Subgroups — C₇₉×#23592 #34135281

Order 20224.

1086 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3461	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×AGL(1,ℤ/8)×C₇₉	C₂	1	2	yes	maximal, complemented
3	C₇₉×#2326	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#2060	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#2039	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉×#2038	C₂	1	2	yes	maximal, complemented
7	C₇₉×#2027	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#2006	C₂	1	1	yes	maximal, characteristic
9	C₇₉×#2003	C₂	1	2	yes	maximal, complemented
10	C₇₉×#1759	C₂	1	2	yes	maximal, complemented
11	C₄×#101×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₇₉	C₂²	1	2	yes	—
13	#544×C₇₉	C₂²	1	1	yes	characteristic
14	#542×C₇₉	—	2	2	no	—
15	#541×C₇₉	—	2	2	no	—
16	#539×C₇₉	—	2	2	no	—
17	#537×C₇₉	C₂²	1	1	yes	characteristic
18	#536×C₇₉	C₂²	1	2	yes	—
19	#533×C₇₉	—	2	2	no	—
20	#529×C₇₉	—	2	2	no	—
21	#529×C₇₉	—	2	2	no	—
22	C₂×#124×C₇₉	C₂²	1	1	yes	characteristic
23	C₄×#41×C₇₉	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
26	#442×C₇₉	—	2	2	no	—
27	#440×C₇₉	—	2	2	no	—
28	C₄×SD₁₆×C₇₉	—	2	2	no	—
29	C₄×D₈×C₇₉	—	2	2	no	—
30	#428×C₇₉	C₂²	1	2	yes	—
31	C₂×#104×C₇₉	C₂²	1	2	yes	—
32	C₂×#104×C₇₉	C₂²	1	2	yes	—
33	#418×C₇₉	C₂²	1	2	yes	—
34	#417×C₇₉	C₂²	1	2	yes	—
35	C₂×#101×C₇₉	C₂²	1	2	yes	—
36	C₄×M₁₆×C₇₉	C₂²	1	2	yes	—
37	#391×C₇₉	C₂²	1	1	yes	characteristic
38	#390×C₇₉	C₂²	1	1	yes	characteristic
39	#388×C₇₉	—	2	2	no	—
40	#385×C₇₉	—	2	2	no	—
41	#384×C₇₉	C₂²	1	1	yes	characteristic
42	#376×C₇₉	C₂²	1	1	yes	characteristic
43	#343×C₇₉	C₂²	1	1	yes	characteristic
44	#343×C₇₉	C₂²	1	1	yes	characteristic
45	#339×C₇₉	C₂²	1	2	yes	—
46	#339×C₇₉	C₂²	1	2	yes	—
47	C₂×#41×C₇₉	C₂³	1	2	yes	—
48	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₇₉	—	2	1	no	—
51	AGL(1,ℤ/8)×C₇₉	—	2	4	no	—
52	AGL(1,ℤ/8)×C₇₉	—	2	4	no	—
53	C₂×SD₁₆×C₇₉	—	2	2	no	—
54	C₂×D₈×C₇₉	—	2	2	no	—
55	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
56	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
57	C₄⋊Q₈×C₇₉	—	2	2	no	—
58	C₄⋊Q₈×C₇₉	—	2	2	no	—
59	#126×C₇₉	—	2	4	no	—
60	#126×C₇₉	—	2	4	no	—
61	#125×C₇₉	—	2	2	no	—
62	#125×C₇₉	—	2	4	no	—
63	#125×C₇₉	—	2	2	no	—
64	#124×C₇₉	—	2	2	no	—
65	#124×C₇₉	—	2	2	no	—
66	#124×C₇₉	—	2	2	no	—
67	#124×C₇₉	—	2	2	no	—
68	#123×C₇₉	—	2	4	no	—
69	#123×C₇₉	—	2	4	no	—
70	C₂²⋊Q₈×C₇₉	—	2	4	no	—
71	C₂²⋊Q₈×C₇₉	—	2	2	no	—
72	C₂²⋊Q₈×C₇₉	—	2	2	no	—
73	C₂²⋊Q₈×C₇₉	—	2	2	no	—
74	C₂²⋊Q₈×C₇₉	—	2	2	no	—
75	#121×C₇₉	—	2	2	no	—
76	#121×C₇₉	—	2	2	no	—
77	C₄×Q₈×C₇₉	—	2	2	no	—
78	C₄×Q₈×C₇₉	—	2	2	no	—
79	C₄×Q₈×C₇₉	—	2	2	no	—
80	C₄×Q₈×C₇₉	D₄	1	2	yes	—
81	C₄×Q₈×C₇₉	D₄	1	2	yes	—
82	C₄×D₄×C₇₉	—	2	2	no	—
83	C₄×D₄×C₇₉	—	2	2	no	—
84	C₄×D₄×C₇₉	—	2	2	no	—
85	C₄×D₄×C₇₉	—	2	2	no	—
86	C₄×D₄×C₇₉	—	2	2	no	—
87	C₄×D₄×C₇₉	D₄	1	2	yes	—
88	C₄×D₄×C₇₉	D₄	1	2	yes	—
89	#117×C₇₉	—	2	4	no	—
90	#117×C₇₉	—	2	2	no	—
91	#117×C₇₉	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
93	C₂×C₄⋊C₄×C₇₉	D₄	1	2	yes	—
94	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
99	C₂×C₄²×C₇₉	—	2	2	no	—
100	C₂×C₄²×C₇₉	D₄	1	2	yes	—
101	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
104	#107×C₇₉	—	2	2	no	—
105	#106×C₇₉	—	2	2	no	—
106	#104×C₇₉	—	2	4	no	—
107	#104×C₇₉	—	2	4	no	—
108	#103×C₇₉	—	2	2	no	—
109	#102×C₇₉	—	2	2	no	—
110	#102×C₇₉	—	2	2	no	—
111	#102×C₇₉	—	2	2	no	—
112	#101×C₇₉	—	2	4	no	—
113	#97×C₇₉	—	2	2	no	—
114	C₄×C₈×C₇₉	—	2	2	no	—
115	#95×C₇₉	—	2	1	no	—
116	#95×C₇₉	—	2	1	no	—
117	#95×C₇₉	—	2	2	no	—
118	C₂⁴×C₇₉	—	2	1	no	—
119	#41×C₇₉	—	2	2	no	—
120	#41×C₇₉	—	2	2	no	—
121	#41×C₇₉	—	2	2	no	—
122	#41×C₇₉	—	2	2	no	—
123	C₂×Q₈×C₇₉	—	2	2	no	—
124	C₂×Q₈×C₇₉	—	2	2	no	—
125	C₂×Q₈×C₇₉	—	2	2	no	—
126	C₂×Q₈×C₇₉	—	2	1	no	—
127	C₂×Q₈×C₇₉	—	2	1	no	—
128	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
129	C₂×D₄×C₇₉	—	2	2	no	—
130	C₂×D₄×C₇₉	—	2	2	no	—
131	C₂×D₄×C₇₉	—	2	2	no	—
132	C₂×D₄×C₇₉	—	2	2	no	—
133	C₂×D₄×C₇₉	—	2	1	no	—
134	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
135	C₂×D₄×C₇₉	#41	1	2	yes	—
136	C₂²×C₄×C₇₉	—	2	1	no	—
137	C₂²×C₄×C₇₉	—	2	2	no	—
138	C₂²×C₄×C₇₉	—	2	2	no	—
139	C₂²×C₄×C₇₉	—	2	2	no	—
140	C₂²×C₄×C₇₉	—	2	1	no	—
141	C₂²×C₄×C₇₉	—	2	1	no	—
142	C₂²×C₄×C₇₉	—	4	2	no	—
143	C₂²×C₄×C₇₉	—	8	2	no	—
144	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
149	SD₁₆×C₇₉	—	2	8	no	—
150	D₈×C₇₉	—	2	8	no	—
151	M₁₆×C₇₉	—	2	2	no	—
152	M₁₆×C₇₉	—	2	2	no	—
153	M₁₆×C₇₉	—	2	2	no	—
154	M₁₆×C₇₉	#41	1	4	yes	—
155	C₂×C₈×C₇₉	—	2	2	no	—
156	C₂×C₈×C₇₉	—	2	2	no	—
157	C₄⋊C₄×C₇₉	—	2	4	no	—
158	C₄⋊C₄×C₇₉	—	2	4	no	—
159	C₄⋊C₄×C₇₉	—	2	2	no	—
160	C₄⋊C₄×C₇₉	—	2	2	no	—
161	C₄⋊C₄×C₇₉	—	2	4	no	—
162	C₄⋊C₄×C₇₉	—	2	4	no	—
163	C₄⋊C₄×C₇₉	—	2	2	no	—
164	C₄⋊C₄×C₇₉	—	2	2	no	—
165	C₄⋊C₄×C₇₉	—	2	2	no	—
166	C₄⋊C₄×C₇₉	—	2	2	no	—
167	C₄⋊C₄×C₇₉	—	8	2	no	—
168	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
169	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
170	C₂²⋊C₄×C₇₉	—	2	8	no	—
171	C₂²⋊C₄×C₇₉	—	2	4	no	—
172	C₂²⋊C₄×C₇₉	—	2	4	no	—
173	C₂²⋊C₄×C₇₉	—	2	4	no	—
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	—	4	1	no	—
178	C₂²⋊C₄×C₇₉	—	4	1	no	—
179	C₂²⋊C₄×C₇₉	—	8	2	no	—
180	C₄²×C₇₉	—	2	2	no	—
181	C₄²×C₇₉	—	2	2	no	—
182	C₄²×C₇₉	—	2	2	no	—
183	C₄²×C₇₉	—	2	2	no	—
184	C₄²×C₇₉	—	2	2	no	—
185	C₄²×C₇₉	—	2	1	no	—
186	C₄²×C₇₉	—	2	2	no	—
187	C₄²×C₇₉	C₂×D₄	1	2	yes	—
188	C₄²×C₇₉	C₂×D₄	1	2	yes	—
189	C₄²×C₇₉	#41	1	2	yes	—
190	C₂³×C₇₉	—	2	2	no	—
191	C₂³×C₇₉	—	2	2	no	—
192	C₂³×C₇₉	—	4	2	no	—
193	C₂³×C₇₉	—	4	2	no	—
194	C₂³×C₇₉	—	4	1	no	—
195	C₂³×C₇₉	—	4	1	no	—
196	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
197	Q₈×C₇₉	—	2	2	no	—
198	Q₈×C₇₉	—	2	2	no	—
199	Q₈×C₇₉	—	4	2	no	—
200	Q₈×C₇₉	—	4	2	no	—
201	Q₈×C₇₉	—	8	2	no	—
202	D₄×C₇₉	—	2	2	no	—
203	D₄×C₇₉	—	2	4	no	—
204	D₄×C₇₉	—	2	2	no	—
205	D₄×C₇₉	—	4	2	no	—
206	D₄×C₇₉	—	4	2	no	—
207	D₄×C₇₉	—	4	2	no	—
208	D₄×C₇₉	—	8	2	no	—
209	C₂×C₄×C₇₉	—	2	2	no	—
210	C₂×C₄×C₇₉	—	2	2	no	—
211	C₂×C₄×C₇₉	—	2	2	no	—
212	C₂×C₄×C₇₉	—	2	2	no	—
213	C₂×C₄×C₇₉	—	2	2	no	—
214	C₂×C₄×C₇₉	—	2	2	no	—
215	C₂×C₄×C₇₉	—	2	2	no	—
216	C₂×C₄×C₇₉	—	2	2	no	—
217	C₂×C₄×C₇₉	—	4	1	no	—
218	C₂×C₄×C₇₉	—	4	1	no	—
219	C₂×C₄×C₇₉	—	4	4	no	—
220	C₂×C₄×C₇₉	—	4	1	no	—
221	C₂×C₄×C₇₉	—	4	1	no	—
222	C₂×C₄×C₇₉	—	4	2	no	—
223	C₂×C₄×C₇₉	—	4	2	no	—
224	C₂×C₄×C₇₉	—	4	2	no	—
225	C₂×C₄×C₇₉	—	4	1	no	—
226	C₂×C₄×C₇₉	—	4	2	no	—
227	C₂×C₄×C₇₉	—	4	1	no	—
228	C₂×C₄×C₇₉	—	4	1	no	—
229	C₂×C₄×C₇₉	—	4	1	no	—
230	C₂×C₄×C₇₉	—	8	2	no	—
231	C₂×C₄×C₇₉	—	8	4	no	—
232	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
233	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
234	C₂×C₄×C₇₉	#120	1	2	yes	—
235	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
236	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
238	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
239	C₈×C₇₉	—	2	4	no	—
240	C₈×C₇₉	—	4	2	no	—
241	C₂²×C₇₉	—	2	1	no	—
242	C₂²×C₇₉	—	2	1	no	—
243	C₂²×C₇₉	—	4	4	no	—
244	C₂²×C₇₉	—	4	2	no	—
245	C₂²×C₇₉	—	4	2	no	—
246	C₂²×C₇₉	—	4	2	no	—
247	C₂²×C₇₉	—	4	2	no	—
248	C₂²×C₇₉	—	8	2	no	—
249	C₂²×C₇₉	—	8	1	no	—
250	C₂²×C₇₉	—	8	1	no	—
251	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
252	C₂²×C₇₉	#525	1	1	yes	characteristic
253	C₂²×C₇₉	#532	1	1	yes	characteristic
254	C₄×C₇₉	—	2	1	no	—
255	C₄×C₇₉	—	2	1	no	—
256	C₄×C₇₉	—	2	2	no	—
257	C₄×C₇₉	—	4	2	no	—
258	C₄×C₇₉	—	4	2	no	—
259	C₄×C₇₉	—	4	2	no	—
260	C₄×C₇₉	—	4	2	no	—
261	C₄×C₇₉	—	4	2	no	—
262	C₄×C₇₉	—	4	2	no	—
263	C₄×C₇₉	—	8	1	no	—
264	C₄×C₇₉	—	8	1	no	—
265	C₄×C₇₉	#525	1	2	yes	—
266	C₄×C₇₉	#532	1	2	yes	—
267	#23592	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
268	C₂×C₇₉	—	2	1	no	—
269	C₂×C₇₉	—	2	1	no	—
270	C₂×C₇₉	—	8	2	no	—
271	C₂×C₇₉	—	8	2	no	—
272	C₂×C₇₉	#2388	1	1	yes	characteristic
273	C₂×C₇₉	#3020	1	1	yes	characteristic
274	C₂×C₇₉	#3021	1	1	yes	characteristic
275	#3461	C₂×C₇₉	1	1	yes	characteristic, complemented
276	C₄×AGL(1,ℤ/8)	C₂×C₇₉	1	2	yes	complemented
277	#2326	C₂×C₇₉	1	1	yes	characteristic, complemented
278	#2060	C₂×C₇₉	1	1	yes	characteristic, complemented
279	#2039	C₂×C₇₉	1	1	yes	characteristic, complemented
280	#2038	C₂×C₇₉	1	2	yes	complemented
281	#2027	C₂×C₇₉	1	1	yes	characteristic, complemented
282	#2006	C₂×C₇₉	1	1	yes	characteristic
283	#2003	C₂×C₇₉	1	2	yes	complemented
284	#1759	C₂×C₇₉	1	2	yes	complemented
285	C₄×#101	C₂×C₇₉	1	1	yes	characteristic, complemented
286	C₇₉	#23592	1	1	yes	characteristic, direct product factor, Sylow
287	C₂×AGL(1,ℤ/8)	C₂²×C₇₉	1	2	yes	—
288	#544	C₂²×C₇₉	1	1	yes	characteristic
289	#542	—	2	2	no	—
290	#541	—	2	2	no	—
291	#539	—	2	2	no	—
292	#537	C₂²×C₇₉	1	1	yes	characteristic
293	#536	C₂²×C₇₉	1	2	yes	—
294	#533	—	2	2	no	—
295	#529	—	2	2	no	—
296	#529	—	2	2	no	—
297	C₂×#124	C₂²×C₇₉	1	1	yes	characteristic
298	C₄×#41	C₂²×C₇₉	1	2	yes	—
299	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
300	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
301	#442	—	2	2	no	—
302	#440	—	2	2	no	—
303	C₄×SD₁₆	—	2	2	no	—
304	C₄×D₈	—	2	2	no	—
305	#428	C₂²×C₇₉	1	2	yes	—
306	C₂×#104	C₂²×C₇₉	1	2	yes	—
307	C₂×#104	C₂²×C₇₉	1	2	yes	—
308	#418	C₂²×C₇₉	1	2	yes	—
309	#417	C₂²×C₇₉	1	2	yes	—
310	C₂×#101	C₂²×C₇₉	1	2	yes	—
311	C₄×M₁₆	C₂²×C₇₉	1	2	yes	—
312	#391	C₂²×C₇₉	1	1	yes	characteristic
313	#390	C₂²×C₇₉	1	1	yes	characteristic
314	#388	—	2	2	no	—
315	#385	—	2	2	no	—
316	#384	C₂²×C₇₉	1	1	yes	characteristic
317	#376	C₂²×C₇₉	1	1	yes	characteristic
318	#343	C₂²×C₇₉	1	1	yes	characteristic
319	#343	C₂²×C₇₉	1	1	yes	characteristic
320	#339	C₂²×C₇₉	1	2	yes	—
321	#339	C₂²×C₇₉	1	2	yes	—
322	C₂×#41	C₂³×C₇₉	1	2	yes	—
323	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
324	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
325	C₂³×C₄	—	2	1	no	—
326	AGL(1,ℤ/8)	—	2	4	no	—
327	AGL(1,ℤ/8)	—	2	4	no	—
328	C₂×SD₁₆	—	2	2	no	—
329	C₂×D₈	—	2	2	no	—
330	C₂×M₁₆	C₂³×C₇₉	1	2	yes	—
331	C₂×M₁₆	C₂³×C₇₉	1	2	yes	—
332	C₄⋊Q₈	—	2	2	no	—
333	C₄⋊Q₈	—	2	2	no	—
334	#126	—	2	4	no	—
335	#126	—	2	4	no	—
336	#125	—	2	2	no	—
337	#125	—	2	4	no	—
338	#125	—	2	2	no	—
339	#124	—	2	2	no	—
340	#124	—	2	2	no	—
341	#124	—	2	2	no	—
342	#124	—	2	2	no	—
343	#123	—	2	4	no	—
344	#123	—	2	4	no	—
345	C₂²⋊Q₈	—	2	4	no	—
346	C₂²⋊Q₈	—	2	2	no	—
347	C₂²⋊Q₈	—	2	2	no	—
348	C₂²⋊Q₈	—	2	2	no	—
349	C₂²⋊Q₈	—	2	2	no	—
350	#121	—	2	2	no	—
351	#121	—	2	2	no	—
352	C₄×Q₈	—	2	2	no	—
353	C₄×Q₈	—	2	2	no	—
354	C₄×Q₈	—	2	2	no	—
355	C₄×Q₈	D₄×C₇₉	1	2	yes	—
356	C₄×Q₈	D₄×C₇₉	1	2	yes	—
357	C₄×D₄	—	2	2	no	—
358	C₄×D₄	—	2	2	no	—
359	C₄×D₄	—	2	2	no	—
360	C₄×D₄	—	2	2	no	—
361	C₄×D₄	—	2	2	no	—
362	C₄×D₄	D₄×C₇₉	1	2	yes	—
363	C₄×D₄	D₄×C₇₉	1	2	yes	—
364	#117	—	2	4	no	—
365	#117	—	2	2	no	—
366	#117	C₂³×C₇₉	1	2	yes	—
367	C₂×C₄⋊C₄	—	2	2	no	—
368	C₂×C₄⋊C₄	D₄×C₇₉	1	2	yes	—
369	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
371	C₂×C₂²⋊C₄	—	2	2	no	—
372	C₂×C₂²⋊C₄	—	2	1	no	—
373	C₂×C₂²⋊C₄	—	2	2	no	—
374	C₂×C₄²	—	2	2	no	—
375	C₂×C₄²	D₄×C₇₉	1	2	yes	—
376	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
377	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
378	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
379	#107	—	2	2	no	—
380	#106	—	2	2	no	—
381	#104	—	2	4	no	—
382	#104	—	2	4	no	—
383	#103	—	2	2	no	—
384	#102	—	2	2	no	—
385	#102	—	2	2	no	—
386	#102	—	2	2	no	—
387	#101	—	2	4	no	—
388	#97	—	2	2	no	—
389	C₄×C₈	—	2	2	no	—
390	#95	—	2	1	no	—
391	#95	—	2	1	no	—
392	#95	—	2	2	no	—
393	C₂⁴	—	2	1	no	—
394	#41	—	2	2	no	—
395	#41	—	2	2	no	—
396	#41	—	2	2	no	—
397	#41	—	2	2	no	—
398	C₂×Q₈	—	2	2	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	1	no	—
402	C₂×Q₈	—	2	1	no	—
403	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
410	C₂×D₄	#41×C₇₉	1	2	yes	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	4	2	no	—
418	C₂²×C₄	—	8	2	no	—
419	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
420	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
421	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
422	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
423	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
424	SD₁₆	—	2	8	no	—
425	D₈	—	2	8	no	—
426	M₁₆	—	2	2	no	—
427	M₁₆	—	2	2	no	—
428	M₁₆	—	2	2	no	—
429	M₁₆	#41×C₇₉	1	4	yes	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	2	2	no	—
432	C₄⋊C₄	—	2	4	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	4	no	—
437	C₄⋊C₄	—	2	4	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	8	2	no	—
443	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
444	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
445	C₂²⋊C₄	—	2	8	no	—
446	C₂²⋊C₄	—	2	4	no	—
447	C₂²⋊C₄	—	2	4	no	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	2	2	no	—
450	C₂²⋊C₄	—	2	2	no	—
451	C₂²⋊C₄	—	2	2	no	—
452	C₂²⋊C₄	—	4	1	no	—
453	C₂²⋊C₄	—	4	1	no	—
454	C₂²⋊C₄	—	8	2	no	—
455	C₄²	—	2	2	no	—
456	C₄²	—	2	2	no	—
457	C₄²	—	2	2	no	—
458	C₄²	—	2	2	no	—
459	C₄²	—	2	2	no	—
460	C₄²	—	2	1	no	—
461	C₄²	—	2	2	no	—
462	C₄²	C₂×D₄×C₇₉	1	2	yes	—
463	C₄²	C₂×D₄×C₇₉	1	2	yes	—
464	C₄²	#41×C₇₉	1	2	yes	—
465	C₂³	—	2	2	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	4	2	no	—
468	C₂³	—	4	2	no	—
469	C₂³	—	4	1	no	—
470	C₂³	—	4	1	no	—
471	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
472	Q₈	—	2	2	no	—
473	Q₈	—	2	2	no	—
474	Q₈	—	4	2	no	—
475	Q₈	—	4	2	no	—
476	Q₈	—	8	2	no	—
477	D₄	—	2	2	no	—
478	D₄	—	2	4	no	—
479	D₄	—	2	2	no	—
480	D₄	—	4	2	no	—
481	D₄	—	4	2	no	—
482	D₄	—	4	2	no	—
483	D₄	—	8	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	4	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	8	2	no	—
506	C₂×C₄	—	8	4	no	—
507	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
508	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
509	C₂×C₄	#120×C₇₉	1	2	yes	—
510	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
511	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
512	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
513	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
514	C₈	—	2	4	no	—
515	C₈	—	4	2	no	—
516	C₂²	—	2	1	no	—
517	C₂²	—	2	1	no	—
518	C₂²	—	4	4	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	8	2	no	—
524	C₂²	—	8	1	no	—
525	C₂²	—	8	1	no	—
526	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
527	C₂²	#525×C₇₉	1	1	yes	characteristic
528	C₂²	#532×C₇₉	1	1	yes	characteristic
529	C₄	—	2	1	no	—
530	C₄	—	2	1	no	—
531	C₄	—	2	2	no	—
532	C₄	—	4	2	no	—
533	C₄	—	4	2	no	—
534	C₄	—	4	2	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	2	no	—
537	C₄	—	4	2	no	—
538	C₄	—	8	1	no	—
539	C₄	—	8	1	no	—
540	C₄	#525×C₇₉	1	2	yes	—
541	C₄	#532×C₇₉	1	2	yes	—
542	C₂	—	2	1	no	—
543	C₂	—	2	1	no	—
544	C₂	—	8	2	no	—
545	C₂	—	8	2	no	—
546	C₂	C₇₉×#2388	1	1	yes	characteristic
547	C₂	C₇₉×#3020	1	1	yes	characteristic
548	C₂	C₇₉×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₇₉×#2006	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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×#3461	C₂	semidirect
2. C₄×AGL(1,ℤ/8)×C₇₉	C₂	semidirect
3. C₇₉×#2326	C₂	semidirect
4. C₇₉×#2060	C₂	semidirect
5. C₇₉×#2039	C₂	semidirect
6. C₇₉×#2038	C₂	semidirect
7. C₇₉×#2027	C₂	semidirect
9. C₇₉×#2003	C₂	semidirect
10. C₇₉×#1759	C₂	semidirect
11. C₄×#101×C₇₉	C₂	semidirect
267. #23592	C₇₉	direct (N × H)
275. #3461	C₂×C₇₉	semidirect
276. C₄×AGL(1,ℤ/8)	C₂×C₇₉	semidirect
277. #2326	C₂×C₇₉	semidirect
278. #2060	C₂×C₇₉	semidirect
279. #2039	C₂×C₇₉	semidirect
280. #2038	C₂×C₇₉	semidirect
281. #2027	C₂×C₇₉	semidirect
283. #2003	C₂×C₇₉	semidirect
284. #1759	C₂×C₇₉	semidirect
285. C₄×#101	C₂×C₇₉	semidirect
286. C₇₉	#23592	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×#3461	2
C₄×AGL(1,ℤ/8)×C₇₉	2
C₇₉×#2326	2
C₇₉×#2060	2
C₇₉×#2039	2
C₇₉×#2038	2
C₇₉×#2027	2
C₇₉×#2006	2
C₇₉×#2003	2
C₇₉×#1759	2
C₄×#101×C₇₉	2
#23592	79

Subgroups — C79×#23592 #34135281

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#23592 #34135281