Subgroups — C₇₉×#17447 #34129136

Order 20224.

1332 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₇₉×#2920	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×M₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#1491	C₂	1	2	yes	maximal, complemented
5	C₇₉×#1490	C₂	1	2	yes	maximal, complemented
6	C₇₉×#1489	C₂	1	4	yes	maximal, complemented
7	C₇₉×#1476	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₇₉	C₄	1	1	yes	characteristic
9	C₂²×M₁₆×C₇₉	—	2	1	no	—
10	C₄×#41×C₇₉	—	2	1	no	—
11	C₄×#41×C₇₉	—	2	1	no	—
12	C₄×#41×C₇₉	—	2	1	no	—
13	C₄×#41×C₇₉	—	2	1	no	—
14	C₄×#41×C₇₉	C₄	1	2	yes	—
15	C₄×#41×C₇₉	C₄	1	2	yes	—
16	C₄×#41×C₇₉	C₂²	1	2	yes	—
17	C₄×#41×C₇₉	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₇₉	C₄	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₇₉	—	2	1	no	—
21	C₂×C₄×D₄×C₇₉	—	2	1	no	—
22	C₂×C₄×D₄×C₇₉	C₄	1	1	yes	characteristic
23	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
24	C₂×#117×C₇₉	—	2	1	no	—
25	C₂×#117×C₇₉	C₄	1	1	yes	characteristic
26	C₂²×C₄²×C₇₉	—	2	1	no	—
27	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
28	#432×C₇₉	—	2	1	no	—
29	#432×C₇₉	C₂²	1	2	yes	—
30	#431×C₇₉	—	2	1	no	—
31	#431×C₇₉	C₂²	1	2	yes	complemented
32	#423×C₇₉	C₂²	1	2	yes	complemented
33	#407×C₇₉	—	2	1	no	—
34	C₄×M₁₆×C₇₉	—	2	1	no	—
35	C₄×M₁₆×C₇₉	—	2	1	no	—
36	C₄×M₁₆×C₇₉	—	2	1	no	—
37	C₄×M₁₆×C₇₉	C₂²	1	2	yes	—
38	C₄×M₁₆×C₇₉	C₂²	1	2	yes	complemented
39	C₂×#97×C₇₉	—	2	1	no	—
40	C₂×C₄×C₈×C₇₉	C₂²	1	2	yes	complemented
41	Q₈⋊C₈×C₇₉	C₂²	1	8	yes	complemented
42	D₄⋊C₈×C₇₉	C₂²	1	8	yes	complemented
43	C₂×#41×C₇₉	—	2	8	no	—
44	C₂×#41×C₇₉	—	2	1	no	—
45	C₂×#41×C₇₉	—	2	1	no	—
46	C₂×#41×C₇₉	C₂×C₄	1	2	yes	—
47	C₂×#41×C₇₉	C₂×C₄	1	2	yes	—
48	C₂²×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
49	C₂²×D₄×C₇₉	—	2	1	no	—
50	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₇₉	—	2	1	no	—
52	C₂³×C₄×C₇₉	—	2	1	no	—
53	C₂³×C₄×C₇₉	—	2	1	no	—
54	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
55	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
57	C₂×M₁₆×C₇₉	—	2	8	no	—
58	C₂×M₁₆×C₇₉	—	2	2	no	—
59	C₂×M₁₆×C₇₉	—	2	2	no	—
60	C₂×M₁₆×C₇₉	—	2	2	no	—
61	C₂²×C₈×C₇₉	—	2	2	no	—
62	C₄×Q₈×C₇₉	—	2	1	no	—
63	C₄×Q₈×C₇₉	—	2	1	no	—
64	C₄×Q₈×C₇₉	—	2	1	no	—
65	C₄×Q₈×C₇₉	—	2	1	no	—
66	C₄×Q₈×C₇₉	C₂×C₄	1	2	yes	—
67	C₄×Q₈×C₇₉	C₂×C₄	1	2	yes	—
68	C₄×Q₈×C₇₉	C₂×C₄	1	2	yes	—
69	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
70	C₄×D₄×C₇₉	—	2	2	no	—
71	C₄×D₄×C₇₉	—	2	2	no	—
72	C₄×D₄×C₇₉	—	2	2	no	—
73	C₄×D₄×C₇₉	—	2	2	no	—
74	C₄×D₄×C₇₉	—	2	2	no	—
75	C₄×D₄×C₇₉	—	2	2	no	—
76	C₄×D₄×C₇₉	—	2	2	no	—
77	C₄×D₄×C₇₉	—	2	2	no	—
78	C₄×D₄×C₇₉	—	2	1	no	—
79	C₄×D₄×C₇₉	—	2	1	no	—
80	C₄×D₄×C₇₉	—	2	1	no	—
81	C₄×D₄×C₇₉	—	2	1	no	—
82	C₄×D₄×C₇₉	C₂×C₄	1	2	yes	—
83	C₄×D₄×C₇₉	C₂×C₄	1	2	yes	—
84	C₄×D₄×C₇₉	C₂×C₄	1	2	yes	—
85	C₄×D₄×C₇₉	C₂³	1	2	yes	—
86	#117×C₇₉	—	2	1	no	—
87	#117×C₇₉	—	2	1	no	—
88	#117×C₇₉	—	2	2	no	—
89	#117×C₇₉	—	2	2	no	—
90	#117×C₇₉	—	2	2	no	—
91	#117×C₇₉	—	2	2	no	—
92	#117×C₇₉	C₂×C₄	1	2	yes	—
93	#117×C₇₉	C₂×C₄	1	2	yes	—
94	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
101	C₂×C₄²×C₇₉	—	2	1	no	—
102	C₂×C₄²×C₇₉	—	2	1	no	—
103	C₂×C₄²×C₇₉	—	2	1	no	—
104	C₂×C₄²×C₇₉	—	2	2	no	—
105	C₂×C₄²×C₇₉	—	2	2	no	—
106	C₂×C₄²×C₇₉	—	2	2	no	—
107	C₂×C₄²×C₇₉	—	2	2	no	—
108	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
109	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
110	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
111	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
112	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
113	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
114	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
115	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
116	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
117	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
120	C₄⋊C₈×C₇₉	—	2	2	no	—
121	C₄⋊C₈×C₇₉	C₂³	1	4	yes	—
122	C₂²⋊C₈×C₇₉	—	2	2	no	—
123	C₂²⋊C₈×C₇₉	—	2	2	no	—
124	#97×C₇₉	—	2	2	no	—
125	#97×C₇₉	—	2	2	no	—
126	#97×C₇₉	—	2	2	no	—
127	C₄×C₈×C₇₉	—	2	2	no	—
128	C₄×C₈×C₇₉	—	2	2	no	—
129	C₄×C₈×C₇₉	C₂³	1	4	yes	—
130	C₂⁴×C₇₉	—	2	1	no	—
131	C₂⁴×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
132	#41×C₇₉	—	2	8	no	—
133	#41×C₇₉	—	2	8	no	—
134	#41×C₇₉	—	2	4	no	—
135	#41×C₇₉	—	2	4	no	—
136	#41×C₇₉	—	2	4	no	—
137	#41×C₇₉	M₁₆	1	8	yes	complemented
138	C₂×Q₈×C₇₉	—	2	4	no	—
139	C₂×Q₈×C₇₉	—	2	1	no	—
140	C₂×Q₈×C₇₉	C₂²×C₄	1	2	yes	—
141	C₂×D₄×C₇₉	—	2	8	no	—
142	C₂×D₄×C₇₉	—	2	2	no	—
143	C₂×D₄×C₇₉	—	2	2	no	—
144	C₂×D₄×C₇₉	—	2	4	no	—
145	C₂×D₄×C₇₉	—	2	1	no	—
146	C₂×D₄×C₇₉	C₂²×C₄	1	2	yes	—
147	C₂²×C₄×C₇₉	—	2	8	no	—
148	C₂²×C₄×C₇₉	—	2	1	no	—
149	C₂²×C₄×C₇₉	—	2	4	no	—
150	C₂²×C₄×C₇₉	—	2	2	no	—
151	C₂²×C₄×C₇₉	—	2	2	no	—
152	C₂²×C₄×C₇₉	—	2	4	no	—
153	C₂²×C₄×C₇₉	—	2	1	no	—
154	C₂²×C₄×C₇₉	—	2	1	no	—
155	C₂²×C₄×C₇₉	—	2	2	no	—
156	C₂²×C₄×C₇₉	—	2	2	no	—
157	C₂²×C₄×C₇₉	—	2	2	no	—
158	C₂²×C₄×C₇₉	—	2	2	no	—
159	C₂²×C₄×C₇₉	—	4	2	no	—
160	C₂²×C₄×C₇₉	—	4	4	no	—
161	C₂²×C₄×C₇₉	—	4	4	no	—
162	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
163	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
164	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
165	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
166	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
167	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
168	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
169	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
170	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
171	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
180	M₁₆×C₇₉	—	2	8	no	—
181	M₁₆×C₇₉	—	2	8	no	—
182	M₁₆×C₇₉	—	4	4	no	—
183	C₂×C₈×C₇₉	—	2	8	no	—
184	C₂×C₈×C₇₉	—	2	4	no	—
185	C₂×C₈×C₇₉	—	2	4	no	—
186	C₄⋊C₄×C₇₉	—	2	2	no	—
187	C₄⋊C₄×C₇₉	—	2	2	no	—
188	C₄⋊C₄×C₇₉	—	2	2	no	—
189	C₄⋊C₄×C₇₉	—	2	1	no	—
190	C₄⋊C₄×C₇₉	—	2	1	no	—
191	C₄⋊C₄×C₇₉	—	2	2	no	—
192	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
193	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
194	C₂²⋊C₄×C₇₉	—	2	2	no	—
195	C₂²⋊C₄×C₇₉	—	2	2	no	—
196	C₂²⋊C₄×C₇₉	—	2	2	no	—
197	C₂²⋊C₄×C₇₉	—	2	2	no	—
198	C₂²⋊C₄×C₇₉	—	2	2	no	—
199	C₂²⋊C₄×C₇₉	—	2	2	no	—
200	C₄²×C₇₉	—	2	2	no	—
201	C₄²×C₇₉	—	2	2	no	—
202	C₄²×C₇₉	—	2	2	no	—
203	C₄²×C₇₉	—	2	2	no	—
204	C₄²×C₇₉	—	2	2	no	—
205	C₄²×C₇₉	—	2	2	no	—
206	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
207	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
208	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
209	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
210	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
211	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
212	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
213	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
214	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
215	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
216	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
217	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
218	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
219	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
220	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
221	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
222	C₂³×C₇₉	—	2	4	no	—
223	C₂³×C₇₉	—	2	2	no	—
224	C₂³×C₇₉	—	2	2	no	—
225	C₂³×C₇₉	—	2	2	no	—
226	C₂³×C₇₉	—	4	1	no	—
227	C₂³×C₇₉	—	4	2	no	—
228	C₂³×C₇₉	—	4	2	no	—
229	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
232	Q₈×C₇₉	—	2	4	no	—
233	Q₈×C₇₉	—	2	2	no	—
234	Q₈×C₇₉	C₂×M₁₆	1	4	yes	complemented
235	D₄×C₇₉	—	2	8	no	—
236	D₄×C₇₉	—	2	4	no	—
237	D₄×C₇₉	—	2	8	no	—
238	D₄×C₇₉	—	2	2	no	—
239	D₄×C₇₉	C₂×M₁₆	1	4	yes	complemented
240	C₂×C₄×C₇₉	—	2	4	no	—
241	C₂×C₄×C₇₉	—	2	8	no	—
242	C₂×C₄×C₇₉	—	2	2	no	—
243	C₂×C₄×C₇₉	—	2	2	no	—
244	C₂×C₄×C₇₉	—	2	2	no	—
245	C₂×C₄×C₇₉	—	2	2	no	—
246	C₂×C₄×C₇₉	—	2	2	no	—
247	C₂×C₄×C₇₉	—	2	2	no	—
248	C₂×C₄×C₇₉	—	2	2	no	—
249	C₂×C₄×C₇₉	—	2	2	no	—
250	C₂×C₄×C₇₉	—	2	2	no	—
251	C₂×C₄×C₇₉	—	2	8	no	—
252	C₂×C₄×C₇₉	—	2	2	no	—
253	C₂×C₄×C₇₉	—	2	2	no	—
254	C₂×C₄×C₇₉	—	2	2	no	—
255	C₂×C₄×C₇₉	—	2	2	no	—
256	C₂×C₄×C₇₉	—	2	2	no	—
257	C₂×C₄×C₇₉	—	2	2	no	—
258	C₂×C₄×C₇₉	—	2	2	no	—
259	C₂×C₄×C₇₉	—	4	1	no	—
260	C₂×C₄×C₇₉	—	4	1	no	—
261	C₂×C₄×C₇₉	—	4	1	no	—
262	C₂×C₄×C₇₉	—	4	4	no	—
263	C₂×C₄×C₇₉	—	4	2	no	—
264	C₂×C₄×C₇₉	—	4	2	no	—
265	C₂×C₄×C₇₉	—	4	4	no	—
266	C₂×C₄×C₇₉	—	4	4	no	—
267	C₂×C₄×C₇₉	—	4	4	no	—
268	C₂×C₄×C₇₉	#104	1	4	yes	—
269	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
271	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
273	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
274	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
275	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
276	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
277	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
278	C₂×C₄×C₇₉	C₂×M₁₆	1	4	yes	—
279	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
280	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
281	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
282	C₈×C₇₉	—	2	8	no	—
283	C₈×C₇₉	—	4	4	no	—
284	C₂²×C₇₉	—	2	1	no	—
285	C₂²×C₇₉	—	2	1	no	—
286	C₂²×C₇₉	—	2	1	no	—
287	C₂²×C₇₉	—	2	1	no	—
288	C₂²×C₇₉	—	2	1	no	—
289	C₂²×C₇₉	—	2	4	no	—
290	C₂²×C₇₉	—	2	1	no	—
291	C₂²×C₇₉	—	2	1	no	—
292	C₂²×C₇₉	—	4	4	no	—
293	C₂²×C₇₉	—	4	8	no	—
294	C₂²×C₇₉	—	4	2	no	—
295	C₂²×C₇₉	—	4	2	no	—
296	C₂²×C₇₉	#407	1	2	yes	—
297	C₂²×C₇₉	C₂×#104	1	2	yes	—
298	C₂²×C₇₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
299	C₄×C₇₉	—	2	1	no	—
300	C₄×C₇₉	—	2	4	no	—
301	C₄×C₇₉	—	2	1	no	—
302	C₄×C₇₉	—	2	1	no	—
303	C₄×C₇₉	—	2	1	no	—
304	C₄×C₇₉	—	2	1	no	—
305	C₄×C₇₉	—	2	1	no	—
306	C₄×C₇₉	—	2	1	no	—
307	C₄×C₇₉	—	4	2	no	—
308	C₄×C₇₉	—	4	2	no	—
309	C₄×C₇₉	#407	1	2	yes	—
310	C₄×C₇₉	C₂×#104	1	2	yes	—
311	C₄×C₇₉	C₂×#104	1	2	yes	—
312	C₄×C₇₉	C₂²×M₁₆	1	2	yes	—
313	C₄×C₇₉	#575	1	2	yes	—
314	#17447	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
315	C₂×C₇₉	—	2	2	no	—
316	C₂×C₇₉	—	2	2	no	—
317	C₂×C₇₉	—	4	1	no	—
318	C₂×C₇₉	—	4	4	no	—
319	C₂×C₇₉	C₂×#407	1	1	yes	characteristic
320	C₂×C₇₉	#2896	1	1	yes	characteristic
321	C₂×C₇₉	C₂²×#104	1	1	yes	characteristic
322	C₂×C₄×#41	C₂×C₇₉	1	1	yes	characteristic
323	#2920	C₂×C₇₉	1	1	yes	characteristic, complemented
324	C₂×C₄×M₁₆	C₂×C₇₉	1	1	yes	characteristic, complemented
325	#1491	C₂×C₇₉	1	2	yes	complemented
326	#1490	C₂×C₇₉	1	2	yes	complemented
327	#1489	C₂×C₇₉	1	4	yes	complemented
328	#1476	C₂×C₇₉	1	4	yes	complemented
329	C₇₉	#17447	1	1	yes	characteristic, direct product factor, Sylow
330	C₂²×#41	C₄×C₇₉	1	1	yes	characteristic
331	C₂²×M₁₆	—	2	1	no	—
332	C₄×#41	—	2	1	no	—
333	C₄×#41	—	2	1	no	—
334	C₄×#41	—	2	1	no	—
335	C₄×#41	—	2	1	no	—
336	C₄×#41	C₄×C₇₉	1	2	yes	—
337	C₄×#41	C₄×C₇₉	1	2	yes	—
338	C₄×#41	C₂²×C₇₉	1	2	yes	—
339	C₄×#41	C₂²×C₇₉	1	2	yes	—
340	C₂×C₄×Q₈	C₄×C₇₉	1	1	yes	characteristic
341	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
342	C₂×C₄×D₄	—	2	1	no	—
343	C₂×C₄×D₄	—	2	1	no	—
344	C₂×C₄×D₄	C₄×C₇₉	1	1	yes	characteristic
345	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
346	C₂×#117	—	2	1	no	—
347	C₂×#117	C₄×C₇₉	1	1	yes	characteristic
348	C₂²×C₄²	—	2	1	no	—
349	C₂²×C₄²	C₂²×C₇₉	1	1	yes	characteristic
350	#432	—	2	1	no	—
351	#432	C₂²×C₇₉	1	2	yes	—
352	#431	—	2	1	no	—
353	#431	C₂²×C₇₉	1	2	yes	complemented
354	#423	C₂²×C₇₉	1	2	yes	complemented
355	#407	—	2	1	no	—
356	C₄×M₁₆	—	2	1	no	—
357	C₄×M₁₆	—	2	1	no	—
358	C₄×M₁₆	—	2	1	no	—
359	C₄×M₁₆	C₂²×C₇₉	1	2	yes	—
360	C₄×M₁₆	C₂²×C₇₉	1	2	yes	complemented
361	C₂×#97	—	2	1	no	—
362	C₂×C₄×C₈	C₂²×C₇₉	1	2	yes	complemented
363	Q₈⋊C₈	C₂²×C₇₉	1	8	yes	complemented
364	D₄⋊C₈	C₂²×C₇₉	1	8	yes	complemented
365	C₂×#41	—	2	8	no	—
366	C₂×#41	—	2	1	no	—
367	C₂×#41	—	2	1	no	—
368	C₂×#41	C₂×C₄×C₇₉	1	2	yes	—
369	C₂×#41	C₂×C₄×C₇₉	1	2	yes	—
370	C₂²×Q₈	C₂×C₄×C₇₉	1	1	yes	characteristic
371	C₂²×D₄	—	2	1	no	—
372	C₂²×D₄	C₂×C₄×C₇₉	1	1	yes	characteristic
373	C₂³×C₄	—	2	1	no	—
374	C₂³×C₄	—	2	1	no	—
375	C₂³×C₄	—	2	1	no	—
376	C₂³×C₄	C₂×C₄×C₇₉	1	1	yes	characteristic
377	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
378	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
379	C₂×M₁₆	—	2	8	no	—
380	C₂×M₁₆	—	2	2	no	—
381	C₂×M₁₆	—	2	2	no	—
382	C₂×M₁₆	—	2	2	no	—
383	C₂²×C₈	—	2	2	no	—
384	C₄×Q₈	—	2	1	no	—
385	C₄×Q₈	—	2	1	no	—
386	C₄×Q₈	—	2	1	no	—
387	C₄×Q₈	—	2	1	no	—
388	C₄×Q₈	C₂×C₄×C₇₉	1	2	yes	—
389	C₄×Q₈	C₂×C₄×C₇₉	1	2	yes	—
390	C₄×Q₈	C₂×C₄×C₇₉	1	2	yes	—
391	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
392	C₄×D₄	—	2	2	no	—
393	C₄×D₄	—	2	2	no	—
394	C₄×D₄	—	2	2	no	—
395	C₄×D₄	—	2	2	no	—
396	C₄×D₄	—	2	2	no	—
397	C₄×D₄	—	2	2	no	—
398	C₄×D₄	—	2	2	no	—
399	C₄×D₄	—	2	2	no	—
400	C₄×D₄	—	2	1	no	—
401	C₄×D₄	—	2	1	no	—
402	C₄×D₄	—	2	1	no	—
403	C₄×D₄	—	2	1	no	—
404	C₄×D₄	C₂×C₄×C₇₉	1	2	yes	—
405	C₄×D₄	C₂×C₄×C₇₉	1	2	yes	—
406	C₄×D₄	C₂×C₄×C₇₉	1	2	yes	—
407	C₄×D₄	C₂³×C₇₉	1	2	yes	—
408	#117	—	2	1	no	—
409	#117	—	2	1	no	—
410	#117	—	2	2	no	—
411	#117	—	2	2	no	—
412	#117	—	2	2	no	—
413	#117	—	2	2	no	—
414	#117	C₂×C₄×C₇₉	1	2	yes	—
415	#117	C₂×C₄×C₇₉	1	2	yes	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	—	2	1	no	—
418	C₂×C₄⋊C₄	C₂×C₄×C₇₉	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂×C₄×C₇₉	1	1	yes	characteristic
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	—	2	1	no	—
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₄²	—	2	1	no	—
424	C₂×C₄²	—	2	1	no	—
425	C₂×C₄²	—	2	1	no	—
426	C₂×C₄²	—	2	2	no	—
427	C₂×C₄²	—	2	2	no	—
428	C₂×C₄²	—	2	2	no	—
429	C₂×C₄²	—	2	2	no	—
430	C₂×C₄²	C₂×C₄×C₇₉	1	1	yes	characteristic
431	C₂×C₄²	C₂×C₄×C₇₉	1	1	yes	characteristic
432	C₂×C₄²	C₂×C₄×C₇₉	1	1	yes	characteristic
433	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
434	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
435	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
436	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
437	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
438	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
439	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
440	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
441	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
442	C₄⋊C₈	—	2	2	no	—
443	C₄⋊C₈	C₂³×C₇₉	1	4	yes	—
444	C₂²⋊C₈	—	2	2	no	—
445	C₂²⋊C₈	—	2	2	no	—
446	#97	—	2	2	no	—
447	#97	—	2	2	no	—
448	#97	—	2	2	no	—
449	C₄×C₈	—	2	2	no	—
450	C₄×C₈	—	2	2	no	—
451	C₄×C₈	C₂³×C₇₉	1	4	yes	—
452	C₂⁴	—	2	1	no	—
453	C₂⁴	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
454	#41	—	2	8	no	—
455	#41	—	2	8	no	—
456	#41	—	2	4	no	—
457	#41	—	2	4	no	—
458	#41	—	2	4	no	—
459	#41	M₁₆×C₇₉	1	8	yes	complemented
460	C₂×Q₈	—	2	4	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	C₂²×C₄×C₇₉	1	2	yes	—
463	C₂×D₄	—	2	8	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	2	4	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	C₂²×C₄×C₇₉	1	2	yes	—
469	C₂²×C₄	—	2	8	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	4	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	4	2	no	—
482	C₂²×C₄	—	4	4	no	—
483	C₂²×C₄	—	4	4	no	—
484	C₂²×C₄	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
485	C₂²×C₄	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
486	C₂²×C₄	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
487	C₂²×C₄	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
488	C₂²×C₄	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
489	C₂²×C₄	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
490	C₂²×C₄	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
491	C₂²×C₄	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
492	C₂²×C₄	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
493	C₂²×C₄	C₂²×C₄×C₇₉	1	1	yes	characteristic
494	C₂²×C₄	C₂²×C₄×C₇₉	1	1	yes	characteristic
495	C₂²×C₄	C₂²×C₄×C₇₉	1	1	yes	characteristic
496	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
497	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
498	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
499	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
500	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
501	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
502	M₁₆	—	2	8	no	—
503	M₁₆	—	2	8	no	—
504	M₁₆	—	4	4	no	—
505	C₂×C₈	—	2	8	no	—
506	C₂×C₈	—	2	4	no	—
507	C₂×C₈	—	2	4	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	2	no	—
514	C₄⋊C₄	C₂²×C₄×C₇₉	1	2	yes	—
515	C₄⋊C₄	C₂²×C₄×C₇₉	1	2	yes	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	2	2	no	—
521	C₂²⋊C₄	—	2	2	no	—
522	C₄²	—	2	2	no	—
523	C₄²	—	2	2	no	—
524	C₄²	—	2	2	no	—
525	C₄²	—	2	2	no	—
526	C₄²	—	2	2	no	—
527	C₄²	—	2	2	no	—
528	C₄²	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
529	C₄²	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
530	C₄²	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
531	C₄²	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
532	C₄²	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
533	C₄²	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
534	C₄²	C₂²×C₄×C₇₉	1	1	yes	characteristic
535	C₄²	C₂²×C₄×C₇₉	1	1	yes	characteristic
536	C₄²	C₂²×C₄×C₇₉	1	1	yes	characteristic
537	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
538	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
539	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
540	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
541	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
542	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
543	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
544	C₂³	—	2	4	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	2	2	no	—
547	C₂³	—	2	2	no	—
548	C₂³	—	4	1	no	—
549	C₂³	—	4	2	no	—
550	C₂³	—	4	2	no	—
551	C₂³	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
552	C₂³	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
553	C₂³	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
554	Q₈	—	2	4	no	—
555	Q₈	—	2	2	no	—
556	Q₈	C₂×M₁₆×C₇₉	1	4	yes	complemented
557	D₄	—	2	8	no	—
558	D₄	—	2	4	no	—
559	D₄	—	2	8	no	—
560	D₄	—	2	2	no	—
561	D₄	C₂×M₁₆×C₇₉	1	4	yes	complemented
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	8	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	8	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	4	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	4	2	no	—
587	C₂×C₄	—	4	4	no	—
588	C₂×C₄	—	4	4	no	—
589	C₂×C₄	—	4	4	no	—
590	C₂×C₄	#104×C₇₉	1	4	yes	—
591	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
592	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
593	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
594	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
595	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
596	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
597	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
598	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
599	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
600	C₂×C₄	C₂×M₁₆×C₇₉	1	4	yes	—
601	C₂×C₄	C₂³×C₄×C₇₉	1	1	yes	characteristic
602	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
603	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
604	C₈	—	2	8	no	—
605	C₈	—	4	4	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	2	1	no	—
611	C₂²	—	2	4	no	—
612	C₂²	—	2	1	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	4	4	no	—
615	C₂²	—	4	8	no	—
616	C₂²	—	4	2	no	—
617	C₂²	—	4	2	no	—
618	C₂²	#407×C₇₉	1	2	yes	—
619	C₂²	C₂×#104×C₇₉	1	2	yes	—
620	C₂²	C₂²×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
621	C₄	—	2	1	no	—
622	C₄	—	2	4	no	—
623	C₄	—	2	1	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	1	no	—
627	C₄	—	2	1	no	—
628	C₄	—	2	1	no	—
629	C₄	—	4	2	no	—
630	C₄	—	4	2	no	—
631	C₄	#407×C₇₉	1	2	yes	—
632	C₄	C₂×#104×C₇₉	1	2	yes	—
633	C₄	C₂×#104×C₇₉	1	2	yes	—
634	C₄	C₂²×M₁₆×C₇₉	1	2	yes	—
635	C₄	#575×C₇₉	1	2	yes	—
636	C₂	—	2	2	no	—
637	C₂	—	2	2	no	—
638	C₂	—	4	1	no	—
639	C₂	—	4	4	no	—
640	C₂	C₂×#407×C₇₉	1	1	yes	characteristic
641	C₂	C₇₉×#2896	1	1	yes	characteristic
642	C₂	C₂²×#104×C₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₄²×C₇₉	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₇₉
Frattini, cosocle	C₄²	C₂⁴×C₇₉
socle	C₂²×C₇₉	C₂²×C₂²⋊C₄
prime radical	C₂²×#41×C₇₉	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₇₉ ◁ C₂²×C₄²×C₇₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₇₉×#2920	C₂	semidirect
3. C₂×C₄×M₁₆×C₇₉	C₂	semidirect
4. C₇₉×#1491	C₂	semidirect
5. C₇₉×#1490	C₂	semidirect
6. C₇₉×#1489	C₂	semidirect
7. C₇₉×#1476	C₂	semidirect
31. #431×C₇₉	C₂²	semidirect
32. #423×C₇₉	C₂²	semidirect
38. C₄×M₁₆×C₇₉	C₂²	semidirect
40. C₂×C₄×C₈×C₇₉	C₂²	semidirect
41. Q₈⋊C₈×C₇₉	C₂²	semidirect
42. D₄⋊C₈×C₇₉	C₂²	semidirect
137. #41×C₇₉	M₁₆	semidirect
234. Q₈×C₇₉	C₂×M₁₆	semidirect
239. D₄×C₇₉	C₂×M₁₆	semidirect
314. #17447	C₇₉	direct (N × H)
323. #2920	C₂×C₇₉	semidirect
324. C₂×C₄×M₁₆	C₂×C₇₉	semidirect
325. #1491	C₂×C₇₉	semidirect
326. #1490	C₂×C₇₉	semidirect
327. #1489	C₂×C₇₉	semidirect
328. #1476	C₂×C₇₉	semidirect
329. C₇₉	#17447	direct (N × H)
353. #431	C₂²×C₇₉	semidirect
354. #423	C₂²×C₇₉	semidirect
360. C₄×M₁₆	C₂²×C₇₉	semidirect
362. C₂×C₄×C₈	C₂²×C₇₉	semidirect
363. Q₈⋊C₈	C₂²×C₇₉	semidirect
364. D₄⋊C₈	C₂²×C₇₉	semidirect
459. #41	M₁₆×C₇₉	semidirect
556. Q₈	C₂×M₁₆×C₇₉	semidirect
561. D₄	C₂×M₁₆×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₇₉	2
C₇₉×#2920	2
C₂×C₄×M₁₆×C₇₉	2
C₇₉×#1491	2
C₇₉×#1490	2
C₇₉×#1489	2
C₇₉×#1476	2
#17447	79

Subgroups — C79×#17447 #34129136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#17447 #34129136