Subgroups — C₇₉×#24505 #34136194

Order 20224.

996 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#452×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#431×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#2855	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#2297	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#2067	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉×#2066	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#2056	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#2055	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#1969	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#1968	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1934	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₉×#1933	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₉×#1873	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₉×#1854	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#1788	C₂	1	1	yes	maximal, characteristic
16	C₂²×#41×C₇₉	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
22	#452×C₇₉	—	2	4	no	—
23	#431×C₇₉	—	2	4	no	—
24	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
25	C₂×#106×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
28	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
29	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
30	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
31	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
32	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
33	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
34	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
35	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
40	#391×C₇₉	C₂²	1	1	yes	characteristic
41	#391×C₇₉	C₂²	1	1	yes	characteristic
42	#391×C₇₉	C₂²	1	1	yes	characteristic
43	#391×C₇₉	C₂²	1	1	yes	characteristic
44	#390×C₇₉	C₂²	1	1	yes	characteristic
45	#390×C₇₉	C₂²	1	1	yes	characteristic
46	#389×C₇₉	C₂²	1	1	yes	characteristic
47	#389×C₇₉	C₂²	1	1	yes	characteristic
48	#387×C₇₉	—	2	1	no	—
49	#387×C₇₉	—	2	1	no	—
50	#386×C₇₉	—	2	1	no	—
51	#386×C₇₉	—	2	1	no	—
52	#385×C₇₉	—	2	1	no	—
53	#381×C₇₉	—	2	1	no	—
54	#380×C₇₉	C₂²	1	1	yes	characteristic
55	C₄×C₂²⋊C₄×C₇₉	—	2	1	no	—
56	C₄×C₂²⋊C₄×C₇₉	—	2	1	no	—
57	#340×C₇₉	C₂²	1	1	yes	characteristic
58	#340×C₇₉	C₂²	1	1	yes	characteristic
59	#340×C₇₉	C₂²	1	1	yes	characteristic
60	#340×C₇₉	C₂²	1	1	yes	characteristic
61	C₂×#41×C₇₉	—	2	2	no	—
62	C₂×#41×C₇₉	—	2	2	no	—
63	C₂×#41×C₇₉	—	2	2	no	—
64	C₂×#41×C₇₉	—	2	2	no	—
65	C₂×#41×C₇₉	—	4	1	no	—
66	C₂×#41×C₇₉	—	4	1	no	—
67	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
68	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₇₉	—	2	1	no	—
70	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₇₉	—	2	1	no	—
72	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
73	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
74	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
75	C₂×Q₁₆×C₇₉	—	2	2	no	—
76	C₂×Q₁₆×C₇₉	—	2	2	no	—
77	C₂×Q₁₆×C₇₉	—	4	1	no	—
78	C₂×SD₁₆×C₇₉	—	2	2	no	—
79	C₂×SD₁₆×C₇₉	—	2	2	no	—
80	C₂×SD₁₆×C₇₉	—	4	1	no	—
81	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
85	C₂²⋊Q₈×C₇₉	—	2	2	no	—
86	C₂²⋊Q₈×C₇₉	—	2	2	no	—
87	#117×C₇₉	—	4	1	no	—
88	#117×C₇₉	—	4	1	no	—
89	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
90	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
91	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
97	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
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×C₂²⋊C₄×C₇₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
104	C₂×C₄²×C₇₉	—	2	2	no	—
105	C₂×C₄²×C₇₉	—	2	2	no	—
106	C₂×C₄²×C₇₉	—	2	1	no	—
107	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
108	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
111	#107×C₇₉	—	4	1	no	—
112	#106×C₇₉	—	4	1	no	—
113	C₄⋊C₈×C₇₉	—	2	2	no	—
114	C₄⋊C₈×C₇₉	—	2	2	no	—
115	#103×C₇₉	—	2	2	no	—
116	#103×C₇₉	—	2	2	no	—
117	#103×C₇₉	—	4	1	no	—
118	#103×C₇₉	—	4	1	no	—
119	#103×C₇₉	—	4	1	no	—
120	#102×C₇₉	—	2	2	no	—
121	#102×C₇₉	—	2	2	no	—
122	#102×C₇₉	—	4	1	no	—
123	C₂²⋊C₈×C₇₉	—	2	2	no	—
124	C₂²⋊C₈×C₇₉	D₄	1	4	yes	—
125	C₄×C₈×C₇₉	—	2	2	no	—
126	C₄×C₈×C₇₉	—	2	2	no	—
127	#95×C₇₉	—	2	1	no	—
128	#95×C₇₉	—	2	1	no	—
129	#95×C₇₉	—	2	1	no	—
130	#95×C₇₉	—	2	1	no	—
131	#95×C₇₉	—	2	1	no	—
132	#95×C₇₉	—	2	1	no	—
133	#95×C₇₉	—	2	1	no	—
134	#95×C₇₉	—	2	1	no	—
135	#95×C₇₉	—	2	1	no	—
136	#95×C₇₉	—	2	1	no	—
137	#95×C₇₉	—	2	1	no	—
138	C₂⁴×C₇₉	—	2	1	no	—
139	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
140	#41×C₇₉	—	4	4	no	—
141	#41×C₇₉	—	4	4	no	—
142	#41×C₇₉	—	4	4	no	—
143	#41×C₇₉	—	4	4	no	—
144	C₂×Q₈×C₇₉	—	2	1	no	—
145	C₂×Q₈×C₇₉	—	2	1	no	—
146	C₂×Q₈×C₇₉	—	2	1	no	—
147	C₂×Q₈×C₇₉	—	2	1	no	—
148	C₂×Q₈×C₇₉	—	2	1	no	—
149	C₂×Q₈×C₇₉	—	2	1	no	—
150	C₂×Q₈×C₇₉	—	2	1	no	—
151	C₂×Q₈×C₇₉	—	2	1	no	—
152	C₂×Q₈×C₇₉	—	2	1	no	—
153	C₂×Q₈×C₇₉	—	2	1	no	—
154	C₂×Q₈×C₇₉	—	2	1	no	—
155	C₂×Q₈×C₇₉	#41	1	2	yes	—
156	C₂×D₄×C₇₉	—	2	4	no	—
157	C₂×D₄×C₇₉	—	2	1	no	—
158	C₂×D₄×C₇₉	—	2	1	no	—
159	C₂×D₄×C₇₉	—	2	1	no	—
160	C₂×D₄×C₇₉	—	2	1	no	—
161	C₂×D₄×C₇₉	—	2	1	no	—
162	C₂×D₄×C₇₉	—	4	2	no	—
163	C₂×D₄×C₇₉	—	4	2	no	—
164	C₂×D₄×C₇₉	#41	1	2	yes	—
165	C₂²×C₄×C₇₉	—	2	2	no	—
166	C₂²×C₄×C₇₉	—	2	2	no	—
167	C₂²×C₄×C₇₉	—	2	2	no	—
168	C₂²×C₄×C₇₉	—	2	1	no	—
169	C₂²×C₄×C₇₉	—	2	1	no	—
170	C₂²×C₄×C₇₉	—	2	1	no	—
171	C₂²×C₄×C₇₉	—	2	1	no	—
172	C₂²×C₄×C₇₉	—	2	4	no	—
173	C₂²×C₄×C₇₉	—	2	2	no	—
174	C₂²×C₄×C₇₉	—	2	1	no	—
175	C₂²×C₄×C₇₉	—	2	2	no	—
176	C₂²×C₄×C₇₉	—	2	1	no	—
177	C₂²×C₄×C₇₉	—	2	1	no	—
178	C₂²×C₄×C₇₉	—	2	1	no	—
179	C₂²×C₄×C₇₉	—	2	1	no	—
180	C₂²×C₄×C₇₉	—	2	1	no	—
181	C₂²×C₄×C₇₉	—	2	1	no	—
182	C₂²×C₄×C₇₉	—	4	1	no	—
183	C₂²×C₄×C₇₉	—	4	2	no	—
184	C₂²×C₄×C₇₉	—	4	2	no	—
185	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
188	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₇₉	#41	1	2	yes	—
192	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
193	Q₁₆×C₇₉	—	4	4	no	—
194	SD₁₆×C₇₉	—	4	4	no	—
195	C₂×C₈×C₇₉	—	2	1	no	—
196	C₂×C₈×C₇₉	—	2	1	no	—
197	C₂×C₈×C₇₉	—	2	1	no	—
198	C₂×C₈×C₇₉	—	2	1	no	—
199	C₂×C₈×C₇₉	—	2	1	no	—
200	C₂×C₈×C₇₉	—	2	1	no	—
201	C₂×C₈×C₇₉	—	2	1	no	—
202	C₂×C₈×C₇₉	—	2	1	no	—
203	C₂×C₈×C₇₉	—	2	1	no	—
204	C₂×C₈×C₇₉	—	2	1	no	—
205	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
206	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
207	C₄⋊C₄×C₇₉	—	2	1	no	—
208	C₄⋊C₄×C₇₉	—	2	1	no	—
209	C₄⋊C₄×C₇₉	—	2	1	no	—
210	C₄⋊C₄×C₇₉	—	2	1	no	—
211	C₄⋊C₄×C₇₉	—	2	1	no	—
212	C₄⋊C₄×C₇₉	—	2	1	no	—
213	C₄⋊C₄×C₇₉	—	2	1	no	—
214	C₄⋊C₄×C₇₉	—	2	1	no	—
215	C₄⋊C₄×C₇₉	—	2	1	no	—
216	C₄⋊C₄×C₇₉	—	2	1	no	—
217	C₄⋊C₄×C₇₉	—	4	2	no	—
218	C₄⋊C₄×C₇₉	—	4	2	no	—
219	C₄⋊C₄×C₇₉	—	4	2	no	—
220	C₂²⋊C₄×C₇₉	—	4	2	no	—
221	C₂²⋊C₄×C₇₉	—	4	2	no	—
222	C₂²⋊C₄×C₇₉	—	4	2	no	—
223	C₂²⋊C₄×C₇₉	—	4	2	no	—
224	C₂²⋊C₄×C₇₉	—	4	2	no	—
225	C₂²⋊C₄×C₇₉	—	4	2	no	—
226	C₂²⋊C₄×C₇₉	—	4	2	no	—
227	C₄²×C₇₉	—	2	2	no	—
228	C₄²×C₇₉	—	2	2	no	—
229	C₄²×C₇₉	—	2	1	no	—
230	C₄²×C₇₉	—	2	1	no	—
231	C₄²×C₇₉	—	2	1	no	—
232	C₄²×C₇₉	—	2	1	no	—
233	C₄²×C₇₉	—	4	2	no	—
234	C₂³×C₇₉	—	2	1	no	—
235	C₂³×C₇₉	—	2	1	no	—
236	C₂³×C₇₉	—	2	1	no	—
237	C₂³×C₇₉	—	2	1	no	—
238	C₂³×C₇₉	—	2	1	no	—
239	C₂³×C₇₉	—	2	1	no	—
240	C₂³×C₇₉	—	2	2	no	—
241	C₂³×C₇₉	—	4	1	no	—
242	C₂³×C₇₉	—	4	1	no	—
243	C₂³×C₇₉	—	4	1	no	—
244	C₂³×C₇₉	—	4	1	no	—
245	C₂³×C₇₉	—	4	1	no	—
246	C₂³×C₇₉	—	4	1	no	—
247	C₂³×C₇₉	#121	1	2	yes	—
248	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
249	Q₈×C₇₉	—	2	2	no	—
250	Q₈×C₇₉	—	2	2	no	—
251	Q₈×C₇₉	—	4	1	no	—
252	Q₈×C₇₉	—	4	1	no	—
253	Q₈×C₇₉	—	4	1	no	—
254	Q₈×C₇₉	—	4	1	no	—
255	Q₈×C₇₉	—	4	1	no	—
256	Q₈×C₇₉	—	4	1	no	—
257	D₄×C₇₉	—	2	2	no	—
258	D₄×C₇₉	—	2	2	no	—
259	D₄×C₇₉	—	4	8	no	—
260	D₄×C₇₉	—	4	1	no	—
261	D₄×C₇₉	—	4	1	no	—
262	C₂×C₄×C₇₉	—	2	8	no	—
263	C₂×C₄×C₇₉	—	2	1	no	—
264	C₂×C₄×C₇₉	—	2	1	no	—
265	C₂×C₄×C₇₉	—	2	1	no	—
266	C₂×C₄×C₇₉	—	2	1	no	—
267	C₂×C₄×C₇₉	—	2	1	no	—
268	C₂×C₄×C₇₉	—	2	1	no	—
269	C₂×C₄×C₇₉	—	2	1	no	—
270	C₂×C₄×C₇₉	—	2	1	no	—
271	C₂×C₄×C₇₉	—	2	2	no	—
272	C₂×C₄×C₇₉	—	2	2	no	—
273	C₂×C₄×C₇₉	—	2	2	no	—
274	C₂×C₄×C₇₉	—	2	2	no	—
275	C₂×C₄×C₇₉	—	2	1	no	—
276	C₂×C₄×C₇₉	—	2	2	no	—
277	C₂×C₄×C₇₉	—	2	1	no	—
278	C₂×C₄×C₇₉	—	2	1	no	—
279	C₂×C₄×C₇₉	—	4	4	no	—
280	C₂×C₄×C₇₉	—	4	8	no	—
281	C₂×C₄×C₇₉	—	4	1	no	—
282	C₂×C₄×C₇₉	—	4	1	no	—
283	C₂×C₄×C₇₉	—	4	1	no	—
284	C₂×C₄×C₇₉	—	4	1	no	—
285	C₂×C₄×C₇₉	—	4	1	no	—
286	C₂×C₄×C₇₉	—	4	1	no	—
287	C₂×C₄×C₇₉	—	4	1	no	—
288	C₂×C₄×C₇₉	—	4	1	no	—
289	C₂×C₄×C₇₉	—	4	1	no	—
290	C₂×C₄×C₇₉	—	4	1	no	—
291	C₂×C₄×C₇₉	—	4	1	no	—
292	C₂×C₄×C₇₉	—	4	1	no	—
293	C₂×C₄×C₇₉	—	4	1	no	—
294	C₂×C₄×C₇₉	—	4	1	no	—
295	C₂×C₄×C₇₉	—	4	1	no	—
296	C₂×C₄×C₇₉	—	4	1	no	—
297	C₂×C₄×C₇₉	—	4	1	no	—
298	C₂×C₄×C₇₉	—	4	1	no	—
299	C₂×C₄×C₇₉	—	4	1	no	—
300	C₂×C₄×C₇₉	—	4	1	no	—
301	C₂×C₄×C₇₉	#121	1	2	yes	—
302	C₂×C₄×C₇₉	#135	1	2	yes	—
303	C₂×C₄×C₇₉	#135	1	2	yes	—
304	C₂×C₄×C₇₉	#137	1	2	yes	—
305	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
307	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
308	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
309	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
310	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
311	C₈×C₇₉	—	2	2	no	—
312	C₈×C₇₉	—	2	2	no	—
313	C₈×C₇₉	—	4	1	no	—
314	C₈×C₇₉	—	4	1	no	—
315	C₂²×C₇₉	—	2	2	no	—
316	C₂²×C₇₉	—	2	2	no	—
317	C₂²×C₇₉	—	2	2	no	—
318	C₂²×C₇₉	—	4	1	no	—
319	C₂²×C₇₉	—	4	1	no	—
320	C₂²×C₇₉	—	4	1	no	—
321	C₂²×C₇₉	—	4	1	no	—
322	C₂²×C₇₉	—	4	2	no	—
323	C₂²×C₇₉	—	4	2	no	—
324	C₂²×C₇₉	—	4	2	no	—
325	C₂²×C₇₉	—	8	1	no	—
326	C₂²×C₇₉	—	8	1	no	—
327	C₂²×C₇₉	—	8	1	no	—
328	C₂²×C₇₉	—	8	1	no	—
329	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
330	C₂²×C₇₉	#525	1	1	yes	characteristic
331	C₂²×C₇₉	#535	1	1	yes	characteristic
332	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
333	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
334	C₂²×C₇₉	C₂×#137	1	1	yes	characteristic
335	C₂²×C₇₉	#575	1	1	yes	characteristic
336	C₄×C₇₉	—	2	2	no	—
337	C₄×C₇₉	—	2	2	no	—
338	C₄×C₇₉	—	2	2	no	—
339	C₄×C₇₉	—	2	2	no	—
340	C₄×C₇₉	—	4	2	no	—
341	C₄×C₇₉	—	4	1	no	—
342	C₄×C₇₉	—	8	1	no	—
343	C₄×C₇₉	—	8	1	no	—
344	C₄×C₇₉	—	8	1	no	—
345	C₄×C₇₉	—	8	1	no	—
346	C₄×C₇₉	—	8	1	no	—
347	C₄×C₇₉	—	8	1	no	—
348	C₄×C₇₉	#546	1	1	yes	characteristic
349	C₄×C₇₉	#546	1	1	yes	characteristic
350	C₄×C₇₉	#551	1	1	yes	characteristic
351	C₄×C₇₉	#551	1	1	yes	characteristic
352	#24505	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
353	C₂×C₇₉	—	4	2	no	—
354	C₂×C₇₉	—	8	2	no	—
355	C₂×C₇₉	#2411	1	1	yes	characteristic
356	C₂×C₇₉	#3050	1	1	yes	characteristic
357	C₂×C₇₉	#3056	1	1	yes	characteristic
358	C₂×C₇₉	#3102	1	1	yes	characteristic
359	C₂×C₇₉	#3107	1	1	yes	characteristic
360	C₂×C₇₉	#3210	1	1	yes	characteristic
361	C₂×C₇₉	#3212	1	1	yes	characteristic
362	C₂×#452	C₂×C₇₉	1	1	yes	characteristic
363	C₂×#431	C₂×C₇₉	1	1	yes	characteristic, complemented
364	#2855	C₂×C₇₉	1	1	yes	characteristic, complemented
365	#2297	C₂×C₇₉	1	1	yes	characteristic
366	#2067	C₂×C₇₉	1	1	yes	characteristic, complemented
367	#2066	C₂×C₇₉	1	1	yes	characteristic, complemented
368	#2056	C₂×C₇₉	1	1	yes	characteristic, complemented
369	#2055	C₂×C₇₉	1	1	yes	characteristic, complemented
370	#1969	C₂×C₇₉	1	1	yes	characteristic, complemented
371	#1968	C₂×C₇₉	1	1	yes	characteristic, complemented
372	#1934	C₂×C₇₉	1	1	yes	characteristic, complemented
373	#1933	C₂×C₇₉	1	1	yes	characteristic, complemented
374	#1873	C₂×C₇₉	1	1	yes	characteristic, complemented
375	#1854	C₂×C₇₉	1	1	yes	characteristic, complemented
376	#1788	C₂×C₇₉	1	1	yes	characteristic
377	C₇₉	#24505	1	1	yes	characteristic, direct product factor, Sylow
378	C₂²×#41	C₂²×C₇₉	1	1	yes	characteristic
379	C₂²×Q₁₆	C₂²×C₇₉	1	1	yes	characteristic
380	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
381	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
382	C₂×#117	C₂²×C₇₉	1	1	yes	characteristic
383	C₂²×C₄²	C₂²×C₇₉	1	1	yes	characteristic
384	#452	—	2	4	no	—
385	#431	—	2	4	no	—
386	C₂×#107	C₂²×C₇₉	1	1	yes	characteristic
387	C₂×#106	C₂²×C₇₉	1	1	yes	characteristic
388	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
389	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
390	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
391	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
392	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
393	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
394	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
395	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
396	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
397	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
398	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
399	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
400	C₂×C₄×C₈	C₂²×C₇₉	1	1	yes	characteristic
401	C₂×C₄×C₈	C₂²×C₇₉	1	1	yes	characteristic
402	#391	C₂²×C₇₉	1	1	yes	characteristic
403	#391	C₂²×C₇₉	1	1	yes	characteristic
404	#391	C₂²×C₇₉	1	1	yes	characteristic
405	#391	C₂²×C₇₉	1	1	yes	characteristic
406	#390	C₂²×C₇₉	1	1	yes	characteristic
407	#390	C₂²×C₇₉	1	1	yes	characteristic
408	#389	C₂²×C₇₉	1	1	yes	characteristic
409	#389	C₂²×C₇₉	1	1	yes	characteristic
410	#387	—	2	1	no	—
411	#387	—	2	1	no	—
412	#386	—	2	1	no	—
413	#386	—	2	1	no	—
414	#385	—	2	1	no	—
415	#381	—	2	1	no	—
416	#380	C₂²×C₇₉	1	1	yes	characteristic
417	C₄×C₂²⋊C₄	—	2	1	no	—
418	C₄×C₂²⋊C₄	—	2	1	no	—
419	#340	C₂²×C₇₉	1	1	yes	characteristic
420	#340	C₂²×C₇₉	1	1	yes	characteristic
421	#340	C₂²×C₇₉	1	1	yes	characteristic
422	#340	C₂²×C₇₉	1	1	yes	characteristic
423	C₂×#41	—	2	2	no	—
424	C₂×#41	—	2	2	no	—
425	C₂×#41	—	2	2	no	—
426	C₂×#41	—	2	2	no	—
427	C₂×#41	—	4	1	no	—
428	C₂×#41	—	4	1	no	—
429	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
430	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
431	C₂²×D₄	—	2	1	no	—
432	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
433	C₂³×C₄	—	2	1	no	—
434	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
435	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
436	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
437	C₂×Q₁₆	—	2	2	no	—
438	C₂×Q₁₆	—	2	2	no	—
439	C₂×Q₁₆	—	4	1	no	—
440	C₂×SD₁₆	—	2	2	no	—
441	C₂×SD₁₆	—	2	2	no	—
442	C₂×SD₁₆	—	4	1	no	—
443	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
444	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
445	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
446	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
447	C₂²⋊Q₈	—	2	2	no	—
448	C₂²⋊Q₈	—	2	2	no	—
449	#117	—	4	1	no	—
450	#117	—	4	1	no	—
451	C₂×C₄⋊C₄	—	2	1	no	—
452	C₂×C₄⋊C₄	—	2	1	no	—
453	C₂×C₄⋊C₄	—	2	1	no	—
454	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
455	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
457	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
458	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
459	C₂×C₂²⋊C₄	—	2	1	no	—
460	C₂×C₂²⋊C₄	—	2	1	no	—
461	C₂×C₂²⋊C₄	—	2	1	no	—
462	C₂×C₂²⋊C₄	—	2	1	no	—
463	C₂×C₂²⋊C₄	—	2	1	no	—
464	C₂×C₂²⋊C₄	—	2	1	no	—
465	C₂×C₂²⋊C₄	—	2	1	no	—
466	C₂×C₄²	—	2	2	no	—
467	C₂×C₄²	—	2	2	no	—
468	C₂×C₄²	—	2	1	no	—
469	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
470	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
471	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
472	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
473	#107	—	4	1	no	—
474	#106	—	4	1	no	—
475	C₄⋊C₈	—	2	2	no	—
476	C₄⋊C₈	—	2	2	no	—
477	#103	—	2	2	no	—
478	#103	—	2	2	no	—
479	#103	—	4	1	no	—
480	#103	—	4	1	no	—
481	#103	—	4	1	no	—
482	#102	—	2	2	no	—
483	#102	—	2	2	no	—
484	#102	—	4	1	no	—
485	C₂²⋊C₈	—	2	2	no	—
486	C₂²⋊C₈	D₄×C₇₉	1	4	yes	—
487	C₄×C₈	—	2	2	no	—
488	C₄×C₈	—	2	2	no	—
489	#95	—	2	1	no	—
490	#95	—	2	1	no	—
491	#95	—	2	1	no	—
492	#95	—	2	1	no	—
493	#95	—	2	1	no	—
494	#95	—	2	1	no	—
495	#95	—	2	1	no	—
496	#95	—	2	1	no	—
497	#95	—	2	1	no	—
498	#95	—	2	1	no	—
499	#95	—	2	1	no	—
500	C₂⁴	—	2	1	no	—
501	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
502	#41	—	4	4	no	—
503	#41	—	4	4	no	—
504	#41	—	4	4	no	—
505	#41	—	4	4	no	—
506	C₂×Q₈	—	2	1	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×Q₈	—	2	1	no	—
510	C₂×Q₈	—	2	1	no	—
511	C₂×Q₈	—	2	1	no	—
512	C₂×Q₈	—	2	1	no	—
513	C₂×Q₈	—	2	1	no	—
514	C₂×Q₈	—	2	1	no	—
515	C₂×Q₈	—	2	1	no	—
516	C₂×Q₈	—	2	1	no	—
517	C₂×Q₈	#41×C₇₉	1	2	yes	—
518	C₂×D₄	—	2	4	no	—
519	C₂×D₄	—	2	1	no	—
520	C₂×D₄	—	2	1	no	—
521	C₂×D₄	—	2	1	no	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	—	2	1	no	—
524	C₂×D₄	—	4	2	no	—
525	C₂×D₄	—	4	2	no	—
526	C₂×D₄	#41×C₇₉	1	2	yes	—
527	C₂²×C₄	—	2	2	no	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	2	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	—	2	2	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	2	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	4	1	no	—
545	C₂²×C₄	—	4	2	no	—
546	C₂²×C₄	—	4	2	no	—
547	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
548	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
549	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
550	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
551	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
552	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
553	C₂²×C₄	#41×C₇₉	1	2	yes	—
554	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
555	Q₁₆	—	4	4	no	—
556	SD₁₆	—	4	4	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
568	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	4	2	no	—
580	C₄⋊C₄	—	4	2	no	—
581	C₄⋊C₄	—	4	2	no	—
582	C₂²⋊C₄	—	4	2	no	—
583	C₂²⋊C₄	—	4	2	no	—
584	C₂²⋊C₄	—	4	2	no	—
585	C₂²⋊C₄	—	4	2	no	—
586	C₂²⋊C₄	—	4	2	no	—
587	C₂²⋊C₄	—	4	2	no	—
588	C₂²⋊C₄	—	4	2	no	—
589	C₄²	—	2	2	no	—
590	C₄²	—	2	2	no	—
591	C₄²	—	2	1	no	—
592	C₄²	—	2	1	no	—
593	C₄²	—	2	1	no	—
594	C₄²	—	2	1	no	—
595	C₄²	—	4	2	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	2	1	no	—
598	C₂³	—	2	1	no	—
599	C₂³	—	2	1	no	—
600	C₂³	—	2	1	no	—
601	C₂³	—	2	1	no	—
602	C₂³	—	2	2	no	—
603	C₂³	—	4	1	no	—
604	C₂³	—	4	1	no	—
605	C₂³	—	4	1	no	—
606	C₂³	—	4	1	no	—
607	C₂³	—	4	1	no	—
608	C₂³	—	4	1	no	—
609	C₂³	#121×C₇₉	1	2	yes	—
610	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
611	Q₈	—	2	2	no	—
612	Q₈	—	2	2	no	—
613	Q₈	—	4	1	no	—
614	Q₈	—	4	1	no	—
615	Q₈	—	4	1	no	—
616	Q₈	—	4	1	no	—
617	Q₈	—	4	1	no	—
618	Q₈	—	4	1	no	—
619	D₄	—	2	2	no	—
620	D₄	—	2	2	no	—
621	D₄	—	4	8	no	—
622	D₄	—	4	1	no	—
623	D₄	—	4	1	no	—
624	C₂×C₄	—	2	8	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	4	4	no	—
642	C₂×C₄	—	4	8	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	#121×C₇₉	1	2	yes	—
664	C₂×C₄	#135×C₇₉	1	2	yes	—
665	C₂×C₄	#135×C₇₉	1	2	yes	—
666	C₂×C₄	#137×C₇₉	1	2	yes	—
667	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
668	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
669	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
670	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
671	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
672	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
673	C₈	—	2	2	no	—
674	C₈	—	2	2	no	—
675	C₈	—	4	1	no	—
676	C₈	—	4	1	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	2	2	no	—
680	C₂²	—	4	1	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	1	no	—
683	C₂²	—	4	1	no	—
684	C₂²	—	4	2	no	—
685	C₂²	—	4	2	no	—
686	C₂²	—	4	2	no	—
687	C₂²	—	8	1	no	—
688	C₂²	—	8	1	no	—
689	C₂²	—	8	1	no	—
690	C₂²	—	8	1	no	—
691	C₂²	C₂×#121×C₇₉	1	1	yes	characteristic
692	C₂²	#525×C₇₉	1	1	yes	characteristic
693	C₂²	#535×C₇₉	1	1	yes	characteristic
694	C₂²	C₂×#135×C₇₉	1	1	yes	characteristic
695	C₂²	C₂×#135×C₇₉	1	1	yes	characteristic
696	C₂²	C₂×#137×C₇₉	1	1	yes	characteristic
697	C₂²	#575×C₇₉	1	1	yes	characteristic
698	C₄	—	2	2	no	—
699	C₄	—	2	2	no	—
700	C₄	—	2	2	no	—
701	C₄	—	2	2	no	—
702	C₄	—	4	1	no	—
703	C₄	—	4	2	no	—
704	C₄	—	8	1	no	—
705	C₄	—	8	1	no	—
706	C₄	—	8	1	no	—
707	C₄	—	8	1	no	—
708	C₄	—	8	1	no	—
709	C₄	—	8	1	no	—
710	C₄	#546×C₇₉	1	1	yes	characteristic
711	C₄	#546×C₇₉	1	1	yes	characteristic
712	C₄	#551×C₇₉	1	1	yes	characteristic
713	C₄	#551×C₇₉	1	1	yes	characteristic
714	C₂	—	4	2	no	—
715	C₂	—	8	2	no	—
716	C₂	C₇₉×#2411	1	1	yes	characteristic
717	C₂	C₇₉×#3050	1	1	yes	characteristic
718	C₂	C₇₉×#3056	1	1	yes	characteristic
719	C₂	C₇₉×#3102	1	1	yes	characteristic
720	C₂	C₇₉×#3107	1	1	yes	characteristic
721	C₂	C₇₉×#3210	1	1	yes	characteristic
722	C₂	C₇₉×#3212	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×#431×C₇₉	C₂	semidirect
3. C₇₉×#2855	C₂	semidirect
5. C₇₉×#2067	C₂	semidirect
6. C₇₉×#2066	C₂	semidirect
7. C₇₉×#2056	C₂	semidirect
8. C₇₉×#2055	C₂	semidirect
9. C₇₉×#1969	C₂	semidirect
10. C₇₉×#1968	C₂	semidirect
11. C₇₉×#1934	C₂	semidirect
12. C₇₉×#1933	C₂	semidirect
13. C₇₉×#1873	C₂	semidirect
14. C₇₉×#1854	C₂	semidirect
352. #24505	C₇₉	direct (N × H)
363. C₂×#431	C₂×C₇₉	semidirect
364. #2855	C₂×C₇₉	semidirect
366. #2067	C₂×C₇₉	semidirect
367. #2066	C₂×C₇₉	semidirect
368. #2056	C₂×C₇₉	semidirect
369. #2055	C₂×C₇₉	semidirect
370. #1969	C₂×C₇₉	semidirect
371. #1968	C₂×C₇₉	semidirect
372. #1934	C₂×C₇₉	semidirect
373. #1933	C₂×C₇₉	semidirect
374. #1873	C₂×C₇₉	semidirect
375. #1854	C₂×C₇₉	semidirect
377. C₇₉	#24505	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#452×C₇₉	2
C₂×#431×C₇₉	2
C₇₉×#2855	2
C₇₉×#2297	2
C₇₉×#2067	2
C₇₉×#2066	2
C₇₉×#2056	2
C₇₉×#2055	2
C₇₉×#1969	2
C₇₉×#1968	2
C₇₉×#1934	2
C₇₉×#1933	2
C₇₉×#1873	2
C₇₉×#1854	2
C₇₉×#1788	2
#24505	79

Subgroups — C79×#24505 #34136194

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#24505 #34136194