Subgroups — C₇₉×#24503 #34136192

Order 20224.

1054 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#448×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#431×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#2854	C₂	1	1	yes	maximal, characteristic
4	C₂×#391×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#2066	C₂	1	2	yes	maximal, complemented
6	C₇₉×#2055	C₂	1	2	yes	maximal, complemented
7	C₇₉×#1968	C₂	1	2	yes	maximal, complemented
8	C₇₉×#1933	C₂	1	2	yes	maximal, complemented
9	C₇₉×#1874	C₂	1	1	yes	maximal, characteristic
10	C₇₉×#1853	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1787	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₇₉	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₇₉	C₂²	1	2	yes	—
14	C₂×#123×C₇₉	—	2	1	no	—
15	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
18	#448×C₇₉	—	2	4	no	—
19	#431×C₇₉	—	2	4	no	—
20	C₂×#106×C₇₉	C₂²	1	2	yes	—
21	C₂×C₄⋊C₈×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×#102×C₇₉	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₇₉	C₂²	1	2	yes	—
29	#391×C₇₉	—	2	1	no	—
30	#391×C₇₉	—	2	1	no	—
31	#391×C₇₉	C₂²	1	2	yes	—
32	#391×C₇₉	C₂²	1	2	yes	—
33	#390×C₇₉	C₂²	1	1	yes	characteristic
34	#390×C₇₉	C₂²	1	1	yes	characteristic
35	#389×C₇₉	C₂²	1	1	yes	characteristic
36	#389×C₇₉	C₂²	1	1	yes	characteristic
37	#388×C₇₉	—	2	1	no	—
38	#388×C₇₉	—	2	1	no	—
39	#386×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	2	yes	—
51	C₂²×D₄×C₇₉	—	2	1	no	—
52	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₇₉	—	2	1	no	—
54	C₂³×C₄×C₇₉	—	2	1	no	—
55	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
58	C₂×SD₁₆×C₇₉	—	2	4	no	—
59	C₂×SD₁₆×C₇₉	—	2	4	no	—
60	C₂×SD₁₆×C₇₉	—	4	2	no	—
61	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
62	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
63	#123×C₇₉	—	4	4	no	—
64	#121×C₇₉	—	2	2	no	—
65	#121×C₇₉	—	2	2	no	—
66	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₇₉	—	4	2	no	—
70	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
80	C₂×C₄²×C₇₉	—	2	2	no	—
81	C₂×C₄²×C₇₉	—	2	2	no	—
82	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
86	#106×C₇₉	—	4	2	no	—
87	C₄⋊C₈×C₇₉	—	2	4	no	—
88	#103×C₇₉	—	2	4	no	—
89	#103×C₇₉	—	2	4	no	—
90	#103×C₇₉	—	4	2	no	—
91	#102×C₇₉	—	4	2	no	—
92	C₂²⋊C₈×C₇₉	—	2	2	no	—
93	C₂²⋊C₈×C₇₉	D₄	1	4	yes	—
94	C₄×C₈×C₇₉	—	2	4	no	—
95	#95×C₇₉	—	2	2	no	—
96	#95×C₇₉	—	2	2	no	—
97	#95×C₇₉	—	2	2	no	—
98	#95×C₇₉	—	2	2	no	—
99	#95×C₇₉	—	2	1	no	—
100	#95×C₇₉	—	2	1	no	—
101	#95×C₇₉	—	2	1	no	—
102	C₂⁴×C₇₉	—	2	1	no	—
103	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
104	C₂×Q₈×C₇₉	—	2	4	no	—
105	C₂×Q₈×C₇₉	—	2	2	no	—
106	C₂×Q₈×C₇₉	—	2	2	no	—
107	C₂×Q₈×C₇₉	—	2	2	no	—
108	C₂×Q₈×C₇₉	—	2	2	no	—
109	C₂×Q₈×C₇₉	—	2	2	no	—
110	C₂×Q₈×C₇₉	—	4	8	no	—
111	C₂×Q₈×C₇₉	—	4	8	no	—
112	C₂×Q₈×C₇₉	—	4	2	no	—
113	C₂×Q₈×C₇₉	—	4	2	no	—
114	C₂×Q₈×C₇₉	#41	1	4	yes	—
115	C₂×D₄×C₇₉	—	2	1	no	—
116	C₂×D₄×C₇₉	—	2	1	no	—
117	C₂×D₄×C₇₉	—	2	2	no	—
118	C₂×D₄×C₇₉	—	2	2	no	—
119	C₂×D₄×C₇₉	—	4	2	no	—
120	C₂×D₄×C₇₉	—	4	2	no	—
121	C₂×D₄×C₇₉	—	4	2	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	2	no	—
126	C₂²×C₄×C₇₉	—	2	4	no	—
127	C₂²×C₄×C₇₉	—	2	2	no	—
128	C₂²×C₄×C₇₉	—	2	2	no	—
129	C₂²×C₄×C₇₉	—	2	2	no	—
130	C₂²×C₄×C₇₉	—	2	2	no	—
131	C₂²×C₄×C₇₉	—	2	1	no	—
132	C₂²×C₄×C₇₉	—	2	1	no	—
133	C₂²×C₄×C₇₉	—	2	1	no	—
134	C₂²×C₄×C₇₉	—	4	1	no	—
135	C₂²×C₄×C₇₉	—	4	2	no	—
136	C₂²×C₄×C₇₉	—	4	2	no	—
137	C₂²×C₄×C₇₉	—	4	2	no	—
138	C₂²×C₄×C₇₉	—	4	2	no	—
139	C₂²×C₄×C₇₉	—	4	2	no	—
140	C₂²×C₄×C₇₉	SD₁₆	1	4	yes	complemented
141	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₇₉	#41	1	2	yes	—
148	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
149	SD₁₆×C₇₉	—	4	8	no	—
150	C₂×C₈×C₇₉	—	2	2	no	—
151	C₂×C₈×C₇₉	—	2	2	no	—
152	C₂×C₈×C₇₉	—	2	2	no	—
153	C₂×C₈×C₇₉	—	2	2	no	—
154	C₂×C₈×C₇₉	—	2	2	no	—
155	C₂×C₈×C₇₉	C₂×D₄	1	4	yes	—
156	C₄⋊C₄×C₇₉	—	2	1	no	—
157	C₄⋊C₄×C₇₉	—	2	2	no	—
158	C₄⋊C₄×C₇₉	—	2	1	no	—
159	C₄⋊C₄×C₇₉	—	2	2	no	—
160	C₄⋊C₄×C₇₉	—	2	2	no	—
161	C₄⋊C₄×C₇₉	—	2	2	no	—
162	C₄⋊C₄×C₇₉	—	4	2	no	—
163	C₄⋊C₄×C₇₉	—	4	2	no	—
164	C₄⋊C₄×C₇₉	—	4	2	no	—
165	C₂²⋊C₄×C₇₉	—	4	2	no	—
166	C₂²⋊C₄×C₇₉	—	4	2	no	—
167	C₂²⋊C₄×C₇₉	—	4	2	no	—
168	C₂²⋊C₄×C₇₉	—	4	2	no	—
169	C₂²⋊C₄×C₇₉	—	4	2	no	—
170	C₂²⋊C₄×C₇₉	—	4	2	no	—
171	C₄²×C₇₉	—	2	2	no	—
172	C₄²×C₇₉	—	2	2	no	—
173	C₄²×C₇₉	—	2	1	no	—
174	C₄²×C₇₉	—	2	1	no	—
175	C₄²×C₇₉	—	2	1	no	—
176	C₄²×C₇₉	—	2	1	no	—
177	C₂³×C₇₉	—	2	1	no	—
178	C₂³×C₇₉	—	2	1	no	—
179	C₂³×C₇₉	—	2	1	no	—
180	C₂³×C₇₉	—	2	1	no	—
181	C₂³×C₇₉	—	4	1	no	—
182	C₂³×C₇₉	—	4	1	no	—
183	C₂³×C₇₉	—	4	1	no	—
184	C₂³×C₇₉	—	4	1	no	—
185	C₂³×C₇₉	—	4	1	no	—
186	C₂³×C₇₉	—	4	1	no	—
187	C₂³×C₇₉	—	4	1	no	—
188	C₂³×C₇₉	#121	1	2	yes	—
189	C₂³×C₇₉	C₂×SD₁₆	1	2	yes	—
190	C₂³×C₇₉	#135	1	2	yes	—
191	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
192	Q₈×C₇₉	—	2	4	no	—
193	Q₈×C₇₉	—	2	4	no	—
194	Q₈×C₇₉	—	4	8	no	—
195	Q₈×C₇₉	—	4	2	no	—
196	Q₈×C₇₉	—	4	2	no	—
197	D₄×C₇₉	—	4	2	no	—
198	D₄×C₇₉	—	4	2	no	—
199	D₄×C₇₉	—	8	4	no	—
200	C₂×C₄×C₇₉	—	2	1	no	—
201	C₂×C₄×C₇₉	—	2	1	no	—
202	C₂×C₄×C₇₉	—	2	1	no	—
203	C₂×C₄×C₇₉	—	2	1	no	—
204	C₂×C₄×C₇₉	—	2	1	no	—
205	C₂×C₄×C₇₉	—	2	1	no	—
206	C₂×C₄×C₇₉	—	2	1	no	—
207	C₂×C₄×C₇₉	—	2	1	no	—
208	C₂×C₄×C₇₉	—	2	8	no	—
209	C₂×C₄×C₇₉	—	2	4	no	—
210	C₂×C₄×C₇₉	—	2	4	no	—
211	C₂×C₄×C₇₉	—	2	1	no	—
212	C₂×C₄×C₇₉	—	2	4	no	—
213	C₂×C₄×C₇₉	—	2	1	no	—
214	C₂×C₄×C₇₉	—	2	1	no	—
215	C₂×C₄×C₇₉	—	4	4	no	—
216	C₂×C₄×C₇₉	—	4	8	no	—
217	C₂×C₄×C₇₉	—	4	2	no	—
218	C₂×C₄×C₇₉	—	4	2	no	—
219	C₂×C₄×C₇₉	—	4	1	no	—
220	C₂×C₄×C₇₉	—	4	1	no	—
221	C₂×C₄×C₇₉	—	4	2	no	—
222	C₂×C₄×C₇₉	—	4	1	no	—
223	C₂×C₄×C₇₉	—	4	1	no	—
224	C₂×C₄×C₇₉	—	4	1	no	—
225	C₂×C₄×C₇₉	—	4	1	no	—
226	C₂×C₄×C₇₉	—	4	2	no	—
227	C₂×C₄×C₇₉	—	4	1	no	—
228	C₂×C₄×C₇₉	—	4	1	no	—
229	C₂×C₄×C₇₉	—	4	1	no	—
230	C₂×C₄×C₇₉	—	4	2	no	—
231	C₂×C₄×C₇₉	—	8	4	no	—
232	C₂×C₄×C₇₉	#121	1	2	yes	—
233	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
234	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
235	C₂×C₄×C₇₉	#137	1	2	yes	—
236	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
238	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
239	C₂×C₄×C₇₉	H(5,𝔽₂)	1	2	yes	—
240	C₈×C₇₉	—	2	4	no	—
241	C₈×C₇₉	—	4	2	no	—
242	C₂²×C₇₉	—	2	2	no	—
243	C₂²×C₇₉	—	2	2	no	—
244	C₂²×C₇₉	—	2	2	no	—
245	C₂²×C₇₉	—	2	2	no	—
246	C₂²×C₇₉	—	2	2	no	—
247	C₂²×C₇₉	—	2	2	no	—
248	C₂²×C₇₉	—	8	1	no	—
249	C₂²×C₇₉	—	8	1	no	—
250	C₂²×C₇₉	—	8	1	no	—
251	C₂²×C₇₉	—	8	1	no	—
252	C₂²×C₇₉	—	8	1	no	—
253	C₂²×C₇₉	—	8	1	no	—
254	C₂²×C₇₉	—	8	1	no	—
255	C₂²×C₇₉	#465	1	4	yes	—
256	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
257	C₂²×C₇₉	#525	1	1	yes	characteristic
258	C₂²×C₇₉	#535	1	1	yes	characteristic
259	C₂²×C₇₉	C₂²×SD₁₆	1	1	yes	characteristic
260	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
261	C₂²×C₇₉	C₂×#137	1	1	yes	characteristic
262	C₂²×C₇₉	#575	1	1	yes	characteristic
263	C₄×C₇₉	—	2	2	no	—
264	C₄×C₇₉	—	2	2	no	—
265	C₄×C₇₉	—	2	2	no	—
266	C₄×C₇₉	—	2	2	no	—
267	C₄×C₇₉	—	4	4	no	—
268	C₄×C₇₉	—	4	1	no	—
269	C₄×C₇₉	—	8	1	no	—
270	C₄×C₇₉	—	8	1	no	—
271	C₄×C₇₉	—	8	2	no	—
272	C₄×C₇₉	—	8	1	no	—
273	C₄×C₇₉	#546	1	2	yes	—
274	C₄×C₇₉	#551	1	2	yes	—
275	#24503	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
276	C₂×C₇₉	—	2	4	no	—
277	C₂×C₇₉	—	16	1	no	—
278	C₂×C₇₉	#2411	1	1	yes	characteristic
279	C₂×C₇₉	C₂×#465	1	1	yes	characteristic
280	C₂×C₇₉	#3056	1	1	yes	characteristic
281	C₂×C₇₉	#3103	1	1	yes	characteristic
282	C₂×C₇₉	#3108	1	1	yes	characteristic
283	C₂×C₇₉	#3206	1	1	yes	characteristic
284	C₂×C₇₉	#3211	1	1	yes	characteristic
285	C₂×#448	C₂×C₇₉	1	1	yes	characteristic
286	C₂×#431	C₂×C₇₉	1	1	yes	characteristic, complemented
287	#2854	C₂×C₇₉	1	1	yes	characteristic
288	C₂×#391	C₂×C₇₉	1	1	yes	characteristic, complemented
289	#2066	C₂×C₇₉	1	2	yes	complemented
290	#2055	C₂×C₇₉	1	2	yes	complemented
291	#1968	C₂×C₇₉	1	2	yes	complemented
292	#1933	C₂×C₇₉	1	2	yes	complemented
293	#1874	C₂×C₇₉	1	1	yes	characteristic
294	#1853	C₂×C₇₉	1	1	yes	characteristic, complemented
295	#1787	C₂×C₇₉	1	1	yes	characteristic, complemented
296	C₇₉	#24503	1	1	yes	characteristic, direct product factor, Sylow
297	C₂³×Q₈	C₂²×C₇₉	1	1	yes	characteristic
298	C₂²×SD₁₆	C₂²×C₇₉	1	2	yes	—
299	C₂×#123	—	2	1	no	—
300	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
301	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
302	C₂²×C₄²	C₂²×C₇₉	1	1	yes	characteristic
303	#448	—	2	4	no	—
304	#431	—	2	4	no	—
305	C₂×#106	C₂²×C₇₉	1	2	yes	—
306	C₂×C₄⋊C₈	C₂²×C₇₉	1	2	yes	—
307	C₂×#103	C₂²×C₇₉	1	2	yes	—
308	C₂×#103	C₂²×C₇₉	1	2	yes	—
309	C₂×#103	C₂²×C₇₉	1	2	yes	—
310	C₂×#102	C₂²×C₇₉	1	2	yes	—
311	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
312	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
313	C₂×C₄×C₈	C₂²×C₇₉	1	2	yes	—
314	#391	—	2	1	no	—
315	#391	—	2	1	no	—
316	#391	C₂²×C₇₉	1	2	yes	—
317	#391	C₂²×C₇₉	1	2	yes	—
318	#390	C₂²×C₇₉	1	1	yes	characteristic
319	#390	C₂²×C₇₉	1	1	yes	characteristic
320	#389	C₂²×C₇₉	1	1	yes	characteristic
321	#389	C₂²×C₇₉	1	1	yes	characteristic
322	#388	—	2	1	no	—
323	#388	—	2	1	no	—
324	#386	—	2	1	no	—
325	#380	C₂²×C₇₉	1	1	yes	characteristic
326	C₂×#95	—	2	1	no	—
327	C₂×#95	—	2	1	no	—
328	#340	C₂²×C₇₉	1	2	yes	—
329	#340	C₂²×C₇₉	1	2	yes	—
330	C₂²×Q₈	—	2	4	no	—
331	C₂²×Q₈	—	2	1	no	—
332	C₂²×Q₈	—	2	2	no	—
333	C₂²×Q₈	—	2	2	no	—
334	C₂²×Q₈	—	4	2	no	—
335	C₂²×Q₈	C₂³×C₇₉	1	2	yes	—
336	C₂²×D₄	—	2	1	no	—
337	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
338	C₂³×C₄	—	2	1	no	—
339	C₂³×C₄	—	2	1	no	—
340	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
341	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
342	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
343	C₂×SD₁₆	—	2	4	no	—
344	C₂×SD₁₆	—	2	4	no	—
345	C₂×SD₁₆	—	4	2	no	—
346	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
347	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
348	#123	—	4	4	no	—
349	#121	—	2	2	no	—
350	#121	—	2	2	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	4	2	no	—
355	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
356	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
358	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
359	C₂×C₂²⋊C₄	—	2	1	no	—
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₂²⋊C₄	—	2	1	no	—
362	C₂×C₂²⋊C₄	—	2	1	no	—
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₄²	—	2	2	no	—
366	C₂×C₄²	—	2	2	no	—
367	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
368	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
369	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
370	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
371	#106	—	4	2	no	—
372	C₄⋊C₈	—	2	4	no	—
373	#103	—	2	4	no	—
374	#103	—	2	4	no	—
375	#103	—	4	2	no	—
376	#102	—	4	2	no	—
377	C₂²⋊C₈	—	2	2	no	—
378	C₂²⋊C₈	D₄×C₇₉	1	4	yes	—
379	C₄×C₈	—	2	4	no	—
380	#95	—	2	2	no	—
381	#95	—	2	2	no	—
382	#95	—	2	2	no	—
383	#95	—	2	2	no	—
384	#95	—	2	1	no	—
385	#95	—	2	1	no	—
386	#95	—	2	1	no	—
387	C₂⁴	—	2	1	no	—
388	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
389	C₂×Q₈	—	2	4	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	2	no	—
392	C₂×Q₈	—	2	2	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×Q₈	—	4	8	no	—
396	C₂×Q₈	—	4	8	no	—
397	C₂×Q₈	—	4	2	no	—
398	C₂×Q₈	—	4	2	no	—
399	C₂×Q₈	#41×C₇₉	1	4	yes	—
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	4	2	no	—
405	C₂×D₄	—	4	2	no	—
406	C₂×D₄	—	4	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	4	1	no	—
420	C₂²×C₄	—	4	2	no	—
421	C₂²×C₄	—	4	2	no	—
422	C₂²×C₄	—	4	2	no	—
423	C₂²×C₄	—	4	2	no	—
424	C₂²×C₄	—	4	2	no	—
425	C₂²×C₄	SD₁₆×C₇₉	1	4	yes	complemented
426	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
429	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
430	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
431	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
432	C₂²×C₄	#41×C₇₉	1	2	yes	—
433	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
434	SD₁₆	—	4	8	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	C₂×D₄×C₇₉	1	4	yes	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	4	2	no	—
448	C₄⋊C₄	—	4	2	no	—
449	C₄⋊C₄	—	4	2	no	—
450	C₂²⋊C₄	—	4	2	no	—
451	C₂²⋊C₄	—	4	2	no	—
452	C₂²⋊C₄	—	4	2	no	—
453	C₂²⋊C₄	—	4	2	no	—
454	C₂²⋊C₄	—	4	2	no	—
455	C₂²⋊C₄	—	4	2	no	—
456	C₄²	—	2	2	no	—
457	C₄²	—	2	2	no	—
458	C₄²	—	2	1	no	—
459	C₄²	—	2	1	no	—
460	C₄²	—	2	1	no	—
461	C₄²	—	2	1	no	—
462	C₂³	—	2	1	no	—
463	C₂³	—	2	1	no	—
464	C₂³	—	2	1	no	—
465	C₂³	—	2	1	no	—
466	C₂³	—	4	1	no	—
467	C₂³	—	4	1	no	—
468	C₂³	—	4	1	no	—
469	C₂³	—	4	1	no	—
470	C₂³	—	4	1	no	—
471	C₂³	—	4	1	no	—
472	C₂³	—	4	1	no	—
473	C₂³	#121×C₇₉	1	2	yes	—
474	C₂³	C₂×SD₁₆×C₇₉	1	2	yes	—
475	C₂³	#135×C₇₉	1	2	yes	—
476	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
477	Q₈	—	2	4	no	—
478	Q₈	—	2	4	no	—
479	Q₈	—	4	8	no	—
480	Q₈	—	4	2	no	—
481	Q₈	—	4	2	no	—
482	D₄	—	4	2	no	—
483	D₄	—	4	2	no	—
484	D₄	—	8	4	no	—
485	C₂×C₄	—	2	8	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	4	4	no	—
501	C₂×C₄	—	4	8	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	8	4	no	—
517	C₂×C₄	#121×C₇₉	1	2	yes	—
518	C₂×C₄	C₂×SD₁₆×C₇₉	1	2	yes	—
519	C₂×C₄	C₂×SD₁₆×C₇₉	1	2	yes	—
520	C₂×C₄	#137×C₇₉	1	2	yes	—
521	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
522	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
523	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
524	C₂×C₄	H(5,𝔽₂)×C₇₉	1	2	yes	—
525	C₈	—	2	4	no	—
526	C₈	—	4	2	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	8	1	no	—
534	C₂²	—	8	1	no	—
535	C₂²	—	8	1	no	—
536	C₂²	—	8	1	no	—
537	C₂²	—	8	1	no	—
538	C₂²	—	8	1	no	—
539	C₂²	—	8	1	no	—
540	C₂²	#465×C₇₉	1	4	yes	—
541	C₂²	C₂×#121×C₇₉	1	1	yes	characteristic
542	C₂²	#525×C₇₉	1	1	yes	characteristic
543	C₂²	#535×C₇₉	1	1	yes	characteristic
544	C₂²	C₂²×SD₁₆×C₇₉	1	1	yes	characteristic
545	C₂²	C₂×#135×C₇₉	1	1	yes	characteristic
546	C₂²	C₂×#137×C₇₉	1	1	yes	characteristic
547	C₂²	#575×C₇₉	1	1	yes	characteristic
548	C₄	—	2	2	no	—
549	C₄	—	2	2	no	—
550	C₄	—	2	2	no	—
551	C₄	—	2	2	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	4	no	—
554	C₄	—	8	1	no	—
555	C₄	—	8	1	no	—
556	C₄	—	8	1	no	—
557	C₄	—	8	2	no	—
558	C₄	#546×C₇₉	1	2	yes	—
559	C₄	#551×C₇₉	1	2	yes	—
560	C₂	—	2	4	no	—
561	C₂	—	16	1	no	—
562	C₂	C₇₉×#2411	1	1	yes	characteristic
563	C₂	C₂×#465×C₇₉	1	1	yes	characteristic
564	C₂	C₇₉×#3056	1	1	yes	characteristic
565	C₂	C₇₉×#3103	1	1	yes	characteristic
566	C₂	C₇₉×#3108	1	1	yes	characteristic
567	C₂	C₇₉×#3206	1	1	yes	characteristic
568	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	C₂×#121×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
4. C₂×#391×C₇₉	C₂	semidirect
5. C₇₉×#2066	C₂	semidirect
6. C₇₉×#2055	C₂	semidirect
7. C₇₉×#1968	C₂	semidirect
8. C₇₉×#1933	C₂	semidirect
10. C₇₉×#1853	C₂	semidirect
11. C₇₉×#1787	C₂	semidirect
140. C₂²×C₄×C₇₉	SD₁₆	semidirect
275. #24503	C₇₉	direct (N × H)
286. C₂×#431	C₂×C₇₉	semidirect
288. C₂×#391	C₂×C₇₉	semidirect
289. #2066	C₂×C₇₉	semidirect
290. #2055	C₂×C₇₉	semidirect
291. #1968	C₂×C₇₉	semidirect
292. #1933	C₂×C₇₉	semidirect
294. #1853	C₂×C₇₉	semidirect
295. #1787	C₂×C₇₉	semidirect
296. C₇₉	#24503	direct (N × H)
425. C₂²×C₄	SD₁₆×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#448×C₇₉	2
C₂×#431×C₇₉	2
C₇₉×#2854	2
C₂×#391×C₇₉	2
C₇₉×#2066	2
C₇₉×#2055	2
C₇₉×#1968	2
C₇₉×#1933	2
C₇₉×#1874	2
C₇₉×#1853	2
C₇₉×#1787	2
#24503	79

Subgroups — C79×#24503 #34136192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#24503 #34136192