Subgroups — C₇₉×#18918 #34130607

Order 20224.

1042 conjugacy classes of subgroups.

The subgroup lattice has 532 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×#3208	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#3205	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#459×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#1625	C₂	1	4	yes	maximal, complemented
6	C₇₉×#1624	C₂	1	4	yes	maximal, complemented
7	C₇₉×#1542	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#1480	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#1478	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×D₈×C₇₉	—	2	1	no	—
11	#559×C₇₉	—	2	2	no	—
12	#556×C₇₉	—	2	1	no	—
13	#555×C₇₉	C₂²	1	2	yes	complemented
14	#553×C₇₉	—	2	2	no	—
15	#550×C₇₉	—	2	1	no	—
16	#547×C₇₉	C₂²	1	2	yes	complemented
17	#538×C₇₉	—	2	2	no	—
18	#535×C₇₉	—	2	1	no	—
19	#533×C₇₉	C₂²	1	1	yes	characteristic
20	#532×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×#127×C₇₉	C₂²	1	1	yes	characteristic
22	#525×C₇₉	—	2	2	no	—
23	#520×C₇₉	—	2	1	no	—
24	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
25	#493×C₇₉	—	2	1	no	—
26	#492×C₇₉	C₂²	1	2	yes	complemented
27	#486×C₇₉	—	2	1	no	—
28	#486×C₇₉	C₂²	1	2	yes	complemented
29	#460×C₇₉	—	2	2	no	—
30	#459×C₇₉	—	2	2	no	—
31	#459×C₇₉	C₂²	1	4	yes	—
32	#459×C₇₉	C₂²	1	4	yes	complemented
33	#450×C₇₉	—	2	2	no	—
34	#447×C₇₉	—	2	2	no	—
35	#431×C₇₉	C₂²	1	1	yes	characteristic
36	#431×C₇₉	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
38	C₂×#102×C₇₉	—	2	1	no	—
39	#333×C₇₉	C₂²	1	2	yes	complemented
40	#332×C₇₉	C₂²	1	2	yes	complemented
41	D₄⋊C₈×C₇₉	C₂²	1	4	yes	complemented
42	D₄⋊C₈×C₇₉	C₂²	1	4	yes	complemented
43	C₂×#41×C₇₉	—	2	2	no	—
44	C₂×#41×C₇₉	—	2	1	no	—
45	C₂²×D₄×C₇₉	—	2	1	no	—
46	C₂²×D₄×C₇₉	—	2	1	no	—
47	C₂²×D₄×C₇₉	—	2	1	no	—
48	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₇₉	—	2	1	no	—
50	C₂×SD₁₆×C₇₉	—	2	4	no	—
51	C₂×D₈×C₇₉	—	2	4	no	—
52	C₂×D₈×C₇₉	—	2	4	no	—
53	C₂×D₈×C₇₉	—	4	4	no	—
54	C₂²×C₈×C₇₉	—	2	1	no	—
55	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
56	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
57	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
58	#127×C₇₉	—	2	2	no	—
59	#127×C₇₉	—	2	1	no	—
60	#127×C₇₉	—	2	1	no	—
61	#127×C₇₉	—	2	1	no	—
62	#127×C₇₉	D₄	1	1	yes	characteristic
63	#127×C₇₉	C₂³	1	2	yes	—
64	#126×C₇₉	—	2	4	no	—
65	#125×C₇₉	—	2	1	no	—
66	#124×C₇₉	—	2	2	no	—
67	#124×C₇₉	—	2	4	no	—
68	#124×C₇₉	—	2	1	no	—
69	#123×C₇₉	—	2	4	no	—
70	#123×C₇₉	—	2	4	no	—
71	C₂²⋊Q₈×C₇₉	—	2	1	no	—
72	C₂²⋊Q₈×C₇₉	—	2	2	no	—
73	C₂²⋊Q₈×C₇₉	D₄	1	2	yes	—
74	#121×C₇₉	—	2	4	no	—
75	#121×C₇₉	—	2	2	no	—
76	#121×C₇₉	—	2	2	no	—
77	#121×C₇₉	—	2	2	no	—
78	#121×C₇₉	—	2	1	no	—
79	#121×C₇₉	D₄	1	2	yes	—
80	#120×C₇₉	—	2	4	no	—
81	C₄×Q₈×C₇₉	—	2	2	no	—
82	C₄×Q₈×C₇₉	—	2	1	no	—
83	C₄×Q₈×C₇₉	D₄	1	2	yes	—
84	C₄×D₄×C₇₉	—	2	4	no	—
85	C₄×D₄×C₇₉	—	2	2	no	—
86	C₄×D₄×C₇₉	—	2	4	no	—
87	C₄×D₄×C₇₉	—	2	1	no	—
88	C₄×D₄×C₇₉	—	2	1	no	—
89	C₄×D₄×C₇₉	—	2	1	no	—
90	C₄×D₄×C₇₉	D₄	1	2	yes	—
91	C₄×D₄×C₇₉	C₂³	1	2	yes	—
92	C₄×D₄×C₇₉	C₂³	1	2	yes	—
93	#117×C₇₉	—	2	1	no	—
94	#117×C₇₉	—	2	2	no	—
95	#117×C₇₉	—	2	2	no	—
96	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
97	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
99	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
100	C₄⋊C₈×C₇₉	—	2	1	no	—
101	C₄⋊C₈×C₇₉	—	2	1	no	—
102	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
103	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
104	#102×C₇₉	—	2	4	no	—
105	#102×C₇₉	—	2	4	no	—
106	#102×C₇₉	—	2	4	no	—
107	C₂²⋊C₈×C₇₉	—	2	1	no	—
108	C₂²⋊C₈×C₇₉	—	2	1	no	—
109	C₄×C₈×C₇₉	—	2	1	no	—
110	C₄×C₈×C₇₉	C₂³	1	2	yes	—
111	C₂⁴×C₇₉	—	2	1	no	—
112	C₂⁴×C₇₉	—	4	1	no	—
113	#41×C₇₉	—	4	2	no	—
114	#41×C₇₉	—	4	2	no	—
115	#41×C₇₉	—	8	4	no	—
116	C₂×Q₈×C₇₉	—	2	1	no	—
117	C₂×Q₈×C₇₉	—	2	1	no	—
118	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
119	C₂×D₄×C₇₉	—	2	2	no	—
120	C₂×D₄×C₇₉	—	2	4	no	—
121	C₂×D₄×C₇₉	—	2	4	no	—
122	C₂×D₄×C₇₉	—	2	1	no	—
123	C₂×D₄×C₇₉	—	2	1	no	—
124	C₂×D₄×C₇₉	—	2	1	no	—
125	C₂×D₄×C₇₉	—	2	2	no	—
126	C₂×D₄×C₇₉	—	2	2	no	—
127	C₂×D₄×C₇₉	—	2	2	no	—
128	C₂×D₄×C₇₉	—	2	2	no	—
129	C₂×D₄×C₇₉	—	2	2	no	—
130	C₂×D₄×C₇₉	—	4	1	no	—
131	C₂×D₄×C₇₉	—	4	1	no	—
132	C₂×D₄×C₇₉	—	4	1	no	—
133	C₂×D₄×C₇₉	—	4	2	no	—
134	C₂×D₄×C₇₉	—	4	2	no	—
135	C₂×D₄×C₇₉	—	8	2	no	—
136	C₂×D₄×C₇₉	—	8	2	no	—
137	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
138	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₇₉	—	2	4	no	—
140	C₂²×C₄×C₇₉	—	2	1	no	—
141	C₂²×C₄×C₇₉	—	2	2	no	—
142	C₂²×C₄×C₇₉	—	2	2	no	—
143	C₂²×C₄×C₇₉	—	2	2	no	—
144	C₂²×C₄×C₇₉	—	8	2	no	—
145	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
148	SD₁₆×C₇₉	—	8	4	no	—
149	D₈×C₇₉	—	4	8	no	—
150	D₈×C₇₉	—	8	4	no	—
151	C₂×C₈×C₇₉	—	2	2	no	—
152	C₂×C₈×C₇₉	—	2	2	no	—
153	C₂×C₈×C₇₉	—	2	2	no	—
154	C₂×C₈×C₇₉	—	4	2	no	—
155	C₄⋊C₄×C₇₉	—	2	4	no	—
156	C₄⋊C₄×C₇₉	—	2	1	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	1	no	—
161	C₄⋊C₄×C₇₉	—	2	1	no	—
162	C₄⋊C₄×C₇₉	—	2	1	no	—
163	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
164	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
165	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
166	C₂²⋊C₄×C₇₉	—	2	4	no	—
167	C₂²⋊C₄×C₇₉	—	2	4	no	—
168	C₂²⋊C₄×C₇₉	—	2	4	no	—
169	C₂²⋊C₄×C₇₉	—	2	2	no	—
170	C₂²⋊C₄×C₇₉	—	2	2	no	—
171	C₂²⋊C₄×C₇₉	—	2	2	no	—
172	C₂²⋊C₄×C₇₉	—	2	2	no	—
173	C₂²⋊C₄×C₇₉	—	2	2	no	—
174	C₄²×C₇₉	—	2	4	no	—
175	C₄²×C₇₉	—	2	2	no	—
176	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
180	C₂³×C₇₉	—	2	2	no	—
181	C₂³×C₇₉	—	2	2	no	—
182	C₂³×C₇₉	—	4	2	no	—
183	C₂³×C₇₉	—	4	2	no	—
184	C₂³×C₇₉	—	8	1	no	—
185	C₂³×C₇₉	—	8	1	no	—
186	C₂³×C₇₉	—	8	2	no	—
187	C₂³×C₇₉	—	8	2	no	—
188	C₂³×C₇₉	—	8	2	no	—
189	C₂³×C₇₉	#120	1	1	yes	characteristic
190	Q₈×C₇₉	—	4	2	no	—
191	Q₈×C₇₉	—	4	2	no	—
192	Q₈×C₇₉	—	4	2	no	—
193	D₄×C₇₉	—	2	2	no	—
194	D₄×C₇₉	—	2	2	no	—
195	D₄×C₇₉	—	2	4	no	—
196	D₄×C₇₉	—	4	4	no	—
197	D₄×C₇₉	—	4	4	no	—
198	D₄×C₇₉	—	4	2	no	—
199	D₄×C₇₉	—	4	2	no	—
200	D₄×C₇₉	—	4	4	no	—
201	D₄×C₇₉	—	4	2	no	—
202	D₄×C₇₉	—	4	2	no	—
203	D₄×C₇₉	—	8	1	no	—
204	D₄×C₇₉	—	8	2	no	—
205	D₄×C₇₉	—	8	2	no	—
206	D₄×C₇₉	—	8	4	no	—
207	D₄×C₇₉	—	8	4	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	—	4	1	no	—
215	C₂×C₄×C₇₉	—	4	2	no	—
216	C₂×C₄×C₇₉	—	4	2	no	—
217	C₂×C₄×C₇₉	—	4	4	no	—
218	C₂×C₄×C₇₉	—	8	2	no	—
219	C₂×C₄×C₇₉	—	8	1	no	—
220	C₂×C₄×C₇₉	—	8	4	no	—
221	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
222	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
223	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
224	C₂×C₄×C₇₉	#135	1	2	yes	—
225	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
226	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
229	C₈×C₇₉	—	4	2	no	—
230	C₈×C₇₉	—	4	2	no	—
231	C₈×C₇₉	—	4	2	no	—
232	C₂²×C₇₉	—	2	1	no	—
233	C₂²×C₇₉	—	2	1	no	—
234	C₂²×C₇₉	—	4	2	no	—
235	C₂²×C₇₉	—	4	2	no	—
236	C₂²×C₇₉	—	4	2	no	—
237	C₂²×C₇₉	—	4	2	no	—
238	C₂²×C₇₉	—	4	2	no	—
239	C₂²×C₇₉	—	4	2	no	—
240	C₂²×C₇₉	—	8	4	no	—
241	C₂²×C₇₉	—	8	2	no	—
242	C₂²×C₇₉	—	8	2	no	—
243	C₂²×C₇₉	—	8	2	no	—
244	C₂²×C₇₉	—	16	4	no	—
245	C₂²×C₇₉	#449	1	2	yes	—
246	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
247	C₄×C₇₉	—	2	1	no	—
248	C₄×C₇₉	—	2	1	no	—
249	C₄×C₇₉	—	2	1	no	—
250	C₄×C₇₉	—	4	2	no	—
251	C₄×C₇₉	—	4	2	no	—
252	C₄×C₇₉	—	4	2	no	—
253	C₄×C₇₉	—	4	2	no	—
254	C₄×C₇₉	#449	1	2	yes	—
255	C₄×C₇₉	C₂×#135	1	1	yes	characteristic
256	C₄×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
257	C₄×C₇₉	#576	1	2	yes	—
258	#18918	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
259	C₂×C₇₉	—	2	2	no	—
260	C₂×C₇₉	—	8	2	no	—
261	C₂×C₇₉	—	8	2	no	—
262	C₂×C₇₉	—	16	2	no	—
263	C₂×C₇₉	C₂×#449	1	1	yes	characteristic
264	C₂×C₇₉	#3008	1	1	yes	characteristic
265	C₂×C₇₉	#3021	1	1	yes	characteristic
266	#3506	C₂×C₇₉	1	1	yes	characteristic, complemented
267	#3208	C₂×C₇₉	1	1	yes	characteristic, complemented
268	#3205	C₂×C₇₉	1	1	yes	characteristic, complemented
269	C₂×#459	C₂×C₇₉	1	1	yes	characteristic, complemented
270	#1625	C₂×C₇₉	1	4	yes	complemented
271	#1624	C₂×C₇₉	1	4	yes	complemented
272	#1542	C₂×C₇₉	1	1	yes	characteristic, complemented
273	#1480	C₂×C₇₉	1	1	yes	characteristic, complemented
274	#1478	C₂×C₇₉	1	1	yes	characteristic, complemented
275	C₇₉	#18918	1	1	yes	characteristic, direct product factor, Sylow
276	C₂²×D₈	—	2	1	no	—
277	#559	—	2	2	no	—
278	#556	—	2	1	no	—
279	#555	C₂²×C₇₉	1	2	yes	complemented
280	#553	—	2	2	no	—
281	#550	—	2	1	no	—
282	#547	C₂²×C₇₉	1	2	yes	complemented
283	#538	—	2	2	no	—
284	#535	—	2	1	no	—
285	#533	C₂²×C₇₉	1	1	yes	characteristic
286	#532	C₂²×C₇₉	1	1	yes	characteristic
287	C₂×#127	C₂²×C₇₉	1	1	yes	characteristic
288	#525	—	2	2	no	—
289	#520	—	2	1	no	—
290	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
291	#493	—	2	1	no	—
292	#492	C₂²×C₇₉	1	2	yes	complemented
293	#486	—	2	1	no	—
294	#486	C₂²×C₇₉	1	2	yes	complemented
295	#460	—	2	2	no	—
296	#459	—	2	2	no	—
297	#459	C₂²×C₇₉	1	4	yes	—
298	#459	C₂²×C₇₉	1	4	yes	complemented
299	#450	—	2	2	no	—
300	#447	—	2	2	no	—
301	#431	C₂²×C₇₉	1	1	yes	characteristic
302	#431	C₂²×C₇₉	1	1	yes	characteristic
303	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
304	C₂×#102	—	2	1	no	—
305	#333	C₂²×C₇₉	1	2	yes	complemented
306	#332	C₂²×C₇₉	1	2	yes	complemented
307	D₄⋊C₈	C₂²×C₇₉	1	4	yes	complemented
308	D₄⋊C₈	C₂²×C₇₉	1	4	yes	complemented
309	C₂×#41	—	2	2	no	—
310	C₂×#41	—	2	1	no	—
311	C₂²×D₄	—	2	1	no	—
312	C₂²×D₄	—	2	1	no	—
313	C₂²×D₄	—	2	1	no	—
314	C₂²×D₄	D₄×C₇₉	1	1	yes	characteristic
315	C₂³×C₄	—	2	1	no	—
316	C₂×SD₁₆	—	2	4	no	—
317	C₂×D₈	—	2	4	no	—
318	C₂×D₈	—	2	4	no	—
319	C₂×D₈	—	4	4	no	—
320	C₂²×C₈	—	2	1	no	—
321	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
322	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
323	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
324	#127	—	2	2	no	—
325	#127	—	2	1	no	—
326	#127	—	2	1	no	—
327	#127	—	2	1	no	—
328	#127	D₄×C₇₉	1	1	yes	characteristic
329	#127	C₂³×C₇₉	1	2	yes	—
330	#126	—	2	4	no	—
331	#125	—	2	1	no	—
332	#124	—	2	2	no	—
333	#124	—	2	4	no	—
334	#124	—	2	1	no	—
335	#123	—	2	4	no	—
336	#123	—	2	4	no	—
337	C₂²⋊Q₈	—	2	1	no	—
338	C₂²⋊Q₈	—	2	2	no	—
339	C₂²⋊Q₈	D₄×C₇₉	1	2	yes	—
340	#121	—	2	4	no	—
341	#121	—	2	2	no	—
342	#121	—	2	2	no	—
343	#121	—	2	2	no	—
344	#121	—	2	1	no	—
345	#121	D₄×C₇₉	1	2	yes	—
346	#120	—	2	4	no	—
347	C₄×Q₈	—	2	2	no	—
348	C₄×Q₈	—	2	1	no	—
349	C₄×Q₈	D₄×C₇₉	1	2	yes	—
350	C₄×D₄	—	2	4	no	—
351	C₄×D₄	—	2	2	no	—
352	C₄×D₄	—	2	4	no	—
353	C₄×D₄	—	2	1	no	—
354	C₄×D₄	—	2	1	no	—
355	C₄×D₄	—	2	1	no	—
356	C₄×D₄	D₄×C₇₉	1	2	yes	—
357	C₄×D₄	C₂³×C₇₉	1	2	yes	—
358	C₄×D₄	C₂³×C₇₉	1	2	yes	—
359	#117	—	2	1	no	—
360	#117	—	2	2	no	—
361	#117	—	2	2	no	—
362	C₂×C₄⋊C₄	—	2	2	no	—
363	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
366	C₄⋊C₈	—	2	1	no	—
367	C₄⋊C₈	—	2	1	no	—
368	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
369	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
370	#102	—	2	4	no	—
371	#102	—	2	4	no	—
372	#102	—	2	4	no	—
373	C₂²⋊C₈	—	2	1	no	—
374	C₂²⋊C₈	—	2	1	no	—
375	C₄×C₈	—	2	1	no	—
376	C₄×C₈	C₂³×C₇₉	1	2	yes	—
377	C₂⁴	—	2	1	no	—
378	C₂⁴	—	4	1	no	—
379	#41	—	4	2	no	—
380	#41	—	4	2	no	—
381	#41	—	8	4	no	—
382	C₂×Q₈	—	2	1	no	—
383	C₂×Q₈	—	2	1	no	—
384	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	4	no	—
387	C₂×D₄	—	2	4	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	4	1	no	—
397	C₂×D₄	—	4	1	no	—
398	C₂×D₄	—	4	1	no	—
399	C₂×D₄	—	4	2	no	—
400	C₂×D₄	—	4	2	no	—
401	C₂×D₄	—	8	2	no	—
402	C₂×D₄	—	8	2	no	—
403	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
404	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	8	2	no	—
411	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
414	SD₁₆	—	8	4	no	—
415	D₈	—	4	8	no	—
416	D₈	—	8	4	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	4	2	no	—
421	C₄⋊C₄	—	2	4	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
430	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
431	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
432	C₂²⋊C₄	—	2	4	no	—
433	C₂²⋊C₄	—	2	4	no	—
434	C₂²⋊C₄	—	2	4	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₂²⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	—	2	2	no	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₄²	—	2	4	no	—
441	C₄²	—	2	2	no	—
442	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
443	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
444	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
445	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
446	C₂³	—	2	2	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	4	2	no	—
450	C₂³	—	8	1	no	—
451	C₂³	—	8	1	no	—
452	C₂³	—	8	2	no	—
453	C₂³	—	8	2	no	—
454	C₂³	—	8	2	no	—
455	C₂³	#120×C₇₉	1	1	yes	characteristic
456	Q₈	—	4	2	no	—
457	Q₈	—	4	2	no	—
458	Q₈	—	4	2	no	—
459	D₄	—	2	2	no	—
460	D₄	—	2	2	no	—
461	D₄	—	2	4	no	—
462	D₄	—	4	4	no	—
463	D₄	—	4	4	no	—
464	D₄	—	4	2	no	—
465	D₄	—	4	2	no	—
466	D₄	—	4	2	no	—
467	D₄	—	4	2	no	—
468	D₄	—	4	4	no	—
469	D₄	—	8	1	no	—
470	D₄	—	8	2	no	—
471	D₄	—	8	2	no	—
472	D₄	—	8	4	no	—
473	D₄	—	8	4	no	—
474	D₄	—	8	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	4	no	—
484	C₂×C₄	—	8	2	no	—
485	C₂×C₄	—	8	1	no	—
486	C₂×C₄	—	8	4	no	—
487	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
488	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
489	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
490	C₂×C₄	#135×C₇₉	1	2	yes	—
491	C₂×C₄	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
492	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
493	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
494	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
495	C₈	—	4	2	no	—
496	C₈	—	4	2	no	—
497	C₈	—	4	2	no	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	8	4	no	—
507	C₂²	—	8	2	no	—
508	C₂²	—	8	2	no	—
509	C₂²	—	8	2	no	—
510	C₂²	—	16	4	no	—
511	C₂²	#449×C₇₉	1	2	yes	—
512	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
513	C₄	—	2	1	no	—
514	C₄	—	2	1	no	—
515	C₄	—	2	1	no	—
516	C₄	—	4	2	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	2	no	—
519	C₄	—	4	2	no	—
520	C₄	#449×C₇₉	1	2	yes	—
521	C₄	C₂×#135×C₇₉	1	1	yes	characteristic
522	C₄	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
523	C₄	#576×C₇₉	1	2	yes	—
524	C₂	—	2	2	no	—
525	C₂	—	8	2	no	—
526	C₂	—	8	2	no	—
527	C₂	—	16	2	no	—
528	C₂	C₂×#449×C₇₉	1	1	yes	characteristic
529	C₂	C₇₉×#3008	1	1	yes	characteristic
530	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×#3208	C₂	semidirect
3. C₇₉×#3205	C₂	semidirect
4. C₂×#459×C₇₉	C₂	semidirect
5. C₇₉×#1625	C₂	semidirect
6. C₇₉×#1624	C₂	semidirect
7. C₇₉×#1542	C₂	semidirect
8. C₇₉×#1480	C₂	semidirect
9. C₇₉×#1478	C₂	semidirect
13. #555×C₇₉	C₂²	semidirect
16. #547×C₇₉	C₂²	semidirect
26. #492×C₇₉	C₂²	semidirect
28. #486×C₇₉	C₂²	semidirect
32. #459×C₇₉	C₂²	semidirect
39. #333×C₇₉	C₂²	semidirect
40. #332×C₇₉	C₂²	semidirect
41. D₄⋊C₈×C₇₉	C₂²	semidirect
42. D₄⋊C₈×C₇₉	C₂²	semidirect
258. #18918	C₇₉	direct (N × H)
266. #3506	C₂×C₇₉	semidirect
267. #3208	C₂×C₇₉	semidirect
268. #3205	C₂×C₇₉	semidirect
269. C₂×#459	C₂×C₇₉	semidirect
270. #1625	C₂×C₇₉	semidirect
271. #1624	C₂×C₇₉	semidirect
272. #1542	C₂×C₇₉	semidirect
273. #1480	C₂×C₇₉	semidirect
274. #1478	C₂×C₇₉	semidirect
275. C₇₉	#18918	direct (N × H)
279. #555	C₂²×C₇₉	semidirect
282. #547	C₂²×C₇₉	semidirect
292. #492	C₂²×C₇₉	semidirect
294. #486	C₂²×C₇₉	semidirect
298. #459	C₂²×C₇₉	semidirect
305. #333	C₂²×C₇₉	semidirect
306. #332	C₂²×C₇₉	semidirect
307. D₄⋊C₈	C₂²×C₇₉	semidirect
308. D₄⋊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×#3208	2
C₇₉×#3205	2
C₂×#459×C₇₉	2
C₇₉×#1625	2
C₇₉×#1624	2
C₇₉×#1542	2
C₇₉×#1480	2
C₇₉×#1478	2
#18918	79

Subgroups — C79×#18918 #34130607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#18918 #34130607