Subgroups — C₇₉×#18666 #34130355

Order 20224.

936 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₉×#3246	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#3169	C₂	1	1	yes	maximal, characteristic
4	C₇₉×#3037	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#1648	C₂	1	2	yes	maximal, complemented
6	C₇₉×#1640	C₂	1	2	yes	maximal, complemented
7	C₇₉×#1626	C₂	1	2	yes	maximal, complemented
8	C₇₉×#1620	C₂	1	2	yes	maximal, complemented
9	C₇₉×#1547	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#1493	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×Q₈⋊C₈×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₇₉	—	2	1	no	—
13	#559×C₇₉	C₂²	1	2	yes	—
14	#557×C₇₉	C₂²	1	2	yes	—
15	#556×C₇₉	—	2	1	no	—
16	#556×C₇₉	—	2	2	no	—
17	#554×C₇₉	—	2	1	no	—
18	#552×C₇₉	—	2	2	no	—
19	#539×C₇₉	—	2	2	no	—
20	#536×C₇₉	—	2	1	no	—
21	#533×C₇₉	C₂²	1	1	yes	characteristic
22	#532×C₇₉	C₂²	1	1	yes	characteristic
23	#532×C₇₉	C₂²	1	1	yes	characteristic
24	#529×C₇₉	—	2	2	no	—
25	#520×C₇₉	—	2	1	no	—
26	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
27	#500×C₇₉	C₂²	1	1	yes	characteristic
28	#493×C₇₉	C₂²	1	1	yes	characteristic
29	#486×C₇₉	C₂²	1	1	yes	characteristic
30	#486×C₇₉	C₂²	1	1	yes	characteristic
31	#476×C₇₉	—	2	1	no	—
32	#475×C₇₉	C₂²	1	2	yes	—
33	#466×C₇₉	—	2	2	no	—
34	#465×C₇₉	—	2	2	no	—
35	#464×C₇₉	—	2	2	no	—
36	#462×C₇₉	C₂²	1	2	yes	—
37	#461×C₇₉	—	2	1	no	—
38	#460×C₇₉	C₂²	1	2	yes	—
39	#460×C₇₉	C₂²	1	2	yes	—
40	C₄×D₈×C₇₉	—	2	2	no	—
41	#423×C₇₉	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
43	#417×C₇₉	—	2	1	no	—
44	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
45	#332×C₇₉	C₂²	1	2	yes	—
46	#331×C₇₉	C₂²	1	2	yes	—
47	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	—
48	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	—
49	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	—
50	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	—
51	C₂×#41×C₇₉	—	2	1	no	—
52	C₂×#41×C₇₉	—	2	1	no	—
53	C₂²×Q₈×C₇₉	D₄	1	1	yes	characteristic
54	#137×C₇₉	—	4	4	no	—
55	C₂×Q₁₆×C₇₉	—	2	2	no	—
56	C₂×SD₁₆×C₇₉	—	2	2	no	—
57	C₂×SD₁₆×C₇₉	—	2	2	no	—
58	C₂×D₈×C₇₉	—	2	2	no	—
59	C₂×M₁₆×C₇₉	—	2	1	no	—
60	C₂²×C₈×C₇₉	—	2	1	no	—
61	C₂²×C₈×C₇₉	—	2	1	no	—
62	C₄⋊Q₈×C₇₉	—	2	2	no	—
63	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
64	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
65	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
66	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
67	#127×C₇₉	C₂³	1	1	yes	characteristic
68	#127×C₇₉	C₂³	1	1	yes	characteristic
69	#126×C₇₉	—	2	4	no	—
70	#126×C₇₉	—	2	4	no	—
71	#125×C₇₉	—	2	2	no	—
72	#125×C₇₉	—	2	4	no	—
73	#125×C₇₉	—	2	1	no	—
74	#124×C₇₉	—	2	2	no	—
75	#124×C₇₉	—	2	2	no	—
76	#124×C₇₉	—	2	1	no	—
77	#124×C₇₉	—	2	1	no	—
78	#123×C₇₉	—	2	4	no	—
79	#123×C₇₉	—	2	4	no	—
80	C₂²⋊Q₈×C₇₉	—	2	2	no	—
81	C₂²⋊Q₈×C₇₉	—	2	2	no	—
82	C₂²⋊Q₈×C₇₉	—	2	4	no	—
83	C₂²⋊Q₈×C₇₉	—	2	1	no	—
84	C₂²⋊Q₈×C₇₉	D₄	1	2	yes	—
85	#121×C₇₉	—	2	1	no	—
86	#121×C₇₉	—	2	1	no	—
87	#121×C₇₉	—	2	1	no	—
88	#121×C₇₉	D₄	1	2	yes	—
89	C₄×Q₈×C₇₉	—	2	2	no	—
90	C₄×Q₈×C₇₉	—	2	2	no	—
91	C₄×Q₈×C₇₉	—	2	1	no	—
92	C₄×Q₈×C₇₉	—	2	1	no	—
93	C₄×Q₈×C₇₉	—	2	1	no	—
94	C₄×Q₈×C₇₉	D₄	1	2	yes	—
95	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
96	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
97	C₄×D₄×C₇₉	—	2	4	no	—
98	C₄×D₄×C₇₉	—	2	2	no	—
99	C₄×D₄×C₇₉	—	2	2	no	—
100	C₄×D₄×C₇₉	—	2	1	no	—
101	C₄×D₄×C₇₉	—	2	1	no	—
102	C₄×D₄×C₇₉	—	2	1	no	—
103	C₄×D₄×C₇₉	D₄	1	2	yes	—
104	#117×C₇₉	—	2	2	no	—
105	#117×C₇₉	—	2	4	no	—
106	#117×C₇₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
108	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
109	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
110	C₂×C₄²×C₇₉	—	2	1	no	—
111	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
112	#107×C₇₉	—	2	2	no	—
113	#106×C₇₉	—	2	2	no	—
114	C₄⋊C₈×C₇₉	—	2	1	no	—
115	C₄⋊C₈×C₇₉	—	2	1	no	—
116	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
117	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
118	#103×C₇₉	—	2	2	no	—
119	#103×C₇₉	—	2	2	no	—
120	#102×C₇₉	—	2	2	no	—
121	#102×C₇₉	—	2	2	no	—
122	#102×C₇₉	—	2	2	no	—
123	#102×C₇₉	—	2	2	no	—
124	C₄×C₈×C₇₉	—	2	1	no	—
125	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
126	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
127	#41×C₇₉	—	4	2	no	—
128	#41×C₇₉	—	4	2	no	—
129	#41×C₇₉	—	4	2	no	—
130	#41×C₇₉	—	4	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	—	2	2	no	—
135	C₂×Q₈×C₇₉	—	2	2	no	—
136	C₂×Q₈×C₇₉	—	2	1	no	—
137	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
138	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
139	C₂×D₄×C₇₉	—	2	2	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	—	2	1	no	—
145	C₂×D₄×C₇₉	—	4	1	no	—
146	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₇₉	—	2	1	no	—
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	—	4	1	no	—
152	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
155	Q₁₆×C₇₉	—	4	4	no	—
156	SD₁₆×C₇₉	—	4	4	no	—
157	SD₁₆×C₇₉	—	8	2	no	—
158	D₈×C₇₉	—	4	4	no	—
159	M₁₆×C₇₉	—	4	2	no	—
160	C₂×C₈×C₇₉	—	2	1	no	—
161	C₂×C₈×C₇₉	—	2	1	no	—
162	C₂×C₈×C₇₉	—	2	2	no	—
163	C₂×C₈×C₇₉	—	2	2	no	—
164	C₂×C₈×C₇₉	—	4	2	no	—
165	C₂×C₈×C₇₉	—	8	1	no	—
166	C₄⋊C₄×C₇₉	—	2	4	no	—
167	C₄⋊C₄×C₇₉	—	2	4	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	2	no	—
172	C₄⋊C₄×C₇₉	—	2	1	no	—
173	C₄⋊C₄×C₇₉	—	2	2	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	2	no	—
178	C₄⋊C₄×C₇₉	—	2	1	no	—
179	C₄⋊C₄×C₇₉	—	2	1	no	—
180	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
181	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
182	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
183	C₂²⋊C₄×C₇₉	—	2	4	no	—
184	C₂²⋊C₄×C₇₉	—	2	4	no	—
185	C₂²⋊C₄×C₇₉	—	2	4	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	—	2	2	no	—
194	C₄²×C₇₉	—	2	2	no	—
195	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
196	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
197	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
198	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
199	C₂³×C₇₉	—	2	2	no	—
200	C₂³×C₇₉	—	4	1	no	—
201	C₂³×C₇₉	#120	1	1	yes	characteristic
202	Q₈×C₇₉	—	2	2	no	—
203	Q₈×C₇₉	—	2	2	no	—
204	Q₈×C₇₉	—	2	2	no	—
205	Q₈×C₇₉	—	2	2	no	—
206	Q₈×C₇₉	—	4	1	no	—
207	Q₈×C₇₉	—	4	1	no	—
208	Q₈×C₇₉	—	4	2	no	—
209	Q₈×C₇₉	—	4	1	no	—
210	Q₈×C₇₉	—	4	1	no	—
211	Q₈×C₇₉	—	8	1	no	—
212	D₄×C₇₉	—	4	2	no	—
213	D₄×C₇₉	—	4	2	no	—
214	D₄×C₇₉	—	4	4	no	—
215	D₄×C₇₉	—	4	1	no	—
216	D₄×C₇₉	—	4	1	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	—	4	1	no	—
222	D₄×C₇₉	—	4	1	no	—
223	D₄×C₇₉	—	8	2	no	—
224	C₂×C₄×C₇₉	—	2	1	no	—
225	C₂×C₄×C₇₉	—	2	1	no	—
226	C₂×C₄×C₇₉	—	2	2	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	2	no	—
233	C₂×C₄×C₇₉	—	4	4	no	—
234	C₂×C₄×C₇₉	—	4	1	no	—
235	C₂×C₄×C₇₉	—	8	1	no	—
236	C₂×C₄×C₇₉	—	8	4	no	—
237	C₂×C₄×C₇₉	—	8	2	no	—
238	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
239	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
240	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
241	C₂×C₄×C₇₉	#135	1	2	yes	—
242	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
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	—	2	2	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	—	4	2	no	—
253	C₂²×C₇₉	—	4	2	no	—
254	C₂²×C₇₉	—	4	2	no	—
255	C₂²×C₇₉	—	8	1	no	—
256	C₂²×C₇₉	—	8	1	no	—
257	C₂²×C₇₉	—	8	1	no	—
258	C₂²×C₇₉	#449	1	2	yes	—
259	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
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	—	4	2	no	—
267	C₄×C₇₉	—	4	2	no	—
268	C₄×C₇₉	—	8	1	no	—
269	C₄×C₇₉	#449	1	2	yes	—
270	C₄×C₇₉	C₂×#135	1	1	yes	characteristic
271	C₄×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
272	C₄×C₇₉	#577	1	1	yes	characteristic
273	C₄×C₇₉	#578	1	1	yes	characteristic
274	#18666	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
275	C₂×C₇₉	—	2	2	no	—
276	C₂×C₇₉	—	8	2	no	—
277	C₂×C₇₉	—	16	1	no	—
278	C₂×C₇₉	C₂×#449	1	1	yes	characteristic
279	C₂×C₇₉	#3013	1	1	yes	characteristic
280	C₂×C₇₉	#3018	1	1	yes	characteristic
281	#3507	C₂×C₇₉	1	1	yes	characteristic, complemented
282	#3246	C₂×C₇₉	1	1	yes	characteristic, complemented
283	#3169	C₂×C₇₉	1	1	yes	characteristic
284	#3037	C₂×C₇₉	1	1	yes	characteristic, complemented
285	#1648	C₂×C₇₉	1	2	yes	complemented
286	#1640	C₂×C₇₉	1	2	yes	complemented
287	#1626	C₂×C₇₉	1	2	yes	complemented
288	#1620	C₂×C₇₉	1	2	yes	complemented
289	#1547	C₂×C₇₉	1	1	yes	characteristic, complemented
290	#1493	C₂×C₇₉	1	1	yes	characteristic, complemented
291	C₂×Q₈⋊C₈	C₂×C₇₉	1	1	yes	characteristic, complemented
292	C₇₉	#18666	1	1	yes	characteristic, direct product factor, Sylow
293	C₂×#137	—	2	1	no	—
294	#559	C₂²×C₇₉	1	2	yes	—
295	#557	C₂²×C₇₉	1	2	yes	—
296	#556	—	2	1	no	—
297	#556	—	2	2	no	—
298	#554	—	2	1	no	—
299	#552	—	2	2	no	—
300	#539	—	2	2	no	—
301	#536	—	2	1	no	—
302	#533	C₂²×C₇₉	1	1	yes	characteristic
303	#532	C₂²×C₇₉	1	1	yes	characteristic
304	#532	C₂²×C₇₉	1	1	yes	characteristic
305	#529	—	2	2	no	—
306	#520	—	2	1	no	—
307	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
308	#500	C₂²×C₇₉	1	1	yes	characteristic
309	#493	C₂²×C₇₉	1	1	yes	characteristic
310	#486	C₂²×C₇₉	1	1	yes	characteristic
311	#486	C₂²×C₇₉	1	1	yes	characteristic
312	#476	—	2	1	no	—
313	#475	C₂²×C₇₉	1	2	yes	—
314	#466	—	2	2	no	—
315	#465	—	2	2	no	—
316	#464	—	2	2	no	—
317	#462	C₂²×C₇₉	1	2	yes	—
318	#461	—	2	1	no	—
319	#460	C₂²×C₇₉	1	2	yes	—
320	#460	C₂²×C₇₉	1	2	yes	—
321	C₄×D₈	—	2	2	no	—
322	#423	C₂²×C₇₉	1	1	yes	characteristic
323	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
324	#417	—	2	1	no	—
325	C₂×C₄×C₈	C₂²×C₇₉	1	1	yes	characteristic
326	#332	C₂²×C₇₉	1	2	yes	—
327	#331	C₂²×C₇₉	1	2	yes	—
328	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	—
329	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	—
330	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	—
331	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	—
332	C₂×#41	—	2	1	no	—
333	C₂×#41	—	2	1	no	—
334	C₂²×Q₈	D₄×C₇₉	1	1	yes	characteristic
335	#137	—	4	4	no	—
336	C₂×Q₁₆	—	2	2	no	—
337	C₂×SD₁₆	—	2	2	no	—
338	C₂×SD₁₆	—	2	2	no	—
339	C₂×D₈	—	2	2	no	—
340	C₂×M₁₆	—	2	1	no	—
341	C₂²×C₈	—	2	1	no	—
342	C₂²×C₈	—	2	1	no	—
343	C₄⋊Q₈	—	2	2	no	—
344	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
345	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
346	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
347	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
348	#127	C₂³×C₇₉	1	1	yes	characteristic
349	#127	C₂³×C₇₉	1	1	yes	characteristic
350	#126	—	2	4	no	—
351	#126	—	2	4	no	—
352	#125	—	2	2	no	—
353	#125	—	2	4	no	—
354	#125	—	2	1	no	—
355	#124	—	2	2	no	—
356	#124	—	2	2	no	—
357	#124	—	2	1	no	—
358	#124	—	2	1	no	—
359	#123	—	2	4	no	—
360	#123	—	2	4	no	—
361	C₂²⋊Q₈	—	2	2	no	—
362	C₂²⋊Q₈	—	2	2	no	—
363	C₂²⋊Q₈	—	2	4	no	—
364	C₂²⋊Q₈	—	2	1	no	—
365	C₂²⋊Q₈	D₄×C₇₉	1	2	yes	—
366	#121	—	2	1	no	—
367	#121	—	2	1	no	—
368	#121	—	2	1	no	—
369	#121	D₄×C₇₉	1	2	yes	—
370	C₄×Q₈	—	2	2	no	—
371	C₄×Q₈	—	2	2	no	—
372	C₄×Q₈	—	2	1	no	—
373	C₄×Q₈	—	2	1	no	—
374	C₄×Q₈	—	2	1	no	—
375	C₄×Q₈	D₄×C₇₉	1	2	yes	—
376	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
377	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
378	C₄×D₄	—	2	4	no	—
379	C₄×D₄	—	2	2	no	—
380	C₄×D₄	—	2	2	no	—
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	—	2	1	no	—
384	C₄×D₄	D₄×C₇₉	1	2	yes	—
385	#117	—	2	2	no	—
386	#117	—	2	4	no	—
387	#117	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	2	no	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
391	C₂×C₄²	—	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	C₄×C₈	—	2	1	no	—
406	C₄×C₈	C₂³×C₇₉	1	1	yes	characteristic
407	C₄×C₈	C₂³×C₇₉	1	1	yes	characteristic
408	#41	—	4	2	no	—
409	#41	—	4	2	no	—
410	#41	—	4	2	no	—
411	#41	—	4	2	no	—
412	C₂×Q₈	—	2	1	no	—
413	C₂×Q₈	—	2	1	no	—
414	C₂×Q₈	—	2	1	no	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	2	2	no	—
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
419	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	2	1	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	—	4	1	no	—
427	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	4	1	no	—
433	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
436	Q₁₆	—	4	4	no	—
437	SD₁₆	—	4	4	no	—
438	SD₁₆	—	8	2	no	—
439	D₈	—	4	4	no	—
440	M₁₆	—	4	2	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	4	2	no	—
446	C₂×C₈	—	8	1	no	—
447	C₄⋊C₄	—	2	4	no	—
448	C₄⋊C₄	—	2	4	no	—
449	C₄⋊C₄	—	2	4	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
462	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
463	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
464	C₂²⋊C₄	—	2	4	no	—
465	C₂²⋊C₄	—	2	4	no	—
466	C₂²⋊C₄	—	2	4	no	—
467	C₂²⋊C₄	—	2	2	no	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₂²⋊C₄	—	4	1	no	—
471	C₂²⋊C₄	—	4	1	no	—
472	C₄²	—	2	4	no	—
473	C₄²	—	2	2	no	—
474	C₄²	—	2	2	no	—
475	C₄²	—	2	2	no	—
476	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
477	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
478	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
479	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
480	C₂³	—	2	2	no	—
481	C₂³	—	4	1	no	—
482	C₂³	#120×C₇₉	1	1	yes	characteristic
483	Q₈	—	2	2	no	—
484	Q₈	—	2	2	no	—
485	Q₈	—	2	2	no	—
486	Q₈	—	2	2	no	—
487	Q₈	—	4	2	no	—
488	Q₈	—	4	1	no	—
489	Q₈	—	4	1	no	—
490	Q₈	—	4	1	no	—
491	Q₈	—	4	1	no	—
492	Q₈	—	8	1	no	—
493	D₄	—	4	2	no	—
494	D₄	—	4	2	no	—
495	D₄	—	4	4	no	—
496	D₄	—	4	1	no	—
497	D₄	—	4	1	no	—
498	D₄	—	4	1	no	—
499	D₄	—	4	1	no	—
500	D₄	—	4	1	no	—
501	D₄	—	4	1	no	—
502	D₄	—	4	1	no	—
503	D₄	—	4	1	no	—
504	D₄	—	8	2	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	4	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	8	1	no	—
517	C₂×C₄	—	8	4	no	—
518	C₂×C₄	—	8	2	no	—
519	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
520	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
521	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
522	C₂×C₄	#135×C₇₉	1	2	yes	—
523	C₂×C₄	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
524	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
525	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
526	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
527	C₈	—	2	2	no	—
528	C₈	—	4	1	no	—
529	C₈	—	4	2	no	—
530	C₈	—	4	2	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	1	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	8	1	no	—
537	C₂²	—	8	1	no	—
538	C₂²	—	8	1	no	—
539	C₂²	#449×C₇₉	1	2	yes	—
540	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	4	2	no	—
545	C₄	—	4	2	no	—
546	C₄	—	4	2	no	—
547	C₄	—	4	2	no	—
548	C₄	—	4	2	no	—
549	C₄	—	8	1	no	—
550	C₄	#449×C₇₉	1	2	yes	—
551	C₄	C₂×#135×C₇₉	1	1	yes	characteristic
552	C₄	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
553	C₄	#577×C₇₉	1	1	yes	characteristic
554	C₄	#578×C₇₉	1	1	yes	characteristic
555	C₂	—	2	2	no	—
556	C₂	—	8	2	no	—
557	C₂	—	16	1	no	—
558	C₂	C₂×#449×C₇₉	1	1	yes	characteristic
559	C₂	C₇₉×#3013	1	1	yes	characteristic
560	C₂	C₇₉×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₉
prime radical	C₇₉×#3169	C₂
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×#3507	C₂	semidirect
2. C₇₉×#3246	C₂	semidirect
4. C₇₉×#3037	C₂	semidirect
5. C₇₉×#1648	C₂	semidirect
6. C₇₉×#1640	C₂	semidirect
7. C₇₉×#1626	C₂	semidirect
8. C₇₉×#1620	C₂	semidirect
9. C₇₉×#1547	C₂	semidirect
10. C₇₉×#1493	C₂	semidirect
11. C₂×Q₈⋊C₈×C₇₉	C₂	semidirect
274. #18666	C₇₉	direct (N × H)
281. #3507	C₂×C₇₉	semidirect
282. #3246	C₂×C₇₉	semidirect
284. #3037	C₂×C₇₉	semidirect
285. #1648	C₂×C₇₉	semidirect
286. #1640	C₂×C₇₉	semidirect
287. #1626	C₂×C₇₉	semidirect
288. #1620	C₂×C₇₉	semidirect
289. #1547	C₂×C₇₉	semidirect
290. #1493	C₂×C₇₉	semidirect
291. C₂×Q₈⋊C₈	C₂×C₇₉	semidirect
292. C₇₉	#18666	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×#3507	2
C₇₉×#3246	2
C₇₉×#3169	2
C₇₉×#3037	2
C₇₉×#1648	2
C₇₉×#1640	2
C₇₉×#1626	2
C₇₉×#1620	2
C₇₉×#1547	2
C₇₉×#1493	2
C₂×Q₈⋊C₈×C₇₉	2
#18666	79

Subgroups — C79×#18666 #34130355

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#18666 #34130355