Subgroups — C₇₉×#18567 #34130256

Order 20224.

980 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₉×#3254	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#3152	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#3106	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#1633	C₂	1	2	yes	maximal, complemented
6	C₇₉×#1632	C₂	1	2	yes	maximal, complemented
7	C₇₉×#1623	C₂	1	2	yes	maximal, complemented
8	C₇₉×#1622	C₂	1	2	yes	maximal, complemented
9	C₇₉×#1548	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#1489	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1485	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₇₉	—	2	2	no	—
13	Q₈²×C₇₉	C₂²	1	2	yes	—
14	#557×C₇₉	—	2	1	no	—
15	#554×C₇₉	—	2	2	no	—
16	#554×C₇₉	C₂²	1	2	yes	—
17	D₄×Q₈×C₇₉	—	2	2	no	—
18	D₄×Q₈×C₇₉	—	2	1	no	—
19	#544×C₇₉	—	2	2	no	—
20	#544×C₇₉	—	2	1	no	—
21	#533×C₇₉	—	2	1	no	—
22	#533×C₇₉	C₂²	1	1	yes	characteristic
23	#532×C₇₉	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₇₉	—	2	1	no	—
25	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
26	#520×C₇₉	—	2	1	no	—
27	C₄×#41×C₇₉	C₂²	1	1	yes	characteristic
28	#497×C₇₉	—	2	2	no	—
29	#494×C₇₉	C₂²	1	2	yes	—
30	#492×C₇₉	C₂²	1	2	yes	—
31	#482×C₇₉	—	2	1	no	—
32	#477×C₇₉	C₂²	1	1	yes	characteristic
33	#477×C₇₉	C₂²	1	2	yes	—
34	#476×C₇₉	C₂²	1	1	yes	characteristic
35	#474×C₇₉	—	2	1	no	—
36	#468×C₇₉	—	2	2	no	—
37	#461×C₇₉	—	2	1	no	—
38	#460×C₇₉	C₂²	1	1	yes	characteristic
39	#460×C₇₉	C₂²	1	2	yes	—
40	#459×C₇₉	C₂²	1	1	yes	characteristic
41	#449×C₇₉	—	2	1	no	—
42	C₄×SD₁₆×C₇₉	—	2	1	no	—
43	C₄×D₈×C₇₉	—	2	1	no	—
44	#431×C₇₉	C₂²	1	1	yes	characteristic
45	#423×C₇₉	C₂²	1	1	yes	characteristic
46	C₄×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
47	#333×C₇₉	C₂²	1	2	yes	—
48	#333×C₇₉	C₂²	1	2	yes	—
49	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	—
50	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	—
51	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	—
52	D₄⋊C₈×C₇₉	C₂²	1	2	yes	—
53	C₂×#41×C₇₉	—	2	1	no	—
54	C₂×#41×C₇₉	D₄	1	1	yes	characteristic
55	C₂²×Q₈×C₇₉	—	2	2	no	—
56	C₂²×Q₈×C₇₉	D₄	1	2	yes	—
57	#137×C₇₉	—	4	8	no	—
58	C₂×Q₁₆×C₇₉	—	2	4	no	—
59	C₂×SD₁₆×C₇₉	—	2	1	no	—
60	C₂×SD₁₆×C₇₉	—	2	4	no	—
61	C₂×SD₁₆×C₇₉	—	2	2	no	—
62	C₂×D₈×C₇₉	—	2	1	no	—
63	C₂×M₁₆×C₇₉	—	2	1	no	—
64	C₂×M₁₆×C₇₉	—	2	1	no	—
65	C₄⋊Q₈×C₇₉	—	2	2	no	—
66	C₄⋊Q₈×C₇₉	—	2	2	no	—
67	C₄⋊Q₈×C₇₉	—	2	4	no	—
68	C₄⋊Q₈×C₇₉	—	2	2	no	—
69	C₄⋊Q₈×C₇₉	—	2	2	no	—
70	C₄⋊Q₈×C₇₉	—	2	1	no	—
71	C₄⋊Q₈×C₇₉	—	2	1	no	—
72	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
73	C₄⋊Q₈×C₇₉	D₄	1	2	yes	—
74	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
75	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
76	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
77	#127×C₇₉	C₂³	1	1	yes	characteristic
78	#125×C₇₉	—	2	2	no	—
79	#125×C₇₉	—	2	4	no	—
80	#125×C₇₉	—	2	2	no	—
81	#125×C₇₉	—	2	1	no	—
82	#124×C₇₉	—	2	1	no	—
83	C₂²⋊Q₈×C₇₉	—	2	2	no	—
84	C₂²⋊Q₈×C₇₉	—	2	4	no	—
85	C₂²⋊Q₈×C₇₉	—	2	4	no	—
86	C₂²⋊Q₈×C₇₉	—	2	2	no	—
87	C₂²⋊Q₈×C₇₉	—	2	4	no	—
88	C₂²⋊Q₈×C₇₉	—	2	1	no	—
89	C₂²⋊Q₈×C₇₉	D₄	1	2	yes	—
90	#121×C₇₉	—	2	1	no	—
91	#121×C₇₉	—	2	1	no	—
92	C₄×Q₈×C₇₉	—	2	2	no	—
93	C₄×Q₈×C₇₉	—	2	2	no	—
94	C₄×Q₈×C₇₉	—	2	2	no	—
95	C₄×Q₈×C₇₉	—	2	1	no	—
96	C₄×Q₈×C₇₉	D₄	1	1	yes	characteristic
97	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
98	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
99	C₄×D₄×C₇₉	—	2	4	no	—
100	C₄×D₄×C₇₉	—	2	2	no	—
101	C₄×D₄×C₇₉	—	2	1	no	—
102	C₄×D₄×C₇₉	—	2	1	no	—
103	C₄×D₄×C₇₉	—	2	1	no	—
104	C₄×D₄×C₇₉	—	2	1	no	—
105	C₄×D₄×C₇₉	D₄	1	1	yes	characteristic
106	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
107	#117×C₇₉	—	2	2	no	—
108	#117×C₇₉	—	2	1	no	—
109	#117×C₇₉	—	2	1	no	—
110	#117×C₇₉	D₄	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
112	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
113	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
114	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
115	C₂×C₄²×C₇₉	—	2	1	no	—
116	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
117	#107×C₇₉	—	2	1	no	—
118	#107×C₇₉	—	2	2	no	—
119	#106×C₇₉	—	2	1	no	—
120	C₄⋊C₈×C₇₉	—	2	1	no	—
121	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
122	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
123	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
124	#103×C₇₉	—	2	1	no	—
125	#103×C₇₉	—	2	2	no	—
126	#102×C₇₉	—	2	1	no	—
127	#102×C₇₉	—	2	1	no	—
128	#102×C₇₉	—	2	1	no	—
129	#102×C₇₉	—	2	2	no	—
130	C₂²⋊C₈×C₇₉	—	2	1	no	—
131	#97×C₇₉	—	2	1	no	—
132	C₄×C₈×C₇₉	—	2	1	no	—
133	C₄×C₈×C₇₉	C₂³	1	2	yes	—
134	#41×C₇₉	—	2	2	no	—
135	#41×C₇₉	—	2	2	no	—
136	#41×C₇₉	—	4	4	no	—
137	C₂×Q₈×C₇₉	—	2	4	no	—
138	C₂×Q₈×C₇₉	—	2	2	no	—
139	C₂×Q₈×C₇₉	—	2	1	no	—
140	C₂×Q₈×C₇₉	—	2	1	no	—
141	C₂×Q₈×C₇₉	—	4	4	no	—
142	C₂×Q₈×C₇₉	—	8	4	no	—
143	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
144	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
145	C₂×Q₈×C₇₉	C₂×D₄	1	4	yes	—
146	C₂×D₄×C₇₉	—	2	1	no	—
147	C₂×D₄×C₇₉	—	2	1	no	—
148	C₂×D₄×C₇₉	—	2	1	no	—
149	C₂×D₄×C₇₉	—	2	1	no	—
150	C₂×D₄×C₇₉	—	4	1	no	—
151	C₂×D₄×C₇₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₇₉	—	2	1	no	—
153	C₂²×C₄×C₇₉	—	2	4	no	—
154	C₂²×C₄×C₇₉	—	2	2	no	—
155	C₂²×C₄×C₇₉	—	2	1	no	—
156	C₂²×C₄×C₇₉	—	2	1	no	—
157	C₂²×C₄×C₇₉	—	4	1	no	—
158	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
161	Q₁₆×C₇₉	—	4	8	no	—
162	SD₁₆×C₇₉	—	4	8	no	—
163	SD₁₆×C₇₉	—	4	2	no	—
164	SD₁₆×C₇₉	—	8	2	no	—
165	D₈×C₇₉	—	4	2	no	—
166	M₁₆×C₇₉	—	2	4	no	—
167	M₁₆×C₇₉	—	8	1	no	—
168	C₂×C₈×C₇₉	—	2	2	no	—
169	C₂×C₈×C₇₉	—	2	1	no	—
170	C₂×C₈×C₇₉	—	2	1	no	—
171	C₂×C₈×C₇₉	—	2	2	no	—
172	C₄⋊C₄×C₇₉	—	2	4	no	—
173	C₄⋊C₄×C₇₉	—	2	4	no	—
174	C₄⋊C₄×C₇₉	—	2	4	no	—
175	C₄⋊C₄×C₇₉	—	2	4	no	—
176	C₄⋊C₄×C₇₉	—	2	2	no	—
177	C₄⋊C₄×C₇₉	—	2	1	no	—
178	C₄⋊C₄×C₇₉	—	2	2	no	—
179	C₄⋊C₄×C₇₉	—	2	1	no	—
180	C₄⋊C₄×C₇₉	—	2	1	no	—
181	C₄⋊C₄×C₇₉	—	2	1	no	—
182	C₄⋊C₄×C₇₉	—	2	2	no	—
183	C₄⋊C₄×C₇₉	—	2	2	no	—
184	C₄⋊C₄×C₇₉	—	2	2	no	—
185	C₄⋊C₄×C₇₉	—	2	1	no	—
186	C₄⋊C₄×C₇₉	—	2	2	no	—
187	C₄⋊C₄×C₇₉	—	2	1	no	—
188	C₄⋊C₄×C₇₉	—	2	1	no	—
189	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
190	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
191	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
192	C₂²⋊C₄×C₇₉	—	2	4	no	—
193	C₂²⋊C₄×C₇₉	—	2	2	no	—
194	C₂²⋊C₄×C₇₉	—	2	1	no	—
195	C₂²⋊C₄×C₇₉	—	2	1	no	—
196	C₂²⋊C₄×C₇₉	—	2	1	no	—
197	C₂²⋊C₄×C₇₉	—	4	1	no	—
198	C₂²⋊C₄×C₇₉	—	4	1	no	—
199	C₄²×C₇₉	—	2	4	no	—
200	C₄²×C₇₉	—	2	1	no	—
201	C₄²×C₇₉	—	2	1	no	—
202	C₄²×C₇₉	—	2	1	no	—
203	C₄²×C₇₉	—	2	2	no	—
204	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
206	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
208	C₂³×C₇₉	—	2	1	no	—
209	C₂³×C₇₉	—	4	1	no	—
210	C₂³×C₇₉	#120	1	1	yes	characteristic
211	Q₈×C₇₉	—	2	1	no	—
212	Q₈×C₇₉	—	2	2	no	—
213	Q₈×C₇₉	—	2	2	no	—
214	Q₈×C₇₉	—	4	4	no	—
215	Q₈×C₇₉	—	4	2	no	—
216	Q₈×C₇₉	—	4	4	no	—
217	Q₈×C₇₉	—	4	2	no	—
218	Q₈×C₇₉	—	8	4	no	—
219	Q₈×C₇₉	#137	1	2	yes	complemented
220	D₄×C₇₉	—	2	4	no	—
221	D₄×C₇₉	—	2	1	no	—
222	D₄×C₇₉	—	4	2	no	—
223	D₄×C₇₉	—	4	1	no	—
224	D₄×C₇₉	—	4	1	no	—
225	D₄×C₇₉	—	4	1	no	—
226	D₄×C₇₉	—	4	1	no	—
227	D₄×C₇₉	—	8	2	no	—
228	D₄×C₇₉	#137	1	2	yes	complemented
229	C₂×C₄×C₇₉	—	2	4	no	—
230	C₂×C₄×C₇₉	—	2	1	no	—
231	C₂×C₄×C₇₉	—	2	1	no	—
232	C₂×C₄×C₇₉	—	2	1	no	—
233	C₂×C₄×C₇₉	—	2	1	no	—
234	C₂×C₄×C₇₉	—	2	1	no	—
235	C₂×C₄×C₇₉	—	2	2	no	—
236	C₂×C₄×C₇₉	—	2	2	no	—
237	C₂×C₄×C₇₉	—	2	1	no	—
238	C₂×C₄×C₇₉	—	2	1	no	—
239	C₂×C₄×C₇₉	—	2	4	no	—
240	C₂×C₄×C₇₉	—	2	2	no	—
241	C₂×C₄×C₇₉	—	4	1	no	—
242	C₂×C₄×C₇₉	—	4	1	no	—
243	C₂×C₄×C₇₉	—	4	2	no	—
244	C₂×C₄×C₇₉	—	4	1	no	—
245	C₂×C₄×C₇₉	—	8	2	no	—
246	C₂×C₄×C₇₉	—	8	4	no	—
247	C₂×C₄×C₇₉	—	8	2	no	—
248	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
249	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
250	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
251	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
254	C₈×C₇₉	—	2	4	no	—
255	C₈×C₇₉	—	4	1	no	—
256	C₈×C₇₉	—	4	1	no	—
257	C₈×C₇₉	—	4	2	no	—
258	C₂²×C₇₉	—	2	1	no	—
259	C₂²×C₇₉	—	2	2	no	—
260	C₂²×C₇₉	—	2	1	no	—
261	C₂²×C₇₉	—	2	1	no	—
262	C₂²×C₇₉	—	4	1	no	—
263	C₂²×C₇₉	—	4	1	no	—
264	C₂²×C₇₉	—	8	1	no	—
265	C₂²×C₇₉	—	8	1	no	—
266	C₂²×C₇₉	—	8	1	no	—
267	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
268	C₄×C₇₉	—	2	1	no	—
269	C₄×C₇₉	—	2	2	no	—
270	C₄×C₇₉	—	2	1	no	—
271	C₄×C₇₉	—	2	1	no	—
272	C₄×C₇₉	—	4	1	no	—
273	C₄×C₇₉	—	4	2	no	—
274	C₄×C₇₉	—	4	1	no	—
275	C₄×C₇₉	—	4	4	no	—
276	C₄×C₇₉	—	4	2	no	—
277	C₄×C₇₉	—	8	1	no	—
278	C₄×C₇₉	#453	1	2	yes	—
279	C₄×C₇₉	C₂×#137	1	1	yes	characteristic
280	C₄×C₇₉	C₂×#137	1	1	yes	characteristic
281	C₄×C₇₉	#577	1	1	yes	characteristic
282	C₄×C₇₉	#578	1	1	yes	characteristic
283	#18567	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
284	C₂×C₇₉	—	4	1	no	—
285	C₂×C₇₉	—	4	2	no	—
286	C₂×C₇₉	—	16	1	no	—
287	C₂×C₇₉	#3004	1	1	yes	characteristic
288	C₂×C₇₉	#3013	1	1	yes	characteristic
289	C₂×C₇₉	C₂×#453	1	1	yes	characteristic
290	#3503	C₂×C₇₉	1	1	yes	characteristic, complemented
291	#3254	C₂×C₇₉	1	1	yes	characteristic, complemented
292	#3152	C₂×C₇₉	1	1	yes	characteristic, complemented
293	#3106	C₂×C₇₉	1	1	yes	characteristic
294	#1633	C₂×C₇₉	1	2	yes	complemented
295	#1632	C₂×C₇₉	1	2	yes	complemented
296	#1623	C₂×C₇₉	1	2	yes	complemented
297	#1622	C₂×C₇₉	1	2	yes	complemented
298	#1548	C₂×C₇₉	1	1	yes	characteristic, complemented
299	#1489	C₂×C₇₉	1	1	yes	characteristic, complemented
300	#1485	C₂×C₇₉	1	1	yes	characteristic, complemented
301	C₇₉	#18567	1	1	yes	characteristic, direct product factor, Sylow
302	C₂×#137	—	2	2	no	—
303	Q₈²	C₂²×C₇₉	1	2	yes	—
304	#557	—	2	1	no	—
305	#554	—	2	2	no	—
306	#554	C₂²×C₇₉	1	2	yes	—
307	D₄×Q₈	—	2	2	no	—
308	D₄×Q₈	—	2	1	no	—
309	#544	—	2	2	no	—
310	#544	—	2	1	no	—
311	#533	—	2	1	no	—
312	#533	C₂²×C₇₉	1	1	yes	characteristic
313	#532	C₂²×C₇₉	1	1	yes	characteristic
314	C₂×C₄⋊Q₈	—	2	1	no	—
315	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
316	#520	—	2	1	no	—
317	C₄×#41	C₂²×C₇₉	1	1	yes	characteristic
318	#497	—	2	2	no	—
319	#494	C₂²×C₇₉	1	2	yes	—
320	#492	C₂²×C₇₉	1	2	yes	—
321	#482	—	2	1	no	—
322	#477	C₂²×C₇₉	1	1	yes	characteristic
323	#477	C₂²×C₇₉	1	2	yes	—
324	#476	C₂²×C₇₉	1	1	yes	characteristic
325	#474	—	2	1	no	—
326	#468	—	2	2	no	—
327	#461	—	2	1	no	—
328	#460	C₂²×C₇₉	1	1	yes	characteristic
329	#460	C₂²×C₇₉	1	2	yes	—
330	#459	C₂²×C₇₉	1	1	yes	characteristic
331	#449	—	2	1	no	—
332	C₄×SD₁₆	—	2	1	no	—
333	C₄×D₈	—	2	1	no	—
334	#431	C₂²×C₇₉	1	1	yes	characteristic
335	#423	C₂²×C₇₉	1	1	yes	characteristic
336	C₄×M₁₆	C₂²×C₇₉	1	1	yes	characteristic
337	#333	C₂²×C₇₉	1	2	yes	—
338	#333	C₂²×C₇₉	1	2	yes	—
339	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	—
340	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	—
341	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	—
342	D₄⋊C₈	C₂²×C₇₉	1	2	yes	—
343	C₂×#41	—	2	1	no	—
344	C₂×#41	D₄×C₇₉	1	1	yes	characteristic
345	C₂²×Q₈	—	2	2	no	—
346	C₂²×Q₈	D₄×C₇₉	1	2	yes	—
347	#137	—	4	8	no	—
348	C₂×Q₁₆	—	2	4	no	—
349	C₂×SD₁₆	—	2	4	no	—
350	C₂×SD₁₆	—	2	1	no	—
351	C₂×SD₁₆	—	2	2	no	—
352	C₂×D₈	—	2	1	no	—
353	C₂×M₁₆	—	2	1	no	—
354	C₂×M₁₆	—	2	1	no	—
355	C₄⋊Q₈	—	2	2	no	—
356	C₄⋊Q₈	—	2	2	no	—
357	C₄⋊Q₈	—	2	4	no	—
358	C₄⋊Q₈	—	2	2	no	—
359	C₄⋊Q₈	—	2	2	no	—
360	C₄⋊Q₈	—	2	1	no	—
361	C₄⋊Q₈	—	2	1	no	—
362	C₄⋊Q₈	D₄×C₇₉	1	2	yes	—
363	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
364	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
365	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
366	C₄⋊Q₈	C₂³×C₇₉	1	2	yes	—
367	#127	C₂³×C₇₉	1	1	yes	characteristic
368	#125	—	2	2	no	—
369	#125	—	2	4	no	—
370	#125	—	2	2	no	—
371	#125	—	2	1	no	—
372	#124	—	2	1	no	—
373	C₂²⋊Q₈	—	2	2	no	—
374	C₂²⋊Q₈	—	2	4	no	—
375	C₂²⋊Q₈	—	2	4	no	—
376	C₂²⋊Q₈	—	2	2	no	—
377	C₂²⋊Q₈	—	2	4	no	—
378	C₂²⋊Q₈	—	2	1	no	—
379	C₂²⋊Q₈	D₄×C₇₉	1	2	yes	—
380	#121	—	2	1	no	—
381	#121	—	2	1	no	—
382	C₄×Q₈	—	2	2	no	—
383	C₄×Q₈	—	2	2	no	—
384	C₄×Q₈	—	2	2	no	—
385	C₄×Q₈	—	2	1	no	—
386	C₄×Q₈	D₄×C₇₉	1	1	yes	characteristic
387	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
388	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
389	C₄×D₄	—	2	4	no	—
390	C₄×D₄	—	2	2	no	—
391	C₄×D₄	—	2	1	no	—
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	—	2	1	no	—
394	C₄×D₄	—	2	1	no	—
395	C₄×D₄	D₄×C₇₉	1	1	yes	characteristic
396	C₄×D₄	C₂³×C₇₉	1	1	yes	characteristic
397	#117	—	2	2	no	—
398	#117	—	2	1	no	—
399	#117	—	2	1	no	—
400	#117	D₄×C₇₉	1	1	yes	characteristic
401	C₂×C₄⋊C₄	—	2	2	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	2	2	no	—
405	C₂×C₄²	—	2	1	no	—
406	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
407	#107	—	2	1	no	—
408	#107	—	2	2	no	—
409	#106	—	2	1	no	—
410	C₄⋊C₈	—	2	1	no	—
411	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
412	C₄⋊C₈	C₂³×C₇₉	1	1	yes	characteristic
413	C₄⋊C₈	C₂³×C₇₉	1	1	yes	characteristic
414	#103	—	2	1	no	—
415	#103	—	2	2	no	—
416	#102	—	2	1	no	—
417	#102	—	2	1	no	—
418	#102	—	2	1	no	—
419	#102	—	2	2	no	—
420	C₂²⋊C₈	—	2	1	no	—
421	#97	—	2	1	no	—
422	C₄×C₈	—	2	1	no	—
423	C₄×C₈	C₂³×C₇₉	1	2	yes	—
424	#41	—	2	2	no	—
425	#41	—	2	2	no	—
426	#41	—	4	4	no	—
427	C₂×Q₈	—	2	4	no	—
428	C₂×Q₈	—	2	2	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	—	4	4	no	—
432	C₂×Q₈	—	8	4	no	—
433	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
434	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
435	C₂×Q₈	C₂×D₄×C₇₉	1	4	yes	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	4	1	no	—
441	C₂×D₄	C₂×D₄×C₇₉	1	1	yes	characteristic
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	4	1	no	—
448	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
449	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
450	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
451	Q₁₆	—	4	8	no	—
452	SD₁₆	—	4	8	no	—
453	SD₁₆	—	4	2	no	—
454	SD₁₆	—	8	2	no	—
455	D₈	—	4	2	no	—
456	M₁₆	—	2	4	no	—
457	M₁₆	—	8	1	no	—
458	C₂×C₈	—	2	2	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	2	no	—
462	C₄⋊C₄	—	2	4	no	—
463	C₄⋊C₄	—	2	4	no	—
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	4	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
480	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
481	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
482	C₂²⋊C₄	—	2	4	no	—
483	C₂²⋊C₄	—	2	2	no	—
484	C₂²⋊C₄	—	2	1	no	—
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	4	1	no	—
488	C₂²⋊C₄	—	4	1	no	—
489	C₄²	—	2	4	no	—
490	C₄²	—	2	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	2	no	—
494	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
495	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
496	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
497	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
498	C₂³	—	2	1	no	—
499	C₂³	—	4	1	no	—
500	C₂³	#120×C₇₉	1	1	yes	characteristic
501	Q₈	—	2	1	no	—
502	Q₈	—	2	2	no	—
503	Q₈	—	2	2	no	—
504	Q₈	—	4	4	no	—
505	Q₈	—	4	2	no	—
506	Q₈	—	4	4	no	—
507	Q₈	—	4	2	no	—
508	Q₈	—	8	4	no	—
509	Q₈	#137×C₇₉	1	2	yes	complemented
510	D₄	—	2	4	no	—
511	D₄	—	2	1	no	—
512	D₄	—	4	2	no	—
513	D₄	—	4	1	no	—
514	D₄	—	4	1	no	—
515	D₄	—	4	1	no	—
516	D₄	—	4	1	no	—
517	D₄	—	8	2	no	—
518	D₄	#137×C₇₉	1	2	yes	complemented
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	8	2	no	—
536	C₂×C₄	—	8	4	no	—
537	C₂×C₄	—	8	2	no	—
538	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
539	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
540	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
541	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
542	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
543	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
544	C₈	—	2	4	no	—
545	C₈	—	4	1	no	—
546	C₈	—	4	1	no	—
547	C₈	—	4	2	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	2	2	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	8	1	no	—
555	C₂²	—	8	1	no	—
556	C₂²	—	8	1	no	—
557	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
558	C₄	—	2	1	no	—
559	C₄	—	2	2	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	4	no	—
566	C₄	—	4	2	no	—
567	C₄	—	8	1	no	—
568	C₄	#453×C₇₉	1	2	yes	—
569	C₄	C₂×#137×C₇₉	1	1	yes	characteristic
570	C₄	C₂×#137×C₇₉	1	1	yes	characteristic
571	C₄	#577×C₇₉	1	1	yes	characteristic
572	C₄	#578×C₇₉	1	1	yes	characteristic
573	C₂	—	4	1	no	—
574	C₂	—	4	2	no	—
575	C₂	—	16	1	no	—
576	C₂	C₇₉×#3004	1	1	yes	characteristic
577	C₂	C₇₉×#3013	1	1	yes	characteristic
578	C₂	C₂×#453×C₇₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₉
prime radical	C₇₉×#3106	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
1. C₇₉×#3503	C₂	semidirect
2. C₇₉×#3254	C₂	semidirect
3. C₇₉×#3152	C₂	semidirect
5. C₇₉×#1633	C₂	semidirect
6. C₇₉×#1632	C₂	semidirect
7. C₇₉×#1623	C₂	semidirect
8. C₇₉×#1622	C₂	semidirect
9. C₇₉×#1548	C₂	semidirect
10. C₇₉×#1489	C₂	semidirect
11. C₇₉×#1485	C₂	semidirect
219. Q₈×C₇₉	#137	semidirect
228. D₄×C₇₉	#137	semidirect
283. #18567	C₇₉	direct (N × H)
290. #3503	C₂×C₇₉	semidirect
291. #3254	C₂×C₇₉	semidirect
292. #3152	C₂×C₇₉	semidirect
294. #1633	C₂×C₇₉	semidirect
295. #1632	C₂×C₇₉	semidirect
296. #1623	C₂×C₇₉	semidirect
297. #1622	C₂×C₇₉	semidirect
298. #1548	C₂×C₇₉	semidirect
299. #1489	C₂×C₇₉	semidirect
300. #1485	C₂×C₇₉	semidirect
301. C₇₉	#18567	direct (N × H)
509. Q₈	#137×C₇₉	semidirect
518. D₄	#137×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₇₉×#3503	2
C₇₉×#3254	2
C₇₉×#3152	2
C₇₉×#3106	2
C₇₉×#1633	2
C₇₉×#1632	2
C₇₉×#1623	2
C₇₉×#1622	2
C₇₉×#1548	2
C₇₉×#1489	2
C₇₉×#1485	2
#18567	79

Subgroups — C79×#18567 #34130256

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#18567 #34130256