Subgroups — C₇₉×#18858 #34130547

Order 20224.

950 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3517	C₂	1	1	yes	maximal, characteristic
2	C₇₉×#3239	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#3227	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#3039	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#1654	C₂	1	2	yes	maximal, complemented
6	C₇₉×#1653	C₂	1	2	yes	maximal, complemented
7	C₇₉×#1642	C₂	1	2	yes	maximal, complemented
8	C₇₉×#1641	C₂	1	2	yes	maximal, complemented
9	C₇₉×#1557	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#1495	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1488	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₇₉	—	2	1	no	—
13	#557×C₇₉	C₂²	1	1	yes	characteristic
14	#553×C₇₉	—	2	2	no	—
15	#553×C₇₉	—	2	1	no	—
16	#550×C₇₉	—	2	1	no	—
17	#550×C₇₉	—	2	1	no	—
18	#550×C₇₉	C₂²	1	1	yes	characteristic
19	#550×C₇₉	C₂²	1	1	yes	characteristic
20	#547×C₇₉	—	2	1	no	—
21	#547×C₇₉	C₂²	1	1	yes	characteristic
22	#540×C₇₉	—	2	2	no	—
23	#540×C₇₉	—	2	1	no	—
24	#532×C₇₉	—	2	1	no	—
25	#532×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
27	#529×C₇₉	—	2	1	no	—
28	#529×C₇₉	C₂²	1	1	yes	characteristic
29	#520×C₇₉	—	2	1	no	—
30	C₄×#41×C₇₉	C₂²	1	1	yes	characteristic
31	#501×C₇₉	—	2	1	no	—
32	#498×C₇₉	C₂²	1	2	yes	—
33	#489×C₇₉	—	2	1	no	—
34	#486×C₇₉	C₂²	1	2	yes	—
35	#484×C₇₉	—	2	1	no	—
36	#481×C₇₉	—	2	2	no	—
37	#481×C₇₉	—	2	1	no	—
38	#476×C₇₉	—	2	2	no	—
39	#475×C₇₉	C₂²	1	2	yes	—
40	#474×C₇₉	C₂²	1	2	yes	—
41	#462×C₇₉	—	2	1	no	—
42	#462×C₇₉	C₂²	1	2	yes	—
43	#461×C₇₉	—	2	1	no	—
44	#461×C₇₉	C₂²	1	2	yes	—
45	#432×C₇₉	C₂²	1	1	yes	characteristic
46	#431×C₇₉	C₂²	1	1	yes	characteristic
47	#423×C₇₉	C₂²	1	1	yes	characteristic
48	#419×C₇₉	—	2	1	no	—
49	#332×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	D₄⋊C₈×C₇₉	C₂²	1	2	yes	—
54	D₄⋊C₈×C₇₉	C₂²	1	2	yes	—
55	C₂×#41×C₇₉	—	2	1	no	—
56	C₂×#41×C₇₉	—	2	1	no	—
57	C₂×#41×C₇₉	—	2	1	no	—
58	C₂×#41×C₇₉	—	2	1	no	—
59	C₂×#41×C₇₉	D₄	1	1	yes	characteristic
60	C₂²×Q₈×C₇₉	—	2	1	no	—
61	#137×C₇₉	—	4	4	no	—
62	C₂×Q₁₆×C₇₉	—	2	2	no	—
63	C₂×SD₁₆×C₇₉	—	2	2	no	—
64	C₂×M₁₆×C₇₉	—	2	1	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	C₂³	1	2	yes	—
70	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
71	#127×C₇₉	—	2	2	no	—
72	#127×C₇₉	—	2	1	no	—
73	#127×C₇₉	—	2	1	no	—
74	#127×C₇₉	C₂³	1	1	yes	characteristic
75	#126×C₇₉	—	2	2	no	—
76	#126×C₇₉	—	2	1	no	—
77	#125×C₇₉	—	2	2	no	—
78	#125×C₇₉	—	2	1	no	—
79	#125×C₇₉	D₄	1	1	yes	characteristic
80	#124×C₇₉	—	2	1	no	—
81	#124×C₇₉	D₄	1	1	yes	characteristic
82	#123×C₇₉	—	2	2	no	—
83	#123×C₇₉	—	2	2	no	—
84	#123×C₇₉	—	2	2	no	—
85	#123×C₇₉	—	2	1	no	—
86	#123×C₇₉	—	2	2	no	—
87	C₂²⋊Q₈×C₇₉	—	2	1	no	—
88	C₂²⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
89	#121×C₇₉	—	2	2	no	—
90	#121×C₇₉	—	2	2	no	—
91	#121×C₇₉	—	2	2	no	—
92	#121×C₇₉	—	2	2	no	—
93	#121×C₇₉	—	2	2	no	—
94	#121×C₇₉	—	2	1	no	—
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	#121×C₇₉	D₄	1	2	yes	—
102	C₄×Q₈×C₇₉	—	2	1	no	—
103	C₄×Q₈×C₇₉	—	2	1	no	—
104	C₄×Q₈×C₇₉	D₄	1	1	yes	characteristic
105	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
106	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
107	C₄×D₄×C₇₉	—	2	2	no	—
108	C₄×D₄×C₇₉	—	2	2	no	—
109	C₄×D₄×C₇₉	—	2	2	no	—
110	C₄×D₄×C₇₉	—	2	2	no	—
111	C₄×D₄×C₇₉	—	2	1	no	—
112	C₄×D₄×C₇₉	—	2	1	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	D₄	1	1	yes	characteristic
118	C₄×D₄×C₇₉	D₄	1	2	yes	—
119	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
120	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
121	#117×C₇₉	—	2	2	no	—
122	#117×C₇₉	—	2	1	no	—
123	#117×C₇₉	—	2	1	no	—
124	#117×C₇₉	D₄	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
126	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
127	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
128	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
129	C₂×C₄²×C₇₉	—	2	1	no	—
130	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
131	#107×C₇₉	—	2	2	no	—
132	#106×C₇₉	—	2	2	no	—
133	#106×C₇₉	—	2	4	no	—
134	C₄⋊C₈×C₇₉	—	2	1	no	—
135	C₄⋊C₈×C₇₉	—	2	1	no	—
136	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
137	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
138	#103×C₇₉	—	2	2	no	—
139	#103×C₇₉	—	2	2	no	—
140	#103×C₇₉	—	2	2	no	—
141	#102×C₇₉	—	2	2	no	—
142	#102×C₇₉	—	2	4	no	—
143	C₂²⋊C₈×C₇₉	—	2	1	no	—
144	C₂²⋊C₈×C₇₉	—	2	1	no	—
145	#97×C₇₉	—	2	1	no	—
146	C₄×C₈×C₇₉	C₂³	1	2	yes	—
147	#41×C₇₉	—	2	2	no	—
148	#41×C₇₉	—	4	1	no	—
149	#41×C₇₉	—	4	2	no	—
150	#41×C₇₉	—	4	2	no	—
151	#41×C₇₉	—	8	2	no	—
152	#41×C₇₉	—	8	2	no	—
153	#41×C₇₉	—	8	2	no	—
154	C₂×Q₈×C₇₉	—	2	1	no	—
155	C₂×Q₈×C₇₉	—	2	2	no	—
156	C₂×Q₈×C₇₉	—	4	2	no	—
157	C₂×Q₈×C₇₉	—	4	2	no	—
158	C₂×Q₈×C₇₉	—	4	1	no	—
159	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
160	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
161	C₂×D₄×C₇₉	—	2	2	no	—
162	C₂×D₄×C₇₉	—	2	1	no	—
163	C₂×D₄×C₇₉	—	2	2	no	—
164	C₂×D₄×C₇₉	—	2	2	no	—
165	C₂×D₄×C₇₉	—	2	2	no	—
166	C₂×D₄×C₇₉	—	2	2	no	—
167	C₂×D₄×C₇₉	—	2	1	no	—
168	C₂×D₄×C₇₉	—	2	2	no	—
169	C₂×D₄×C₇₉	—	2	1	no	—
170	C₂×D₄×C₇₉	—	2	1	no	—
171	C₂×D₄×C₇₉	C₂×D₄	1	1	yes	characteristic
172	C₂×D₄×C₇₉	C₂×D₄	1	1	yes	characteristic
173	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
174	C₂²×C₄×C₇₉	—	2	2	no	—
175	C₂²×C₄×C₇₉	—	2	2	no	—
176	C₂²×C₄×C₇₉	—	2	2	no	—
177	C₂²×C₄×C₇₉	—	2	1	no	—
178	C₂²×C₄×C₇₉	—	2	1	no	—
179	C₂²×C₄×C₇₉	—	2	1	no	—
180	C₂²×C₄×C₇₉	—	2	1	no	—
181	C₂²×C₄×C₇₉	—	2	2	no	—
182	C₂²×C₄×C₇₉	—	4	1	no	—
183	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
186	Q₁₆×C₇₉	—	4	4	no	—
187	SD₁₆×C₇₉	—	4	4	no	—
188	M₁₆×C₇₉	—	4	2	no	—
189	C₂×C₈×C₇₉	—	2	2	no	—
190	C₂×C₈×C₇₉	—	2	2	no	—
191	C₂×C₈×C₇₉	—	2	2	no	—
192	C₄⋊C₄×C₇₉	—	2	2	no	—
193	C₄⋊C₄×C₇₉	—	2	2	no	—
194	C₄⋊C₄×C₇₉	—	2	2	no	—
195	C₄⋊C₄×C₇₉	—	2	2	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	1	no	—
203	C₄⋊C₄×C₇₉	—	2	2	no	—
204	C₄⋊C₄×C₇₉	—	2	2	no	—
205	C₄⋊C₄×C₇₉	—	4	1	no	—
206	C₄⋊C₄×C₇₉	—	4	1	no	—
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	2	yes	—
210	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
211	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
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	1	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	C₂²⋊C₄×C₇₉	—	2	2	no	—
223	C₂²⋊C₄×C₇₉	—	2	1	no	—
224	C₂²⋊C₄×C₇₉	—	2	1	no	—
225	C₄²×C₇₉	—	2	2	no	—
226	C₄²×C₇₉	—	2	1	no	—
227	C₄²×C₇₉	—	2	1	no	—
228	C₄²×C₇₉	—	2	1	no	—
229	C₄²×C₇₉	—	2	1	no	—
230	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
231	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
232	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
233	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
234	C₂³×C₇₉	—	2	1	no	—
235	C₂³×C₇₉	—	2	1	no	—
236	C₂³×C₇₉	—	2	2	no	—
237	C₂³×C₇₉	#120	1	1	yes	characteristic
238	Q₈×C₇₉	—	2	1	no	—
239	Q₈×C₇₉	—	2	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	AGL(1,ℤ/8)	1	2	yes	—
245	D₄×C₇₉	—	2	1	no	—
246	D₄×C₇₉	—	2	1	no	—
247	D₄×C₇₉	—	2	2	no	—
248	D₄×C₇₉	—	4	2	no	—
249	D₄×C₇₉	—	4	2	no	—
250	D₄×C₇₉	—	4	4	no	—
251	D₄×C₇₉	—	4	1	no	—
252	D₄×C₇₉	—	4	1	no	—
253	D₄×C₇₉	—	4	2	no	—
254	D₄×C₇₉	—	8	1	no	—
255	D₄×C₇₉	—	8	2	no	—
256	D₄×C₇₉	—	8	2	no	—
257	D₄×C₇₉	—	8	2	no	—
258	D₄×C₇₉	—	8	2	no	—
259	D₄×C₇₉	—	8	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	2	no	—
264	C₂×C₄×C₇₉	—	2	1	no	—
265	C₂×C₄×C₇₉	—	2	1	no	—
266	C₂×C₄×C₇₉	—	2	1	no	—
267	C₂×C₄×C₇₉	—	2	1	no	—
268	C₂×C₄×C₇₉	—	2	2	no	—
269	C₂×C₄×C₇₉	—	2	1	no	—
270	C₂×C₄×C₇₉	—	4	1	no	—
271	C₂×C₄×C₇₉	—	4	2	no	—
272	C₂×C₄×C₇₉	—	4	4	no	—
273	C₂×C₄×C₇₉	—	4	1	no	—
274	C₂×C₄×C₇₉	—	4	1	no	—
275	C₂×C₄×C₇₉	—	4	2	no	—
276	C₂×C₄×C₇₉	—	4	2	no	—
277	C₂×C₄×C₇₉	—	8	1	no	—
278	C₂×C₄×C₇₉	—	8	2	no	—
279	C₂×C₄×C₇₉	—	8	2	no	—
280	C₂×C₄×C₇₉	—	8	2	no	—
281	C₂×C₄×C₇₉	—	8	2	no	—
282	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
283	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
284	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
285	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
286	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
287	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
288	C₈×C₇₉	—	4	2	no	—
289	C₈×C₇₉	—	4	2	no	—
290	C₈×C₇₉	—	4	2	no	—
291	C₂²×C₇₉	—	2	1	no	—
292	C₂²×C₇₉	—	2	1	no	—
293	C₂²×C₇₉	—	2	1	no	—
294	C₂²×C₇₉	—	4	1	no	—
295	C₂²×C₇₉	—	4	2	no	—
296	C₂²×C₇₉	—	4	1	no	—
297	C₂²×C₇₉	—	4	1	no	—
298	C₂²×C₇₉	—	4	1	no	—
299	C₂²×C₇₉	—	4	2	no	—
300	C₂²×C₇₉	—	4	1	no	—
301	C₂²×C₇₉	—	4	2	no	—
302	C₂²×C₇₉	—	4	1	no	—
303	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
304	C₄×C₇₉	—	2	1	no	—
305	C₄×C₇₉	—	2	2	no	—
306	C₄×C₇₉	—	2	1	no	—
307	C₄×C₇₉	—	2	1	no	—
308	C₄×C₇₉	—	2	1	no	—
309	C₄×C₇₉	—	4	1	no	—
310	C₄×C₇₉	—	4	1	no	—
311	C₄×C₇₉	—	4	1	no	—
312	C₄×C₇₉	—	4	2	no	—
313	C₄×C₇₉	—	4	1	no	—
314	C₄×C₇₉	—	4	1	no	—
315	C₄×C₇₉	—	8	2	no	—
316	C₄×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
317	C₄×C₇₉	#575	1	1	yes	characteristic
318	C₄×C₇₉	#577	1	2	yes	—
319	#18858	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
320	C₂×C₇₉	—	4	1	no	—
321	C₂×C₇₉	—	8	1	no	—
322	C₂×C₇₉	—	8	1	no	—
323	C₂×C₇₉	—	8	2	no	—
324	C₂×C₇₉	#3006	1	1	yes	characteristic
325	C₂×C₇₉	#3009	1	1	yes	characteristic
326	C₂×C₇₉	#3022	1	1	yes	characteristic
327	#3517	C₂×C₇₉	1	1	yes	characteristic
328	#3239	C₂×C₇₉	1	1	yes	characteristic, complemented
329	#3227	C₂×C₇₉	1	1	yes	characteristic, complemented
330	#3039	C₂×C₇₉	1	1	yes	characteristic, complemented
331	#1654	C₂×C₇₉	1	2	yes	complemented
332	#1653	C₂×C₇₉	1	2	yes	complemented
333	#1642	C₂×C₇₉	1	2	yes	complemented
334	#1641	C₂×C₇₉	1	2	yes	complemented
335	#1557	C₂×C₇₉	1	1	yes	characteristic, complemented
336	#1495	C₂×C₇₉	1	1	yes	characteristic, complemented
337	#1488	C₂×C₇₉	1	1	yes	characteristic, complemented
338	C₇₉	#18858	1	1	yes	characteristic, direct product factor, Sylow
339	C₂×#137	—	2	1	no	—
340	#557	C₂²×C₇₉	1	1	yes	characteristic
341	#553	—	2	2	no	—
342	#553	—	2	1	no	—
343	#550	—	2	1	no	—
344	#550	—	2	1	no	—
345	#550	C₂²×C₇₉	1	1	yes	characteristic
346	#550	C₂²×C₇₉	1	1	yes	characteristic
347	#547	—	2	1	no	—
348	#547	C₂²×C₇₉	1	1	yes	characteristic
349	#540	—	2	2	no	—
350	#540	—	2	1	no	—
351	#532	—	2	1	no	—
352	#532	C₂²×C₇₉	1	1	yes	characteristic
353	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
354	#529	—	2	1	no	—
355	#529	C₂²×C₇₉	1	1	yes	characteristic
356	#520	—	2	1	no	—
357	C₄×#41	C₂²×C₇₉	1	1	yes	characteristic
358	#501	—	2	1	no	—
359	#498	C₂²×C₇₉	1	2	yes	—
360	#489	—	2	1	no	—
361	#486	C₂²×C₇₉	1	2	yes	—
362	#484	—	2	1	no	—
363	#481	—	2	2	no	—
364	#481	—	2	1	no	—
365	#476	—	2	2	no	—
366	#475	C₂²×C₇₉	1	2	yes	—
367	#474	C₂²×C₇₉	1	2	yes	—
368	#462	—	2	1	no	—
369	#462	C₂²×C₇₉	1	2	yes	—
370	#461	—	2	1	no	—
371	#461	C₂²×C₇₉	1	2	yes	—
372	#432	C₂²×C₇₉	1	1	yes	characteristic
373	#431	C₂²×C₇₉	1	1	yes	characteristic
374	#423	C₂²×C₇₉	1	1	yes	characteristic
375	#419	—	2	1	no	—
376	#332	C₂²×C₇₉	1	2	yes	—
377	#331	C₂²×C₇₉	1	2	yes	—
378	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	—
379	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	—
380	D₄⋊C₈	C₂²×C₇₉	1	2	yes	—
381	D₄⋊C₈	C₂²×C₇₉	1	2	yes	—
382	C₂×#41	—	2	1	no	—
383	C₂×#41	—	2	1	no	—
384	C₂×#41	—	2	1	no	—
385	C₂×#41	—	2	1	no	—
386	C₂×#41	D₄×C₇₉	1	1	yes	characteristic
387	C₂²×Q₈	—	2	1	no	—
388	#137	—	4	4	no	—
389	C₂×Q₁₆	—	2	2	no	—
390	C₂×SD₁₆	—	2	2	no	—
391	C₂×M₁₆	—	2	1	no	—
392	C₄⋊Q₈	—	2	1	no	—
393	C₄⋊Q₈	—	2	1	no	—
394	C₄⋊Q₈	—	2	1	no	—
395	C₄⋊Q₈	—	2	1	no	—
396	C₄⋊Q₈	C₂³×C₇₉	1	2	yes	—
397	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
398	#127	—	2	2	no	—
399	#127	—	2	1	no	—
400	#127	—	2	1	no	—
401	#127	C₂³×C₇₉	1	1	yes	characteristic
402	#126	—	2	2	no	—
403	#126	—	2	1	no	—
404	#125	—	2	2	no	—
405	#125	—	2	1	no	—
406	#125	D₄×C₇₉	1	1	yes	characteristic
407	#124	—	2	1	no	—
408	#124	D₄×C₇₉	1	1	yes	characteristic
409	#123	—	2	2	no	—
410	#123	—	2	2	no	—
411	#123	—	2	2	no	—
412	#123	—	2	1	no	—
413	#123	—	2	2	no	—
414	C₂²⋊Q₈	—	2	1	no	—
415	C₂²⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
416	#121	—	2	2	no	—
417	#121	—	2	2	no	—
418	#121	—	2	2	no	—
419	#121	—	2	2	no	—
420	#121	—	2	2	no	—
421	#121	—	2	1	no	—
422	#121	—	2	2	no	—
423	#121	—	2	2	no	—
424	#121	—	2	1	no	—
425	#121	—	2	1	no	—
426	#121	—	2	1	no	—
427	#121	D₄×C₇₉	1	1	yes	characteristic
428	#121	D₄×C₇₉	1	2	yes	—
429	C₄×Q₈	—	2	1	no	—
430	C₄×Q₈	—	2	1	no	—
431	C₄×Q₈	D₄×C₇₉	1	1	yes	characteristic
432	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
433	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
434	C₄×D₄	—	2	2	no	—
435	C₄×D₄	—	2	2	no	—
436	C₄×D₄	—	2	2	no	—
437	C₄×D₄	—	2	2	no	—
438	C₄×D₄	—	2	1	no	—
439	C₄×D₄	—	2	1	no	—
440	C₄×D₄	—	2	1	no	—
441	C₄×D₄	—	2	1	no	—
442	C₄×D₄	—	2	1	no	—
443	C₄×D₄	—	2	1	no	—
444	C₄×D₄	D₄×C₇₉	1	1	yes	characteristic
445	C₄×D₄	D₄×C₇₉	1	2	yes	—
446	C₄×D₄	C₂³×C₇₉	1	1	yes	characteristic
447	C₄×D₄	C₂³×C₇₉	1	1	yes	characteristic
448	#117	—	2	2	no	—
449	#117	—	2	1	no	—
450	#117	—	2	1	no	—
451	#117	D₄×C₇₉	1	1	yes	characteristic
452	C₂×C₄⋊C₄	—	2	2	no	—
453	C₂×C₄⋊C₄	—	2	1	no	—
454	C₂×C₄⋊C₄	—	2	1	no	—
455	C₂×C₄⋊C₄	—	2	1	no	—
456	C₂×C₄²	—	2	1	no	—
457	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
458	#107	—	2	2	no	—
459	#106	—	2	2	no	—
460	#106	—	2	4	no	—
461	C₄⋊C₈	—	2	1	no	—
462	C₄⋊C₈	—	2	1	no	—
463	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
464	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
465	#103	—	2	2	no	—
466	#103	—	2	2	no	—
467	#103	—	2	2	no	—
468	#102	—	2	2	no	—
469	#102	—	2	4	no	—
470	C₂²⋊C₈	—	2	1	no	—
471	C₂²⋊C₈	—	2	1	no	—
472	#97	—	2	1	no	—
473	C₄×C₈	C₂³×C₇₉	1	2	yes	—
474	#41	—	2	2	no	—
475	#41	—	4	1	no	—
476	#41	—	4	2	no	—
477	#41	—	4	2	no	—
478	#41	—	8	2	no	—
479	#41	—	8	2	no	—
480	#41	—	8	2	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	—	2	2	no	—
483	C₂×Q₈	—	4	2	no	—
484	C₂×Q₈	—	4	2	no	—
485	C₂×Q₈	—	4	1	no	—
486	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
487	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
488	C₂×D₄	—	2	2	no	—
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	2	2	no	—
491	C₂×D₄	—	2	2	no	—
492	C₂×D₄	—	2	2	no	—
493	C₂×D₄	—	2	2	no	—
494	C₂×D₄	—	2	1	no	—
495	C₂×D₄	—	2	2	no	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	2	1	no	—
498	C₂×D₄	C₂×D₄×C₇₉	1	1	yes	characteristic
499	C₂×D₄	C₂×D₄×C₇₉	1	1	yes	characteristic
500	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	2	2	no	—
503	C₂²×C₄	—	2	2	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	2	no	—
509	C₂²×C₄	—	4	1	no	—
510	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
511	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
512	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
513	Q₁₆	—	4	4	no	—
514	SD₁₆	—	4	4	no	—
515	M₁₆	—	4	2	no	—
516	C₂×C₈	—	2	2	no	—
517	C₂×C₈	—	2	2	no	—
518	C₂×C₈	—	2	2	no	—
519	C₄⋊C₄	—	2	2	no	—
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	2	2	no	—
522	C₄⋊C₄	—	2	2	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	2	no	—
531	C₄⋊C₄	—	2	2	no	—
532	C₄⋊C₄	—	4	1	no	—
533	C₄⋊C₄	—	4	1	no	—
534	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
535	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
536	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
537	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
538	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
539	C₂²⋊C₄	—	2	2	no	—
540	C₂²⋊C₄	—	2	2	no	—
541	C₂²⋊C₄	—	2	2	no	—
542	C₂²⋊C₄	—	2	1	no	—
543	C₂²⋊C₄	—	2	1	no	—
544	C₂²⋊C₄	—	2	1	no	—
545	C₂²⋊C₄	—	2	1	no	—
546	C₂²⋊C₄	—	2	2	no	—
547	C₂²⋊C₄	—	2	1	no	—
548	C₂²⋊C₄	—	2	1	no	—
549	C₂²⋊C₄	—	2	2	no	—
550	C₂²⋊C₄	—	2	1	no	—
551	C₂²⋊C₄	—	2	1	no	—
552	C₄²	—	2	2	no	—
553	C₄²	—	2	1	no	—
554	C₄²	—	2	1	no	—
555	C₄²	—	2	1	no	—
556	C₄²	—	2	1	no	—
557	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
558	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
559	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
560	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
561	C₂³	—	2	1	no	—
562	C₂³	—	2	2	no	—
563	C₂³	—	2	1	no	—
564	C₂³	#120×C₇₉	1	1	yes	characteristic
565	Q₈	—	2	1	no	—
566	Q₈	—	2	2	no	—
567	Q₈	—	4	2	no	—
568	Q₈	—	4	2	no	—
569	Q₈	—	4	2	no	—
570	Q₈	—	8	2	no	—
571	Q₈	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
572	D₄	—	2	1	no	—
573	D₄	—	2	1	no	—
574	D₄	—	2	2	no	—
575	D₄	—	4	2	no	—
576	D₄	—	4	2	no	—
577	D₄	—	4	4	no	—
578	D₄	—	4	1	no	—
579	D₄	—	4	1	no	—
580	D₄	—	4	2	no	—
581	D₄	—	8	1	no	—
582	D₄	—	8	2	no	—
583	D₄	—	8	2	no	—
584	D₄	—	8	2	no	—
585	D₄	—	8	2	no	—
586	D₄	—	8	2	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	4	4	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	2	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	8	1	no	—
605	C₂×C₄	—	8	2	no	—
606	C₂×C₄	—	8	2	no	—
607	C₂×C₄	—	8	2	no	—
608	C₂×C₄	—	8	2	no	—
609	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
610	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
611	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
612	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
613	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
614	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
615	C₈	—	4	2	no	—
616	C₈	—	4	2	no	—
617	C₈	—	4	2	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	4	2	no	—
623	C₂²	—	4	1	no	—
624	C₂²	—	4	1	no	—
625	C₂²	—	4	2	no	—
626	C₂²	—	4	1	no	—
627	C₂²	—	4	1	no	—
628	C₂²	—	4	1	no	—
629	C₂²	—	4	2	no	—
630	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
631	C₄	—	2	1	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	1	no	—
636	C₄	—	4	1	no	—
637	C₄	—	4	1	no	—
638	C₄	—	4	1	no	—
639	C₄	—	4	1	no	—
640	C₄	—	4	1	no	—
641	C₄	—	4	2	no	—
642	C₄	—	8	2	no	—
643	C₄	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
644	C₄	#575×C₇₉	1	1	yes	characteristic
645	C₄	#577×C₇₉	1	2	yes	—
646	C₂	—	4	1	no	—
647	C₂	—	8	1	no	—
648	C₂	—	8	2	no	—
649	C₂	—	8	1	no	—
650	C₂	C₇₉×#3006	1	1	yes	characteristic
651	C₂	C₇₉×#3009	1	1	yes	characteristic
652	C₂	C₇₉×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₉
prime radical	C₇₉×#3517	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×#3239	C₂	semidirect
3. C₇₉×#3227	C₂	semidirect
4. C₇₉×#3039	C₂	semidirect
5. C₇₉×#1654	C₂	semidirect
6. C₇₉×#1653	C₂	semidirect
7. C₇₉×#1642	C₂	semidirect
8. C₇₉×#1641	C₂	semidirect
9. C₇₉×#1557	C₂	semidirect
10. C₇₉×#1495	C₂	semidirect
11. C₇₉×#1488	C₂	semidirect
319. #18858	C₇₉	direct (N × H)
328. #3239	C₂×C₇₉	semidirect
329. #3227	C₂×C₇₉	semidirect
330. #3039	C₂×C₇₉	semidirect
331. #1654	C₂×C₇₉	semidirect
332. #1653	C₂×C₇₉	semidirect
333. #1642	C₂×C₇₉	semidirect
334. #1641	C₂×C₇₉	semidirect
335. #1557	C₂×C₇₉	semidirect
336. #1495	C₂×C₇₉	semidirect
337. #1488	C₂×C₇₉	semidirect
338. C₇₉	#18858	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×#3517	2
C₇₉×#3239	2
C₇₉×#3227	2
C₇₉×#3039	2
C₇₉×#1654	2
C₇₉×#1653	2
C₇₉×#1642	2
C₇₉×#1641	2
C₇₉×#1557	2
C₇₉×#1495	2
C₇₉×#1488	2
#18858	79

Subgroups — C79×#18858 #34130547

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#18858 #34130547