Subgroups — C₇₉×#25495 #34137184

Order 20224.

1412 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#532×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#465×C₇₉	C₂	1	2	yes	maximal, complemented
3	C₇₉×#2855	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#2058	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#2041	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉×#2024	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#2014	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#1893	C₂	1	2	yes	maximal, complemented
9	C₇₉×#1877	C₂	1	2	yes	maximal, complemented
10	C₇₉×#1864	C₂	1	2	yes	maximal, complemented
11	C₂×#336×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₇₉	—	2	1	no	—
13	C₂²×SD₁₆×C₇₉	C₂²	1	2	yes	—
14	C₂³×C₈×C₇₉	C₂²	1	2	yes	—
15	#532×C₇₉	—	2	8	no	—
16	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×#127×C₇₉	C₂²	1	1	yes	characteristic
18	C₂×#124×C₇₉	—	2	1	no	—
19	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×#121×C₇₉	—	2	1	no	—
21	C₂×#121×C₇₉	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₇₉	—	2	1	no	—
23	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	—
24	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
25	#465×C₇₉	—	2	8	no	—
26	C₂×#106×C₇₉	C₂²	1	2	yes	—
27	C₂×#103×C₇₉	C₂²	1	2	yes	—
28	C₂×#102×C₇₉	C₂²	1	2	yes	—
29	C₂×#102×C₇₉	C₂²	1	2	yes	—
30	C₂×#102×C₇₉	C₂²	1	2	yes	—
31	#391×C₇₉	C₂²	1	1	yes	characteristic
32	#391×C₇₉	C₂²	1	1	yes	characteristic
33	#389×C₇₉	C₂²	1	1	yes	characteristic
34	#389×C₇₉	C₂²	1	1	yes	characteristic
35	#387×C₇₉	—	2	1	no	—
36	#387×C₇₉	—	2	1	no	—
37	#385×C₇₉	—	2	1	no	—
38	#381×C₇₉	—	2	1	no	—
39	#380×C₇₉	C₂²	1	1	yes	characteristic
40	#340×C₇₉	C₂²	1	2	yes	—
41	#340×C₇₉	C₂²	1	2	yes	—
42	#336×C₇₉	C₂²	1	1	yes	characteristic
43	#336×C₇₉	C₂²	1	1	yes	characteristic
44	#336×C₇₉	C₂²	1	2	yes	—
45	C₂×#41×C₇₉	—	2	8	no	—
46	C₂×#41×C₇₉	—	4	4	no	—
47	C₂×#41×C₇₉	—	4	4	no	—
48	C₂²×Q₈×C₇₉	—	2	1	no	—
49	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₇₉	—	2	2	no	—
51	C₂²×D₄×C₇₉	—	2	1	no	—
52	C₂²×D₄×C₇₉	—	2	1	no	—
53	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
54	C₂³×C₄×C₇₉	—	2	2	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	—	2	4	no	—
62	C₂²×C₈×C₇₉	—	2	4	no	—
63	C₂²×C₈×C₇₉	—	4	2	no	—
64	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
65	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
66	C₄⋊Q₈×C₇₉	—	2	4	no	—
67	#127×C₇₉	—	2	4	no	—
68	#124×C₇₉	—	2	8	no	—
69	C₂²⋊Q₈×C₇₉	—	2	4	no	—
70	#121×C₇₉	—	2	8	no	—
71	#121×C₇₉	—	2	4	no	—
72	#121×C₇₉	D₄	1	8	yes	—
73	C₄×D₄×C₇₉	—	2	8	no	—
74	C₄×D₄×C₇₉	—	2	4	no	—
75	C₄×D₄×C₇₉	—	2	4	no	—
76	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
84	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
88	C₂×C₄²×C₇₉	—	2	4	no	—
89	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
90	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
91	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
93	#106×C₇₉	—	2	4	no	—
94	#103×C₇₉	—	2	4	no	—
95	#102×C₇₉	—	2	4	no	—
96	#102×C₇₉	—	2	4	no	—
97	#102×C₇₉	—	4	2	no	—
98	#95×C₇₉	—	2	1	no	—
99	#95×C₇₉	—	2	1	no	—
100	#95×C₇₉	—	2	1	no	—
101	#95×C₇₉	—	2	1	no	—
102	#95×C₇₉	—	2	1	no	—
103	#95×C₇₉	—	2	1	no	—
104	#95×C₇₉	—	2	1	no	—
105	C₂⁴×C₇₉	—	2	2	no	—
106	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
107	#41×C₇₉	—	4	32	no	—
108	C₂×Q₈×C₇₉	—	2	4	no	—
109	C₂×Q₈×C₇₉	—	2	2	no	—
110	C₂×Q₈×C₇₉	—	2	2	no	—
111	C₂×Q₈×C₇₉	—	2	1	no	—
112	C₂×Q₈×C₇₉	—	2	1	no	—
113	C₂×Q₈×C₇₉	—	4	2	no	—
114	C₂×Q₈×C₇₉	—	4	2	no	—
115	C₂×D₄×C₇₉	—	2	4	no	—
116	C₂×D₄×C₇₉	—	2	4	no	—
117	C₂×D₄×C₇₉	—	2	8	no	—
118	C₂×D₄×C₇₉	—	2	2	no	—
119	C₂×D₄×C₇₉	—	2	2	no	—
120	C₂×D₄×C₇₉	—	2	2	no	—
121	C₂×D₄×C₇₉	—	2	2	no	—
122	C₂×D₄×C₇₉	—	2	2	no	—
123	C₂×D₄×C₇₉	—	4	2	no	—
124	C₂×D₄×C₇₉	—	4	2	no	—
125	C₂×D₄×C₇₉	—	4	4	no	—
126	C₂×D₄×C₇₉	—	4	4	no	—
127	C₂×D₄×C₇₉	—	4	2	no	—
128	C₂×D₄×C₇₉	—	4	2	no	—
129	C₂×D₄×C₇₉	C₂×D₄	1	4	yes	—
130	C₂²×C₄×C₇₉	—	2	2	no	—
131	C₂²×C₄×C₇₉	—	2	2	no	—
132	C₂²×C₄×C₇₉	—	2	2	no	—
133	C₂²×C₄×C₇₉	—	2	1	no	—
134	C₂²×C₄×C₇₉	—	2	1	no	—
135	C₂²×C₄×C₇₉	—	2	8	no	—
136	C₂²×C₄×C₇₉	—	2	2	no	—
137	C₂²×C₄×C₇₉	—	2	2	no	—
138	C₂²×C₄×C₇₉	—	2	2	no	—
139	C₂²×C₄×C₇₉	—	2	1	no	—
140	C₂²×C₄×C₇₉	—	2	1	no	—
141	C₂²×C₄×C₇₉	—	2	1	no	—
142	C₂²×C₄×C₇₉	—	2	1	no	—
143	C₂²×C₄×C₇₉	—	4	1	no	—
144	C₂²×C₄×C₇₉	—	4	4	no	—
145	C₂²×C₄×C₇₉	—	4	4	no	—
146	C₂²×C₄×C₇₉	SD₁₆	1	4	yes	complemented
147	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₇₉	C₂×D₄	1	4	yes	—
150	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
154	SD₁₆×C₇₉	—	4	8	no	—
155	C₂×C₈×C₇₉	—	2	2	no	—
156	C₂×C₈×C₇₉	—	2	2	no	—
157	C₂×C₈×C₇₉	—	2	2	no	—
158	C₂×C₈×C₇₉	—	2	2	no	—
159	C₂×C₈×C₇₉	—	2	2	no	—
160	C₂×C₈×C₇₉	—	4	8	no	—
161	C₂×C₈×C₇₉	#41	1	4	yes	complemented
162	C₄⋊C₄×C₇₉	—	2	4	no	—
163	C₄⋊C₄×C₇₉	—	2	2	no	—
164	C₄⋊C₄×C₇₉	—	2	2	no	—
165	C₄⋊C₄×C₇₉	—	2	2	no	—
166	C₄⋊C₄×C₇₉	—	2	1	no	—
167	C₄⋊C₄×C₇₉	—	2	1	no	—
168	C₄⋊C₄×C₇₉	—	4	2	no	—
169	C₄⋊C₄×C₇₉	—	4	2	no	—
170	C₄⋊C₄×C₇₉	—	4	2	no	—
171	C₄⋊C₄×C₇₉	C₂×D₄	1	4	yes	—
172	C₂²⋊C₄×C₇₉	—	2	8	no	—
173	C₂²⋊C₄×C₇₉	—	2	8	no	—
174	C₂²⋊C₄×C₇₉	—	4	2	no	—
175	C₂²⋊C₄×C₇₉	—	4	2	no	—
176	C₄²×C₇₉	—	2	2	no	—
177	C₄²×C₇₉	—	2	2	no	—
178	C₄²×C₇₉	—	2	2	no	—
179	C₄²×C₇₉	—	2	2	no	—
180	C₂³×C₇₉	—	2	1	no	—
181	C₂³×C₇₉	—	2	1	no	—
182	C₂³×C₇₉	—	2	1	no	—
183	C₂³×C₇₉	—	2	1	no	—
184	C₂³×C₇₉	—	2	4	no	—
185	C₂³×C₇₉	—	4	2	no	—
186	C₂³×C₇₉	—	4	2	no	—
187	C₂³×C₇₉	—	4	2	no	—
188	C₂³×C₇₉	—	4	2	no	—
189	C₂³×C₇₉	—	4	2	no	—
190	C₂³×C₇₉	—	4	2	no	—
191	C₂³×C₇₉	#120	1	2	yes	—
192	C₂³×C₇₉	C₂×SD₁₆	1	2	yes	—
193	C₂³×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
194	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
195	Q₈×C₇₉	—	4	8	no	—
196	Q₈×C₇₉	—	4	2	no	—
197	Q₈×C₇₉	—	4	2	no	—
198	D₄×C₇₉	—	2	4	no	—
199	D₄×C₇₉	—	2	4	no	—
200	D₄×C₇₉	—	4	8	no	—
201	D₄×C₇₉	—	4	8	no	—
202	D₄×C₇₉	—	4	16	no	—
203	D₄×C₇₉	—	4	2	no	—
204	D₄×C₇₉	—	4	2	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	1	no	—
209	C₂×C₄×C₇₉	—	2	1	no	—
210	C₂×C₄×C₇₉	—	2	1	no	—
211	C₂×C₄×C₇₉	—	2	1	no	—
212	C₂×C₄×C₇₉	—	2	1	no	—
213	C₂×C₄×C₇₉	—	2	8	no	—
214	C₂×C₄×C₇₉	—	2	4	no	—
215	C₂×C₄×C₇₉	—	2	4	no	—
216	C₂×C₄×C₇₉	—	2	1	no	—
217	C₂×C₄×C₇₉	—	2	4	no	—
218	C₂×C₄×C₇₉	—	2	1	no	—
219	C₂×C₄×C₇₉	—	2	1	no	—
220	C₂×C₄×C₇₉	—	4	4	no	—
221	C₂×C₄×C₇₉	—	4	16	no	—
222	C₂×C₄×C₇₉	—	4	2	no	—
223	C₂×C₄×C₇₉	—	4	2	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	—	4	1	no	—
228	C₂×C₄×C₇₉	—	4	1	no	—
229	C₂×C₄×C₇₉	—	4	1	no	—
230	C₂×C₄×C₇₉	—	4	1	no	—
231	C₂×C₄×C₇₉	—	4	1	no	—
232	C₂×C₄×C₇₉	—	4	1	no	—
233	C₂×C₄×C₇₉	—	4	1	no	—
234	C₂×C₄×C₇₉	—	4	1	no	—
235	C₂×C₄×C₇₉	—	4	1	no	—
236	C₂×C₄×C₇₉	#120	1	2	yes	—
237	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
238	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
239	C₂×C₄×C₇₉	#135	1	2	yes	—
240	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
241	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
242	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
243	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
244	C₈×C₇₉	—	2	4	no	—
245	C₈×C₇₉	—	4	2	no	—
246	C₂²×C₇₉	—	2	2	no	—
247	C₂²×C₇₉	—	2	2	no	—
248	C₂²×C₇₉	—	2	2	no	—
249	C₂²×C₇₉	—	2	2	no	—
250	C₂²×C₇₉	—	2	2	no	—
251	C₂²×C₇₉	—	2	2	no	—
252	C₂²×C₇₉	—	4	4	no	—
253	C₂²×C₇₉	—	4	4	no	—
254	C₂²×C₇₉	—	4	4	no	—
255	C₂²×C₇₉	—	8	2	no	—
256	C₂²×C₇₉	—	8	2	no	—
257	C₂²×C₇₉	—	8	2	no	—
258	C₂²×C₇₉	—	8	2	no	—
259	C₂²×C₇₉	#450	1	4	yes	—
260	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
261	C₂²×C₇₉	#532	1	1	yes	characteristic
262	C₂²×C₇₉	#537	1	1	yes	characteristic
263	C₂²×C₇₉	C₂²×SD₁₆	1	1	yes	characteristic
264	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
265	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
266	C₂²×C₇₉	#575	1	1	yes	characteristic
267	C₄×C₇₉	—	2	2	no	—
268	C₄×C₇₉	—	2	2	no	—
269	C₄×C₇₉	—	2	2	no	—
270	C₄×C₇₉	—	2	2	no	—
271	C₄×C₇₉	—	4	4	no	—
272	C₄×C₇₉	—	4	1	no	—
273	C₄×C₇₉	—	8	1	no	—
274	C₄×C₇₉	—	8	1	no	—
275	C₄×C₇₉	—	8	1	no	—
276	C₄×C₇₉	—	8	1	no	—
277	C₄×C₇₉	#546	1	2	yes	—
278	C₄×C₇₉	#547	1	2	yes	—
279	#25495	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
280	C₂×C₇₉	—	2	4	no	—
281	C₂×C₇₉	—	8	4	no	—
282	C₂×C₇₉	#2430	1	1	yes	characteristic
283	C₂×C₇₉	C₂×#450	1	1	yes	characteristic
284	C₂×C₇₉	#3002	1	1	yes	characteristic
285	C₂×C₇₉	#3167	1	1	yes	characteristic
286	C₂×C₇₉	#3180	1	1	yes	characteristic
287	C₂×C₇₉	#3246	1	1	yes	characteristic
288	C₂×C₇₉	#3247	1	1	yes	characteristic
289	C₂×#532	C₂×C₇₉	1	1	yes	characteristic
290	C₂×#465	C₂×C₇₉	1	2	yes	complemented
291	#2855	C₂×C₇₉	1	1	yes	characteristic, complemented
292	#2058	C₂×C₇₉	1	1	yes	characteristic, complemented
293	#2041	C₂×C₇₉	1	1	yes	characteristic, complemented
294	#2024	C₂×C₇₉	1	1	yes	characteristic, complemented
295	#2014	C₂×C₇₉	1	1	yes	characteristic, complemented
296	#1893	C₂×C₇₉	1	2	yes	complemented
297	#1877	C₂×C₇₉	1	2	yes	complemented
298	#1864	C₂×C₇₉	1	2	yes	complemented
299	C₂×#336	C₂×C₇₉	1	1	yes	characteristic, complemented
300	C₇₉	#25495	1	1	yes	characteristic, direct product factor, Sylow
301	C₂²×#41	—	2	1	no	—
302	C₂²×SD₁₆	C₂²×C₇₉	1	2	yes	—
303	C₂³×C₈	C₂²×C₇₉	1	2	yes	—
304	#532	—	2	8	no	—
305	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
306	C₂×#127	C₂²×C₇₉	1	1	yes	characteristic
307	C₂×#124	—	2	1	no	—
308	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
309	C₂×#121	—	2	1	no	—
310	C₂×#121	C₂²×C₇₉	1	2	yes	—
311	C₂×C₄×D₄	—	2	1	no	—
312	C₂×C₄×D₄	C₂²×C₇₉	1	2	yes	—
313	C₂²×C₄²	C₂²×C₇₉	1	1	yes	characteristic
314	#465	—	2	8	no	—
315	C₂×#106	C₂²×C₇₉	1	2	yes	—
316	C₂×#103	C₂²×C₇₉	1	2	yes	—
317	C₂×#102	C₂²×C₇₉	1	2	yes	—
318	C₂×#102	C₂²×C₇₉	1	2	yes	—
319	C₂×#102	C₂²×C₇₉	1	2	yes	—
320	#391	C₂²×C₇₉	1	1	yes	characteristic
321	#391	C₂²×C₇₉	1	1	yes	characteristic
322	#389	C₂²×C₇₉	1	1	yes	characteristic
323	#389	C₂²×C₇₉	1	1	yes	characteristic
324	#387	—	2	1	no	—
325	#387	—	2	1	no	—
326	#385	—	2	1	no	—
327	#381	—	2	1	no	—
328	#380	C₂²×C₇₉	1	1	yes	characteristic
329	#340	C₂²×C₇₉	1	2	yes	—
330	#340	C₂²×C₇₉	1	2	yes	—
331	#336	C₂²×C₇₉	1	1	yes	characteristic
332	#336	C₂²×C₇₉	1	2	yes	—
333	#336	C₂²×C₇₉	1	1	yes	characteristic
334	C₂×#41	—	2	8	no	—
335	C₂×#41	—	4	4	no	—
336	C₂×#41	—	4	4	no	—
337	C₂²×Q₈	—	2	1	no	—
338	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
339	C₂²×D₄	—	2	2	no	—
340	C₂²×D₄	—	2	1	no	—
341	C₂²×D₄	—	2	1	no	—
342	C₂²×D₄	C₂³×C₇₉	1	2	yes	—
343	C₂³×C₄	—	2	2	no	—
344	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
345	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
346	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
347	C₂×SD₁₆	—	2	4	no	—
348	C₂×SD₁₆	—	2	4	no	—
349	C₂×SD₁₆	—	4	2	no	—
350	C₂²×C₈	—	2	4	no	—
351	C₂²×C₈	—	2	4	no	—
352	C₂²×C₈	—	4	2	no	—
353	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
354	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
355	C₄⋊Q₈	—	2	4	no	—
356	#127	—	2	4	no	—
357	#124	—	2	8	no	—
358	C₂²⋊Q₈	—	2	4	no	—
359	#121	—	2	8	no	—
360	#121	—	2	4	no	—
361	#121	D₄×C₇₉	1	8	yes	—
362	C₄×D₄	—	2	8	no	—
363	C₄×D₄	—	2	4	no	—
364	C₄×D₄	—	2	4	no	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	—	2	1	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
373	C₂×C₂²⋊C₄	—	2	2	no	—
374	C₂×C₂²⋊C₄	—	2	2	no	—
375	C₂×C₂²⋊C₄	—	2	1	no	—
376	C₂×C₂²⋊C₄	—	2	1	no	—
377	C₂×C₄²	—	2	4	no	—
378	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
379	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
380	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
381	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
382	#106	—	2	4	no	—
383	#103	—	2	4	no	—
384	#102	—	2	4	no	—
385	#102	—	2	4	no	—
386	#102	—	4	2	no	—
387	#95	—	2	1	no	—
388	#95	—	2	1	no	—
389	#95	—	2	1	no	—
390	#95	—	2	1	no	—
391	#95	—	2	1	no	—
392	#95	—	2	1	no	—
393	#95	—	2	1	no	—
394	C₂⁴	—	2	2	no	—
395	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
396	#41	—	4	32	no	—
397	C₂×Q₈	—	2	4	no	—
398	C₂×Q₈	—	2	2	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	1	no	—
401	C₂×Q₈	—	2	1	no	—
402	C₂×Q₈	—	4	2	no	—
403	C₂×Q₈	—	4	2	no	—
404	C₂×D₄	—	2	4	no	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	—	2	8	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	4	2	no	—
413	C₂×D₄	—	4	2	no	—
414	C₂×D₄	—	4	4	no	—
415	C₂×D₄	—	4	4	no	—
416	C₂×D₄	—	4	2	no	—
417	C₂×D₄	—	4	2	no	—
418	C₂×D₄	C₂×D₄×C₇₉	1	4	yes	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	8	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	4	1	no	—
433	C₂²×C₄	—	4	4	no	—
434	C₂²×C₄	—	4	4	no	—
435	C₂²×C₄	SD₁₆×C₇₉	1	4	yes	complemented
436	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₇₉	1	4	yes	—
439	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
440	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
442	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
443	SD₁₆	—	4	8	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	2	2	no	—
446	C₂×C₈	—	2	2	no	—
447	C₂×C₈	—	2	2	no	—
448	C₂×C₈	—	2	2	no	—
449	C₂×C₈	—	4	8	no	—
450	C₂×C₈	#41×C₇₉	1	4	yes	complemented
451	C₄⋊C₄	—	2	4	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	4	2	no	—
458	C₄⋊C₄	—	4	2	no	—
459	C₄⋊C₄	—	4	2	no	—
460	C₄⋊C₄	C₂×D₄×C₇₉	1	4	yes	—
461	C₂²⋊C₄	—	2	8	no	—
462	C₂²⋊C₄	—	2	8	no	—
463	C₂²⋊C₄	—	4	2	no	—
464	C₂²⋊C₄	—	4	2	no	—
465	C₄²	—	2	2	no	—
466	C₄²	—	2	2	no	—
467	C₄²	—	2	2	no	—
468	C₄²	—	2	2	no	—
469	C₂³	—	2	1	no	—
470	C₂³	—	2	1	no	—
471	C₂³	—	2	1	no	—
472	C₂³	—	2	1	no	—
473	C₂³	—	2	4	no	—
474	C₂³	—	4	2	no	—
475	C₂³	—	4	2	no	—
476	C₂³	—	4	2	no	—
477	C₂³	—	4	2	no	—
478	C₂³	—	4	2	no	—
479	C₂³	—	4	2	no	—
480	C₂³	#120×C₇₉	1	2	yes	—
481	C₂³	C₂×SD₁₆×C₇₉	1	2	yes	—
482	C₂³	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
483	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
484	Q₈	—	4	8	no	—
485	Q₈	—	4	2	no	—
486	Q₈	—	4	2	no	—
487	D₄	—	2	4	no	—
488	D₄	—	2	4	no	—
489	D₄	—	4	8	no	—
490	D₄	—	4	8	no	—
491	D₄	—	4	16	no	—
492	D₄	—	4	2	no	—
493	D₄	—	4	2	no	—
494	C₂×C₄	—	2	8	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	4	4	no	—
510	C₂×C₄	—	4	16	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	#120×C₇₉	1	2	yes	—
526	C₂×C₄	C₂×SD₁₆×C₇₉	1	2	yes	—
527	C₂×C₄	C₂×SD₁₆×C₇₉	1	2	yes	—
528	C₂×C₄	#135×C₇₉	1	2	yes	—
529	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
530	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
531	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
532	C₂×C₄	2₋¹⁺⁴×C₇₉	1	1	yes	characteristic
533	C₈	—	2	4	no	—
534	C₈	—	4	2	no	—
535	C₂²	—	2	2	no	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	2	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	2	2	no	—
541	C₂²	—	4	4	no	—
542	C₂²	—	4	4	no	—
543	C₂²	—	4	4	no	—
544	C₂²	—	8	2	no	—
545	C₂²	—	8	2	no	—
546	C₂²	—	8	2	no	—
547	C₂²	—	8	2	no	—
548	C₂²	#450×C₇₉	1	4	yes	—
549	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
550	C₂²	#532×C₇₉	1	1	yes	characteristic
551	C₂²	#537×C₇₉	1	1	yes	characteristic
552	C₂²	C₂²×SD₁₆×C₇₉	1	1	yes	characteristic
553	C₂²	C₂×#135×C₇₉	1	1	yes	characteristic
554	C₂²	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
555	C₂²	#575×C₇₉	1	1	yes	characteristic
556	C₄	—	2	2	no	—
557	C₄	—	2	2	no	—
558	C₄	—	2	2	no	—
559	C₄	—	2	2	no	—
560	C₄	—	4	4	no	—
561	C₄	—	4	1	no	—
562	C₄	—	8	1	no	—
563	C₄	—	8	1	no	—
564	C₄	—	8	1	no	—
565	C₄	—	8	1	no	—
566	C₄	#546×C₇₉	1	2	yes	—
567	C₄	#547×C₇₉	1	2	yes	—
568	C₂	—	2	4	no	—
569	C₂	—	8	4	no	—
570	C₂	C₇₉×#2430	1	1	yes	characteristic
571	C₂	C₂×#450×C₇₉	1	1	yes	characteristic
572	C₂	C₇₉×#3002	1	1	yes	characteristic
573	C₂	C₇₉×#3167	1	1	yes	characteristic
574	C₂	C₇₉×#3180	1	1	yes	characteristic
575	C₂	C₇₉×#3246	1	1	yes	characteristic
576	C₂	C₇₉×#3247	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₂×#532×C₇₉	C₂
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×#465×C₇₉	C₂	semidirect
3. C₇₉×#2855	C₂	semidirect
4. C₇₉×#2058	C₂	semidirect
5. C₇₉×#2041	C₂	semidirect
6. C₇₉×#2024	C₂	semidirect
7. C₇₉×#2014	C₂	semidirect
8. C₇₉×#1893	C₂	semidirect
9. C₇₉×#1877	C₂	semidirect
10. C₇₉×#1864	C₂	semidirect
11. C₂×#336×C₇₉	C₂	semidirect
146. C₂²×C₄×C₇₉	SD₁₆	semidirect
161. C₂×C₈×C₇₉	#41	semidirect
279. #25495	C₇₉	direct (N × H)
290. C₂×#465	C₂×C₇₉	semidirect
291. #2855	C₂×C₇₉	semidirect
292. #2058	C₂×C₇₉	semidirect
293. #2041	C₂×C₇₉	semidirect
294. #2024	C₂×C₇₉	semidirect
295. #2014	C₂×C₇₉	semidirect
296. #1893	C₂×C₇₉	semidirect
297. #1877	C₂×C₇₉	semidirect
298. #1864	C₂×C₇₉	semidirect
299. C₂×#336	C₂×C₇₉	semidirect
300. C₇₉	#25495	direct (N × H)
435. C₂²×C₄	SD₁₆×C₇₉	semidirect
450. C₂×C₈	#41×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#532×C₇₉	2
C₂×#465×C₇₉	2
C₇₉×#2855	2
C₇₉×#2058	2
C₇₉×#2041	2
C₇₉×#2024	2
C₇₉×#2014	2
C₇₉×#1893	2
C₇₉×#1877	2
C₇₉×#1864	2
C₂×#336×C₇₉	2
#25495	79

Subgroups — C79×#25495 #34137184

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#25495 #34137184