Subgroups — C₇₉×#18593 #34130282

Order 20224.

916 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3511	C₂	1	1	yes	maximal, characteristic
2	C₇₉×#3254	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#3165	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#3107	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#1654	C₂	1	2	yes	maximal, complemented
6	C₇₉×#1652	C₂	1	2	yes	maximal, complemented
7	C₇₉×#1650	C₂	1	2	yes	maximal, complemented
8	C₇₉×#1647	C₂	1	2	yes	maximal, complemented
9	C₇₉×#1546	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#1489	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1484	C₂	1	1	yes	maximal, characteristic, complemented
12	#556×C₇₉	C₂²	1	2	yes	—
13	#555×C₇₉	—	2	1	no	—
14	#554×C₇₉	—	2	1	no	—
15	#553×C₇₉	—	2	2	no	—
16	#548×C₇₉	—	2	2	no	—
17	#547×C₇₉	C₂²	1	2	yes	—
18	#542×C₇₉	—	2	2	no	—
19	#537×C₇₉	—	2	1	no	—
20	#533×C₇₉	—	2	1	no	—
21	#533×C₇₉	C₂²	1	1	yes	characteristic
22	#532×C₇₉	—	2	1	no	—
23	#532×C₇₉	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
25	#520×C₇₉	—	2	1	no	—
26	C₄×#41×C₇₉	C₂²	1	1	yes	characteristic
27	#501×C₇₉	—	2	2	no	—
28	#500×C₇₉	C₂²	1	2	yes	—
29	#498×C₇₉	C₂²	1	2	yes	—
30	#485×C₇₉	—	2	1	no	—
31	#477×C₇₉	—	2	1	no	—
32	#475×C₇₉	C₂²	1	1	yes	characteristic
33	#474×C₇₉	C₂²	1	1	yes	characteristic
34	#474×C₇₉	C₂²	1	2	yes	—
35	#468×C₇₉	—	2	2	no	—
36	#462×C₇₉	C₂²	1	1	yes	characteristic
37	#461×C₇₉	C₂²	1	1	yes	characteristic
38	#461×C₇₉	C₂²	1	2	yes	—
39	#460×C₇₉	—	2	1	no	—
40	#452×C₇₉	—	2	1	no	—
41	C₄×Q₁₆×C₇₉	—	2	1	no	—
42	C₄×SD₁₆×C₇₉	—	2	1	no	—
43	#431×C₇₉	C₂²	1	1	yes	characteristic
44	#428×C₇₉	—	2	2	no	—
45	#423×C₇₉	C₂²	1	1	yes	characteristic
46	C₄×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
47	#332×C₇₉	C₂²	1	2	yes	—
48	#332×C₇₉	C₂²	1	2	yes	—
49	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	—
50	D₄⋊C₈×C₇₉	C₂²	1	2	yes	—
51	D₄⋊C₈×C₇₉	C₂²	1	2	yes	—
52	D₄⋊C₈×C₇₉	C₂²	1	2	yes	—
53	C₂×#41×C₇₉	—	2	2	no	—
54	C₂×#41×C₇₉	—	2	1	no	—
55	C₂×#41×C₇₉	D₄	1	1	yes	characteristic
56	C₂²×Q₈×C₇₉	—	2	1	no	—
57	C₂×Q₁₆×C₇₉	—	2	1	no	—
58	C₂×SD₁₆×C₇₉	—	2	1	no	—
59	C₂×SD₁₆×C₇₉	—	2	2	no	—
60	C₂×M₁₆×C₇₉	—	2	1	no	—
61	C₂×M₁₆×C₇₉	—	2	1	no	—
62	C₄⋊Q₈×C₇₉	—	2	1	no	—
63	C₄⋊Q₈×C₇₉	—	2	1	no	—
64	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
65	C₄⋊Q₈×C₇₉	D₄	1	2	yes	—
66	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
67	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
68	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
69	#127×C₇₉	D₄	1	1	yes	characteristic
70	#126×C₇₉	—	2	4	no	—
71	#125×C₇₉	—	2	2	no	—
72	#125×C₇₉	—	2	1	no	—
73	#124×C₇₉	—	2	4	no	—
74	#124×C₇₉	—	2	2	no	—
75	#124×C₇₉	—	2	1	no	—
76	#123×C₇₉	—	2	4	no	—
77	C₂²⋊Q₈×C₇₉	—	2	2	no	—
78	C₂²⋊Q₈×C₇₉	—	2	4	no	—
79	C₂²⋊Q₈×C₇₉	—	2	2	no	—
80	C₂²⋊Q₈×C₇₉	—	2	2	no	—
81	C₂²⋊Q₈×C₇₉	—	2	1	no	—
82	C₂²⋊Q₈×C₇₉	—	2	1	no	—
83	#121×C₇₉	—	2	2	no	—
84	#121×C₇₉	—	2	2	no	—
85	#121×C₇₉	—	2	4	no	—
86	#121×C₇₉	—	2	2	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	D₄	1	1	yes	characteristic
94	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
95	C₄×D₄×C₇₉	—	2	2	no	—
96	C₄×D₄×C₇₉	—	2	4	no	—
97	C₄×D₄×C₇₉	—	2	2	no	—
98	C₄×D₄×C₇₉	—	2	1	no	—
99	C₄×D₄×C₇₉	—	2	1	no	—
100	C₄×D₄×C₇₉	—	2	1	no	—
101	C₄×D₄×C₇₉	D₄	1	1	yes	characteristic
102	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
103	C₄×D₄×C₇₉	C₂³	1	2	yes	—
104	#117×C₇₉	—	2	2	no	—
105	#117×C₇₉	—	2	2	no	—
106	#117×C₇₉	—	2	1	no	—
107	#117×C₇₉	—	2	1	no	—
108	#117×C₇₉	D₄	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
110	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
111	C₂×C₄⋊C₄×C₇₉	D₄	1	2	yes	—
112	C₂×C₄²×C₇₉	—	2	1	no	—
113	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
114	#107×C₇₉	—	2	4	no	—
115	#107×C₇₉	—	2	1	no	—
116	#107×C₇₉	—	2	2	no	—
117	#106×C₇₉	—	2	4	no	—
118	#106×C₇₉	—	2	1	no	—
119	C₄⋊C₈×C₇₉	—	2	1	no	—
120	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
121	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
122	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
123	#103×C₇₉	—	2	1	no	—
124	#103×C₇₉	—	2	1	no	—
125	#103×C₇₉	—	2	1	no	—
126	#103×C₇₉	—	2	2	no	—
127	#102×C₇₉	—	2	1	no	—
128	#102×C₇₉	—	2	2	no	—
129	C₂²⋊C₈×C₇₉	—	2	1	no	—
130	#97×C₇₉	—	2	1	no	—
131	C₄×C₈×C₇₉	—	2	1	no	—
132	C₄×C₈×C₇₉	C₂³	1	2	yes	—
133	#41×C₇₉	—	4	1	no	—
134	#41×C₇₉	—	4	1	no	—
135	#41×C₇₉	—	4	2	no	—
136	#41×C₇₉	—	4	2	no	—
137	#41×C₇₉	—	8	2	no	—
138	#41×C₇₉	—	8	2	no	—
139	C₂×Q₈×C₇₉	—	2	1	no	—
140	C₂×Q₈×C₇₉	—	2	2	no	—
141	C₂×Q₈×C₇₉	—	2	2	no	—
142	C₂×Q₈×C₇₉	—	2	1	no	—
143	C₂×Q₈×C₇₉	—	2	1	no	—
144	C₂×Q₈×C₇₉	—	8	1	no	—
145	C₂×Q₈×C₇₉	—	8	1	no	—
146	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
147	C₂×D₄×C₇₉	—	2	1	no	—
148	C₂×D₄×C₇₉	—	2	2	no	—
149	C₂×D₄×C₇₉	—	2	4	no	—
150	C₂×D₄×C₇₉	—	2	1	no	—
151	C₂×D₄×C₇₉	—	2	1	no	—
152	C₂×D₄×C₇₉	C₂×D₄	1	1	yes	characteristic
153	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₇₉	—	2	4	no	—
155	C₂²×C₄×C₇₉	—	2	2	no	—
156	C₂²×C₄×C₇₉	—	2	1	no	—
157	C₂²×C₄×C₇₉	—	2	1	no	—
158	C₂²×C₄×C₇₉	—	2	1	no	—
159	C₂²×C₄×C₇₉	—	2	2	no	—
160	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
163	Q₁₆×C₇₉	—	4	2	no	—
164	SD₁₆×C₇₉	—	4	2	no	—
165	SD₁₆×C₇₉	—	8	2	no	—
166	M₁₆×C₇₉	—	2	4	no	—
167	M₁₆×C₇₉	—	8	1	no	—
168	C₂×C₈×C₇₉	—	2	2	no	—
169	C₂×C₈×C₇₉	—	2	1	no	—
170	C₂×C₈×C₇₉	—	2	1	no	—
171	C₂×C₈×C₇₉	—	2	2	no	—
172	C₄⋊C₄×C₇₉	—	2	4	no	—
173	C₄⋊C₄×C₇₉	—	2	4	no	—
174	C₄⋊C₄×C₇₉	—	2	2	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	—	2	2	no	—
179	C₄⋊C₄×C₇₉	—	2	1	no	—
180	C₄⋊C₄×C₇₉	—	2	1	no	—
181	C₄⋊C₄×C₇₉	—	2	1	no	—
182	C₄⋊C₄×C₇₉	—	2	1	no	—
183	C₄⋊C₄×C₇₉	—	2	1	no	—
184	C₄⋊C₄×C₇₉	—	4	1	no	—
185	C₄⋊C₄×C₇₉	—	4	1	no	—
186	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
187	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
188	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
189	C₄⋊C₄×C₇₉	C₂×D₄	1	4	yes	—
190	C₂²⋊C₄×C₇₉	—	2	4	no	—
191	C₂²⋊C₄×C₇₉	—	2	4	no	—
192	C₂²⋊C₄×C₇₉	—	2	4	no	—
193	C₂²⋊C₄×C₇₉	—	2	1	no	—
194	C₂²⋊C₄×C₇₉	—	2	1	no	—
195	C₂²⋊C₄×C₇₉	—	2	2	no	—
196	C₂²⋊C₄×C₇₉	—	2	1	no	—
197	C₂²⋊C₄×C₇₉	—	2	2	no	—
198	C₂²⋊C₄×C₇₉	—	4	1	no	—
199	C₄²×C₇₉	—	2	4	no	—
200	C₄²×C₇₉	—	2	1	no	—
201	C₄²×C₇₉	—	2	1	no	—
202	C₄²×C₇₉	—	2	1	no	—
203	C₄²×C₇₉	—	4	1	no	—
204	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
206	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
208	C₂³×C₇₉	—	2	1	no	—
209	C₂³×C₇₉	—	2	2	no	—
210	C₂³×C₇₉	#120	1	1	yes	characteristic
211	Q₈×C₇₉	—	2	1	no	—
212	Q₈×C₇₉	—	2	1	no	—
213	Q₈×C₇₉	—	4	2	no	—
214	Q₈×C₇₉	—	4	2	no	—
215	Q₈×C₇₉	—	4	2	no	—
216	Q₈×C₇₉	—	4	1	no	—
217	Q₈×C₇₉	—	4	1	no	—
218	Q₈×C₇₉	—	4	1	no	—
219	Q₈×C₇₉	—	4	1	no	—
220	Q₈×C₇₉	—	8	2	no	—
221	D₄×C₇₉	—	2	1	no	—
222	D₄×C₇₉	—	2	1	no	—
223	D₄×C₇₉	—	2	2	no	—
224	D₄×C₇₉	—	2	2	no	—
225	D₄×C₇₉	—	4	2	no	—
226	D₄×C₇₉	—	4	2	no	—
227	D₄×C₇₉	—	4	4	no	—
228	D₄×C₇₉	—	4	2	no	—
229	D₄×C₇₉	—	8	4	no	—
230	C₂×C₄×C₇₉	—	2	1	no	—
231	C₂×C₄×C₇₉	—	2	1	no	—
232	C₂×C₄×C₇₉	—	2	1	no	—
233	C₂×C₄×C₇₉	—	2	1	no	—
234	C₂×C₄×C₇₉	—	2	2	no	—
235	C₂×C₄×C₇₉	—	2	1	no	—
236	C₂×C₄×C₇₉	—	2	1	no	—
237	C₂×C₄×C₇₉	—	2	2	no	—
238	C₂×C₄×C₇₉	—	2	1	no	—
239	C₂×C₄×C₇₉	—	2	4	no	—
240	C₂×C₄×C₇₉	—	4	2	no	—
241	C₂×C₄×C₇₉	—	4	2	no	—
242	C₂×C₄×C₇₉	—	4	2	no	—
243	C₂×C₄×C₇₉	—	4	1	no	—
244	C₂×C₄×C₇₉	—	4	1	no	—
245	C₂×C₄×C₇₉	—	4	2	no	—
246	C₂×C₄×C₇₉	—	4	1	no	—
247	C₂×C₄×C₇₉	—	4	1	no	—
248	C₂×C₄×C₇₉	—	8	2	no	—
249	C₂×C₄×C₇₉	—	8	4	no	—
250	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
251	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
252	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
253	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
256	C₈×C₇₉	—	2	4	no	—
257	C₈×C₇₉	—	4	1	no	—
258	C₈×C₇₉	—	4	1	no	—
259	C₈×C₇₉	—	4	2	no	—
260	C₂²×C₇₉	—	2	1	no	—
261	C₂²×C₇₉	—	2	1	no	—
262	C₂²×C₇₉	—	2	1	no	—
263	C₂²×C₇₉	—	4	1	no	—
264	C₂²×C₇₉	—	4	2	no	—
265	C₂²×C₇₉	—	4	1	no	—
266	C₂²×C₇₉	—	4	2	no	—
267	C₂²×C₇₉	—	4	1	no	—
268	C₂²×C₇₉	—	4	2	no	—
269	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
270	C₄×C₇₉	—	2	1	no	—
271	C₄×C₇₉	—	2	1	no	—
272	C₄×C₇₉	—	2	1	no	—
273	C₄×C₇₉	—	4	1	no	—
274	C₄×C₇₉	—	4	2	no	—
275	C₄×C₇₉	—	4	1	no	—
276	C₄×C₇₉	—	4	4	no	—
277	C₄×C₇₉	—	4	1	no	—
278	C₄×C₇₉	—	8	1	no	—
279	C₄×C₇₉	—	8	1	no	—
280	C₄×C₇₉	#456	1	2	yes	—
281	C₄×C₇₉	#575	1	1	yes	characteristic
282	C₄×C₇₉	#575	1	1	yes	characteristic
283	C₄×C₇₉	#576	1	1	yes	characteristic
284	C₄×C₇₉	#577	1	1	yes	characteristic
285	#18593	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
286	C₂×C₇₉	—	4	1	no	—
287	C₂×C₇₉	—	8	1	no	—
288	C₂×C₇₉	—	8	2	no	—
289	C₂×C₇₉	#3005	1	1	yes	characteristic
290	C₂×C₇₉	#3012	1	1	yes	characteristic
291	C₂×C₇₉	C₂×#456	1	1	yes	characteristic
292	#3511	C₂×C₇₉	1	1	yes	characteristic
293	#3254	C₂×C₇₉	1	1	yes	characteristic, complemented
294	#3165	C₂×C₇₉	1	1	yes	characteristic, complemented
295	#3107	C₂×C₇₉	1	1	yes	characteristic, complemented
296	#1654	C₂×C₇₉	1	2	yes	complemented
297	#1652	C₂×C₇₉	1	2	yes	complemented
298	#1650	C₂×C₇₉	1	2	yes	complemented
299	#1647	C₂×C₇₉	1	2	yes	complemented
300	#1546	C₂×C₇₉	1	1	yes	characteristic, complemented
301	#1489	C₂×C₇₉	1	1	yes	characteristic, complemented
302	#1484	C₂×C₇₉	1	1	yes	characteristic, complemented
303	C₇₉	#18593	1	1	yes	characteristic, direct product factor, Sylow
304	#556	C₂²×C₇₉	1	2	yes	—
305	#555	—	2	1	no	—
306	#554	—	2	1	no	—
307	#553	—	2	2	no	—
308	#548	—	2	2	no	—
309	#547	C₂²×C₇₉	1	2	yes	—
310	#542	—	2	2	no	—
311	#537	—	2	1	no	—
312	#533	—	2	1	no	—
313	#533	C₂²×C₇₉	1	1	yes	characteristic
314	#532	—	2	1	no	—
315	#532	C₂²×C₇₉	1	1	yes	characteristic
316	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
317	#520	—	2	1	no	—
318	C₄×#41	C₂²×C₇₉	1	1	yes	characteristic
319	#501	—	2	2	no	—
320	#500	C₂²×C₇₉	1	2	yes	—
321	#498	C₂²×C₇₉	1	2	yes	—
322	#485	—	2	1	no	—
323	#477	—	2	1	no	—
324	#475	C₂²×C₇₉	1	1	yes	characteristic
325	#474	C₂²×C₇₉	1	1	yes	characteristic
326	#474	C₂²×C₇₉	1	2	yes	—
327	#468	—	2	2	no	—
328	#462	C₂²×C₇₉	1	1	yes	characteristic
329	#461	C₂²×C₇₉	1	1	yes	characteristic
330	#461	C₂²×C₇₉	1	2	yes	—
331	#460	—	2	1	no	—
332	#452	—	2	1	no	—
333	C₄×Q₁₆	—	2	1	no	—
334	C₄×SD₁₆	—	2	1	no	—
335	#431	C₂²×C₇₉	1	1	yes	characteristic
336	#428	—	2	2	no	—
337	#423	C₂²×C₇₉	1	1	yes	characteristic
338	C₄×M₁₆	C₂²×C₇₉	1	1	yes	characteristic
339	#332	C₂²×C₇₉	1	2	yes	—
340	#332	C₂²×C₇₉	1	2	yes	—
341	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	—
342	D₄⋊C₈	C₂²×C₇₉	1	2	yes	—
343	D₄⋊C₈	C₂²×C₇₉	1	2	yes	—
344	D₄⋊C₈	C₂²×C₇₉	1	2	yes	—
345	C₂×#41	—	2	2	no	—
346	C₂×#41	—	2	1	no	—
347	C₂×#41	D₄×C₇₉	1	1	yes	characteristic
348	C₂²×Q₈	—	2	1	no	—
349	C₂×Q₁₆	—	2	1	no	—
350	C₂×SD₁₆	—	2	1	no	—
351	C₂×SD₁₆	—	2	2	no	—
352	C₂×M₁₆	—	2	1	no	—
353	C₂×M₁₆	—	2	1	no	—
354	C₄⋊Q₈	—	2	1	no	—
355	C₄⋊Q₈	—	2	1	no	—
356	C₄⋊Q₈	D₄×C₇₉	1	2	yes	—
357	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
358	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
359	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
360	C₄⋊Q₈	C₂³×C₇₉	1	2	yes	—
361	#127	D₄×C₇₉	1	1	yes	characteristic
362	#126	—	2	4	no	—
363	#125	—	2	2	no	—
364	#125	—	2	1	no	—
365	#124	—	2	4	no	—
366	#124	—	2	2	no	—
367	#124	—	2	1	no	—
368	#123	—	2	4	no	—
369	C₂²⋊Q₈	—	2	2	no	—
370	C₂²⋊Q₈	—	2	4	no	—
371	C₂²⋊Q₈	—	2	2	no	—
372	C₂²⋊Q₈	—	2	2	no	—
373	C₂²⋊Q₈	—	2	1	no	—
374	C₂²⋊Q₈	—	2	1	no	—
375	#121	—	2	2	no	—
376	#121	—	2	2	no	—
377	#121	—	2	4	no	—
378	#121	—	2	2	no	—
379	#121	—	2	1	no	—
380	#121	D₄×C₇₉	1	2	yes	—
381	C₄×Q₈	—	2	2	no	—
382	C₄×Q₈	—	2	2	no	—
383	C₄×Q₈	—	2	1	no	—
384	C₄×Q₈	—	2	1	no	—
385	C₄×Q₈	D₄×C₇₉	1	1	yes	characteristic
386	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
387	C₄×D₄	—	2	2	no	—
388	C₄×D₄	—	2	4	no	—
389	C₄×D₄	—	2	2	no	—
390	C₄×D₄	—	2	1	no	—
391	C₄×D₄	—	2	1	no	—
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	D₄×C₇₉	1	1	yes	characteristic
394	C₄×D₄	C₂³×C₇₉	1	1	yes	characteristic
395	C₄×D₄	C₂³×C₇₉	1	2	yes	—
396	#117	—	2	2	no	—
397	#117	—	2	2	no	—
398	#117	—	2	1	no	—
399	#117	—	2	1	no	—
400	#117	D₄×C₇₉	1	1	yes	characteristic
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	—	2	2	no	—
403	C₂×C₄⋊C₄	D₄×C₇₉	1	2	yes	—
404	C₂×C₄²	—	2	1	no	—
405	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
406	#107	—	2	4	no	—
407	#107	—	2	1	no	—
408	#107	—	2	2	no	—
409	#106	—	2	4	no	—
410	#106	—	2	1	no	—
411	C₄⋊C₈	—	2	1	no	—
412	C₄⋊C₈	C₂³×C₇₉	1	1	yes	characteristic
413	C₄⋊C₈	C₂³×C₇₉	1	1	yes	characteristic
414	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
415	#103	—	2	1	no	—
416	#103	—	2	1	no	—
417	#103	—	2	1	no	—
418	#103	—	2	2	no	—
419	#102	—	2	1	no	—
420	#102	—	2	2	no	—
421	C₂²⋊C₈	—	2	1	no	—
422	#97	—	2	1	no	—
423	C₄×C₈	—	2	1	no	—
424	C₄×C₈	C₂³×C₇₉	1	2	yes	—
425	#41	—	4	1	no	—
426	#41	—	4	1	no	—
427	#41	—	4	2	no	—
428	#41	—	4	2	no	—
429	#41	—	8	2	no	—
430	#41	—	8	2	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	2	no	—
433	C₂×Q₈	—	2	2	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	8	1	no	—
437	C₂×Q₈	—	8	1	no	—
438	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	4	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	C₂×D₄×C₇₉	1	1	yes	characteristic
445	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
446	C₂²×C₄	—	2	4	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
455	Q₁₆	—	4	2	no	—
456	SD₁₆	—	4	2	no	—
457	SD₁₆	—	8	2	no	—
458	M₁₆	—	2	4	no	—
459	M₁₆	—	8	1	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	2	no	—
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	4	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	4	1	no	—
477	C₄⋊C₄	—	4	1	no	—
478	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
479	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
480	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
481	C₄⋊C₄	C₂×D₄×C₇₉	1	4	yes	—
482	C₂²⋊C₄	—	2	4	no	—
483	C₂²⋊C₄	—	2	4	no	—
484	C₂²⋊C₄	—	2	4	no	—
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	2	2	no	—
488	C₂²⋊C₄	—	2	1	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	4	1	no	—
491	C₄²	—	2	4	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	2	1	no	—
495	C₄²	—	4	1	no	—
496	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
497	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
498	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
499	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
500	C₂³	—	2	1	no	—
501	C₂³	—	2	2	no	—
502	C₂³	#120×C₇₉	1	1	yes	characteristic
503	Q₈	—	2	1	no	—
504	Q₈	—	2	1	no	—
505	Q₈	—	4	2	no	—
506	Q₈	—	4	2	no	—
507	Q₈	—	4	2	no	—
508	Q₈	—	4	1	no	—
509	Q₈	—	4	1	no	—
510	Q₈	—	4	1	no	—
511	Q₈	—	4	1	no	—
512	Q₈	—	8	2	no	—
513	D₄	—	2	1	no	—
514	D₄	—	2	1	no	—
515	D₄	—	2	2	no	—
516	D₄	—	2	2	no	—
517	D₄	—	4	2	no	—
518	D₄	—	4	2	no	—
519	D₄	—	4	4	no	—
520	D₄	—	4	2	no	—
521	D₄	—	8	4	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	8	2	no	—
541	C₂×C₄	—	8	4	no	—
542	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
543	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
544	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
545	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
546	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
547	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
548	C₈	—	2	4	no	—
549	C₈	—	4	1	no	—
550	C₈	—	4	1	no	—
551	C₈	—	4	2	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	2	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	2	no	—
561	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
562	C₄	—	2	1	no	—
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	2	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	4	no	—
569	C₄	—	4	1	no	—
570	C₄	—	8	1	no	—
571	C₄	—	8	1	no	—
572	C₄	#456×C₇₉	1	2	yes	—
573	C₄	#575×C₇₉	1	1	yes	characteristic
574	C₄	#575×C₇₉	1	1	yes	characteristic
575	C₄	#576×C₇₉	1	1	yes	characteristic
576	C₄	#577×C₇₉	1	1	yes	characteristic
577	C₂	—	4	1	no	—
578	C₂	—	8	1	no	—
579	C₂	—	8	2	no	—
580	C₂	C₇₉×#3005	1	1	yes	characteristic
581	C₂	C₇₉×#3012	1	1	yes	characteristic
582	C₂	C₂×#456×C₇₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₉
prime radical	C₇₉×#3511	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
2. C₇₉×#3254	C₂	semidirect
3. C₇₉×#3165	C₂	semidirect
4. C₇₉×#3107	C₂	semidirect
5. C₇₉×#1654	C₂	semidirect
6. C₇₉×#1652	C₂	semidirect
7. C₇₉×#1650	C₂	semidirect
8. C₇₉×#1647	C₂	semidirect
9. C₇₉×#1546	C₂	semidirect
10. C₇₉×#1489	C₂	semidirect
11. C₇₉×#1484	C₂	semidirect
285. #18593	C₇₉	direct (N × H)
293. #3254	C₂×C₇₉	semidirect
294. #3165	C₂×C₇₉	semidirect
295. #3107	C₂×C₇₉	semidirect
296. #1654	C₂×C₇₉	semidirect
297. #1652	C₂×C₇₉	semidirect
298. #1650	C₂×C₇₉	semidirect
299. #1647	C₂×C₇₉	semidirect
300. #1546	C₂×C₇₉	semidirect
301. #1489	C₂×C₇₉	semidirect
302. #1484	C₂×C₇₉	semidirect
303. C₇₉	#18593	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×#3511	2
C₇₉×#3254	2
C₇₉×#3165	2
C₇₉×#3107	2
C₇₉×#1654	2
C₇₉×#1652	2
C₇₉×#1650	2
C₇₉×#1647	2
C₇₉×#1546	2
C₇₉×#1489	2
C₇₉×#1484	2
#18593	79

Subgroups — C79×#18593 #34130282

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#18593 #34130282