Subgroups — C₇₉×#18912 #34130601

Order 20224.

1218 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3497	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₉×#3205	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#3205	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#460×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#1627	C₂	1	4	yes	maximal, complemented
6	C₇₉×#1621	C₂	1	4	yes	maximal, complemented
7	C₇₉×#1540	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#1480	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#1479	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×2₋¹⁺⁴×C₇₉	—	2	1	no	—
11	C₂²×SD₁₆×C₇₉	—	2	1	no	—
12	#550×C₇₉	—	2	1	no	—
13	#550×C₇₉	C₂²	1	2	yes	complemented
14	D₄×Q₈×C₇₉	—	2	1	no	—
15	D₄×Q₈×C₇₉	C₂²	1	2	yes	complemented
16	#548×C₇₉	—	2	2	no	—
17	#548×C₇₉	—	2	2	no	—
18	#537×C₇₉	—	2	2	no	—
19	#537×C₇₉	—	2	1	no	—
20	#532×C₇₉	—	2	2	no	—
21	#532×C₇₉	C₂²	1	1	yes	characteristic
22	#532×C₇₉	C₂²	1	1	yes	characteristic
23	C₂×#127×C₇₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
25	#493×C₇₉	—	2	1	no	—
26	#493×C₇₉	C₂²	1	2	yes	—
27	#486×C₇₉	—	2	1	no	—
28	#486×C₇₉	C₂²	1	2	yes	—
29	#460×C₇₉	—	2	2	no	—
30	#460×C₇₉	C₂²	1	4	yes	—
31	#459×C₇₉	—	2	2	no	—
32	#459×C₇₉	C₂²	1	4	yes	—
33	#447×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	#332×C₇₉	C₂²	1	2	yes	complemented
40	#331×C₇₉	C₂²	1	2	yes	complemented
41	Q₈⋊C₈×C₇₉	C₂²	1	4	yes	complemented
42	D₄⋊C₈×C₇₉	C₂²	1	4	yes	complemented
43	2₋¹⁺⁴×C₇₉	—	4	4	no	—
44	2₋¹⁺⁴×C₇₉	—	4	4	no	—
45	C₂×#41×C₇₉	—	2	4	no	—
46	C₂×#41×C₇₉	—	2	2	no	—
47	C₂×#41×C₇₉	—	2	2	no	—
48	C₂×#41×C₇₉	—	2	1	no	—
49	C₂×#41×C₇₉	—	2	1	no	—
50	C₂²×Q₈×C₇₉	—	2	2	no	—
51	C₂²×Q₈×C₇₉	—	2	2	no	—
52	C₂²×Q₈×C₇₉	D₄	1	1	yes	characteristic
53	C₂²×D₄×C₇₉	—	2	1	no	—
54	C₂²×D₄×C₇₉	—	2	1	no	—
55	C₂²×D₄×C₇₉	—	2	1	no	—
56	C₂×SD₁₆×C₇₉	—	2	4	no	—
57	C₂×SD₁₆×C₇₉	—	4	4	no	—
58	C₂×D₈×C₇₉	—	2	4	no	—
59	C₂×D₈×C₇₉	—	2	4	no	—
60	C₂²×C₈×C₇₉	—	2	1	no	—
61	C₄⋊Q₈×C₇₉	—	2	2	no	—
62	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
63	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
64	#127×C₇₉	—	2	2	no	—
65	#127×C₇₉	—	2	1	no	—
66	#127×C₇₉	—	2	1	no	—
67	#127×C₇₉	—	2	1	no	—
68	#127×C₇₉	D₄	1	1	yes	characteristic
69	#127×C₇₉	C₂³	1	2	yes	—
70	#127×C₇₉	C₂³	1	1	yes	characteristic
71	#124×C₇₉	—	2	4	no	—
72	#124×C₇₉	—	2	1	no	—
73	#124×C₇₉	—	2	1	no	—
74	C₂²⋊Q₈×C₇₉	—	2	2	no	—
75	C₂²⋊Q₈×C₇₉	—	2	4	no	—
76	C₂²⋊Q₈×C₇₉	—	2	2	no	—
77	C₂²⋊Q₈×C₇₉	—	2	4	no	—
78	#121×C₇₉	—	2	4	no	—
79	#121×C₇₉	—	2	2	no	—
80	#121×C₇₉	—	2	4	no	—
81	#121×C₇₉	—	2	4	no	—
82	#121×C₇₉	—	2	1	no	—
83	#121×C₇₉	—	2	1	no	—
84	#121×C₇₉	—	2	2	no	—
85	#121×C₇₉	D₄	1	2	yes	—
86	#121×C₇₉	D₄	1	2	yes	—
87	C₄×Q₈×C₇₉	—	2	1	no	—
88	C₄×Q₈×C₇₉	—	2	1	no	—
89	C₄×Q₈×C₇₉	D₄	1	2	yes	—
90	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
91	C₄×D₄×C₇₉	—	2	4	no	—
92	C₄×D₄×C₇₉	—	2	2	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	D₄	1	2	yes	—
97	C₄×D₄×C₇₉	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₇₉	—	2	1	no	—
101	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
102	C₄⋊C₈×C₇₉	—	2	1	no	—
103	C₄⋊C₈×C₇₉	—	2	1	no	—
104	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
105	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
106	#102×C₇₉	—	2	4	no	—
107	#102×C₇₉	—	2	4	no	—
108	#102×C₇₉	—	2	4	no	—
109	C₂²⋊C₈×C₇₉	—	2	1	no	—
110	C₂²⋊C₈×C₇₉	—	2	1	no	—
111	C₄×C₈×C₇₉	—	2	1	no	—
112	C₄×C₈×C₇₉	C₂³	1	2	yes	—
113	C₂⁴×C₇₉	—	4	1	no	—
114	#41×C₇₉	—	4	16	no	—
115	#41×C₇₉	—	4	4	no	—
116	#41×C₇₉	—	4	8	no	—
117	#41×C₇₉	—	4	4	no	—
118	#41×C₇₉	—	4	2	no	—
119	#41×C₇₉	—	4	2	no	—
120	#41×C₇₉	—	4	2	no	—
121	#41×C₇₉	—	4	2	no	—
122	C₂×Q₈×C₇₉	—	2	4	no	—
123	C₂×Q₈×C₇₉	—	2	1	no	—
124	C₂×Q₈×C₇₉	—	2	1	no	—
125	C₂×Q₈×C₇₉	—	2	2	no	—
126	C₂×Q₈×C₇₉	—	2	1	no	—
127	C₂×Q₈×C₇₉	—	4	4	no	—
128	C₂×Q₈×C₇₉	—	4	8	no	—
129	C₂×Q₈×C₇₉	—	4	4	no	—
130	C₂×Q₈×C₇₉	D₈	1	4	yes	complemented
131	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
132	C₂×D₄×C₇₉	—	2	4	no	—
133	C₂×D₄×C₇₉	—	2	2	no	—
134	C₂×D₄×C₇₉	—	2	2	no	—
135	C₂×D₄×C₇₉	—	2	4	no	—
136	C₂×D₄×C₇₉	—	2	1	no	—
137	C₂×D₄×C₇₉	—	2	1	no	—
138	C₂×D₄×C₇₉	—	2	1	no	—
139	C₂×D₄×C₇₉	—	2	1	no	—
140	C₂×D₄×C₇₉	—	2	2	no	—
141	C₂×D₄×C₇₉	—	2	2	no	—
142	C₂×D₄×C₇₉	—	2	2	no	—
143	C₂×D₄×C₇₉	—	4	1	no	—
144	C₂×D₄×C₇₉	—	4	1	no	—
145	C₂×D₄×C₇₉	—	4	1	no	—
146	C₂×D₄×C₇₉	—	4	2	no	—
147	C₂×D₄×C₇₉	—	4	2	no	—
148	C₂×D₄×C₇₉	—	8	2	no	—
149	C₂×D₄×C₇₉	—	8	2	no	—
150	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
151	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₇₉	—	2	1	no	—
153	C₂²×C₄×C₇₉	—	2	4	no	—
154	C₂²×C₄×C₇₉	—	2	4	no	—
155	C₂²×C₄×C₇₉	—	2	1	no	—
156	C₂²×C₄×C₇₉	—	2	2	no	—
157	C₂²×C₄×C₇₉	—	2	2	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	SD₁₆×C₇₉	—	4	8	no	—
162	D₈×C₇₉	—	8	4	no	—
163	D₈×C₇₉	—	8	4	no	—
164	C₂×C₈×C₇₉	—	2	2	no	—
165	C₂×C₈×C₇₉	—	2	2	no	—
166	C₂×C₈×C₇₉	—	2	2	no	—
167	C₂×C₈×C₇₉	—	4	2	no	—
168	C₄⋊C₄×C₇₉	—	2	4	no	—
169	C₄⋊C₄×C₇₉	—	2	2	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	C₂×D₄	1	2	yes	—
175	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
176	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
177	C₂²⋊C₄×C₇₉	—	2	4	no	—
178	C₂²⋊C₄×C₇₉	—	2	4	no	—
179	C₂²⋊C₄×C₇₉	—	2	2	no	—
180	C₂²⋊C₄×C₇₉	—	2	2	no	—
181	C₂²⋊C₄×C₇₉	—	2	2	no	—
182	C₂²⋊C₄×C₇₉	—	2	2	no	—
183	C₄²×C₇₉	—	2	2	no	—
184	C₄²×C₇₉	—	2	2	no	—
185	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
186	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
189	C₂³×C₇₉	—	2	2	no	—
190	C₂³×C₇₉	—	2	2	no	—
191	C₂³×C₇₉	—	4	2	no	—
192	C₂³×C₇₉	—	8	2	no	—
193	C₂³×C₇₉	—	8	2	no	—
194	C₂³×C₇₉	—	8	2	no	—
195	C₂³×C₇₉	#120	1	1	yes	characteristic
196	Q₈×C₇₉	—	2	2	no	—
197	Q₈×C₇₉	—	2	4	no	—
198	Q₈×C₇₉	—	4	8	no	—
199	Q₈×C₇₉	—	4	1	no	—
200	Q₈×C₇₉	—	4	1	no	—
201	Q₈×C₇₉	—	4	2	no	—
202	Q₈×C₇₉	C₂×D₈	1	4	yes	—
203	D₄×C₇₉	—	2	4	no	—
204	D₄×C₇₉	—	4	2	no	—
205	D₄×C₇₉	—	4	8	no	—
206	D₄×C₇₉	—	4	4	no	—
207	D₄×C₇₉	—	4	4	no	—
208	D₄×C₇₉	—	4	4	no	—
209	D₄×C₇₉	—	4	1	no	—
210	D₄×C₇₉	—	4	2	no	—
211	D₄×C₇₉	—	4	1	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	—	8	1	no	—
217	D₄×C₇₉	—	8	2	no	—
218	D₄×C₇₉	—	8	2	no	—
219	D₄×C₇₉	—	8	4	no	—
220	D₄×C₇₉	—	8	2	no	—
221	C₂×C₄×C₇₉	—	2	2	no	—
222	C₂×C₄×C₇₉	—	2	4	no	—
223	C₂×C₄×C₇₉	—	2	2	no	—
224	C₂×C₄×C₇₉	—	2	2	no	—
225	C₂×C₄×C₇₉	—	2	2	no	—
226	C₂×C₄×C₇₉	—	2	2	no	—
227	C₂×C₄×C₇₉	—	4	1	no	—
228	C₂×C₄×C₇₉	—	4	8	no	—
229	C₂×C₄×C₇₉	—	4	8	no	—
230	C₂×C₄×C₇₉	—	4	2	no	—
231	C₂×C₄×C₇₉	—	4	2	no	—
232	C₂×C₄×C₇₉	—	4	4	no	—
233	C₂×C₄×C₇₉	—	8	1	no	—
234	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
235	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
236	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
237	C₂×C₄×C₇₉	C₂×D₈	1	2	yes	—
238	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
239	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
242	C₈×C₇₉	—	4	2	no	—
243	C₈×C₇₉	—	4	2	no	—
244	C₈×C₇₉	—	4	2	no	—
245	C₂²×C₇₉	—	2	1	no	—
246	C₂²×C₇₉	—	2	1	no	—
247	C₂²×C₇₉	—	4	2	no	—
248	C₂²×C₇₉	—	4	2	no	—
249	C₂²×C₇₉	—	4	2	no	—
250	C₂²×C₇₉	—	4	2	no	—
251	C₂²×C₇₉	—	4	2	no	—
252	C₂²×C₇₉	—	4	2	no	—
253	C₂²×C₇₉	—	8	2	no	—
254	C₂²×C₇₉	—	8	2	no	—
255	C₂²×C₇₉	—	8	2	no	—
256	C₂²×C₇₉	—	16	4	no	—
257	C₂²×C₇₉	#447	1	2	yes	—
258	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
259	C₄×C₇₉	—	2	4	no	—
260	C₄×C₇₉	—	2	1	no	—
261	C₄×C₇₉	—	2	1	no	—
262	C₄×C₇₉	—	2	1	no	—
263	C₄×C₇₉	—	4	2	no	—
264	C₄×C₇₉	—	4	2	no	—
265	C₄×C₇₉	—	4	2	no	—
266	C₄×C₇₉	#447	1	2	yes	—
267	C₄×C₇₉	C₂²×D₈	1	1	yes	characteristic
268	C₄×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
269	C₄×C₇₉	#577	1	2	yes	—
270	#18912	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
271	C₂×C₇₉	—	2	2	no	—
272	C₂×C₇₉	—	8	2	no	—
273	C₂×C₇₉	—	8	2	no	—
274	C₂×C₇₉	—	16	2	no	—
275	C₂×C₇₉	C₂×#447	1	1	yes	characteristic
276	C₂×C₇₉	#3010	1	1	yes	characteristic
277	C₂×C₇₉	#3021	1	1	yes	characteristic
278	#3497	C₂×C₇₉	1	1	yes	characteristic, complemented
279	#3205	C₂×C₇₉	1	1	yes	characteristic, complemented
280	#3205	C₂×C₇₉	1	1	yes	characteristic, complemented
281	C₂×#460	C₂×C₇₉	1	1	yes	characteristic, complemented
282	#1627	C₂×C₇₉	1	4	yes	complemented
283	#1621	C₂×C₇₉	1	4	yes	complemented
284	#1540	C₂×C₇₉	1	1	yes	characteristic, complemented
285	#1480	C₂×C₇₉	1	1	yes	characteristic, complemented
286	#1479	C₂×C₇₉	1	1	yes	characteristic, complemented
287	C₇₉	#18912	1	1	yes	characteristic, direct product factor, Sylow
288	C₂×2₋¹⁺⁴	—	2	1	no	—
289	C₂²×SD₁₆	—	2	1	no	—
290	#550	—	2	1	no	—
291	#550	C₂²×C₇₉	1	2	yes	complemented
292	D₄×Q₈	—	2	1	no	—
293	D₄×Q₈	C₂²×C₇₉	1	2	yes	complemented
294	#548	—	2	2	no	—
295	#548	—	2	2	no	—
296	#537	—	2	2	no	—
297	#537	—	2	1	no	—
298	#532	—	2	2	no	—
299	#532	C₂²×C₇₉	1	1	yes	characteristic
300	#532	C₂²×C₇₉	1	1	yes	characteristic
301	C₂×#127	C₂²×C₇₉	1	1	yes	characteristic
302	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
303	#493	—	2	1	no	—
304	#493	C₂²×C₇₉	1	2	yes	—
305	#486	—	2	1	no	—
306	#486	C₂²×C₇₉	1	2	yes	—
307	#460	—	2	2	no	—
308	#460	C₂²×C₇₉	1	4	yes	—
309	#459	—	2	2	no	—
310	#459	C₂²×C₇₉	1	4	yes	—
311	#447	—	2	2	no	—
312	#447	—	2	2	no	—
313	#431	C₂²×C₇₉	1	1	yes	characteristic
314	#431	C₂²×C₇₉	1	1	yes	characteristic
315	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
316	C₂×#102	—	2	1	no	—
317	#332	C₂²×C₇₉	1	2	yes	complemented
318	#331	C₂²×C₇₉	1	2	yes	complemented
319	Q₈⋊C₈	C₂²×C₇₉	1	4	yes	complemented
320	D₄⋊C₈	C₂²×C₇₉	1	4	yes	complemented
321	2₋¹⁺⁴	—	4	4	no	—
322	2₋¹⁺⁴	—	4	4	no	—
323	C₂×#41	—	2	4	no	—
324	C₂×#41	—	2	2	no	—
325	C₂×#41	—	2	2	no	—
326	C₂×#41	—	2	1	no	—
327	C₂×#41	—	2	1	no	—
328	C₂²×Q₈	—	2	2	no	—
329	C₂²×Q₈	—	2	2	no	—
330	C₂²×Q₈	D₄×C₇₉	1	1	yes	characteristic
331	C₂²×D₄	—	2	1	no	—
332	C₂²×D₄	—	2	1	no	—
333	C₂²×D₄	—	2	1	no	—
334	C₂×SD₁₆	—	2	4	no	—
335	C₂×SD₁₆	—	4	4	no	—
336	C₂×D₈	—	2	4	no	—
337	C₂×D₈	—	2	4	no	—
338	C₂²×C₈	—	2	1	no	—
339	C₄⋊Q₈	—	2	2	no	—
340	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
341	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
342	#127	—	2	2	no	—
343	#127	—	2	1	no	—
344	#127	—	2	1	no	—
345	#127	—	2	1	no	—
346	#127	D₄×C₇₉	1	1	yes	characteristic
347	#127	C₂³×C₇₉	1	2	yes	—
348	#127	C₂³×C₇₉	1	1	yes	characteristic
349	#124	—	2	4	no	—
350	#124	—	2	1	no	—
351	#124	—	2	1	no	—
352	C₂²⋊Q₈	—	2	2	no	—
353	C₂²⋊Q₈	—	2	4	no	—
354	C₂²⋊Q₈	—	2	2	no	—
355	C₂²⋊Q₈	—	2	4	no	—
356	#121	—	2	4	no	—
357	#121	—	2	2	no	—
358	#121	—	2	4	no	—
359	#121	—	2	4	no	—
360	#121	—	2	1	no	—
361	#121	—	2	1	no	—
362	#121	—	2	2	no	—
363	#121	D₄×C₇₉	1	2	yes	—
364	#121	D₄×C₇₉	1	2	yes	—
365	C₄×Q₈	—	2	1	no	—
366	C₄×Q₈	—	2	1	no	—
367	C₄×Q₈	D₄×C₇₉	1	2	yes	—
368	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
369	C₄×D₄	—	2	4	no	—
370	C₄×D₄	—	2	2	no	—
371	C₄×D₄	—	2	2	no	—
372	C₄×D₄	—	2	1	no	—
373	C₄×D₄	—	2	1	no	—
374	C₄×D₄	D₄×C₇₉	1	2	yes	—
375	C₄×D₄	C₂³×C₇₉	1	2	yes	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
378	C₂×C₄²	—	2	1	no	—
379	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
380	C₄⋊C₈	—	2	1	no	—
381	C₄⋊C₈	—	2	1	no	—
382	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
383	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
384	#102	—	2	4	no	—
385	#102	—	2	4	no	—
386	#102	—	2	4	no	—
387	C₂²⋊C₈	—	2	1	no	—
388	C₂²⋊C₈	—	2	1	no	—
389	C₄×C₈	—	2	1	no	—
390	C₄×C₈	C₂³×C₇₉	1	2	yes	—
391	C₂⁴	—	4	1	no	—
392	#41	—	4	16	no	—
393	#41	—	4	8	no	—
394	#41	—	4	4	no	—
395	#41	—	4	4	no	—
396	#41	—	4	2	no	—
397	#41	—	4	2	no	—
398	#41	—	4	2	no	—
399	#41	—	4	2	no	—
400	C₂×Q₈	—	2	4	no	—
401	C₂×Q₈	—	2	1	no	—
402	C₂×Q₈	—	2	1	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	1	no	—
405	C₂×Q₈	—	4	8	no	—
406	C₂×Q₈	—	4	4	no	—
407	C₂×Q₈	—	4	4	no	—
408	C₂×Q₈	D₈×C₇₉	1	4	yes	complemented
409	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
410	C₂×D₄	—	2	4	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	4	no	—
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	4	1	no	—
422	C₂×D₄	—	4	1	no	—
423	C₂×D₄	—	4	1	no	—
424	C₂×D₄	—	4	2	no	—
425	C₂×D₄	—	4	2	no	—
426	C₂×D₄	—	8	2	no	—
427	C₂×D₄	—	8	2	no	—
428	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
429	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	4	no	—
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	C₂×D₄×C₇₉	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
439	SD₁₆	—	4	8	no	—
440	D₈	—	8	4	no	—
441	D₈	—	8	4	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	4	2	no	—
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
453	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
454	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	—	2	4	no	—
457	C₂²⋊C₄	—	2	2	no	—
458	C₂²⋊C₄	—	2	2	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	—	2	2	no	—
461	C₄²	—	2	2	no	—
462	C₄²	—	2	2	no	—
463	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
464	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
465	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
466	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
467	C₂³	—	2	2	no	—
468	C₂³	—	2	2	no	—
469	C₂³	—	4	2	no	—
470	C₂³	—	8	2	no	—
471	C₂³	—	8	2	no	—
472	C₂³	—	8	2	no	—
473	C₂³	#120×C₇₉	1	1	yes	characteristic
474	Q₈	—	2	4	no	—
475	Q₈	—	2	2	no	—
476	Q₈	—	4	8	no	—
477	Q₈	—	4	2	no	—
478	Q₈	—	4	1	no	—
479	Q₈	—	4	1	no	—
480	Q₈	C₂×D₈×C₇₉	1	4	yes	—
481	D₄	—	2	4	no	—
482	D₄	—	4	2	no	—
483	D₄	—	4	8	no	—
484	D₄	—	4	4	no	—
485	D₄	—	4	4	no	—
486	D₄	—	4	4	no	—
487	D₄	—	4	2	no	—
488	D₄	—	4	1	no	—
489	D₄	—	4	2	no	—
490	D₄	—	4	1	no	—
491	D₄	—	4	2	no	—
492	D₄	—	4	2	no	—
493	D₄	—	4	4	no	—
494	D₄	—	8	1	no	—
495	D₄	—	8	2	no	—
496	D₄	—	8	2	no	—
497	D₄	—	8	4	no	—
498	D₄	—	8	2	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	8	no	—
507	C₂×C₄	—	4	8	no	—
508	C₂×C₄	—	4	4	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	8	1	no	—
512	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
513	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
514	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
515	C₂×C₄	C₂×D₈×C₇₉	1	2	yes	—
516	C₂×C₄	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
517	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
518	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
519	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
520	C₈	—	4	2	no	—
521	C₈	—	4	2	no	—
522	C₈	—	4	2	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	8	2	no	—
532	C₂²	—	8	2	no	—
533	C₂²	—	8	2	no	—
534	C₂²	—	16	4	no	—
535	C₂²	#447×C₇₉	1	2	yes	—
536	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
537	C₄	—	2	1	no	—
538	C₄	—	2	1	no	—
539	C₄	—	2	4	no	—
540	C₄	—	2	1	no	—
541	C₄	—	4	2	no	—
542	C₄	—	4	2	no	—
543	C₄	—	4	2	no	—
544	C₄	#447×C₇₉	1	2	yes	—
545	C₄	C₂²×D₈×C₇₉	1	1	yes	characteristic
546	C₄	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
547	C₄	#577×C₇₉	1	2	yes	—
548	C₂	—	2	2	no	—
549	C₂	—	8	2	no	—
550	C₂	—	8	2	no	—
551	C₂	—	16	2	no	—
552	C₂	C₂×#447×C₇₉	1	1	yes	characteristic
553	C₂	C₇₉×#3010	1	1	yes	characteristic
554	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×#3497	C₂	semidirect
2. C₇₉×#3205	C₂	semidirect
3. C₇₉×#3205	C₂	semidirect
4. C₂×#460×C₇₉	C₂	semidirect
5. C₇₉×#1627	C₂	semidirect
6. C₇₉×#1621	C₂	semidirect
7. C₇₉×#1540	C₂	semidirect
8. C₇₉×#1480	C₂	semidirect
9. C₇₉×#1479	C₂	semidirect
13. #550×C₇₉	C₂²	semidirect
15. D₄×Q₈×C₇₉	C₂²	semidirect
39. #332×C₇₉	C₂²	semidirect
40. #331×C₇₉	C₂²	semidirect
41. Q₈⋊C₈×C₇₉	C₂²	semidirect
42. D₄⋊C₈×C₇₉	C₂²	semidirect
130. C₂×Q₈×C₇₉	D₈	semidirect
270. #18912	C₇₉	direct (N × H)
278. #3497	C₂×C₇₉	semidirect
279. #3205	C₂×C₇₉	semidirect
280. #3205	C₂×C₇₉	semidirect
281. C₂×#460	C₂×C₇₉	semidirect
282. #1627	C₂×C₇₉	semidirect
283. #1621	C₂×C₇₉	semidirect
284. #1540	C₂×C₇₉	semidirect
285. #1480	C₂×C₇₉	semidirect
286. #1479	C₂×C₇₉	semidirect
287. C₇₉	#18912	direct (N × H)
291. #550	C₂²×C₇₉	semidirect
293. D₄×Q₈	C₂²×C₇₉	semidirect
317. #332	C₂²×C₇₉	semidirect
318. #331	C₂²×C₇₉	semidirect
319. Q₈⋊C₈	C₂²×C₇₉	semidirect
320. D₄⋊C₈	C₂²×C₇₉	semidirect
408. C₂×Q₈	D₈×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₇₉×#3497	2
C₇₉×#3205	2
C₂×#460×C₇₉	2
C₇₉×#1627	2
C₇₉×#1621	2
C₇₉×#1540	2
C₇₉×#1480	2
C₇₉×#1479	2
#18912	79

Subgroups — C79×#18912 #34130601

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#18912 #34130601