Subgroups — C₇₉×#24478 #34136167

Order 20224.

1232 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#481×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#102×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#2433	C₂	1	1	yes	maximal, characteristic
4	C₇₉×#2345	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#2065	C₂	1	2	yes	maximal, complemented
6	C₇₉×#2041	C₂	1	2	yes	maximal, complemented
7	C₇₉×#1982	C₂	1	2	yes	maximal, complemented
8	C₇₉×#1926	C₂	1	2	yes	maximal, complemented
9	C₇₉×#1893	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#1850	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1786	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₇₉	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₇₉	C₂²	1	1	yes	characteristic
14	C₂×#127×C₇₉	C₂²	1	2	yes	—
15	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
16	C₂×#120×C₇₉	—	2	1	no	—
17	C₂×#120×C₇₉	—	2	1	no	—
18	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
19	#481×C₇₉	—	2	4	no	—
20	C₂×#106×C₇₉	C₂²	1	1	yes	characteristic, complemented
21	C₂×#106×C₇₉	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₄⋊C₈×C₇₉	C₂²	1	2	yes	complemented
23	C₂×#102×C₇₉	—	2	4	no	—
24	C₂×#102×C₇₉	C₂²	1	2	yes	—
25	C₂×#102×C₇₉	C₂²	1	2	yes	—
26	C₂×#102×C₇₉	C₂²	1	2	yes	—
27	C₂×#102×C₇₉	C₂²	1	2	yes	—
28	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic, complemented
29	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic, complemented
30	C₂×#102×C₇₉	C₂²	1	2	yes	complemented
31	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
32	#392×C₇₉	—	2	2	no	—
33	#390×C₇₉	C₂²	1	2	yes	—
34	#389×C₇₉	C₂²	1	2	yes	complemented
35	#387×C₇₉	—	2	2	no	—
36	#380×C₇₉	—	2	1	no	—
37	#380×C₇₉	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₇₉	C₂²	1	2	yes	complemented
39	C₄×C₂²⋊C₄×C₇₉	—	2	1	no	—
40	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
41	#340×C₇₉	C₂²	1	2	yes	complemented
42	#336×C₇₉	C₂²	1	2	yes	complemented
43	C₂⁵×C₇₉	—	2	1	no	—
44	C₂²×D₄×C₇₉	—	2	4	no	—
45	C₂²×D₄×C₇₉	—	2	1	no	—
46	C₂²×D₄×C₇₉	—	2	2	no	—
47	C₂²×D₄×C₇₉	—	2	1	no	—
48	C₂²×D₄×C₇₉	—	2	2	no	—
49	C₂²×D₄×C₇₉	—	2	2	no	—
50	C₂²×D₄×C₇₉	—	2	2	no	—
51	C₂²×D₄×C₇₉	—	4	2	no	—
52	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
54	C₂³×C₄×C₇₉	—	2	1	no	—
55	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₇₉	—	2	2	no	—
57	C₂²×C₈×C₇₉	—	4	2	no	—
58	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
60	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
61	#127×C₇₉	—	2	4	no	—
62	#127×C₇₉	—	4	2	no	—
63	#121×C₇₉	—	2	2	no	—
64	#121×C₇₉	—	2	2	no	—
65	#120×C₇₉	—	4	4	no	—
66	#120×C₇₉	—	4	4	no	—
67	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
70	C₂×C₄⋊C₄×C₇₉	D₄	1	4	yes	complemented
71	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
80	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₇₉	—	2	2	no	—
82	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
83	#106×C₇₉	—	2	2	no	—
84	#106×C₇₉	—	2	2	no	—
85	C₄⋊C₈×C₇₉	—	4	2	no	—
86	#102×C₇₉	—	2	4	no	—
87	#102×C₇₉	—	2	2	no	—
88	#102×C₇₉	—	2	2	no	—
89	#102×C₇₉	—	2	4	no	—
90	#102×C₇₉	—	2	4	no	—
91	#102×C₇₉	—	4	2	no	—
92	#102×C₇₉	—	4	2	no	—
93	C₂²⋊C₈×C₇₉	—	2	2	no	—
94	#95×C₇₉	—	2	2	no	—
95	#95×C₇₉	—	2	2	no	—
96	#95×C₇₉	—	2	1	no	—
97	#95×C₇₉	D₄	1	2	yes	—
98	C₂⁴×C₇₉	—	2	2	no	—
99	C₂⁴×C₇₉	—	2	1	no	—
100	C₂⁴×C₇₉	—	4	4	no	—
101	C₂⁴×C₇₉	—	4	2	no	—
102	C₂⁴×C₇₉	—	4	2	no	—
103	C₂⁴×C₇₉	—	4	2	no	—
104	C₂⁴×C₇₉	—	8	2	no	—
105	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
106	C₂×D₄×C₇₉	—	2	8	no	—
107	C₂×D₄×C₇₉	—	2	2	no	—
108	C₂×D₄×C₇₉	—	2	1	no	—
109	C₂×D₄×C₇₉	—	2	2	no	—
110	C₂×D₄×C₇₉	—	2	2	no	—
111	C₂×D₄×C₇₉	—	2	1	no	—
112	C₂×D₄×C₇₉	—	2	2	no	—
113	C₂×D₄×C₇₉	—	2	2	no	—
114	C₂×D₄×C₇₉	—	2	2	no	—
115	C₂×D₄×C₇₉	—	2	2	no	—
116	C₂×D₄×C₇₉	—	4	8	no	—
117	C₂×D₄×C₇₉	—	4	4	no	—
118	C₂×D₄×C₇₉	—	4	4	no	—
119	C₂×D₄×C₇₉	—	4	4	no	—
120	C₂×D₄×C₇₉	—	4	4	no	—
121	C₂×D₄×C₇₉	—	4	4	no	—
122	C₂×D₄×C₇₉	—	4	2	no	—
123	C₂×D₄×C₇₉	—	4	2	no	—
124	C₂×D₄×C₇₉	—	4	2	no	—
125	C₂×D₄×C₇₉	—	4	2	no	—
126	C₂×D₄×C₇₉	—	4	4	no	—
127	C₂×D₄×C₇₉	—	8	2	no	—
128	C₂×D₄×C₇₉	—	8	2	no	—
129	C₂×D₄×C₇₉	#41	1	4	yes	—
130	C₂²×C₄×C₇₉	—	2	2	no	—
131	C₂²×C₄×C₇₉	—	2	2	no	—
132	C₂²×C₄×C₇₉	—	2	1	no	—
133	C₂²×C₄×C₇₉	—	2	1	no	—
134	C₂²×C₄×C₇₉	—	2	4	no	—
135	C₂²×C₄×C₇₉	—	2	2	no	—
136	C₂²×C₄×C₇₉	—	2	1	no	—
137	C₂²×C₄×C₇₉	—	8	2	no	—
138	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₇₉	#41	1	2	yes	—
143	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
144	C₂×C₈×C₇₉	—	2	1	no	—
145	C₂×C₈×C₇₉	—	2	1	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	—	4	4	no	—
152	C₄⋊C₄×C₇₉	—	2	4	no	—
153	C₄⋊C₄×C₇₉	—	2	1	no	—
154	C₄⋊C₄×C₇₉	—	2	1	no	—
155	C₄⋊C₄×C₇₉	—	2	1	no	—
156	C₄⋊C₄×C₇₉	—	2	2	no	—
157	C₄⋊C₄×C₇₉	—	2	1	no	—
158	C₄⋊C₄×C₇₉	—	2	2	no	—
159	C₄⋊C₄×C₇₉	—	8	2	no	—
160	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
161	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
162	C₂²⋊C₄×C₇₉	—	2	2	no	—
163	C₂²⋊C₄×C₇₉	—	4	4	no	—
164	C₂²⋊C₄×C₇₉	—	4	2	no	—
165	C₂²⋊C₄×C₇₉	—	4	2	no	—
166	C₂²⋊C₄×C₇₉	—	4	4	no	—
167	C₂²⋊C₄×C₇₉	SD₁₆	1	4	yes	—
168	C₄²×C₇₉	—	2	2	no	—
169	C₄²×C₇₉	—	2	2	no	—
170	C₄²×C₇₉	—	8	2	no	—
171	C₂³×C₇₉	—	2	2	no	—
172	C₂³×C₇₉	—	2	2	no	—
173	C₂³×C₇₉	—	2	4	no	—
174	C₂³×C₇₉	—	4	8	no	—
175	C₂³×C₇₉	—	4	2	no	—
176	C₂³×C₇₉	—	4	2	no	—
177	C₂³×C₇₉	—	4	2	no	—
178	C₂³×C₇₉	—	4	2	no	—
179	C₂³×C₇₉	—	4	2	no	—
180	C₂³×C₇₉	—	4	2	no	—
181	C₂³×C₇₉	—	4	1	no	—
182	C₂³×C₇₉	—	4	2	no	—
183	C₂³×C₇₉	—	4	1	no	—
184	C₂³×C₇₉	—	4	1	no	—
185	C₂³×C₇₉	—	4	2	no	—
186	C₂³×C₇₉	—	8	8	no	—
187	C₂³×C₇₉	—	8	8	no	—
188	C₂³×C₇₉	—	8	4	no	—
189	C₂³×C₇₉	—	8	4	no	—
190	C₂³×C₇₉	#121	1	2	yes	—
191	C₂³×C₇₉	C₂×SD₁₆	1	2	yes	—
192	C₂³×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
193	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
194	D₄×C₇₉	—	2	4	no	—
195	D₄×C₇₉	—	2	4	no	—
196	D₄×C₇₉	—	4	8	no	—
197	D₄×C₇₉	—	4	1	no	—
198	D₄×C₇₉	—	4	2	no	—
199	D₄×C₇₉	—	4	1	no	—
200	D₄×C₇₉	—	4	2	no	—
201	D₄×C₇₉	—	4	2	no	—
202	D₄×C₇₉	—	8	8	no	—
203	D₄×C₇₉	—	8	8	no	—
204	D₄×C₇₉	—	8	4	no	—
205	C₂×C₄×C₇₉	—	2	2	no	—
206	C₂×C₄×C₇₉	—	2	2	no	—
207	C₂×C₄×C₇₉	—	2	2	no	—
208	C₂×C₄×C₇₉	—	2	2	no	—
209	C₂×C₄×C₇₉	—	2	2	no	—
210	C₂×C₄×C₇₉	—	2	4	no	—
211	C₂×C₄×C₇₉	—	2	2	no	—
212	C₂×C₄×C₇₉	—	2	2	no	—
213	C₂×C₄×C₇₉	—	2	2	no	—
214	C₂×C₄×C₇₉	—	2	2	no	—
215	C₂×C₄×C₇₉	—	2	2	no	—
216	C₂×C₄×C₇₉	—	4	2	no	—
217	C₂×C₄×C₇₉	—	4	2	no	—
218	C₂×C₄×C₇₉	—	4	1	no	—
219	C₂×C₄×C₇₉	—	4	2	no	—
220	C₂×C₄×C₇₉	—	4	1	no	—
221	C₂×C₄×C₇₉	—	4	1	no	—
222	C₂×C₄×C₇₉	—	4	2	no	—
223	C₂×C₄×C₇₉	—	4	2	no	—
224	C₂×C₄×C₇₉	—	8	4	no	—
225	C₂×C₄×C₇₉	#121	1	2	yes	—
226	C₂×C₄×C₇₉	C₂×SD₁₆	1	4	yes	—
227	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
229	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
230	C₂×C₄×C₇₉	H(5,𝔽₂)	1	2	yes	—
231	C₈×C₇₉	—	4	1	no	—
232	C₈×C₇₉	—	4	1	no	—
233	C₈×C₇₉	—	4	2	no	—
234	C₂²×C₇₉	—	2	2	no	—
235	C₂²×C₇₉	—	2	4	no	—
236	C₂²×C₇₉	—	2	2	no	—
237	C₂²×C₇₉	—	2	4	no	—
238	C₂²×C₇₉	—	4	4	no	—
239	C₂²×C₇₉	—	4	4	no	—
240	C₂²×C₇₉	—	4	4	no	—
241	C₂²×C₇₉	—	8	16	no	—
242	C₂²×C₇₉	—	8	2	no	—
243	C₂²×C₇₉	—	8	2	no	—
244	C₂²×C₇₉	—	8	2	no	—
245	C₂²×C₇₉	—	8	2	no	—
246	C₂²×C₇₉	—	8	1	no	—
247	C₂²×C₇₉	—	8	1	no	—
248	C₂²×C₇₉	—	8	2	no	—
249	C₂²×C₇₉	—	8	1	no	—
250	C₂²×C₇₉	—	8	2	no	—
251	C₂²×C₇₉	#460	1	4	yes	—
252	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
253	C₂²×C₇₉	#546	1	2	yes	—
254	C₂²×C₇₉	C₂²×SD₁₆	1	1	yes	characteristic
255	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
256	C₂²×C₇₉	#576	1	2	yes	—
257	C₄×C₇₉	—	2	2	no	—
258	C₄×C₇₉	—	2	4	no	—
259	C₄×C₇₉	—	4	2	no	—
260	C₄×C₇₉	—	4	2	no	—
261	C₄×C₇₉	—	4	2	no	—
262	C₄×C₇₉	—	8	1	no	—
263	C₄×C₇₉	—	8	2	no	—
264	C₄×C₇₉	#525	1	1	yes	characteristic
265	C₄×C₇₉	#535	1	1	yes	characteristic
266	C₄×C₇₉	#551	1	2	yes	—
267	#24478	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
268	C₂×C₇₉	—	2	4	no	—
269	C₂×C₇₉	—	8	4	no	—
270	C₂×C₇₉	—	16	1	no	—
271	C₂×C₇₉	#2411	1	1	yes	characteristic
272	C₂×C₇₉	C₂×#460	1	1	yes	characteristic
273	C₂×C₇₉	#3041	1	1	yes	characteristic
274	C₂×C₇₉	#3295	1	2	yes	—
275	C₂×C₇₉	#3318	1	2	yes	—
276	C₂×#481	C₂×C₇₉	1	1	yes	characteristic, complemented
277	C₂²×#102	C₂×C₇₉	1	1	yes	characteristic, complemented
278	#2433	C₂×C₇₉	1	1	yes	characteristic
279	#2345	C₂×C₇₉	1	1	yes	characteristic, complemented
280	#2065	C₂×C₇₉	1	2	yes	complemented
281	#2041	C₂×C₇₉	1	2	yes	complemented
282	#1982	C₂×C₇₉	1	2	yes	complemented
283	#1926	C₂×C₇₉	1	2	yes	complemented
284	#1893	C₂×C₇₉	1	1	yes	characteristic, complemented
285	#1850	C₂×C₇₉	1	1	yes	characteristic, complemented
286	#1786	C₂×C₇₉	1	1	yes	characteristic, complemented
287	C₇₉	#24478	1	1	yes	characteristic, direct product factor, Sylow
288	C₂³×D₄	C₂²×C₇₉	1	1	yes	characteristic
289	C₂³×C₈	C₂²×C₇₉	1	1	yes	characteristic
290	C₂×#127	C₂²×C₇₉	1	2	yes	—
291	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
292	C₂×#120	—	2	1	no	—
293	C₂×#120	—	2	1	no	—
294	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
295	#481	—	2	4	no	—
296	C₂×#106	C₂²×C₇₉	1	1	yes	characteristic, complemented
297	C₂×#106	C₂²×C₇₉	1	1	yes	characteristic, complemented
298	C₂×C₄⋊C₈	C₂²×C₇₉	1	2	yes	complemented
299	C₂×#102	—	2	4	no	—
300	C₂×#102	C₂²×C₇₉	1	2	yes	—
301	C₂×#102	C₂²×C₇₉	1	2	yes	—
302	C₂×#102	C₂²×C₇₉	1	2	yes	—
303	C₂×#102	C₂²×C₇₉	1	2	yes	—
304	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic, complemented
305	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic, complemented
306	C₂×#102	C₂²×C₇₉	1	2	yes	complemented
307	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
308	#392	—	2	2	no	—
309	#390	C₂²×C₇₉	1	2	yes	—
310	#389	C₂²×C₇₉	1	2	yes	complemented
311	#387	—	2	2	no	—
312	#380	—	2	1	no	—
313	#380	C₂²×C₇₉	1	1	yes	characteristic
314	C₄×C₄⋊C₄	C₂²×C₇₉	1	2	yes	complemented
315	C₄×C₂²⋊C₄	—	2	1	no	—
316	C₄×C₂²⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
317	#340	C₂²×C₇₉	1	2	yes	complemented
318	#336	C₂²×C₇₉	1	2	yes	complemented
319	C₂⁵	—	2	1	no	—
320	C₂²×D₄	—	2	4	no	—
321	C₂²×D₄	—	2	1	no	—
322	C₂²×D₄	—	2	2	no	—
323	C₂²×D₄	—	2	1	no	—
324	C₂²×D₄	—	2	2	no	—
325	C₂²×D₄	—	2	2	no	—
326	C₂²×D₄	—	2	2	no	—
327	C₂²×D₄	—	4	2	no	—
328	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
329	C₂²×D₄	C₂³×C₇₉	1	2	yes	—
330	C₂³×C₄	—	2	1	no	—
331	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
332	C₂²×C₈	—	2	2	no	—
333	C₂²×C₈	—	4	2	no	—
334	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
335	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
336	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
337	#127	—	2	4	no	—
338	#127	—	4	2	no	—
339	#121	—	2	2	no	—
340	#121	—	2	2	no	—
341	#120	—	4	4	no	—
342	#120	—	4	4	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	—	2	2	no	—
345	C₂×C₄⋊C₄	—	2	2	no	—
346	C₂×C₄⋊C₄	D₄×C₇₉	1	4	yes	complemented
347	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
348	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
349	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
351	C₂×C₂²⋊C₄	—	2	1	no	—
352	C₂×C₂²⋊C₄	—	2	2	no	—
353	C₂×C₂²⋊C₄	—	2	2	no	—
354	C₂×C₂²⋊C₄	—	2	1	no	—
355	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
356	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
357	C₂×C₄²	—	2	2	no	—
358	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
359	#106	—	2	2	no	—
360	#106	—	2	2	no	—
361	C₄⋊C₈	—	4	2	no	—
362	#102	—	2	4	no	—
363	#102	—	2	4	no	—
364	#102	—	2	4	no	—
365	#102	—	2	2	no	—
366	#102	—	2	2	no	—
367	#102	—	4	2	no	—
368	#102	—	4	2	no	—
369	C₂²⋊C₈	—	2	2	no	—
370	#95	—	2	2	no	—
371	#95	—	2	2	no	—
372	#95	—	2	1	no	—
373	#95	D₄×C₇₉	1	2	yes	—
374	C₂⁴	—	2	2	no	—
375	C₂⁴	—	2	1	no	—
376	C₂⁴	—	4	4	no	—
377	C₂⁴	—	4	2	no	—
378	C₂⁴	—	4	2	no	—
379	C₂⁴	—	4	2	no	—
380	C₂⁴	—	8	2	no	—
381	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
382	C₂×D₄	—	2	8	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	1	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	4	8	no	—
393	C₂×D₄	—	4	4	no	—
394	C₂×D₄	—	4	4	no	—
395	C₂×D₄	—	4	4	no	—
396	C₂×D₄	—	4	4	no	—
397	C₂×D₄	—	4	4	no	—
398	C₂×D₄	—	4	2	no	—
399	C₂×D₄	—	4	2	no	—
400	C₂×D₄	—	4	2	no	—
401	C₂×D₄	—	4	2	no	—
402	C₂×D₄	—	4	4	no	—
403	C₂×D₄	—	8	2	no	—
404	C₂×D₄	—	8	2	no	—
405	C₂×D₄	#41×C₇₉	1	4	yes	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	8	2	no	—
414	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
415	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
416	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
417	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
418	C₂²×C₄	#41×C₇₉	1	2	yes	—
419	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	4	4	no	—
428	C₄⋊C₄	—	2	4	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	8	2	no	—
436	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
437	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
438	C₂²⋊C₄	—	2	2	no	—
439	C₂²⋊C₄	—	4	4	no	—
440	C₂²⋊C₄	—	4	2	no	—
441	C₂²⋊C₄	—	4	2	no	—
442	C₂²⋊C₄	—	4	4	no	—
443	C₂²⋊C₄	SD₁₆×C₇₉	1	4	yes	—
444	C₄²	—	2	2	no	—
445	C₄²	—	2	2	no	—
446	C₄²	—	8	2	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	2	4	no	—
450	C₂³	—	4	8	no	—
451	C₂³	—	4	2	no	—
452	C₂³	—	4	2	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	4	2	no	—
456	C₂³	—	4	2	no	—
457	C₂³	—	4	1	no	—
458	C₂³	—	4	2	no	—
459	C₂³	—	4	1	no	—
460	C₂³	—	4	1	no	—
461	C₂³	—	4	2	no	—
462	C₂³	—	8	8	no	—
463	C₂³	—	8	8	no	—
464	C₂³	—	8	4	no	—
465	C₂³	—	8	4	no	—
466	C₂³	#121×C₇₉	1	2	yes	—
467	C₂³	C₂×SD₁₆×C₇₉	1	2	yes	—
468	C₂³	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
469	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
470	D₄	—	2	4	no	—
471	D₄	—	2	4	no	—
472	D₄	—	4	8	no	—
473	D₄	—	4	1	no	—
474	D₄	—	4	2	no	—
475	D₄	—	4	1	no	—
476	D₄	—	4	2	no	—
477	D₄	—	4	2	no	—
478	D₄	—	8	8	no	—
479	D₄	—	8	8	no	—
480	D₄	—	8	4	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	8	4	no	—
501	C₂×C₄	#121×C₇₉	1	2	yes	—
502	C₂×C₄	C₂×SD₁₆×C₇₉	1	4	yes	—
503	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
504	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
505	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
506	C₂×C₄	H(5,𝔽₂)×C₇₉	1	2	yes	—
507	C₈	—	4	1	no	—
508	C₈	—	4	2	no	—
509	C₈	—	4	1	no	—
510	C₂²	—	2	4	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	2	4	no	—
513	C₂²	—	2	2	no	—
514	C₂²	—	4	4	no	—
515	C₂²	—	4	4	no	—
516	C₂²	—	4	4	no	—
517	C₂²	—	8	16	no	—
518	C₂²	—	8	2	no	—
519	C₂²	—	8	2	no	—
520	C₂²	—	8	2	no	—
521	C₂²	—	8	2	no	—
522	C₂²	—	8	1	no	—
523	C₂²	—	8	2	no	—
524	C₂²	—	8	1	no	—
525	C₂²	—	8	2	no	—
526	C₂²	—	8	1	no	—
527	C₂²	#460×C₇₉	1	4	yes	—
528	C₂²	C₂×#121×C₇₉	1	1	yes	characteristic
529	C₂²	#546×C₇₉	1	2	yes	—
530	C₂²	C₂²×SD₁₆×C₇₉	1	1	yes	characteristic
531	C₂²	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
532	C₂²	#576×C₇₉	1	2	yes	—
533	C₄	—	2	4	no	—
534	C₄	—	2	2	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	2	no	—
537	C₄	—	4	2	no	—
538	C₄	—	8	1	no	—
539	C₄	—	8	2	no	—
540	C₄	#525×C₇₉	1	1	yes	characteristic
541	C₄	#535×C₇₉	1	1	yes	characteristic
542	C₄	#551×C₇₉	1	2	yes	—
543	C₂	—	2	4	no	—
544	C₂	—	8	4	no	—
545	C₂	—	16	1	no	—
546	C₂	C₇₉×#2411	1	1	yes	characteristic
547	C₂	C₂×#460×C₇₉	1	1	yes	characteristic
548	C₂	C₇₉×#3041	1	1	yes	characteristic
549	C₂	C₇₉×#3295	1	2	yes	—
550	C₂	C₇₉×#3318	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₇₉×#2433	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₄×C₂²⋊C₄×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#481×C₇₉	C₂	semidirect
2. C₂²×#102×C₇₉	C₂	semidirect
4. C₇₉×#2345	C₂	semidirect
5. C₇₉×#2065	C₂	semidirect
6. C₇₉×#2041	C₂	semidirect
7. C₇₉×#1982	C₂	semidirect
8. C₇₉×#1926	C₂	semidirect
9. C₇₉×#1893	C₂	semidirect
10. C₇₉×#1850	C₂	semidirect
11. C₇₉×#1786	C₂	semidirect
20. C₂×#106×C₇₉	C₂²	semidirect
21. C₂×#106×C₇₉	C₂²	semidirect
22. C₂×C₄⋊C₈×C₇₉	C₂²	semidirect
28. C₂×#102×C₇₉	C₂²	semidirect
29. C₂×#102×C₇₉	C₂²	semidirect
30. C₂×#102×C₇₉	C₂²	semidirect
34. #389×C₇₉	C₂²	semidirect
38. C₄×C₄⋊C₄×C₇₉	C₂²	semidirect
41. #340×C₇₉	C₂²	semidirect
42. #336×C₇₉	C₂²	semidirect
70. C₂×C₄⋊C₄×C₇₉	D₄	semidirect
267. #24478	C₇₉	direct (N × H)
276. C₂×#481	C₂×C₇₉	semidirect
277. C₂²×#102	C₂×C₇₉	semidirect
279. #2345	C₂×C₇₉	semidirect
280. #2065	C₂×C₇₉	semidirect
281. #2041	C₂×C₇₉	semidirect
282. #1982	C₂×C₇₉	semidirect
283. #1926	C₂×C₇₉	semidirect
284. #1893	C₂×C₇₉	semidirect
285. #1850	C₂×C₇₉	semidirect
286. #1786	C₂×C₇₉	semidirect
287. C₇₉	#24478	direct (N × H)
296. C₂×#106	C₂²×C₇₉	semidirect
297. C₂×#106	C₂²×C₇₉	semidirect
298. C₂×C₄⋊C₈	C₂²×C₇₉	semidirect
304. C₂×#102	C₂²×C₇₉	semidirect
305. C₂×#102	C₂²×C₇₉	semidirect
306. C₂×#102	C₂²×C₇₉	semidirect
310. #389	C₂²×C₇₉	semidirect
314. C₄×C₄⋊C₄	C₂²×C₇₉	semidirect
317. #340	C₂²×C₇₉	semidirect
318. #336	C₂²×C₇₉	semidirect
346. C₂×C₄⋊C₄	D₄×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#481×C₇₉	2
C₂²×#102×C₇₉	2
C₇₉×#2433	2
C₇₉×#2345	2
C₇₉×#2065	2
C₇₉×#2041	2
C₇₉×#1982	2
C₇₉×#1926	2
C₇₉×#1893	2
C₇₉×#1850	2
C₇₉×#1786	2
#24478	79

Subgroups — C79×#24478 #34136167

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#24478 #34136167