Subgroups — C₇₉×#18653 #34130342

Order 20224.

918 conjugacy classes of subgroups.

The subgroup lattice has 498 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
2	C₇₉×#3209	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#500×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#3079	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#1649	C₂	1	4	yes	maximal, complemented
6	C₇₉×#1648	C₂	1	4	yes	maximal, complemented
7	C₇₉×#1549	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#1493	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#1476	C₂	1	1	yes	maximal, characteristic
10	Q₈²×C₇₉	—	2	1	no	—
11	#557×C₇₉	C₂²	1	2	yes	—
12	#554×C₇₉	—	2	1	no	—
13	#554×C₇₉	—	2	2	no	—
14	D₄×Q₈×C₇₉	—	2	2	no	—
15	D₄×Q₈×C₇₉	C₂²	1	2	yes	—
16	#544×C₇₉	—	2	2	no	—
17	#544×C₇₉	—	2	1	no	—
18	#533×C₇₉	—	2	1	no	—
19	#533×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊Q₈×C₇₉	—	2	1	no	—
21	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
23	#520×C₇₉	—	2	1	no	—
24	C₄×#41×C₇₉	C₂²	1	1	yes	characteristic
25	#500×C₇₉	—	2	2	no	—
26	#500×C₇₉	C₂²	1	4	yes	—
27	#494×C₇₉	—	2	1	no	—
28	#487×C₇₉	—	2	1	no	—
29	#477×C₇₉	—	2	1	no	—
30	#476×C₇₉	—	2	1	no	—
31	#475×C₇₉	C₂²	1	2	yes	—
32	#474×C₇₉	C₂²	1	2	yes	—
33	#462×C₇₉	C₂²	1	4	yes	—
34	#451×C₇₉	—	2	2	no	—
35	#431×C₇₉	C₂²	1	1	yes	characteristic
36	#428×C₇₉	—	2	1	no	—
37	C₂×#107×C₇₉	—	2	2	no	—
38	#423×C₇₉	C₂²	1	1	yes	characteristic
39	#417×C₇₉	—	2	1	no	—
40	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
41	#332×C₇₉	C₂²	1	4	yes	—
42	Q₈⋊C₈×C₇₉	C₂²	1	4	yes	—
43	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	—
44	D₄⋊C₈×C₇₉	C₂²	1	2	yes	—
45	C₂×#41×C₇₉	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₇₉	—	2	2	no	—
47	C₂²×Q₈×C₇₉	—	2	1	no	—
48	C₂²×Q₈×C₇₉	—	2	1	no	—
49	C₂×Q₁₆×C₇₉	—	2	4	no	—
50	C₂×M₁₆×C₇₉	—	2	1	no	—
51	C₂²×C₈×C₇₉	—	2	1	no	—
52	C₄⋊Q₈×C₇₉	—	2	2	no	—
53	C₄⋊Q₈×C₇₉	—	2	2	no	—
54	C₄⋊Q₈×C₇₉	—	2	4	no	—
55	C₄⋊Q₈×C₇₉	—	2	2	no	—
56	C₄⋊Q₈×C₇₉	—	2	2	no	—
57	C₄⋊Q₈×C₇₉	—	2	1	no	—
58	C₄⋊Q₈×C₇₉	—	2	1	no	—
59	C₄⋊Q₈×C₇₉	—	2	1	no	—
60	C₄⋊Q₈×C₇₉	—	2	1	no	—
61	C₄⋊Q₈×C₇₉	—	2	1	no	—
62	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
63	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
64	C₄⋊Q₈×C₇₉	D₄	1	2	yes	—
65	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
66	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
67	#125×C₇₉	—	2	2	no	—
68	#125×C₇₉	—	2	4	no	—
69	#125×C₇₉	—	2	2	no	—
70	#125×C₇₉	—	2	1	no	—
71	C₂²⋊Q₈×C₇₉	—	2	2	no	—
72	C₂²⋊Q₈×C₇₉	—	2	4	no	—
73	C₂²⋊Q₈×C₇₉	—	2	4	no	—
74	C₂²⋊Q₈×C₇₉	—	2	1	no	—
75	C₂²⋊Q₈×C₇₉	—	2	2	no	—
76	C₂²⋊Q₈×C₇₉	—	2	4	no	—
77	C₂²⋊Q₈×C₇₉	D₄	1	2	yes	—
78	C₄×Q₈×C₇₉	—	2	2	no	—
79	C₄×Q₈×C₇₉	—	2	2	no	—
80	C₄×Q₈×C₇₉	—	2	2	no	—
81	C₄×Q₈×C₇₉	—	2	1	no	—
82	C₄×Q₈×C₇₉	D₄	1	1	yes	characteristic
83	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
84	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
85	C₄×D₄×C₇₉	—	2	4	no	—
86	C₄×D₄×C₇₉	—	2	2	no	—
87	C₄×D₄×C₇₉	—	2	1	no	—
88	C₄×D₄×C₇₉	—	2	1	no	—
89	C₄×D₄×C₇₉	D₄	1	1	yes	characteristic
90	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
91	#117×C₇₉	—	2	2	no	—
92	#117×C₇₉	—	2	1	no	—
93	#117×C₇₉	—	2	1	no	—
94	#117×C₇₉	D₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
96	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
97	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
98	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
100	C₂×C₄⋊C₄×C₇₉	D₄	1	2	yes	—
101	C₂×C₄²×C₇₉	—	2	1	no	—
102	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
103	#107×C₇₉	—	2	8	no	—
104	#107×C₇₉	—	2	2	no	—
105	#106×C₇₉	—	2	2	no	—
106	C₄⋊C₈×C₇₉	—	2	1	no	—
107	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
108	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
109	#103×C₇₉	—	2	2	no	—
110	#103×C₇₉	—	2	4	no	—
111	#102×C₇₉	—	2	2	no	—
112	C₂²⋊C₈×C₇₉	—	2	1	no	—
113	C₄×C₈×C₇₉	—	2	1	no	—
114	C₄×C₈×C₇₉	—	2	1	no	—
115	C₄×C₈×C₇₉	C₂³	1	2	yes	—
116	#41×C₇₉	—	2	2	no	—
117	#41×C₇₉	Q₁₆	1	4	yes	complemented
118	C₂×Q₈×C₇₉	—	2	4	no	—
119	C₂×Q₈×C₇₉	—	2	1	no	—
120	C₂×Q₈×C₇₉	—	2	2	no	—
121	C₂×Q₈×C₇₉	—	2	2	no	—
122	C₂×Q₈×C₇₉	—	2	2	no	—
123	C₂×Q₈×C₇₉	—	4	1	no	—
124	C₂×Q₈×C₇₉	—	8	2	no	—
125	C₂×Q₈×C₇₉	—	8	2	no	—
126	C₂×Q₈×C₇₉	—	8	4	no	—
127	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
128	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
129	C₂×D₄×C₇₉	—	2	1	no	—
130	C₂×D₄×C₇₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₇₉	—	2	1	no	—
132	C₂²×C₄×C₇₉	—	2	4	no	—
133	C₂²×C₄×C₇₉	—	2	2	no	—
134	C₂²×C₄×C₇₉	—	2	1	no	—
135	C₂²×C₄×C₇₉	—	2	1	no	—
136	C₂²×C₄×C₇₉	—	4	1	no	—
137	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
140	Q₁₆×C₇₉	—	8	4	no	—
141	M₁₆×C₇₉	—	4	2	no	—
142	C₂×C₈×C₇₉	—	2	4	no	—
143	C₂×C₈×C₇₉	—	2	2	no	—
144	C₂×C₈×C₇₉	—	2	2	no	—
145	C₂×C₈×C₇₉	—	2	2	no	—
146	C₄⋊C₄×C₇₉	—	2	4	no	—
147	C₄⋊C₄×C₇₉	—	2	4	no	—
148	C₄⋊C₄×C₇₉	—	2	4	no	—
149	C₄⋊C₄×C₇₉	—	2	4	no	—
150	C₄⋊C₄×C₇₉	—	2	1	no	—
151	C₄⋊C₄×C₇₉	—	2	2	no	—
152	C₄⋊C₄×C₇₉	—	2	1	no	—
153	C₄⋊C₄×C₇₉	—	2	2	no	—
154	C₄⋊C₄×C₇₉	—	2	1	no	—
155	C₄⋊C₄×C₇₉	—	2	1	no	—
156	C₄⋊C₄×C₇₉	—	2	2	no	—
157	C₄⋊C₄×C₇₉	—	2	2	no	—
158	C₄⋊C₄×C₇₉	—	2	1	no	—
159	C₄⋊C₄×C₇₉	—	2	2	no	—
160	C₄⋊C₄×C₇₉	—	2	2	no	—
161	C₄⋊C₄×C₇₉	—	2	2	no	—
162	C₄⋊C₄×C₇₉	—	4	1	no	—
163	C₄⋊C₄×C₇₉	—	4	1	no	—
164	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
165	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
166	C₄⋊C₄×C₇₉	C₂×D₄	1	4	yes	—
167	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
168	C₂²⋊C₄×C₇₉	—	2	4	no	—
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	1	no	—
173	C₄²×C₇₉	—	2	4	no	—
174	C₄²×C₇₉	—	2	1	no	—
175	C₄²×C₇₉	—	2	1	no	—
176	C₄²×C₇₉	—	2	1	no	—
177	C₄²×C₇₉	—	2	2	no	—
178	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
182	C₂³×C₇₉	—	2	1	no	—
183	C₂³×C₇₉	#120	1	1	yes	characteristic
184	Q₈×C₇₉	—	2	1	no	—
185	Q₈×C₇₉	—	2	4	no	—
186	Q₈×C₇₉	—	4	4	no	—
187	Q₈×C₇₉	—	4	2	no	—
188	Q₈×C₇₉	—	4	4	no	—
189	Q₈×C₇₉	—	8	2	no	—
190	Q₈×C₇₉	—	8	2	no	—
191	Q₈×C₇₉	—	8	4	no	—
192	Q₈×C₇₉	C₂×Q₁₆	1	2	yes	—
193	D₄×C₇₉	—	2	4	no	—
194	D₄×C₇₉	—	2	1	no	—
195	D₄×C₇₉	C₂×Q₁₆	1	2	yes	—
196	C₂×C₄×C₇₉	—	2	1	no	—
197	C₂×C₄×C₇₉	—	2	2	no	—
198	C₂×C₄×C₇₉	—	2	4	no	—
199	C₂×C₄×C₇₉	—	2	2	no	—
200	C₂×C₄×C₇₉	—	2	2	no	—
201	C₂×C₄×C₇₉	—	2	1	no	—
202	C₂×C₄×C₇₉	—	2	1	no	—
203	C₂×C₄×C₇₉	—	2	2	no	—
204	C₂×C₄×C₇₉	—	2	4	no	—
205	C₂×C₄×C₇₉	—	4	2	no	—
206	C₂×C₄×C₇₉	—	4	2	no	—
207	C₂×C₄×C₇₉	—	4	2	no	—
208	C₂×C₄×C₇₉	—	8	2	no	—
209	C₂×C₄×C₇₉	—	8	4	no	—
210	C₂×C₄×C₇₉	—	8	2	no	—
211	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
212	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
213	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
214	C₂×C₄×C₇₉	C₂×Q₁₆	1	2	yes	—
215	C₂×C₄×C₇₉	#137	1	2	yes	—
216	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
219	C₈×C₇₉	—	2	4	no	—
220	C₈×C₇₉	—	4	2	no	—
221	C₈×C₇₉	—	4	2	no	—
222	C₂²×C₇₉	—	2	1	no	—
223	C₂²×C₇₉	—	2	1	no	—
224	C₂²×C₇₉	—	2	2	no	—
225	C₂²×C₇₉	—	4	1	no	—
226	C₂²×C₇₉	—	4	1	no	—
227	C₂²×C₇₉	#451	1	2	yes	—
228	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
229	C₄×C₇₉	—	2	2	no	—
230	C₄×C₇₉	—	2	1	no	—
231	C₄×C₇₉	—	2	1	no	—
232	C₄×C₇₉	—	4	1	no	—
233	C₄×C₇₉	—	4	2	no	—
234	C₄×C₇₉	—	4	4	no	—
235	C₄×C₇₉	—	4	1	no	—
236	C₄×C₇₉	—	4	2	no	—
237	C₄×C₇₉	—	8	2	no	—
238	C₄×C₇₉	#451	1	2	yes	—
239	C₄×C₇₉	#456	1	2	yes	—
240	C₄×C₇₉	C₂²×Q₁₆	1	1	yes	characteristic
241	C₄×C₇₉	C₂×#137	1	1	yes	characteristic
242	C₄×C₇₉	#576	1	2	yes	—
243	#18653	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
244	C₂×C₇₉	—	2	2	no	—
245	C₂×C₇₉	—	4	2	no	—
246	C₂×C₇₉	C₂×#451	1	1	yes	characteristic
247	C₂×C₇₉	#3008	1	1	yes	characteristic
248	C₂×C₇₉	C₂×#456	1	1	yes	characteristic
249	#3503	C₂×C₇₉	1	1	yes	characteristic
250	#3209	C₂×C₇₉	1	1	yes	characteristic, complemented
251	C₂×#500	C₂×C₇₉	1	1	yes	characteristic, complemented
252	#3079	C₂×C₇₉	1	1	yes	characteristic
253	#1649	C₂×C₇₉	1	4	yes	complemented
254	#1648	C₂×C₇₉	1	4	yes	complemented
255	#1549	C₂×C₇₉	1	1	yes	characteristic, complemented
256	#1493	C₂×C₇₉	1	1	yes	characteristic, complemented
257	#1476	C₂×C₇₉	1	1	yes	characteristic
258	C₇₉	#18653	1	1	yes	characteristic, direct product factor, Sylow
259	Q₈²	—	2	1	no	—
260	#557	C₂²×C₇₉	1	2	yes	—
261	#554	—	2	1	no	—
262	#554	—	2	2	no	—
263	D₄×Q₈	—	2	2	no	—
264	D₄×Q₈	C₂²×C₇₉	1	2	yes	—
265	#544	—	2	2	no	—
266	#544	—	2	1	no	—
267	#533	—	2	1	no	—
268	#533	C₂²×C₇₉	1	1	yes	characteristic
269	C₂×C₄⋊Q₈	—	2	1	no	—
270	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
271	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
272	#520	—	2	1	no	—
273	C₄×#41	C₂²×C₇₉	1	1	yes	characteristic
274	#500	—	2	2	no	—
275	#500	C₂²×C₇₉	1	4	yes	—
276	#494	—	2	1	no	—
277	#487	—	2	1	no	—
278	#477	—	2	1	no	—
279	#476	—	2	1	no	—
280	#475	C₂²×C₇₉	1	2	yes	—
281	#474	C₂²×C₇₉	1	2	yes	—
282	#462	C₂²×C₇₉	1	4	yes	—
283	#451	—	2	2	no	—
284	#431	C₂²×C₇₉	1	1	yes	characteristic
285	#428	—	2	1	no	—
286	C₂×#107	—	2	2	no	—
287	#423	C₂²×C₇₉	1	1	yes	characteristic
288	#417	—	2	1	no	—
289	C₂×C₄×C₈	C₂²×C₇₉	1	1	yes	characteristic
290	#332	C₂²×C₇₉	1	4	yes	—
291	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	—
292	Q₈⋊C₈	C₂²×C₇₉	1	4	yes	—
293	D₄⋊C₈	C₂²×C₇₉	1	2	yes	—
294	C₂×#41	D₄×C₇₉	1	1	yes	characteristic
295	C₂²×Q₈	—	2	2	no	—
296	C₂²×Q₈	—	2	1	no	—
297	C₂²×Q₈	—	2	1	no	—
298	C₂×Q₁₆	—	2	4	no	—
299	C₂×M₁₆	—	2	1	no	—
300	C₂²×C₈	—	2	1	no	—
301	C₄⋊Q₈	—	2	2	no	—
302	C₄⋊Q₈	—	2	2	no	—
303	C₄⋊Q₈	—	2	4	no	—
304	C₄⋊Q₈	—	2	2	no	—
305	C₄⋊Q₈	—	2	2	no	—
306	C₄⋊Q₈	—	2	1	no	—
307	C₄⋊Q₈	—	2	1	no	—
308	C₄⋊Q₈	—	2	1	no	—
309	C₄⋊Q₈	—	2	1	no	—
310	C₄⋊Q₈	—	2	1	no	—
311	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
312	C₄⋊Q₈	D₄×C₇₉	1	2	yes	—
313	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
314	C₄⋊Q₈	C₂³×C₇₉	1	2	yes	—
315	C₄⋊Q₈	C₂³×C₇₉	1	2	yes	—
316	#125	—	2	2	no	—
317	#125	—	2	4	no	—
318	#125	—	2	2	no	—
319	#125	—	2	1	no	—
320	C₂²⋊Q₈	—	2	2	no	—
321	C₂²⋊Q₈	—	2	4	no	—
322	C₂²⋊Q₈	—	2	4	no	—
323	C₂²⋊Q₈	—	2	1	no	—
324	C₂²⋊Q₈	—	2	2	no	—
325	C₂²⋊Q₈	—	2	4	no	—
326	C₂²⋊Q₈	D₄×C₇₉	1	2	yes	—
327	C₄×Q₈	—	2	2	no	—
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	—	2	2	no	—
330	C₄×Q₈	—	2	1	no	—
331	C₄×Q₈	D₄×C₇₉	1	1	yes	characteristic
332	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
333	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
334	C₄×D₄	—	2	4	no	—
335	C₄×D₄	—	2	2	no	—
336	C₄×D₄	—	2	1	no	—
337	C₄×D₄	—	2	1	no	—
338	C₄×D₄	D₄×C₇₉	1	1	yes	characteristic
339	C₄×D₄	C₂³×C₇₉	1	1	yes	characteristic
340	#117	—	2	2	no	—
341	#117	—	2	1	no	—
342	#117	—	2	1	no	—
343	#117	D₄×C₇₉	1	1	yes	characteristic
344	C₂×C₄⋊C₄	—	2	2	no	—
345	C₂×C₄⋊C₄	—	2	2	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	D₄×C₇₉	1	2	yes	—
350	C₂×C₄²	—	2	1	no	—
351	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
352	#107	—	2	8	no	—
353	#107	—	2	2	no	—
354	#106	—	2	2	no	—
355	C₄⋊C₈	—	2	1	no	—
356	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
357	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
358	#103	—	2	2	no	—
359	#103	—	2	4	no	—
360	#102	—	2	2	no	—
361	C₂²⋊C₈	—	2	1	no	—
362	C₄×C₈	—	2	1	no	—
363	C₄×C₈	—	2	1	no	—
364	C₄×C₈	C₂³×C₇₉	1	2	yes	—
365	#41	—	2	2	no	—
366	#41	Q₁₆×C₇₉	1	4	yes	complemented
367	C₂×Q₈	—	2	4	no	—
368	C₂×Q₈	—	2	1	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	4	1	no	—
373	C₂×Q₈	—	8	2	no	—
374	C₂×Q₈	—	8	2	no	—
375	C₂×Q₈	—	8	4	no	—
376	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
377	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	C₂×D₄×C₇₉	1	1	yes	characteristic
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	4	1	no	—
386	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
387	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
389	Q₁₆	—	8	4	no	—
390	M₁₆	—	4	2	no	—
391	C₂×C₈	—	2	4	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₄⋊C₄	—	2	4	no	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	—	2	4	no	—
398	C₄⋊C₄	—	2	4	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	4	1	no	—
412	C₄⋊C₄	—	4	1	no	—
413	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
414	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
415	C₄⋊C₄	C₂×D₄×C₇₉	1	4	yes	—
416	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
417	C₂²⋊C₄	—	2	4	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	1	no	—
420	C₂²⋊C₄	—	2	1	no	—
421	C₂²⋊C₄	—	2	1	no	—
422	C₄²	—	2	4	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	1	no	—
425	C₄²	—	2	1	no	—
426	C₄²	—	2	2	no	—
427	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
428	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
429	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
430	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
431	C₂³	—	2	1	no	—
432	C₂³	#120×C₇₉	1	1	yes	characteristic
433	Q₈	—	2	1	no	—
434	Q₈	—	2	4	no	—
435	Q₈	—	4	2	no	—
436	Q₈	—	4	4	no	—
437	Q₈	—	4	4	no	—
438	Q₈	—	8	2	no	—
439	Q₈	—	8	2	no	—
440	Q₈	—	8	4	no	—
441	Q₈	C₂×Q₁₆×C₇₉	1	2	yes	—
442	D₄	—	2	4	no	—
443	D₄	—	2	1	no	—
444	D₄	C₂×Q₁₆×C₇₉	1	2	yes	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	8	2	no	—
458	C₂×C₄	—	8	4	no	—
459	C₂×C₄	—	8	2	no	—
460	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
461	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
462	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
463	C₂×C₄	C₂×Q₁₆×C₇₉	1	2	yes	—
464	C₂×C₄	#137×C₇₉	1	2	yes	—
465	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
466	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
467	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
468	C₈	—	2	4	no	—
469	C₈	—	4	2	no	—
470	C₈	—	4	2	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	2	1	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	4	1	no	—
476	C₂²	#451×C₇₉	1	2	yes	—
477	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
478	C₄	—	2	2	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	4	1	no	—
482	C₄	—	4	2	no	—
483	C₄	—	4	4	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	2	no	—
486	C₄	—	8	2	no	—
487	C₄	#451×C₇₉	1	2	yes	—
488	C₄	#456×C₇₉	1	2	yes	—
489	C₄	C₂²×Q₁₆×C₇₉	1	1	yes	characteristic
490	C₄	C₂×#137×C₇₉	1	1	yes	characteristic
491	C₄	#576×C₇₉	1	2	yes	—
492	C₂	—	2	2	no	—
493	C₂	—	4	2	no	—
494	C₂	C₂×#451×C₇₉	1	1	yes	characteristic
495	C₂	C₇₉×#3008	1	1	yes	characteristic
496	C₂	C₂×#456×C₇₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₉
prime radical	C₂×#41×C₇₉	D₄
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×#3209	C₂	semidirect
3. C₂×#500×C₇₉	C₂	semidirect
5. C₇₉×#1649	C₂	semidirect
6. C₇₉×#1648	C₂	semidirect
7. C₇₉×#1549	C₂	semidirect
8. C₇₉×#1493	C₂	semidirect
117. #41×C₇₉	Q₁₆	semidirect
243. #18653	C₇₉	direct (N × H)
250. #3209	C₂×C₇₉	semidirect
251. C₂×#500	C₂×C₇₉	semidirect
253. #1649	C₂×C₇₉	semidirect
254. #1648	C₂×C₇₉	semidirect
255. #1549	C₂×C₇₉	semidirect
256. #1493	C₂×C₇₉	semidirect
258. C₇₉	#18653	direct (N × H)
366. #41	Q₁₆×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×#3209	2
C₂×#500×C₇₉	2
C₇₉×#3079	2
C₇₉×#1649	2
C₇₉×#1648	2
C₇₉×#1549	2
C₇₉×#1493	2
C₇₉×#1476	2
#18653	79

Subgroups — C79×#18653 #34130342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#18653 #34130342