Subgroups — C₇₉×#24502 #34136191

Order 20224.

992 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#451×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#431×C₇₉	C₂	1	1	yes	maximal, characteristic
3	C₇₉×#2855	C₂	1	1	yes	maximal, characteristic
4	C₂×#391×C₇₉	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#2068	C₂	1	2	yes	maximal, complemented
6	C₇₉×#2056	C₂	1	2	yes	maximal, complemented
7	C₇₉×#1969	C₂	1	2	yes	maximal, complemented
8	C₇₉×#1933	C₂	1	2	yes	maximal, complemented
9	C₇₉×#1872	C₂	1	1	yes	maximal, characteristic
10	C₇₉×#1852	C₂	1	1	yes	maximal, characteristic
11	C₇₉×#1787	C₂	1	1	yes	maximal, characteristic
12	C₂³×Q₈×C₇₉	C₂²	1	1	yes	characteristic
13	C₂²×Q₁₆×C₇₉	C₂²	1	2	yes	—
14	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
17	#451×C₇₉	—	2	4	no	—
18	#431×C₇₉	—	2	4	no	—
19	C₂×#107×C₇₉	C₂²	1	2	yes	—
20	C₂×C₄⋊C₈×C₇₉	C₂²	1	2	yes	—
21	C₂×#103×C₇₉	C₂²	1	2	yes	—
22	C₂×#103×C₇₉	C₂²	1	2	yes	—
23	C₂×#103×C₇₉	C₂²	1	2	yes	—
24	C₂×#103×C₇₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₇₉	C₂²	1	2	yes	—
28	#391×C₇₉	—	2	1	no	—
29	#391×C₇₉	—	2	1	no	—
30	#391×C₇₉	C₂²	1	2	yes	—
31	#391×C₇₉	C₂²	1	2	yes	—
32	#391×C₇₉	C₂²	1	1	yes	characteristic
33	#391×C₇₉	C₂²	1	1	yes	characteristic
34	#389×C₇₉	C₂²	1	1	yes	characteristic
35	#389×C₇₉	C₂²	1	1	yes	characteristic
36	#387×C₇₉	—	2	1	no	—
37	#387×C₇₉	—	2	1	no	—
38	#385×C₇₉	—	2	1	no	—
39	#381×C₇₉	—	2	1	no	—
40	#380×C₇₉	C₂²	1	1	yes	characteristic
41	C₂×#95×C₇₉	—	2	1	no	—
42	C₂×#95×C₇₉	—	2	1	no	—
43	#340×C₇₉	C₂²	1	2	yes	—
44	#340×C₇₉	C₂²	1	2	yes	—
45	C₂²×Q₈×C₇₉	—	2	4	no	—
46	C₂²×Q₈×C₇₉	—	2	1	no	—
47	C₂²×Q₈×C₇₉	—	2	2	no	—
48	C₂²×Q₈×C₇₉	—	2	2	no	—
49	C₂²×Q₈×C₇₉	—	4	2	no	—
50	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
51	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
52	C₂³×C₄×C₇₉	—	2	1	no	—
53	C₂³×C₄×C₇₉	—	2	1	no	—
54	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
57	C₂×Q₁₆×C₇₉	—	2	4	no	—
58	C₂×Q₁₆×C₇₉	—	2	4	no	—
59	C₂×Q₁₆×C₇₉	—	4	2	no	—
60	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
61	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
62	C₂²⋊Q₈×C₇₉	—	2	2	no	—
63	C₂²⋊Q₈×C₇₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₇₉	—	4	2	no	—
69	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
75	C₂×C₄²×C₇₉	—	2	2	no	—
76	C₂×C₄²×C₇₉	—	2	2	no	—
77	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
81	#107×C₇₉	—	4	2	no	—
82	C₄⋊C₈×C₇₉	—	2	4	no	—
83	#103×C₇₉	—	2	4	no	—
84	#103×C₇₉	—	2	4	no	—
85	#103×C₇₉	—	4	2	no	—
86	#103×C₇₉	—	4	2	no	—
87	C₂²⋊C₈×C₇₉	—	2	2	no	—
88	C₂²⋊C₈×C₇₉	D₄	1	4	yes	—
89	C₄×C₈×C₇₉	—	2	4	no	—
90	#95×C₇₉	—	2	2	no	—
91	#95×C₇₉	—	2	2	no	—
92	#95×C₇₉	—	2	2	no	—
93	#95×C₇₉	—	2	2	no	—
94	#95×C₇₉	—	2	1	no	—
95	#95×C₇₉	—	2	1	no	—
96	#95×C₇₉	—	2	1	no	—
97	#95×C₇₉	—	2	1	no	—
98	#95×C₇₉	—	2	1	no	—
99	#95×C₇₉	—	2	1	no	—
100	#95×C₇₉	—	2	1	no	—
101	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
102	C₂×Q₈×C₇₉	—	2	4	no	—
103	C₂×Q₈×C₇₉	—	2	2	no	—
104	C₂×Q₈×C₇₉	—	2	2	no	—
105	C₂×Q₈×C₇₉	—	2	1	no	—
106	C₂×Q₈×C₇₉	—	2	2	no	—
107	C₂×Q₈×C₇₉	—	2	1	no	—
108	C₂×Q₈×C₇₉	—	2	2	no	—
109	C₂×Q₈×C₇₉	—	2	2	no	—
110	C₂×Q₈×C₇₉	—	2	2	no	—
111	C₂×Q₈×C₇₉	—	2	2	no	—
112	C₂×Q₈×C₇₉	—	4	8	no	—
113	C₂×Q₈×C₇₉	—	4	8	no	—
114	C₂×Q₈×C₇₉	—	4	2	no	—
115	C₂×Q₈×C₇₉	—	4	2	no	—
116	C₂×Q₈×C₇₉	#41	1	4	yes	—
117	C₂²×C₄×C₇₉	—	2	2	no	—
118	C₂²×C₄×C₇₉	—	2	2	no	—
119	C₂²×C₄×C₇₉	—	2	2	no	—
120	C₂²×C₄×C₇₉	—	2	2	no	—
121	C₂²×C₄×C₇₉	—	2	4	no	—
122	C₂²×C₄×C₇₉	—	2	2	no	—
123	C₂²×C₄×C₇₉	—	2	2	no	—
124	C₂²×C₄×C₇₉	—	2	2	no	—
125	C₂²×C₄×C₇₉	—	2	1	no	—
126	C₂²×C₄×C₇₉	—	2	1	no	—
127	C₂²×C₄×C₇₉	—	2	1	no	—
128	C₂²×C₄×C₇₉	—	2	2	no	—
129	C₂²×C₄×C₇₉	—	2	1	no	—
130	C₂²×C₄×C₇₉	—	4	1	no	—
131	C₂²×C₄×C₇₉	—	4	2	no	—
132	C₂²×C₄×C₇₉	—	4	2	no	—
133	C₂²×C₄×C₇₉	—	4	2	no	—
134	C₂²×C₄×C₇₉	—	4	2	no	—
135	C₂²×C₄×C₇₉	—	4	2	no	—
136	C₂²×C₄×C₇₉	Q₁₆	1	4	yes	complemented
137	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₇₉	#41	1	2	yes	—
144	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
145	Q₁₆×C₇₉	—	4	8	no	—
146	C₂×C₈×C₇₉	—	2	2	no	—
147	C₂×C₈×C₇₉	—	2	2	no	—
148	C₂×C₈×C₇₉	—	2	2	no	—
149	C₂×C₈×C₇₉	—	2	2	no	—
150	C₂×C₈×C₇₉	—	2	2	no	—
151	C₂×C₈×C₇₉	C₂×D₄	1	4	yes	—
152	C₄⋊C₄×C₇₉	—	2	1	no	—
153	C₄⋊C₄×C₇₉	—	2	2	no	—
154	C₄⋊C₄×C₇₉	—	2	1	no	—
155	C₄⋊C₄×C₇₉	—	2	2	no	—
156	C₄⋊C₄×C₇₉	—	2	2	no	—
157	C₄⋊C₄×C₇₉	—	2	2	no	—
158	C₄⋊C₄×C₇₉	—	4	2	no	—
159	C₄⋊C₄×C₇₉	—	4	2	no	—
160	C₄⋊C₄×C₇₉	—	4	2	no	—
161	C₄⋊C₄×C₇₉	—	4	2	no	—
162	C₂²⋊C₄×C₇₉	—	4	2	no	—
163	C₂²⋊C₄×C₇₉	—	4	2	no	—
164	C₄²×C₇₉	—	2	2	no	—
165	C₄²×C₇₉	—	2	2	no	—
166	C₄²×C₇₉	—	2	1	no	—
167	C₄²×C₇₉	—	2	1	no	—
168	C₄²×C₇₉	—	2	1	no	—
169	C₄²×C₇₉	—	2	1	no	—
170	C₂³×C₇₉	—	2	1	no	—
171	C₂³×C₇₉	—	2	1	no	—
172	C₂³×C₇₉	—	2	1	no	—
173	C₂³×C₇₉	—	2	1	no	—
174	C₂³×C₇₉	#121	1	2	yes	—
175	C₂³×C₇₉	C₂×Q₁₆	1	2	yes	—
176	C₂³×C₇₉	#135	1	2	yes	—
177	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
178	Q₈×C₇₉	—	2	4	no	—
179	Q₈×C₇₉	—	2	4	no	—
180	Q₈×C₇₉	—	4	8	no	—
181	Q₈×C₇₉	—	4	2	no	—
182	Q₈×C₇₉	—	4	2	no	—
183	Q₈×C₇₉	—	4	2	no	—
184	Q₈×C₇₉	—	4	2	no	—
185	C₂×C₄×C₇₉	—	2	1	no	—
186	C₂×C₄×C₇₉	—	2	1	no	—
187	C₂×C₄×C₇₉	—	2	1	no	—
188	C₂×C₄×C₇₉	—	2	1	no	—
189	C₂×C₄×C₇₉	—	2	1	no	—
190	C₂×C₄×C₇₉	—	2	1	no	—
191	C₂×C₄×C₇₉	—	2	1	no	—
192	C₂×C₄×C₇₉	—	2	1	no	—
193	C₂×C₄×C₇₉	—	2	8	no	—
194	C₂×C₄×C₇₉	—	2	4	no	—
195	C₂×C₄×C₇₉	—	2	4	no	—
196	C₂×C₄×C₇₉	—	2	1	no	—
197	C₂×C₄×C₇₉	—	2	4	no	—
198	C₂×C₄×C₇₉	—	2	1	no	—
199	C₂×C₄×C₇₉	—	2	1	no	—
200	C₂×C₄×C₇₉	—	4	4	no	—
201	C₂×C₄×C₇₉	—	4	8	no	—
202	C₂×C₄×C₇₉	—	4	2	no	—
203	C₂×C₄×C₇₉	—	4	2	no	—
204	C₂×C₄×C₇₉	—	4	1	no	—
205	C₂×C₄×C₇₉	—	4	1	no	—
206	C₂×C₄×C₇₉	—	4	1	no	—
207	C₂×C₄×C₇₉	—	4	1	no	—
208	C₂×C₄×C₇₉	—	4	2	no	—
209	C₂×C₄×C₇₉	—	4	1	no	—
210	C₂×C₄×C₇₉	—	4	1	no	—
211	C₂×C₄×C₇₉	—	4	1	no	—
212	C₂×C₄×C₇₉	—	4	1	no	—
213	C₂×C₄×C₇₉	—	4	2	no	—
214	C₂×C₄×C₇₉	—	4	1	no	—
215	C₂×C₄×C₇₉	—	4	1	no	—
216	C₂×C₄×C₇₉	—	4	1	no	—
217	C₂×C₄×C₇₉	—	4	1	no	—
218	C₂×C₄×C₇₉	—	4	2	no	—
219	C₂×C₄×C₇₉	—	8	4	no	—
220	C₂×C₄×C₇₉	#121	1	2	yes	—
221	C₂×C₄×C₇₉	C₂×Q₁₆	1	2	yes	—
222	C₂×C₄×C₇₉	C₂×Q₁₆	1	2	yes	—
223	C₂×C₄×C₇₉	#137	1	2	yes	—
224	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
226	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
227	C₂×C₄×C₇₉	H(5,𝔽₂)	1	2	yes	—
228	C₈×C₇₉	—	2	4	no	—
229	C₈×C₇₉	—	4	2	no	—
230	C₂²×C₇₉	—	2	2	no	—
231	C₂²×C₇₉	—	2	2	no	—
232	C₂²×C₇₉	—	2	2	no	—
233	C₂²×C₇₉	—	2	2	no	—
234	C₂²×C₇₉	—	2	2	no	—
235	C₂²×C₇₉	—	2	2	no	—
236	C₂²×C₇₉	#467	1	4	yes	—
237	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
238	C₂²×C₇₉	#525	1	1	yes	characteristic
239	C₂²×C₇₉	#535	1	1	yes	characteristic
240	C₂²×C₇₉	C₂²×Q₁₆	1	1	yes	characteristic
241	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
242	C₂²×C₇₉	C₂×#137	1	1	yes	characteristic
243	C₂²×C₇₉	#575	1	1	yes	characteristic
244	C₄×C₇₉	—	2	2	no	—
245	C₄×C₇₉	—	2	2	no	—
246	C₄×C₇₉	—	2	2	no	—
247	C₄×C₇₉	—	2	2	no	—
248	C₄×C₇₉	—	4	4	no	—
249	C₄×C₇₉	—	4	1	no	—
250	C₄×C₇₉	—	8	1	no	—
251	C₄×C₇₉	—	8	1	no	—
252	C₄×C₇₉	—	8	1	no	—
253	C₄×C₇₉	—	8	2	no	—
254	C₄×C₇₉	—	8	1	no	—
255	C₄×C₇₉	#546	1	2	yes	—
256	C₄×C₇₉	#551	1	2	yes	—
257	#24502	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
258	C₂×C₇₉	—	2	4	no	—
259	C₂×C₇₉	#2411	1	1	yes	characteristic
260	C₂×C₇₉	C₂×#467	1	1	yes	characteristic
261	C₂×C₇₉	#3056	1	1	yes	characteristic
262	C₂×C₇₉	#3104	1	1	yes	characteristic
263	C₂×C₇₉	#3108	1	1	yes	characteristic
264	C₂×C₇₉	#3209	1	1	yes	characteristic
265	C₂×C₇₉	#3211	1	1	yes	characteristic
266	C₂×#451	C₂×C₇₉	1	1	yes	characteristic
267	C₂×#431	C₂×C₇₉	1	1	yes	characteristic
268	#2855	C₂×C₇₉	1	1	yes	characteristic
269	C₂×#391	C₂×C₇₉	1	1	yes	characteristic
270	#2068	C₂×C₇₉	1	2	yes	complemented
271	#2056	C₂×C₇₉	1	2	yes	complemented
272	#1969	C₂×C₇₉	1	2	yes	complemented
273	#1933	C₂×C₇₉	1	2	yes	complemented
274	#1872	C₂×C₇₉	1	1	yes	characteristic
275	#1852	C₂×C₇₉	1	1	yes	characteristic
276	#1787	C₂×C₇₉	1	1	yes	characteristic
277	C₇₉	#24502	1	1	yes	characteristic, direct product factor, Sylow
278	C₂³×Q₈	C₂²×C₇₉	1	1	yes	characteristic
279	C₂²×Q₁₆	C₂²×C₇₉	1	2	yes	—
280	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
281	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
282	C₂²×C₄²	C₂²×C₇₉	1	1	yes	characteristic
283	#451	—	2	4	no	—
284	#431	—	2	4	no	—
285	C₂×#107	C₂²×C₇₉	1	2	yes	—
286	C₂×C₄⋊C₈	C₂²×C₇₉	1	2	yes	—
287	C₂×#103	C₂²×C₇₉	1	2	yes	—
288	C₂×#103	C₂²×C₇₉	1	2	yes	—
289	C₂×#103	C₂²×C₇₉	1	2	yes	—
290	C₂×#103	C₂²×C₇₉	1	2	yes	—
291	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
292	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
293	C₂×C₄×C₈	C₂²×C₇₉	1	2	yes	—
294	#391	—	2	1	no	—
295	#391	—	2	1	no	—
296	#391	C₂²×C₇₉	1	1	yes	characteristic
297	#391	C₂²×C₇₉	1	2	yes	—
298	#391	C₂²×C₇₉	1	1	yes	characteristic
299	#391	C₂²×C₇₉	1	2	yes	—
300	#389	C₂²×C₇₉	1	1	yes	characteristic
301	#389	C₂²×C₇₉	1	1	yes	characteristic
302	#387	—	2	1	no	—
303	#387	—	2	1	no	—
304	#385	—	2	1	no	—
305	#381	—	2	1	no	—
306	#380	C₂²×C₇₉	1	1	yes	characteristic
307	C₂×#95	—	2	1	no	—
308	C₂×#95	—	2	1	no	—
309	#340	C₂²×C₇₉	1	2	yes	—
310	#340	C₂²×C₇₉	1	2	yes	—
311	C₂²×Q₈	—	2	4	no	—
312	C₂²×Q₈	—	2	1	no	—
313	C₂²×Q₈	—	2	2	no	—
314	C₂²×Q₈	—	2	2	no	—
315	C₂²×Q₈	—	4	2	no	—
316	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
317	C₂²×Q₈	C₂³×C₇₉	1	2	yes	—
318	C₂³×C₄	—	2	1	no	—
319	C₂³×C₄	—	2	1	no	—
320	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
321	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
322	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
323	C₂×Q₁₆	—	2	4	no	—
324	C₂×Q₁₆	—	2	4	no	—
325	C₂×Q₁₆	—	4	2	no	—
326	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
327	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
328	C₂²⋊Q₈	—	2	2	no	—
329	C₂²⋊Q₈	—	2	2	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	4	2	no	—
335	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
336	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
337	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
338	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
339	C₂×C₂²⋊C₄	—	2	1	no	—
340	C₂×C₂²⋊C₄	—	2	1	no	—
341	C₂×C₄²	—	2	2	no	—
342	C₂×C₄²	—	2	2	no	—
343	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
344	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
345	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
346	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
347	#107	—	4	2	no	—
348	C₄⋊C₈	—	2	4	no	—
349	#103	—	2	4	no	—
350	#103	—	2	4	no	—
351	#103	—	4	2	no	—
352	#103	—	4	2	no	—
353	C₂²⋊C₈	—	2	2	no	—
354	C₂²⋊C₈	D₄×C₇₉	1	4	yes	—
355	C₄×C₈	—	2	4	no	—
356	#95	—	2	2	no	—
357	#95	—	2	2	no	—
358	#95	—	2	2	no	—
359	#95	—	2	2	no	—
360	#95	—	2	1	no	—
361	#95	—	2	1	no	—
362	#95	—	2	1	no	—
363	#95	—	2	1	no	—
364	#95	—	2	1	no	—
365	#95	—	2	1	no	—
366	#95	—	2	1	no	—
367	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
368	C₂×Q₈	—	2	4	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	1	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	4	8	no	—
379	C₂×Q₈	—	4	8	no	—
380	C₂×Q₈	—	4	2	no	—
381	C₂×Q₈	—	4	2	no	—
382	C₂×Q₈	#41×C₇₉	1	4	yes	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	4	1	no	—
397	C₂²×C₄	—	4	2	no	—
398	C₂²×C₄	—	4	2	no	—
399	C₂²×C₄	—	4	2	no	—
400	C₂²×C₄	—	4	2	no	—
401	C₂²×C₄	—	4	2	no	—
402	C₂²×C₄	Q₁₆×C₇₉	1	4	yes	complemented
403	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
405	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
406	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
407	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
409	C₂²×C₄	#41×C₇₉	1	2	yes	—
410	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
411	Q₁₆	—	4	8	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	C₂×D₄×C₇₉	1	4	yes	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	4	2	no	—
425	C₄⋊C₄	—	4	2	no	—
426	C₄⋊C₄	—	4	2	no	—
427	C₄⋊C₄	—	4	2	no	—
428	C₂²⋊C₄	—	4	2	no	—
429	C₂²⋊C₄	—	4	2	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	2	2	no	—
432	C₄²	—	2	1	no	—
433	C₄²	—	2	1	no	—
434	C₄²	—	2	1	no	—
435	C₄²	—	2	1	no	—
436	C₂³	—	2	1	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	2	1	no	—
439	C₂³	—	2	1	no	—
440	C₂³	#121×C₇₉	1	2	yes	—
441	C₂³	C₂×Q₁₆×C₇₉	1	2	yes	—
442	C₂³	#135×C₇₉	1	2	yes	—
443	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
444	Q₈	—	2	4	no	—
445	Q₈	—	2	4	no	—
446	Q₈	—	4	8	no	—
447	Q₈	—	4	2	no	—
448	Q₈	—	4	2	no	—
449	Q₈	—	4	2	no	—
450	Q₈	—	4	2	no	—
451	C₂×C₄	—	2	8	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	4	4	no	—
467	C₂×C₄	—	4	8	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	8	4	no	—
486	C₂×C₄	#121×C₇₉	1	2	yes	—
487	C₂×C₄	C₂×Q₁₆×C₇₉	1	2	yes	—
488	C₂×C₄	C₂×Q₁₆×C₇₉	1	2	yes	—
489	C₂×C₄	#137×C₇₉	1	2	yes	—
490	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
491	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
492	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
493	C₂×C₄	H(5,𝔽₂)×C₇₉	1	2	yes	—
494	C₈	—	2	4	no	—
495	C₈	—	4	2	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	2	2	no	—
501	C₂²	—	2	2	no	—
502	C₂²	#467×C₇₉	1	4	yes	—
503	C₂²	C₂×#121×C₇₉	1	1	yes	characteristic
504	C₂²	#525×C₇₉	1	1	yes	characteristic
505	C₂²	#535×C₇₉	1	1	yes	characteristic
506	C₂²	C₂²×Q₁₆×C₇₉	1	1	yes	characteristic
507	C₂²	C₂×#135×C₇₉	1	1	yes	characteristic
508	C₂²	C₂×#137×C₇₉	1	1	yes	characteristic
509	C₂²	#575×C₇₉	1	1	yes	characteristic
510	C₄	—	2	2	no	—
511	C₄	—	2	2	no	—
512	C₄	—	2	2	no	—
513	C₄	—	2	2	no	—
514	C₄	—	4	1	no	—
515	C₄	—	4	4	no	—
516	C₄	—	8	1	no	—
517	C₄	—	8	1	no	—
518	C₄	—	8	1	no	—
519	C₄	—	8	2	no	—
520	C₄	—	8	1	no	—
521	C₄	#546×C₇₉	1	2	yes	—
522	C₄	#551×C₇₉	1	2	yes	—
523	C₂	—	2	4	no	—
524	C₂	C₇₉×#2411	1	1	yes	characteristic
525	C₂	C₂×#467×C₇₉	1	1	yes	characteristic
526	C₂	C₇₉×#3056	1	1	yes	characteristic
527	C₂	C₇₉×#3104	1	1	yes	characteristic
528	C₂	C₇₉×#3108	1	1	yes	characteristic
529	C₂	C₇₉×#3209	1	1	yes	characteristic
530	C₂	C₇₉×#3211	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₂⁴×C₇₉	C₂×D₄
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
5. C₇₉×#2068	C₂	semidirect
6. C₇₉×#2056	C₂	semidirect
7. C₇₉×#1969	C₂	semidirect
8. C₇₉×#1933	C₂	semidirect
136. C₂²×C₄×C₇₉	Q₁₆	semidirect
257. #24502	C₇₉	direct (N × H)
270. #2068	C₂×C₇₉	semidirect
271. #2056	C₂×C₇₉	semidirect
272. #1969	C₂×C₇₉	semidirect
273. #1933	C₂×C₇₉	semidirect
277. C₇₉	#24502	direct (N × H)
402. C₂²×C₄	Q₁₆×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#451×C₇₉	2
C₂×#431×C₇₉	2
C₇₉×#2855	2
C₂×#391×C₇₉	2
C₇₉×#2068	2
C₇₉×#2056	2
C₇₉×#1969	2
C₇₉×#1933	2
C₇₉×#1872	2
C₇₉×#1852	2
C₇₉×#1787	2
#24502	79

Subgroups — C79×#24502 #34136191

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#24502 #34136191