no	—
156	C₂×Q₈×C₇₉	—	8	2	no	—
157	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
158	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
159	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
160	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
161	C₂×D₄×C₇₉	—	2	2	no	—
162	C₂×D₄×C₇₉	—	2	2	no	—
163	C₂×D₄×C₇₉	—	2	1	no	—
164	C₂×D₄×C₇₉	—	2	2	no	—
165	C₂×D₄×C₇₉	—	2	1	no	—
166	C₂×D₄×C₇₉	—	2	1	no	—
167	C₂×D₄×C₇₉	C₂×D₄	1	1	yes	characteristic
168	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
169	C₂²×C₄×C₇₉	—	2	2	no	—
170	C₂²×C₄×C₇₉	—	2	1	no	—
171	C₂²×C₄×C₇₉	—	2	1	no	—
172	C₂²×C₄×C₇₉	—	2	2	no	—
173	C₂²×C₄×C₇₉	—	2	2	no	—
174	C₂²×C₄×C₇₉	—	2	1	no	—
175	C₂²×C₄×C₇₉	—	2	2	no	—
176	C₂²×C₄×C₇₉	—	4	1	no	—
177	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
180	Q₁₆×C₇₉	—	8	2	no	—
181	SD₁₆×C₇₉	—	8	2	no	—
182	M₁₆×C₇₉	—	4	2	no	—
183	C₂×C₈×C₇₉	—	2	2	no	—
184	C₂×C₈×C₇₉	—	2	2	no	—
185	C₂×C₈×C₇₉	—	2	2	no	—
186	C₂×C₈×C₇₉	—	4	2	no	—
187	C₄⋊C₄×C₇₉	—	2	2	no	—
188	C₄⋊C₄×C₇₉	—	2	2	no	—
189	C₄⋊C₄×C₇₉	—	2	2	no	—
190	C₄⋊C₄×C₇₉	—	2	2	no	—
191	C₄⋊C₄×C₇₉	—	2	1	no	—
192	C₄⋊C₄×C₇₉	—	2	1	no	—
193	C₄⋊C₄×C₇₉	—	2	1	no	—
194	C₄⋊C₄×C₇₉	—	2	1	no	—
195	C₄⋊C₄×C₇₉	—	2	1	no	—
196	C₄⋊C₄×C₇₉	—	2	1	no	—
197	C₄⋊C₄×C₇₉	—	2	1	no	—
198	C₄⋊C₄×C₇₉	—	2	1	no	—
199	C₄⋊C₄×C₇₉	—	2	1	no	—
200	C₄⋊C₄×C₇₉	—	2	1	no	—
201	C₄⋊C₄×C₇₉	—	2	1	no	—
202	C₄⋊C₄×C₇₉	—	2	2	no	—
203	C₄⋊C₄×C₇₉	—	2	2	no	—
204	C₄⋊C₄×C₇₉	—	4	1	no	—
205	C₄⋊C₄×C₇₉	—	4	1	no	—
206	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
207	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
208	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
209	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
210	C₂²⋊C₄×C₇₉	—	2	2	no	—
211	C₂²⋊C₄×C₇₉	—	2	2	no	—
212	C₂²⋊C₄×C₇₉	—	2	2	no	—
213	C₂²⋊C₄×C₇₉	—	2	2	no	—
214	C₂²⋊C₄×C₇₉	—	2	2	no	—
215	C₂²⋊C₄×C₇₉	—	2	1	no	—
216	C₂²⋊C₄×C₇₉	—	2	2	no	—
217	C₂²⋊C₄×C₇₉	—	2	1	no	—
218	C₂²⋊C₄×C₇₉	—	2	1	no	—
219	C₂²⋊C₄×C₇₉	—	2	2	no	—
220	C₂²⋊C₄×C₇₉	—	2	1	no	—
221	C₂²⋊C₄×C₇₉	—	2	1	no	—
222	C₄²×C₇₉	—	2	2	no	—
223	C₄²×C₇₉	—	2	1	no	—
224	C₄²×C₇₉	—	2	1	no	—
225	C₄²×C₇₉	—	2	1	no	—
226	C₄²×C₇₉	—	2	1	no	—
227	C₄²×C₇₉	—	2	1	no	—
228	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
229	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
230	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
231	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
232	C₂³×C₇₉	—	2	1	no	—
233	C₂³×C₇₉	—	2	2	no	—
234	C₂³×C₇₉	#120	1	1	yes	characteristic
235	Q₈×C₇₉	—	2	1	no	—
236	Q₈×C₇₉	—	2	1	no	—
237	Q₈×C₇₉	—	2	1	no	—
238	Q₈×C₇₉	—	2	2	no	—
239	Q₈×C₇₉	—	4	2	no	—
240	Q₈×C₇₉	—	4	2	no	—
241	Q₈×C₇₉	—	4	2	no	—
242	Q₈×C₇₉	—	4	2	no	—
243	Q₈×C₇₉	—	8	2	no	—
244	Q₈×C₇₉	—	8	2	no	—
245	Q₈×C₇₉	#137	1	2	yes	—
246	D₄×C₇₉	—	2	2	no	—
247	D₄×C₇₉	—	4	2	no	—
248	D₄×C₇₉	—	4	4	no	—
249	D₄×C₇₉	—	4	4	no	—
250	D₄×C₇₉	—	4	2	no	—
251	D₄×C₇₉	—	4	1	no	—
252	D₄×C₇₉	—	4	1	no	—
253	D₄×C₇₉	—	4	2	no	—
254	D₄×C₇₉	—	8	2	no	—
255	C₂×C₄×C₇₉	—	2	1	no	—
256	C₂×C₄×C₇₉	—	2	2	no	—
257	C₂×C₄×C₇₉	—	2	1	no	—
258	C₂×C₄×C₇₉	—	2	1	no	—
259	C₂×C₄×C₇₉	—	2	2	no	—
260	C₂×C₄×C₇₉	—	2	1	no	—
261	C₂×C₄×C₇₉	—	2	1	no	—
262	C₂×C₄×C₇₉	—	2	1	no	—
263	C₂×C₄×C₇₉	—	2	1	no	—
264	C₂×C₄×C₇₉	—	2	2	no	—
265	C₂×C₄×C₇₉	—	2	1	no	—
266	C₂×C₄×C₇₉	—	2	1	no	—
267	C₂×C₄×C₇₉	—	4	2	no	—
268	C₂×C₄×C₇₉	—	4	4	no	—
269	C₂×C₄×C₇₉	—	4	2	no	—
270	C₂×C₄×C₇₉	—	4	1	no	—
271	C₂×C₄×C₇₉	—	4	1	no	—
272	C₂×C₄×C₇₉	—	4	2	no	—
273	C₂×C₄×C₇₉	—	8	2	no	—
274	C₂×C₄×C₇₉	—	8	2	no	—
275	C₂×C₄×C₇₉	—	8	2	no	—
276	C₂×C₄×C₇₉	—	8	2	no	—
277	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
278	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
279	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
280	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
281	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
283	C₈×C₇₉	—	4	2	no	—
284	C₈×C₇₉	—	4	2	no	—
285	C₈×C₇₉	—	4	2	no	—
286	C₂²×C₇₉	—	2	1	no	—
287	C₂²×C₇₉	—	2	1	no	—
288	C₂²×C₇₉	—	4	2	no	—
289	C₂²×C₇₉	—	4	1	no	—
290	C₂²×C₇₉	—	4	1	no	—
291	C₂²×C₇₉	—	4	2	no	—
292	C₂²×C₇₉	—	4	2	no	—
293	C₂²×C₇₉	—	4	1	no	—
294	C₂²×C₇₉	#455	1	2	yes	—
295	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
296	C₄×C₇₉	—	2	1	no	—
297	C₄×C₇₉	—	2	2	no	—
298	C₄×C₇₉	—	2	1	no	—
299	C₄×C₇₉	—	2	1	no	—
300	C₄×C₇₉	—	2	1	no	—
301	C₄×C₇₉	—	4	1	no	—
302	C₄×C₇₉	—	4	1	no	—
303	C₄×C₇₉	—	4	1	no	—
304	C₄×C₇₉	—	4	1	no	—
305	C₄×C₇₉	—	4	1	no	—
306	C₄×C₇₉	—	4	2	no	—
307	C₄×C₇₉	—	4	1	no	—
308	C₄×C₇₉	—	8	2	no	—
309	C₄×C₇₉	C₂×#137	1	1	yes	characteristic
310	C₄×C₇₉	#575	1	1	yes	characteristic
311	C₄×C₇₉	#577	1	2	yes	—
312	#18573	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
313	C₂×C₇₉	—	2	2	no	—
314	C₂×C₇₉	—	8	1	no	—
315	C₂×C₇₉	—	8	2	no	—
316	C₂×C₇₉	#3007	1	1	yes	characteristic
317	C₂×C₇₉	#3010	1	1	yes	characteristic
318	C₂×C₇₉	C₂×#455	1	1	yes	characteristic
319	#3522	C₂×C₇₉	1	1	yes	characteristic
320	#3218	C₂×C₇₉	1	1	yes	characteristic, complemented
321	#3141	C₂×C₇₉	1	1	yes	characteristic, complemented
322	C₂×#475	C₂×C₇₉	1	1	yes	characteristic, complemented
323	#1645	C₂×C₇₉	1	2	yes	complemented
324	#1643	C₂×C₇₉	1	2	yes	complemented
325	#1642	C₂×C₇₉	1	2	yes	complemented
326	#1640	C₂×C₇₉	1	2	yes	complemented
327	#1551	C₂×C₇₉	1	1	yes	characteristic, complemented
328	#1491	C₂×C₇₉	1	1	yes	characteristic, complemented
329	#1483	C₂×C₇₉	1	1	yes	characteristic, complemented
330	C₇₉	#18573	1	1	yes	characteristic, direct product factor, Sylow
331	#559	—	2	1	no	—
332	#559	C₂²×C₇₉	1	1	yes	characteristic
333	Q₈²	C₂²×C₇₉	1	1	yes	characteristic
334	#554	—	2	1	no	—
335	#554	C₂²×C₇₉	1	1	yes	characteristic
336	#550	C₂²×C₇₉	1	1	yes	characteristic
337	#548	—	2	1	no	—
338	#547	—	2	2	no	—
339	#547	—	2	1	no	—
340	#542	—	2	2	no	—
341	#542	—	2	1	no	—
342	#532	—	2	1	no	—
343	#532	C₂²×C₇₉	1	1	yes	characteristic
344	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
345	#529	—	2	1	no	—
346	#529	C₂²×C₇₉	1	1	yes	characteristic
347	#520	—	2	1	no	—
348	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
349	#497	—	2	1	no	—
350	#491	—	2	1	no	—
351	#489	—	2	2	no	—
352	#487	C₂²×C₇₉	1	2	yes	—
353	#486	C₂²×C₇₉	1	2	yes	—
354	#475	—	2	1	no	—
355	#475	—	2	1	no	—
356	#475	C₂²×C₇₉	1	2	yes	—
357	#475	C₂²×C₇₉	1	2	yes	—
358	#462	C₂²×C₇₉	1	2	yes	—
359	#461	C₂²×C₇₉	1	2	yes	—
360	#451	—	2	1	no	—
361	#448	—	2	1	no	—
362	#432	C₂²×C₇₉	1	1	yes	characteristic
363	C₂×#106	—	2	1	no	—
364	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
365	#417	—	2	2	no	—
366	C₂×#103	—	2	1	no	—
367	C₄×M₁₆	C₂²×C₇₉	1	1	yes	characteristic
368	#333	C₂²×C₇₉	1	2	yes	—
369	#331	C₂²×C₇₉	1	2	yes	—
370	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	—
371	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	—
372	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	—
373	D₄⋊C₈	C₂²×C₇₉	1	2	yes	—
374	C₂×#41	—	2	2	no	—
375	C₂×#41	—	2	1	no	—
376	C₂×#41	D₄×C₇₉	1	2	yes	—
377	C₂²×Q₈	—	2	1	no	—
378	C₂²×Q₈	D₄×C₇₉	1	1	yes	characteristic
379	C₂×Q₁₆	—	2	2	no	—
380	C₂×SD₁₆	—	2	2	no	—
381	C₂×M₁₆	—	2	1	no	—
382	C₂²×C₈	—	2	1	no	—
383	C₄⋊Q₈	—	2	2	no	—
384	C₄⋊Q₈	—	2	1	no	—
385	C₄⋊Q₈	—	2	1	no	—
386	C₄⋊Q₈	—	2	1	no	—
387	C₄⋊Q₈	—	2	1	no	—
388	C₄⋊Q₈	—	2	1	no	—
389	C₄⋊Q₈	C₂³×C₇₉	1	2	yes	—
390	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
391	#127	—	2	1	no	—
392	#127	C₂³×C₇₉	1	1	yes	characteristic
393	#126	—	2	2	no	—
394	#126	—	2	1	no	—
395	#125	—	2	1	no	—
396	#125	D₄×C₇₉	1	1	yes	characteristic
397	#124	—	2	2	no	—
398	#124	—	2	2	no	—
399	#124	—	2	1	no	—
400	#124	—	2	1	no	—
401	#124	D₄×C₇₉	1	1	yes	characteristic
402	#124	D₄×C₇₉	1	2	yes	—
403	#123	—	2	2	no	—
404	#123	—	2	2	no	—
405	#123	—	2	2	no	—
406	#123	—	2	2	no	—
407	#123	—	2	1	no	—
408	C₂²⋊Q₈	—	2	2	no	—
409	C₂²⋊Q₈	—	2	2	no	—
410	C₂²⋊Q₈	—	2	2	no	—
411	C₂²⋊Q₈	—	2	2	no	—
412	C₂²⋊Q₈	—	2	1	no	—
413	C₂²⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
414	#121	—	2	2	no	—
415	#121	—	2	2	no	—
416	#121	—	2	1	no	—
417	#121	—	2	1	no	—
418	#121	—	2	1	no	—
419	#121	D₄×C₇₉	1	1	yes	characteristic
420	C₄×Q₈	—	2	1	no	—
421	C₄×Q₈	—	2	1	no	—
422	C₄×Q₈	—	2	1	no	—
423	C₄×Q₈	—	2	1	no	—
424	C₄×Q₈	D₄×C₇₉	1	1	yes	characteristic
425	C₄×Q₈	D₄×C₇₉	1	1	yes	characteristic
426	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
427	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
428	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
429	C₄×D₄	—	2	2	no	—
430	C₄×D₄	—	2	2	no	—
431	C₄×D₄	—	2	2	no	—
432	C₄×D₄	—	2	1	no	—
433	C₄×D₄	—	2	1	no	—
434	C₄×D₄	—	2	1	no	—
435	C₄×D₄	—	2	1	no	—
436	C₄×D₄	—	2	1	no	—
437	C₄×D₄	—	2	1	no	—
438	C₄×D₄	—	2	1	no	—
439	C₄×D₄	C₂³×C₇₉	1	1	yes	characteristic
440	#117	—	2	2	no	—
441	#117	—	2	1	no	—
442	C₂×C₄⋊C₄	—	2	2	no	—
443	C₂×C₄⋊C₄	—	2	1	no	—
444	C₂×C₄⋊C₄	—	2	1	no	—
445	C₂×C₄⋊C₄	—	2	1	no	—
446	C₂×C₄⋊C₄	—	2	1	no	—
447	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
448	C₂×C₄²	—	2	1	no	—
449	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
450	#106	—	2	2	no	—
451	#106	—	2	2	no	—
452	C₄⋊C₈	—	2	1	no	—
453	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
454	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
455	#103	—	2	2	no	—
456	#103	—	2	2	no	—
457	#103	—	2	4	no	—
458	#103	—	2	2	no	—
459	#103	—	2	2	no	—
460	#102	—	2	4	no	—
461	C₂²⋊C₈	—	2	1	no	—
462	#97	—	2	1	no	—
463	#97	—	2	1	no	—
464	C₄×C₈	C₂³×C₇₉	1	2	yes	—
465	#41	—	4	4	no	—
466	#41	—	4	2	no	—
467	#41	—	4	2	no	—
468	#41	—	8	4	no	—
469	C₂×Q₈	—	2	2	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	—	2	2	no	—
472	C₂×Q₈	—	2	2	no	—
473	C₂×Q₈	—	4	1	no	—
474	C₂×Q₈	—	4	1	no	—
475	C₂×Q₈	—	8	2	no	—
476	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
477	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
478	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
479	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
480	C₂×D₄	—	2	2	no	—
481	C₂×D₄	—	2	2	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	2	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	2	1	no	—
486	C₂×D₄	C₂×D₄×C₇₉	1	1	yes	characteristic
487	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	2	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	4	1	no	—
496	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
497	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
498	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
499	Q₁₆	—	8	2	no	—
500	SD₁₆	—	8	2	no	—
501	M₁₆	—	4	2	no	—
502	C₂×C₈	—	2	2	no	—
503	C₂×C₈	—	2	2	no	—
504	C₂×C₈	—	2	2	no	—
505	C₂×C₈	—	4	2	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	2	no	—
522	C₄⋊C₄	—	2	2	no	—
523	C₄⋊C₄	—	4	1	no	—
524	C₄⋊C₄	—	4	1	no	—
525	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
526	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
527	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
528	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
529	C₂²⋊C₄	—	2	2	no	—
530	C₂²⋊C₄	—	2	2	no	—
531	C₂²⋊C₄	—	2	2	no	—
532	C₂²⋊C₄	—	2	2	no	—
533	C₂²⋊C₄	—	2	2	no	—
534	C₂²⋊C₄	—	2	1	no	—
535	C₂²⋊C₄	—	2	2	no	—
536	C₂²⋊C₄	—	2	1	no	—
537	C₂²⋊C₄	—	2	1	no	—
538	C₂²⋊C₄	—	2	2	no	—
539	C₂²⋊C₄	—	2	1	no	—
540	C₂²⋊C₄	—	2	1	no	—
541	C₄²	—	2	2	no	—
542	C₄²	—	2	1	no	—
543	C₄²	—	2	1	no	—
544	C₄²	—	2	1	no	—
545	C₄²	—	2	1	no	—
546	C₄²	—	2	1	no	—
547	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
548	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
549	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
550	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
551	C₂³	—	2	1	no	—
552	C₂³	—	2	2	no	—
553	C₂³	#120×C₇₉	1	1	yes	characteristic
554	Q₈	—	2	1	no	—
555	Q₈	—	2	1	no	—
556	Q₈	—	2	1	no	—
557	Q₈	—	2	2	no	—
558	Q₈	—	4	2	no	—
559	Q₈	—	4	2	no	—
560	Q₈	—	4	2	no	—
561	Q₈	—	4	2	no	—
562	Q₈	—	8	2	no	—
563	Q₈	—	8	2	no	—
564	Q₈	#137×C₇₉	1	2	yes	—
565	D₄	—	2	2	no	—
566	D₄	—	4	2	no	—
567	D₄	—	4	4	no	—
568	D₄	—	4	4	no	—
569	D₄	—	4	2	no	—
570	D₄	—	4	1	no	—
571	D₄	—	4	1	no	—
572	D₄	—	4	2	no	—
573	D₄	—	8	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	4	2	no	—
587	C₂×C₄	—	4	4	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	—	8	2	no	—
593	C₂×C₄	—	8	2	no	—
594	C₂×C₄	—	8	2	no	—
595	C₂×C₄	—	8	2	no	—
596	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
597	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
598	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
599	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
600	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
601	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
602	C₈	—	4	2	no	—
603	C₈	—	4	2	no	—
604	C₈	—	4	2	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	4	1	no	—
613	C₂²	#455×C₇₉	1	2	yes	—
614	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
615	C₄	—	2	1	no	—
616	C₄	—	2	2	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	4	1	no	—
621	C₄	—	4	1	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	1	no	—
624	C₄	—	4	1	no	—
625	C₄	—	4	2	no	—
626	C₄	—	4	1	no	—
627	C₄	—	8	2	no	—
628	C₄	C₂×#137×C₇₉	1	1	yes	characteristic
629	C₄	#575×C₇₉	1	1	yes	characteristic
630	C₄	#577×C₇₉	1	2	yes	—
631	C₂	—	2	2	no	—
632	C₂	—	8	1	no	—
633	C₂	—	8	2	no	—
634	C₂	C₇₉×#3007	1	1	yes	characteristic
635	C₂	C₇₉×#3010	1	1	yes	characteristic
636	C₂	C₂×#455×C₇₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₉
prime radical	C₇₉×#3522	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ C₂×C₄²×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇₉×#3218	C₂	semidirect
3. C₇₉×#3141	C₂	semidirect
4. C₂×#475×C₇₉	C₂	semidirect
5. C₇₉×#1645	C₂	semidirect
6. C₇₉×#1643	C₂	semidirect
7. C₇₉×#1642	C₂	semidirect
8. C₇₉×#1640	C₂	semidirect
9. C₇₉×#1551	C₂	semidirect
10. C₇₉×#1491	C₂	semidirect
11. C₇₉×#1483	C₂	semidirect
312. #18573	C₇₉	direct (N × H)
320. #3218	C₂×C₇₉	semidirect
321. #3141	C₂×C₇₉	semidirect
322. C₂×#475	C₂×C₇₉	semidirect
323. #1645	C₂×C₇₉	semidirect
324. #1643	C₂×C₇₉	semidirect
325. #1642	C₂×C₇₉	semidirect
326. #1640	C₂×C₇₉	semidirect
327. #1551	C₂×C₇₉	semidirect
328. #1491	C₂×C₇₉	semidirect
329. #1483	C₂×C₇₉	semidirect
330. C₇₉	#18573	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇₉×#3522	2
C₇₉×#3218	2
C₇₉×#3141	2
C₂×#475×C₇₉	2
C₇₉×#1645	2
C₇₉×#1643	2
C₇₉×#1642	2
C₇₉×#1640	2
C₇₉×#1551	2
C₇₉×#1491	2
C₇₉×#1483	2
#18573	79

Subgroups — C79×#18573 #34130262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#18573 #34130262