Subgroups — C₇₉×#18856 #34130545

Order 20224.

956 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₉×#3254	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#3207	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#3109	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#1638	C₂	1	2	yes	maximal, complemented
6	C₇₉×#1631	C₂	1	2	yes	maximal, complemented
7	C₇₉×#1628	C₂	1	2	yes	maximal, complemented
8	C₇₉×#1621	C₂	1	2	yes	maximal, complemented
9	C₇₉×#1557	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#1497	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1486	C₂	1	1	yes	maximal, characteristic, complemented
12	#559×C₇₉	—	2	2	no	—
13	#556×C₇₉	C₂²	1	2	yes	—
14	#555×C₇₉	—	2	1	no	—
15	#553×C₇₉	—	2	2	no	—
16	#550×C₇₉	C₂²	1	2	yes	—
17	#547×C₇₉	—	2	1	no	—
18	#538×C₇₉	—	2	2	no	—
19	#535×C₇₉	—	2	1	no	—
20	#533×C₇₉	C₂²	1	1	yes	characteristic
21	#532×C₇₉	C₂²	1	1	yes	characteristic
22	#532×C₇₉	C₂²	1	1	yes	characteristic
23	#525×C₇₉	—	2	2	no	—
24	#520×C₇₉	—	2	1	no	—
25	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
26	#493×C₇₉	C₂²	1	1	yes	characteristic, complemented
27	#492×C₇₉	C₂²	1	1	yes	characteristic, complemented
28	#487×C₇₉	C₂²	1	1	yes	characteristic, complemented
29	#486×C₇₉	C₂²	1	1	yes	characteristic, complemented
30	#481×C₇₉	—	2	1	no	—
31	#477×C₇₉	C₂²	1	2	yes	complemented
32	#476×C₇₉	C₂²	1	2	yes	—
33	#474×C₇₉	—	2	1	no	—
34	#468×C₇₉	—	2	2	no	—
35	#463×C₇₉	—	2	2	no	—
36	#461×C₇₉	—	2	1	no	—
37	#460×C₇₉	C₂²	1	2	yes	complemented
38	#459×C₇₉	C₂²	1	2	yes	—
39	#449×C₇₉	—	2	2	no	—
40	#447×C₇₉	—	2	1	no	—
41	#442×C₇₉	—	2	2	no	—
42	#432×C₇₉	C₂²	1	1	yes	characteristic
43	#431×C₇₉	C₂²	1	1	yes	characteristic
44	#423×C₇₉	C₂²	1	1	yes	characteristic
45	#332×C₇₉	C₂²	1	2	yes	complemented
46	#331×C₇₉	C₂²	1	2	yes	complemented
47	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	complemented
48	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	complemented
49	D₄⋊C₈×C₇₉	C₂²	1	2	yes	—
50	D₄⋊C₈×C₇₉	C₂²	1	2	yes	—
51	C₂×#41×C₇₉	—	2	2	no	—
52	C₂×#41×C₇₉	—	2	1	no	—
53	C₂×#41×C₇₉	—	2	1	no	—
54	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₇₉	—	2	1	no	—
56	C₂×SD₁₆×C₇₉	—	2	2	no	—
57	C₂×SD₁₆×C₇₉	—	2	2	no	—
58	C₂×D₈×C₇₉	—	2	2	no	—
59	C₂×D₈×C₇₉	—	2	2	no	—
60	C₂×M₁₆×C₇₉	—	2	1	no	—
61	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
62	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
63	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
64	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
65	#127×C₇₉	—	2	2	no	—
66	#127×C₇₉	C₂³	1	1	yes	characteristic
67	#127×C₇₉	C₂³	1	1	yes	characteristic
68	#126×C₇₉	—	2	4	no	—
69	#125×C₇₉	—	2	1	no	—
70	#124×C₇₉	—	2	4	no	—
71	#124×C₇₉	—	2	2	no	—
72	#124×C₇₉	—	2	1	no	—
73	#124×C₇₉	—	2	1	no	—
74	#123×C₇₉	—	2	4	no	—
75	#123×C₇₉	—	2	4	no	—
76	C₂²⋊Q₈×C₇₉	—	2	2	no	—
77	C₂²⋊Q₈×C₇₉	—	2	1	no	—
78	C₂²⋊Q₈×C₇₉	D₄	1	2	yes	—
79	#121×C₇₉	—	2	2	no	—
80	#121×C₇₉	—	2	2	no	—
81	#121×C₇₉	—	2	4	no	—
82	#121×C₇₉	—	2	1	no	—
83	#121×C₇₉	—	2	2	no	—
84	#121×C₇₉	—	2	1	no	—
85	#121×C₇₉	—	2	1	no	—
86	#121×C₇₉	D₄	1	2	yes	—
87	#120×C₇₉	—	2	4	no	—
88	C₄×Q₈×C₇₉	—	2	2	no	—
89	C₄×Q₈×C₇₉	—	2	1	no	—
90	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
91	C₄×D₄×C₇₉	—	2	4	no	—
92	C₄×D₄×C₇₉	—	2	4	no	—
93	C₄×D₄×C₇₉	—	2	2	no	—
94	C₄×D₄×C₇₉	—	2	1	no	—
95	C₄×D₄×C₇₉	—	2	1	no	—
96	C₄×D₄×C₇₉	—	2	1	no	—
97	C₄×D₄×C₇₉	—	2	1	no	—
98	C₄×D₄×C₇₉	—	2	1	no	—
99	C₄×D₄×C₇₉	D₄	1	2	yes	—
100	C₄×D₄×C₇₉	D₄	1	2	yes	—
101	C₄×D₄×C₇₉	C₂³	1	2	yes	—
102	#117×C₇₉	—	2	2	no	—
103	#117×C₇₉	—	2	1	no	—
104	#117×C₇₉	—	2	2	no	—
105	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
106	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
108	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
109	#107×C₇₉	—	2	2	no	—
110	#106×C₇₉	—	2	2	no	—
111	C₄⋊C₈×C₇₉	—	2	1	no	—
112	C₄⋊C₈×C₇₉	—	2	1	no	—
113	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
114	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
115	#103×C₇₉	—	2	2	no	—
116	#103×C₇₉	—	2	2	no	—
117	#102×C₇₉	—	2	2	no	—
118	#102×C₇₉	—	2	2	no	—
119	#102×C₇₉	—	2	2	no	—
120	#102×C₇₉	—	2	2	no	—
121	C₂²⋊C₈×C₇₉	—	2	1	no	—
122	C₂²⋊C₈×C₇₉	—	2	1	no	—
123	#97×C₇₉	—	2	1	no	—
124	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
125	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
126	C₂⁴×C₇₉	—	2	1	no	—
127	#41×C₇₉	—	4	4	no	—
128	#41×C₇₉	—	8	2	no	—
129	#41×C₇₉	—	8	2	no	—
130	#41×C₇₉	—	8	2	no	—
131	C₂×Q₈×C₇₉	—	2	1	no	—
132	C₂×Q₈×C₇₉	—	2	1	no	—
133	C₂×Q₈×C₇₉	—	2	1	no	—
134	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
135	C₂×D₄×C₇₉	—	2	2	no	—
136	C₂×D₄×C₇₉	—	2	4	no	—
137	C₂×D₄×C₇₉	—	2	4	no	—
138	C₂×D₄×C₇₉	—	2	1	no	—
139	C₂×D₄×C₇₉	—	2	1	no	—
140	C₂×D₄×C₇₉	—	2	1	no	—
141	C₂×D₄×C₇₉	—	2	1	no	—
142	C₂×D₄×C₇₉	—	2	1	no	—
143	C₂×D₄×C₇₉	—	2	1	no	—
144	C₂×D₄×C₇₉	—	4	2	no	—
145	C₂×D₄×C₇₉	—	4	1	no	—
146	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
147	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₇₉	—	2	4	no	—
149	C₂²×C₄×C₇₉	—	2	1	no	—
150	C₂²×C₄×C₇₉	—	2	2	no	—
151	C₂²×C₄×C₇₉	—	2	2	no	—
152	C₂²×C₄×C₇₉	—	2	2	no	—
153	C₂²×C₄×C₇₉	—	4	1	no	—
154	C₂²×C₄×C₇₉	—	8	1	no	—
155	C₂²×C₄×C₇₉	—	8	1	no	—
156	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
159	SD₁₆×C₇₉	—	8	2	no	—
160	SD₁₆×C₇₉	—	8	2	no	—
161	D₈×C₇₉	—	4	4	no	—
162	D₈×C₇₉	—	8	2	no	—
163	M₁₆×C₇₉	—	8	1	no	—
164	C₂×C₈×C₇₉	—	2	1	no	—
165	C₂×C₈×C₇₉	—	2	1	no	—
166	C₂×C₈×C₇₉	—	2	2	no	—
167	C₂×C₈×C₇₉	—	2	2	no	—
168	C₄⋊C₄×C₇₉	—	2	4	no	—
169	C₄⋊C₄×C₇₉	—	2	1	no	—
170	C₄⋊C₄×C₇₉	—	2	1	no	—
171	C₄⋊C₄×C₇₉	—	2	1	no	—
172	C₄⋊C₄×C₇₉	—	2	2	no	—
173	C₄⋊C₄×C₇₉	—	2	1	no	—
174	C₄⋊C₄×C₇₉	—	2	1	no	—
175	C₄⋊C₄×C₇₉	—	2	2	no	—
176	C₄⋊C₄×C₇₉	—	2	1	no	—
177	C₄⋊C₄×C₇₉	—	2	1	no	—
178	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
179	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
180	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
181	C₂²⋊C₄×C₇₉	—	2	4	no	—
182	C₂²⋊C₄×C₇₉	—	2	4	no	—
183	C₂²⋊C₄×C₇₉	—	2	4	no	—
184	C₂²⋊C₄×C₇₉	—	2	2	no	—
185	C₂²⋊C₄×C₇₉	—	2	2	no	—
186	C₂²⋊C₄×C₇₉	—	2	2	no	—
187	C₂²⋊C₄×C₇₉	—	2	2	no	—
188	C₂²⋊C₄×C₇₉	—	2	2	no	—
189	C₂²⋊C₄×C₇₉	—	4	1	no	—
190	C₂²⋊C₄×C₇₉	—	4	1	no	—
191	C₄²×C₇₉	—	2	4	no	—
192	C₄²×C₇₉	—	2	2	no	—
193	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
195	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
196	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
197	C₂³×C₇₉	—	2	2	no	—
198	C₂³×C₇₉	—	2	2	no	—
199	C₂³×C₇₉	—	4	2	no	—
200	C₂³×C₇₉	—	4	1	no	—
201	C₂³×C₇₉	—	8	1	no	—
202	C₂³×C₇₉	—	8	1	no	—
203	C₂³×C₇₉	#120	1	1	yes	characteristic
204	Q₈×C₇₉	—	2	2	no	—
205	Q₈×C₇₉	—	2	2	no	—
206	Q₈×C₇₉	—	4	2	no	—
207	Q₈×C₇₉	—	4	2	no	—
208	Q₈×C₇₉	—	8	1	no	—
209	D₄×C₇₉	—	2	2	no	—
210	D₄×C₇₉	—	2	2	no	—
211	D₄×C₇₉	—	4	2	no	—
212	D₄×C₇₉	—	4	2	no	—
213	D₄×C₇₉	—	4	2	no	—
214	D₄×C₇₉	—	4	4	no	—
215	D₄×C₇₉	—	4	2	no	—
216	D₄×C₇₉	—	4	2	no	—
217	D₄×C₇₉	—	4	1	no	—
218	D₄×C₇₉	—	4	1	no	—
219	D₄×C₇₉	—	4	1	no	—
220	D₄×C₇₉	—	4	1	no	—
221	D₄×C₇₉	—	8	4	no	—
222	D₄×C₇₉	—	8	4	no	—
223	D₄×C₇₉	—	8	2	no	—
224	C₂×C₄×C₇₉	—	2	2	no	—
225	C₂×C₄×C₇₉	—	2	1	no	—
226	C₂×C₄×C₇₉	—	2	1	no	—
227	C₂×C₄×C₇₉	—	2	2	no	—
228	C₂×C₄×C₇₉	—	2	2	no	—
229	C₂×C₄×C₇₉	—	2	2	no	—
230	C₂×C₄×C₇₉	—	2	2	no	—
231	C₂×C₄×C₇₉	—	4	1	no	—
232	C₂×C₄×C₇₉	—	4	4	no	—
233	C₂×C₄×C₇₉	—	4	2	no	—
234	C₂×C₄×C₇₉	—	4	2	no	—
235	C₂×C₄×C₇₉	—	4	1	no	—
236	C₂×C₄×C₇₉	—	8	2	no	—
237	C₂×C₄×C₇₉	—	8	2	no	—
238	C₂×C₄×C₇₉	—	8	1	no	—
239	C₂×C₄×C₇₉	—	8	4	no	—
240	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
241	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
242	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
243	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
246	C₈×C₇₉	—	4	1	no	—
247	C₈×C₇₉	—	4	1	no	—
248	C₈×C₇₉	—	4	2	no	—
249	C₈×C₇₉	—	4	2	no	—
250	C₂²×C₇₉	—	2	1	no	—
251	C₂²×C₇₉	—	2	1	no	—
252	C₂²×C₇₉	—	2	1	no	—
253	C₂²×C₇₉	—	4	2	no	—
254	C₂²×C₇₉	—	4	2	no	—
255	C₂²×C₇₉	—	4	2	no	—
256	C₂²×C₇₉	—	4	2	no	—
257	C₂²×C₇₉	—	4	2	no	—
258	C₂²×C₇₉	—	4	2	no	—
259	C₂²×C₇₉	—	8	4	no	—
260	C₂²×C₇₉	—	8	1	no	—
261	C₂²×C₇₉	—	8	1	no	—
262	C₂²×C₇₉	—	8	1	no	—
263	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
264	C₄×C₇₉	—	2	1	no	—
265	C₄×C₇₉	—	2	1	no	—
266	C₄×C₇₉	—	2	1	no	—
267	C₄×C₇₉	—	2	1	no	—
268	C₄×C₇₉	—	4	2	no	—
269	C₄×C₇₉	—	4	2	no	—
270	C₄×C₇₉	—	4	2	no	—
271	C₄×C₇₉	—	4	2	no	—
272	C₄×C₇₉	—	8	1	no	—
273	C₄×C₇₉	#575	1	2	yes	—
274	C₄×C₇₉	#576	1	1	yes	characteristic
275	C₄×C₇₉	#577	1	1	yes	characteristic
276	#18856	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
277	C₂×C₇₉	—	4	1	no	—
278	C₂×C₇₉	—	8	2	no	—
279	C₂×C₇₉	—	8	2	no	—
280	C₂×C₇₉	—	16	1	no	—
281	C₂×C₇₉	#3005	1	1	yes	characteristic
282	C₂×C₇₉	#3012	1	1	yes	characteristic
283	C₂×C₇₉	#3021	1	1	yes	characteristic
284	#3506	C₂×C₇₉	1	1	yes	characteristic, complemented
285	#3254	C₂×C₇₉	1	1	yes	characteristic, complemented
286	#3207	C₂×C₇₉	1	1	yes	characteristic, complemented
287	#3109	C₂×C₇₉	1	1	yes	characteristic, complemented
288	#1638	C₂×C₇₉	1	2	yes	complemented
289	#1631	C₂×C₇₉	1	2	yes	complemented
290	#1628	C₂×C₇₉	1	2	yes	complemented
291	#1621	C₂×C₇₉	1	2	yes	complemented
292	#1557	C₂×C₇₉	1	1	yes	characteristic, complemented
293	#1497	C₂×C₇₉	1	1	yes	characteristic, complemented
294	#1486	C₂×C₇₉	1	1	yes	characteristic, complemented
295	C₇₉	#18856	1	1	yes	characteristic, direct product factor, Sylow
296	#559	—	2	2	no	—
297	#556	C₂²×C₇₉	1	2	yes	—
298	#555	—	2	1	no	—
299	#553	—	2	2	no	—
300	#550	C₂²×C₇₉	1	2	yes	—
301	#547	—	2	1	no	—
302	#538	—	2	2	no	—
303	#535	—	2	1	no	—
304	#533	C₂²×C₇₉	1	1	yes	characteristic
305	#532	C₂²×C₇₉	1	1	yes	characteristic
306	#532	C₂²×C₇₉	1	1	yes	characteristic
307	#525	—	2	2	no	—
308	#520	—	2	1	no	—
309	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
310	#493	C₂²×C₇₉	1	1	yes	characteristic, complemented
311	#492	C₂²×C₇₉	1	1	yes	characteristic, complemented
312	#487	C₂²×C₇₉	1	1	yes	characteristic, complemented
313	#486	C₂²×C₇₉	1	1	yes	characteristic, complemented
314	#481	—	2	1	no	—
315	#477	C₂²×C₇₉	1	2	yes	complemented
316	#476	C₂²×C₇₉	1	2	yes	—
317	#474	—	2	1	no	—
318	#468	—	2	2	no	—
319	#463	—	2	2	no	—
320	#461	—	2	1	no	—
321	#460	C₂²×C₇₉	1	2	yes	complemented
322	#459	C₂²×C₇₉	1	2	yes	—
323	#449	—	2	2	no	—
324	#447	—	2	1	no	—
325	#442	—	2	2	no	—
326	#432	C₂²×C₇₉	1	1	yes	characteristic
327	#431	C₂²×C₇₉	1	1	yes	characteristic
328	#423	C₂²×C₇₉	1	1	yes	characteristic
329	#332	C₂²×C₇₉	1	2	yes	complemented
330	#331	C₂²×C₇₉	1	2	yes	complemented
331	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	complemented
332	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	complemented
333	D₄⋊C₈	C₂²×C₇₉	1	2	yes	—
334	D₄⋊C₈	C₂²×C₇₉	1	2	yes	—
335	C₂×#41	—	2	2	no	—
336	C₂×#41	—	2	1	no	—
337	C₂×#41	—	2	1	no	—
338	C₂²×D₄	D₄×C₇₉	1	1	yes	characteristic
339	C₂³×C₄	—	2	1	no	—
340	C₂×SD₁₆	—	2	2	no	—
341	C₂×SD₁₆	—	2	2	no	—
342	C₂×D₈	—	2	2	no	—
343	C₂×D₈	—	2	2	no	—
344	C₂×M₁₆	—	2	1	no	—
345	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
346	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
347	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
348	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
349	#127	—	2	2	no	—
350	#127	C₂³×C₇₉	1	1	yes	characteristic
351	#127	C₂³×C₇₉	1	1	yes	characteristic
352	#126	—	2	4	no	—
353	#125	—	2	1	no	—
354	#124	—	2	4	no	—
355	#124	—	2	2	no	—
356	#124	—	2	1	no	—
357	#124	—	2	1	no	—
358	#123	—	2	4	no	—
359	#123	—	2	4	no	—
360	C₂²⋊Q₈	—	2	2	no	—
361	C₂²⋊Q₈	—	2	1	no	—
362	C₂²⋊Q₈	D₄×C₇₉	1	2	yes	—
363	#121	—	2	2	no	—
364	#121	—	2	2	no	—
365	#121	—	2	4	no	—
366	#121	—	2	1	no	—
367	#121	—	2	2	no	—
368	#121	—	2	1	no	—
369	#121	—	2	1	no	—
370	#121	D₄×C₇₉	1	2	yes	—
371	#120	—	2	4	no	—
372	C₄×Q₈	—	2	2	no	—
373	C₄×Q₈	—	2	1	no	—
374	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
375	C₄×D₄	—	2	4	no	—
376	C₄×D₄	—	2	4	no	—
377	C₄×D₄	—	2	2	no	—
378	C₄×D₄	—	2	1	no	—
379	C₄×D₄	—	2	1	no	—
380	C₄×D₄	—	2	1	no	—
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	D₄×C₇₉	1	2	yes	—
384	C₄×D₄	D₄×C₇₉	1	2	yes	—
385	C₄×D₄	C₂³×C₇₉	1	2	yes	—
386	#117	—	2	2	no	—
387	#117	—	2	1	no	—
388	#117	—	2	2	no	—
389	C₂×C₄⋊C₄	—	2	2	no	—
390	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
391	C₂×C₂²⋊C₄	—	2	1	no	—
392	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
393	#107	—	2	2	no	—
394	#106	—	2	2	no	—
395	C₄⋊C₈	—	2	1	no	—
396	C₄⋊C₈	—	2	1	no	—
397	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
398	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
399	#103	—	2	2	no	—
400	#103	—	2	2	no	—
401	#102	—	2	2	no	—
402	#102	—	2	2	no	—
403	#102	—	2	2	no	—
404	#102	—	2	2	no	—
405	C₂²⋊C₈	—	2	1	no	—
406	C₂²⋊C₈	—	2	1	no	—
407	#97	—	2	1	no	—
408	C₄×C₈	C₂³×C₇₉	1	1	yes	characteristic
409	C₄×C₈	C₂³×C₇₉	1	1	yes	characteristic
410	C₂⁴	—	2	1	no	—
411	#41	—	4	4	no	—
412	#41	—	8	2	no	—
413	#41	—	8	2	no	—
414	#41	—	8	2	no	—
415	C₂×Q₈	—	2	1	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	—	2	4	no	—
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	—	2	1	no	—
427	C₂×D₄	—	2	1	no	—
428	C₂×D₄	—	4	2	no	—
429	C₂×D₄	—	4	1	no	—
430	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
431	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	4	1	no	—
438	C₂²×C₄	—	8	1	no	—
439	C₂²×C₄	—	8	1	no	—
440	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
443	SD₁₆	—	8	2	no	—
444	SD₁₆	—	8	2	no	—
445	D₈	—	4	4	no	—
446	D₈	—	8	2	no	—
447	M₁₆	—	8	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	2	no	—
451	C₂×C₈	—	2	2	no	—
452	C₄⋊C₄	—	2	4	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
463	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
464	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
465	C₂²⋊C₄	—	2	4	no	—
466	C₂²⋊C₄	—	2	4	no	—
467	C₂²⋊C₄	—	2	4	no	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₂²⋊C₄	—	2	2	no	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	—	4	1	no	—
474	C₂²⋊C₄	—	4	1	no	—
475	C₄²	—	2	4	no	—
476	C₄²	—	2	2	no	—
477	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
478	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
479	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
480	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
481	C₂³	—	2	2	no	—
482	C₂³	—	2	2	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	4	1	no	—
485	C₂³	—	8	1	no	—
486	C₂³	—	8	1	no	—
487	C₂³	#120×C₇₉	1	1	yes	characteristic
488	Q₈	—	2	2	no	—
489	Q₈	—	2	2	no	—
490	Q₈	—	4	2	no	—
491	Q₈	—	4	2	no	—
492	Q₈	—	8	1	no	—
493	D₄	—	2	2	no	—
494	D₄	—	2	2	no	—
495	D₄	—	4	2	no	—
496	D₄	—	4	2	no	—
497	D₄	—	4	2	no	—
498	D₄	—	4	4	no	—
499	D₄	—	4	2	no	—
500	D₄	—	4	2	no	—
501	D₄	—	4	1	no	—
502	D₄	—	4	1	no	—
503	D₄	—	4	1	no	—
504	D₄	—	4	1	no	—
505	D₄	—	8	4	no	—
506	D₄	—	8	4	no	—
507	D₄	—	8	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	4	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	8	2	no	—
521	C₂×C₄	—	8	2	no	—
522	C₂×C₄	—	8	1	no	—
523	C₂×C₄	—	8	4	no	—
524	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
525	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
526	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
527	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
528	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
529	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
530	C₈	—	4	1	no	—
531	C₈	—	4	1	no	—
532	C₈	—	4	2	no	—
533	C₈	—	4	2	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	4	2	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	2	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	8	4	no	—
544	C₂²	—	8	1	no	—
545	C₂²	—	8	1	no	—
546	C₂²	—	8	1	no	—
547	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	2	no	—
554	C₄	—	4	2	no	—
555	C₄	—	4	2	no	—
556	C₄	—	8	1	no	—
557	C₄	#575×C₇₉	1	2	yes	—
558	C₄	#576×C₇₉	1	1	yes	characteristic
559	C₄	#577×C₇₉	1	1	yes	characteristic
560	C₂	—	4	1	no	—
561	C₂	—	8	2	no	—
562	C₂	—	8	2	no	—
563	C₂	—	16	1	no	—
564	C₂	C₇₉×#3005	1	1	yes	characteristic
565	C₂	C₇₉×#3012	1	1	yes	characteristic
566	C₂	C₇₉×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₉
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×#3506	C₂	semidirect
2. C₇₉×#3254	C₂	semidirect
3. C₇₉×#3207	C₂	semidirect
4. C₇₉×#3109	C₂	semidirect
5. C₇₉×#1638	C₂	semidirect
6. C₇₉×#1631	C₂	semidirect
7. C₇₉×#1628	C₂	semidirect
8. C₇₉×#1621	C₂	semidirect
9. C₇₉×#1557	C₂	semidirect
10. C₇₉×#1497	C₂	semidirect
11. C₇₉×#1486	C₂	semidirect
26. #493×C₇₉	C₂²	semidirect
27. #492×C₇₉	C₂²	semidirect
28. #487×C₇₉	C₂²	semidirect
29. #486×C₇₉	C₂²	semidirect
31. #477×C₇₉	C₂²	semidirect
37. #460×C₇₉	C₂²	semidirect
45. #332×C₇₉	C₂²	semidirect
46. #331×C₇₉	C₂²	semidirect
47. Q₈⋊C₈×C₇₉	C₂²	semidirect
48. Q₈⋊C₈×C₇₉	C₂²	semidirect
276. #18856	C₇₉	direct (N × H)
284. #3506	C₂×C₇₉	semidirect
285. #3254	C₂×C₇₉	semidirect
286. #3207	C₂×C₇₉	semidirect
287. #3109	C₂×C₇₉	semidirect
288. #1638	C₂×C₇₉	semidirect
289. #1631	C₂×C₇₉	semidirect
290. #1628	C₂×C₇₉	semidirect
291. #1621	C₂×C₇₉	semidirect
292. #1557	C₂×C₇₉	semidirect
293. #1497	C₂×C₇₉	semidirect
294. #1486	C₂×C₇₉	semidirect
295. C₇₉	#18856	direct (N × H)
310. #493	C₂²×C₇₉	semidirect
311. #492	C₂²×C₇₉	semidirect
312. #487	C₂²×C₇₉	semidirect
313. #486	C₂²×C₇₉	semidirect
315. #477	C₂²×C₇₉	semidirect
321. #460	C₂²×C₇₉	semidirect
329. #332	C₂²×C₇₉	semidirect
330. #331	C₂²×C₇₉	semidirect
331. Q₈⋊C₈	C₂²×C₇₉	semidirect
332. Q₈⋊C₈	C₂²×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₇₉×#3506	2
C₇₉×#3254	2
C₇₉×#3207	2
C₇₉×#3109	2
C₇₉×#1638	2
C₇₉×#1631	2
C₇₉×#1628	2
C₇₉×#1621	2
C₇₉×#1557	2
C₇₉×#1497	2
C₇₉×#1486	2
#18856	79

Subgroups — C79×#18856 #34130545

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#18856 #34130545