Subgroups — C₇₉×#17620 #34129309

Order 20224.

1270 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3496	C₂	1	1	yes	maximal, characteristic
2	C₇₉×#2973	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#2353	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#1519	C₂	1	2	yes	maximal, complemented
5	C₇₉×#1514	C₂	1	2	yes	maximal, complemented
6	C₇₉×#1510	C₂	1	2	yes	maximal, complemented
7	C₇₉×#1507	C₂	1	2	yes	maximal, complemented
8	C₇₉×#1505	C₂	1	2	yes	maximal, complemented
9	C₂×#327×C₇₉	C₂	1	2	yes	maximal, complemented
10	C₂×H(5,𝔽₂)×C₇₉	—	2	1	no	—
11	#547×C₇₉	C₄	1	4	yes	complemented
12	#546×C₇₉	—	2	4	no	—
13	D₄²×C₇₉	C₄	1	4	yes	complemented
14	#537×C₇₉	—	2	1	no	—
15	#534×C₇₉	—	2	1	no	—
16	#534×C₇₉	—	2	1	no	—
17	#532×C₇₉	C₂²	1	2	yes	—
18	C₂×#121×C₇₉	C₂²	1	2	yes	—
19	C₂×#121×C₇₉	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
21	#435×C₇₉	—	2	4	no	—
22	#432×C₇₉	C₂²	1	2	yes	complemented
23	#407×C₇₉	C₂²	1	2	yes	complemented
24	C₂×C₂²⋊C₈×C₇₉	C₂²	1	2	yes	complemented
25	#388×C₇₉	—	2	1	no	—
26	#387×C₇₉	—	2	1	no	—
27	#386×C₇₉	—	2	1	no	—
28	#383×C₇₉	C₂²	1	1	yes	characteristic, complemented
29	#381×C₇₉	C₂²	1	1	yes	characteristic, complemented
30	#380×C₇₉	C₂²	1	1	yes	characteristic, complemented
31	C₄×C₂²⋊C₄×C₇₉	—	2	1	no	—
32	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
33	#376×C₇₉	C₂²	1	1	yes	characteristic, complemented
34	C₂×#95×C₇₉	C₂²	1	1	yes	characteristic, complemented
35	#327×C₇₉	C₂²	1	4	yes	complemented
36	#327×C₇₉	C₂²	1	4	yes	complemented
37	#327×C₇₉	C₂²	1	4	yes	complemented
38	#327×C₇₉	C₂²	1	4	yes	complemented
39	H(5,𝔽₂)×C₇₉	—	4	4	no	—
40	H(5,𝔽₂)×C₇₉	—	4	4	no	—
41	C₂×#41×C₇₉	—	2	4	no	—
42	C₂×#41×C₇₉	—	2	2	no	—
43	C₂²×D₄×C₇₉	—	2	2	no	—
44	C₂²×D₄×C₇₉	—	2	2	no	—
45	C₂²×D₄×C₇₉	—	2	4	no	—
46	C₂²×D₄×C₇₉	C₂×C₄	1	2	yes	—
47	C₂²×D₄×C₇₉	C₂×C₄	1	2	yes	complemented
48	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₇₉	—	2	1	no	—
50	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
52	C₂×M₁₆×C₇₉	—	2	2	no	—
53	C₂²×C₈×C₇₉	—	2	2	no	—
54	C₄⋊Q₈×C₇₉	C₂×C₄	1	2	yes	complemented
55	#127×C₇₉	C₂×C₄	1	2	yes	complemented
56	#124×C₇₉	—	2	2	no	—
57	#123×C₇₉	—	2	4	no	—
58	#123×C₇₉	—	2	4	no	—
59	C₂²⋊Q₈×C₇₉	—	2	4	no	—
60	#121×C₇₉	—	2	2	no	—
61	#121×C₇₉	—	2	2	no	—
62	#121×C₇₉	—	2	2	no	—
63	#121×C₇₉	—	2	2	no	—
64	#121×C₇₉	—	2	2	no	—
65	#121×C₇₉	—	2	4	no	—
66	#121×C₇₉	C₂×C₄	1	4	yes	—
67	#121×C₇₉	C₂×C₄	1	4	yes	complemented
68	#121×C₇₉	C₂³	1	4	yes	—
69	#120×C₇₉	—	2	4	no	—
70	#120×C₇₉	—	2	4	no	—
71	C₄×D₄×C₇₉	—	2	2	no	—
72	C₄×D₄×C₇₉	C₂×C₄	1	4	yes	—
73	C₄×D₄×C₇₉	C₂×C₄	1	4	yes	complemented
74	C₄×D₄×C₇₉	D₄	1	4	yes	—
75	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
77	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	complemented
78	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
85	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₇₉	—	2	1	no	—
87	C₂×C₄²×C₇₉	—	2	1	no	—
88	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₇₉	—	2	2	no	—
90	C₂²⋊C₈×C₇₉	—	2	2	no	—
91	C₂²⋊C₈×C₇₉	—	2	2	no	—
92	C₂²⋊C₈×C₇₉	C₂³	1	4	yes	—
93	#97×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	C₂³	1	1	yes	characteristic
100	#95×C₇₉	C₂³	1	1	yes	characteristic
101	#95×C₇₉	C₂³	1	1	yes	characteristic
102	#95×C₇₉	C₂³	1	1	yes	characteristic
103	C₂⁴×C₇₉	—	2	2	no	—
104	C₂⁴×C₇₉	—	2	2	no	—
105	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
106	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
107	#41×C₇₉	—	4	4	no	—
108	#41×C₇₉	—	4	4	no	—
109	#41×C₇₉	—	4	16	no	—
110	C₂×Q₈×C₇₉	—	2	2	no	—
111	C₂×D₄×C₇₉	—	2	2	no	—
112	C₂×D₄×C₇₉	—	2	2	no	—
113	C₂×D₄×C₇₉	—	2	4	no	—
114	C₂×D₄×C₇₉	—	2	4	no	—
115	C₂×D₄×C₇₉	—	2	4	no	—
116	C₂×D₄×C₇₉	—	2	2	no	—
117	C₂×D₄×C₇₉	—	2	2	no	—
118	C₂×D₄×C₇₉	—	2	2	no	—
119	C₂×D₄×C₇₉	—	2	2	no	—
120	C₂×D₄×C₇₉	—	4	16	no	—
121	C₂×D₄×C₇₉	—	4	4	no	—
122	C₂×D₄×C₇₉	—	4	4	no	—
123	C₂×D₄×C₇₉	—	4	4	no	—
124	C₂×D₄×C₇₉	—	4	4	no	—
125	C₂×D₄×C₇₉	—	8	2	no	—
126	C₂×D₄×C₇₉	—	8	2	no	—
127	C₂×D₄×C₇₉	C₂²⋊C₄	1	4	yes	—
128	C₂×D₄×C₇₉	C₂²×C₄	1	4	yes	—
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	4	no	—
133	C₂²×C₄×C₇₉	—	2	1	no	—
134	C₂²×C₄×C₇₉	—	2	1	no	—
135	C₂²×C₄×C₇₉	—	2	1	no	—
136	C₂²×C₄×C₇₉	—	4	2	no	—
137	C₂²×C₄×C₇₉	—	4	2	no	—
138	C₂²×C₄×C₇₉	—	8	1	no	—
139	C₂²×C₄×C₇₉	—	8	1	no	—
140	C₂²×C₄×C₇₉	—	8	1	no	—
141	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
143	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
150	M₁₆×C₇₉	—	8	2	no	—
151	C₂×C₈×C₇₉	—	2	4	no	—
152	C₂×C₈×C₇₉	—	8	2	no	—
153	C₄⋊C₄×C₇₉	—	2	2	no	—
154	C₄⋊C₄×C₇₉	—	2	2	no	—
155	C₄⋊C₄×C₇₉	—	2	2	no	—
156	C₄⋊C₄×C₇₉	—	8	1	no	—
157	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	4	yes	—
158	C₄⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
159	C₂²⋊C₄×C₇₉	—	2	4	no	—
160	C₂²⋊C₄×C₇₉	—	2	4	no	—
161	C₂²⋊C₄×C₇₉	—	2	4	no	—
162	C₂²⋊C₄×C₇₉	—	2	4	no	—
163	C₂²⋊C₄×C₇₉	—	4	2	no	—
164	C₂²⋊C₄×C₇₉	—	4	2	no	—
165	C₂²⋊C₄×C₇₉	—	8	1	no	—
166	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	4	yes	—
167	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	4	yes	—
168	C₄²×C₇₉	—	4	2	no	—
169	C₄²×C₇₉	—	8	1	no	—
170	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
171	C₄²×C₇₉	C₂×D₄	1	2	yes	—
172	C₂³×C₇₉	—	2	1	no	—
173	C₂³×C₇₉	—	2	1	no	—
174	C₂³×C₇₉	—	2	4	no	—
175	C₂³×C₇₉	—	4	1	no	—
176	C₂³×C₇₉	—	4	1	no	—
177	C₂³×C₇₉	—	4	1	no	—
178	C₂³×C₇₉	—	4	1	no	—
179	C₂³×C₇₉	—	4	4	no	—
180	C₂³×C₇₉	—	4	4	no	—
181	C₂³×C₇₉	—	8	2	no	—
182	C₂³×C₇₉	—	8	2	no	—
183	C₂³×C₇₉	—	8	2	no	—
184	C₂³×C₇₉	—	8	2	no	—
185	C₂³×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
186	C₂³×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
187	C₂³×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
188	C₂³×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
189	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
190	Q₈×C₇₉	—	4	4	no	—
191	D₄×C₇₉	—	2	8	no	—
192	D₄×C₇₉	—	4	4	no	—
193	D₄×C₇₉	—	4	4	no	—
194	D₄×C₇₉	—	4	8	no	—
195	D₄×C₇₉	—	4	4	no	—
196	D₄×C₇₉	—	4	4	no	—
197	D₄×C₇₉	—	4	8	no	—
198	D₄×C₇₉	—	8	2	no	—
199	D₄×C₇₉	—	8	2	no	—
200	D₄×C₇₉	—	8	2	no	—
201	C₂×C₄×C₇₉	—	2	1	no	—
202	C₂×C₄×C₇₉	—	2	1	no	—
203	C₂×C₄×C₇₉	—	2	2	no	—
204	C₂×C₄×C₇₉	—	2	4	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	2	no	—
210	C₂×C₄×C₇₉	—	4	1	no	—
211	C₂×C₄×C₇₉	—	4	2	no	—
212	C₂×C₄×C₇₉	—	4	2	no	—
213	C₂×C₄×C₇₉	—	4	8	no	—
214	C₂×C₄×C₇₉	—	4	1	no	—
215	C₂×C₄×C₇₉	—	4	4	no	—
216	C₂×C₄×C₇₉	—	4	1	no	—
217	C₂×C₄×C₇₉	—	4	4	no	—
218	C₂×C₄×C₇₉	—	4	1	no	—
219	C₂×C₄×C₇₉	—	4	1	no	—
220	C₂×C₄×C₇₉	—	4	1	no	—
221	C₂×C₄×C₇₉	—	4	1	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	1	no	—
227	C₂×C₄×C₇₉	—	8	4	no	—
228	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
229	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
230	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
231	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
232	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
233	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
234	C₈×C₇₉	—	4	4	no	—
235	C₂²×C₇₉	—	2	1	no	—
236	C₂²×C₇₉	—	2	2	no	—
237	C₂²×C₇₉	—	2	1	no	—
238	C₂²×C₇₉	—	2	2	no	—
239	C₂²×C₇₉	—	2	2	no	—
240	C₂²×C₇₉	—	2	2	no	—
241	C₂²×C₇₉	—	2	2	no	—
242	C₂²×C₇₉	—	4	2	no	—
243	C₂²×C₇₉	—	4	2	no	—
244	C₂²×C₇₉	—	4	4	no	—
245	C₂²×C₇₉	—	4	4	no	—
246	C₂²×C₇₉	—	4	4	no	—
247	C₂²×C₇₉	—	8	1	no	—
248	C₂²×C₇₉	—	8	1	no	—
249	C₂²×C₇₉	—	16	4	no	—
250	C₂²×C₇₉	—	16	4	no	—
251	C₂²×C₇₉	#418	1	4	yes	—
252	C₂²×C₇₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
253	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
254	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
255	C₄×C₇₉	—	2	1	no	—
256	C₄×C₇₉	—	2	1	no	—
257	C₄×C₇₉	—	2	2	no	—
258	C₄×C₇₉	—	2	2	no	—
259	C₄×C₇₉	—	2	2	no	—
260	C₄×C₇₉	—	2	2	no	—
261	C₄×C₇₉	—	4	2	no	—
262	C₄×C₇₉	—	4	4	no	—
263	C₄×C₇₉	—	8	1	no	—
264	C₄×C₇₉	—	8	1	no	—
265	C₄×C₇₉	—	8	1	no	—
266	#17620	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
267	C₂×C₇₉	—	2	1	no	—
268	C₂×C₇₉	—	2	1	no	—
269	C₂×C₇₉	—	2	4	no	—
270	C₂×C₇₉	—	4	2	no	—
271	C₂×C₇₉	—	8	4	no	—
272	C₂×C₇₉	#2883	1	1	yes	characteristic
273	C₂×C₇₉	C₂×#418	1	1	yes	characteristic
274	C₂×C₇₉	#2901	1	1	yes	characteristic
275	#3496	C₂×C₇₉	1	1	yes	characteristic
276	#2973	C₂×C₇₉	1	1	yes	characteristic, complemented
277	#2353	C₂×C₇₉	1	1	yes	characteristic, complemented
278	#1519	C₂×C₇₉	1	2	yes	complemented
279	#1514	C₂×C₇₉	1	2	yes	complemented
280	#1510	C₂×C₇₉	1	2	yes	complemented
281	#1507	C₂×C₇₉	1	2	yes	complemented
282	#1505	C₂×C₇₉	1	2	yes	complemented
283	C₂×#327	C₂×C₇₉	1	2	yes	complemented
284	C₇₉	#17620	1	1	yes	characteristic, direct product factor, Sylow
285	C₂×H(5,𝔽₂)	—	2	1	no	—
286	#547	C₄×C₇₉	1	4	yes	complemented
287	#546	—	2	4	no	—
288	D₄²	C₄×C₇₉	1	4	yes	complemented
289	#537	—	2	1	no	—
290	#534	—	2	1	no	—
291	#534	—	2	1	no	—
292	#532	C₂²×C₇₉	1	2	yes	—
293	C₂×#121	C₂²×C₇₉	1	2	yes	—
294	C₂×#121	C₂²×C₇₉	1	2	yes	—
295	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
296	#435	—	2	4	no	—
297	#432	C₂²×C₇₉	1	2	yes	complemented
298	#407	C₂²×C₇₉	1	2	yes	complemented
299	C₂×C₂²⋊C₈	C₂²×C₇₉	1	2	yes	complemented
300	#388	—	2	1	no	—
301	#387	—	2	1	no	—
302	#386	—	2	1	no	—
303	#383	C₂²×C₇₉	1	1	yes	characteristic, complemented
304	#381	C₂²×C₇₉	1	1	yes	characteristic, complemented
305	#380	C₂²×C₇₉	1	1	yes	characteristic, complemented
306	C₄×C₂²⋊C₄	—	2	1	no	—
307	C₄×C₂²⋊C₄	C₂²×C₇₉	1	1	yes	characteristic, complemented
308	#376	C₂²×C₇₉	1	1	yes	characteristic, complemented
309	C₂×#95	C₂²×C₇₉	1	1	yes	characteristic, complemented
310	#327	C₂²×C₇₉	1	4	yes	complemented
311	#327	C₂²×C₇₉	1	4	yes	complemented
312	#327	C₂²×C₇₉	1	4	yes	complemented
313	#327	C₂²×C₇₉	1	4	yes	complemented
314	H(5,𝔽₂)	—	4	4	no	—
315	H(5,𝔽₂)	—	4	4	no	—
316	C₂×#41	—	2	4	no	—
317	C₂×#41	—	2	2	no	—
318	C₂²×D₄	—	2	2	no	—
319	C₂²×D₄	—	2	2	no	—
320	C₂²×D₄	—	2	4	no	—
321	C₂²×D₄	C₂×C₄×C₇₉	1	2	yes	—
322	C₂²×D₄	C₂×C₄×C₇₉	1	2	yes	complemented
323	C₂²×D₄	D₄×C₇₉	1	1	yes	characteristic
324	C₂³×C₄	—	2	1	no	—
325	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
326	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
327	C₂×M₁₆	—	2	2	no	—
328	C₂²×C₈	—	2	2	no	—
329	C₄⋊Q₈	C₂×C₄×C₇₉	1	2	yes	complemented
330	#127	C₂×C₄×C₇₉	1	2	yes	complemented
331	#124	—	2	2	no	—
332	#123	—	2	4	no	—
333	#123	—	2	4	no	—
334	C₂²⋊Q₈	—	2	4	no	—
335	#121	—	2	2	no	—
336	#121	—	2	2	no	—
337	#121	—	2	2	no	—
338	#121	—	2	2	no	—
339	#121	—	2	2	no	—
340	#121	—	2	4	no	—
341	#121	C₂×C₄×C₇₉	1	4	yes	—
342	#121	C₂×C₄×C₇₉	1	4	yes	complemented
343	#121	C₂³×C₇₉	1	4	yes	—
344	#120	—	2	4	no	—
345	#120	—	2	4	no	—
346	C₄×D₄	—	2	2	no	—
347	C₄×D₄	C₂×C₄×C₇₉	1	4	yes	—
348	C₄×D₄	C₂×C₄×C₇₉	1	4	yes	complemented
349	C₄×D₄	D₄×C₇₉	1	4	yes	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	C₂×C₄×C₇₉	1	2	yes	—
352	C₂×C₄⋊C₄	C₂×C₄×C₇₉	1	2	yes	complemented
353	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
354	C₂×C₂²⋊C₄	—	2	2	no	—
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₂²⋊C₄	—	2	1	no	—
357	C₂×C₂²⋊C₄	—	2	1	no	—
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
360	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
361	C₂×C₄²	—	2	1	no	—
362	C₂×C₄²	—	2	1	no	—
363	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
364	C₄⋊C₈	—	2	2	no	—
365	C₂²⋊C₈	—	2	2	no	—
366	C₂²⋊C₈	—	2	2	no	—
367	C₂²⋊C₈	C₂³×C₇₉	1	4	yes	—
368	#97	—	2	2	no	—
369	#95	—	2	1	no	—
370	#95	—	2	1	no	—
371	#95	—	2	1	no	—
372	#95	—	2	1	no	—
373	#95	—	2	1	no	—
374	#95	C₂³×C₇₉	1	1	yes	characteristic
375	#95	C₂³×C₇₉	1	1	yes	characteristic
376	#95	C₂³×C₇₉	1	1	yes	characteristic
377	#95	C₂³×C₇₉	1	1	yes	characteristic
378	C₂⁴	—	2	2	no	—
379	C₂⁴	—	2	2	no	—
380	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
381	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
382	#41	—	4	4	no	—
383	#41	—	4	4	no	—
384	#41	—	4	16	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	4	no	—
389	C₂×D₄	—	2	4	no	—
390	C₂×D₄	—	2	4	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	4	16	no	—
396	C₂×D₄	—	4	4	no	—
397	C₂×D₄	—	4	4	no	—
398	C₂×D₄	—	4	4	no	—
399	C₂×D₄	—	4	4	no	—
400	C₂×D₄	—	8	2	no	—
401	C₂×D₄	—	8	2	no	—
402	C₂×D₄	C₂²⋊C₄×C₇₉	1	4	yes	—
403	C₂×D₄	C₂²×C₄×C₇₉	1	4	yes	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	4	2	no	—
412	C₂²×C₄	—	4	2	no	—
413	C₂²×C₄	—	8	1	no	—
414	C₂²×C₄	—	8	1	no	—
415	C₂²×C₄	—	8	1	no	—
416	C₂²×C₄	C₂²×C₄×C₇₉	1	2	yes	—
417	C₂²×C₄	C₂²×C₄×C₇₉	1	2	yes	—
418	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
421	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
422	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
423	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
424	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
425	M₁₆	—	8	2	no	—
426	C₂×C₈	—	2	4	no	—
427	C₂×C₈	—	8	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	8	1	no	—
432	C₄⋊C₄	C₂²⋊C₄×C₇₉	1	4	yes	—
433	C₄⋊C₄	C₂²×C₄×C₇₉	1	4	yes	—
434	C₂²⋊C₄	—	2	4	no	—
435	C₂²⋊C₄	—	2	4	no	—
436	C₂²⋊C₄	—	2	4	no	—
437	C₂²⋊C₄	—	2	4	no	—
438	C₂²⋊C₄	—	4	2	no	—
439	C₂²⋊C₄	—	4	2	no	—
440	C₂²⋊C₄	—	8	1	no	—
441	C₂²⋊C₄	C₂²⋊C₄×C₇₉	1	4	yes	—
442	C₂²⋊C₄	C₂²⋊C₄×C₇₉	1	4	yes	—
443	C₄²	—	4	2	no	—
444	C₄²	—	8	1	no	—
445	C₄²	C₂²×C₄×C₇₉	1	2	yes	—
446	C₄²	C₂×D₄×C₇₉	1	2	yes	—
447	C₂³	—	2	1	no	—
448	C₂³	—	2	1	no	—
449	C₂³	—	2	4	no	—
450	C₂³	—	4	1	no	—
451	C₂³	—	4	1	no	—
452	C₂³	—	4	1	no	—
453	C₂³	—	4	1	no	—
454	C₂³	—	4	4	no	—
455	C₂³	—	4	4	no	—
456	C₂³	—	8	2	no	—
457	C₂³	—	8	2	no	—
458	C₂³	—	8	2	no	—
459	C₂³	—	8	2	no	—
460	C₂³	C₂×C₂²⋊C₄×C₇₉	1	2	yes	—
461	C₂³	C₂×C₂²⋊C₄×C₇₉	1	2	yes	—
462	C₂³	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
463	C₂³	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
464	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
465	Q₈	—	4	4	no	—
466	D₄	—	2	8	no	—
467	D₄	—	4	4	no	—
468	D₄	—	4	4	no	—
469	D₄	—	4	8	no	—
470	D₄	—	4	8	no	—
471	D₄	—	4	4	no	—
472	D₄	—	4	4	no	—
473	D₄	—	8	2	no	—
474	D₄	—	8	2	no	—
475	D₄	—	8	2	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	8	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	4	no	—
491	C₂×C₄	—	4	4	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	8	4	no	—
503	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	2	yes	—
504	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	2	yes	—
505	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	2	yes	—
506	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	2	yes	—
507	C₂×C₄	C₂³×C₄×C₇₉	1	1	yes	characteristic
508	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
509	C₈	—	4	4	no	—
510	C₂²	—	2	1	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	2	1	no	—
513	C₂²	—	2	2	no	—
514	C₂²	—	2	2	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	4	no	—
520	C₂²	—	4	4	no	—
521	C₂²	—	4	4	no	—
522	C₂²	—	8	1	no	—
523	C₂²	—	8	1	no	—
524	C₂²	—	16	4	no	—
525	C₂²	—	16	4	no	—
526	C₂²	#418×C₇₉	1	4	yes	—
527	C₂²	C₂²×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
528	C₂²	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
529	C₂²	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
530	C₄	—	2	1	no	—
531	C₄	—	2	1	no	—
532	C₄	—	2	2	no	—
533	C₄	—	2	2	no	—
534	C₄	—	2	2	no	—
535	C₄	—	2	2	no	—
536	C₄	—	4	2	no	—
537	C₄	—	4	4	no	—
538	C₄	—	8	1	no	—
539	C₄	—	8	1	no	—
540	C₄	—	8	1	no	—
541	C₂	—	2	1	no	—
542	C₂	—	2	1	no	—
543	C₂	—	2	4	no	—
544	C₂	—	4	2	no	—
545	C₂	—	8	4	no	—
546	C₂	C₇₉×#2883	1	1	yes	characteristic
547	C₂	C₂×#418×C₇₉	1	1	yes	characteristic
548	C₂	C₇₉×#2901	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₇₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₇₉×#3496	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ C₂×C₄×D₄×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇₉×#2973	C₂	semidirect
3. C₇₉×#2353	C₂	semidirect
4. C₇₉×#1519	C₂	semidirect
5. C₇₉×#1514	C₂	semidirect
6. C₇₉×#1510	C₂	semidirect
7. C₇₉×#1507	C₂	semidirect
8. C₇₉×#1505	C₂	semidirect
9. C₂×#327×C₇₉	C₂	semidirect
11. #547×C₇₉	C₄	semidirect
13. D₄²×C₇₉	C₄	semidirect
22. #432×C₇₉	C₂²	semidirect
23. #407×C₇₉	C₂²	semidirect
24. C₂×C₂²⋊C₈×C₇₉	C₂²	semidirect
28. #383×C₇₉	C₂²	semidirect
29. #381×C₇₉	C₂²	semidirect
30. #380×C₇₉	C₂²	semidirect
32. C₄×C₂²⋊C₄×C₇₉	C₂²	semidirect
33. #376×C₇₉	C₂²	semidirect
34. C₂×#95×C₇₉	C₂²	semidirect
35. #327×C₇₉	C₂²	semidirect
36. #327×C₇₉	C₂²	semidirect
37. #327×C₇₉	C₂²	semidirect
38. #327×C₇₉	C₂²	semidirect
47. C₂²×D₄×C₇₉	C₂×C₄	semidirect
54. C₄⋊Q₈×C₇₉	C₂×C₄	semidirect
55. #127×C₇₉	C₂×C₄	semidirect
67. #121×C₇₉	C₂×C₄	semidirect
73. C₄×D₄×C₇₉	C₂×C₄	semidirect
77. C₂×C₄⋊C₄×C₇₉	C₂×C₄	semidirect
266. #17620	C₇₉	direct (N × H)
276. #2973	C₂×C₇₉	semidirect
277. #2353	C₂×C₇₉	semidirect
278. #1519	C₂×C₇₉	semidirect
279. #1514	C₂×C₇₉	semidirect
280. #1510	C₂×C₇₉	semidirect
281. #1507	C₂×C₇₉	semidirect
282. #1505	C₂×C₇₉	semidirect
283. C₂×#327	C₂×C₇₉	semidirect
284. C₇₉	#17620	direct (N × H)
286. #547	C₄×C₇₉	semidirect
288. D₄²	C₄×C₇₉	semidirect
297. #432	C₂²×C₇₉	semidirect
298. #407	C₂²×C₇₉	semidirect
299. C₂×C₂²⋊C₈	C₂²×C₇₉	semidirect
303. #383	C₂²×C₇₉	semidirect
304. #381	C₂²×C₇₉	semidirect
305. #380	C₂²×C₇₉	semidirect
307. C₄×C₂²⋊C₄	C₂²×C₇₉	semidirect
308. #376	C₂²×C₇₉	semidirect
309. C₂×#95	C₂²×C₇₉	semidirect
310. #327	C₂²×C₇₉	semidirect
311. #327	C₂²×C₇₉	semidirect
312. #327	C₂²×C₇₉	semidirect
313. #327	C₂²×C₇₉	semidirect
322. C₂²×D₄	C₂×C₄×C₇₉	semidirect
329. C₄⋊Q₈	C₂×C₄×C₇₉	semidirect
330. #127	C₂×C₄×C₇₉	semidirect
342. #121	C₂×C₄×C₇₉	semidirect
348. C₄×D₄	C₂×C₄×C₇₉	semidirect
352. C₂×C₄⋊C₄	C₂×C₄×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₇₉×#3496	2
C₇₉×#2973	2
C₇₉×#2353	2
C₇₉×#1519	2
C₇₉×#1514	2
C₇₉×#1510	2
C₇₉×#1507	2
C₇₉×#1505	2
C₂×#327×C₇₉	2
#17620	79

Subgroups — C79×#17620 #34129309

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#17620 #34129309