Subgroups — C₂×#442×D₇₉ #35152310

Order 20224.

3654 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₈×D₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₄×D₇₉	C₂	1	2	yes	maximal, complemented
3	C₂×#19098676	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#19098675	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#19098674	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#19098673	C₂	1	2	yes	maximal, complemented
7	C₂×#19098672	C₂	1	2	yes	maximal, complemented
8	#442×D₇₉	C₂	1	16	yes	maximal, direct product factor
9	C₂×#106×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#102×D₇₉	C₂	1	2	yes	maximal, complemented
11	C₂×#97×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#442×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×D₄×D₇₉	C₂²	1	2	yes	—
14	C₂³×C₄×D₇₉	—	2	2	no	—
15	C₂²×D₆₃₂	C₂²	1	1	yes	characteristic
16	C₂²×#11929609	C₂²	1	2	yes	—
17	C₂×D₈×D₇₉	C₄	1	16	yes	complemented
18	C₂×D₈×D₇₉	C₂²	1	8	yes	—
19	C₂²×C₈×D₇₉	C₂²	1	1	yes	characteristic
20	C₂²×C₈×D₇₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₃₁₆	C₂²	1	2	yes	complemented
22	C₂×D₄×Dic₇₉	C₂²	1	2	yes	complemented
23	C₂×#14579123	C₂²	1	2	yes	complemented
24	C₂×C₄×C₂²⋊D₇₉	—	2	2	no	—
25	C₂×(C₂²⋊D₇₉)⋊C₄	—	2	2	no	—
26	C₄×D₄×D₇₉	—	2	8	no	—
27	C₄×D₄×D₇₉	C₂²	1	16	yes	complemented
28	C₂×C₄⋊C₄×D₇₉	C₂²	1	2	yes	—
29	C₂×C₂²⋊C₄×D₇₉	—	2	2	no	—
30	C₂×C₄²×D₇₉	C₂²	1	1	yes	characteristic
31	#19098676	C₂²	1	8	yes	complemented
32	#19098675	C₂²	1	8	yes	complemented
33	#19098674	C₂²	1	8	yes	complemented
34	#19098673	C₂²	1	16	yes	complemented
35	#19098672	C₂²	1	16	yes	complemented
36	C₂×#14579093	C₂²	1	1	yes	characteristic, complemented
37	C₂×#14579092	C₂²	1	2	yes	complemented
38	#106×D₇₉	C₂²	1	8	yes	complemented
39	C₂×#14579083	C₂²	1	2	yes	complemented
40	C₂×#14579082	C₂²	1	2	yes	complemented
41	C₂×#14579081	C₂²	1	2	yes	complemented
42	#102×D₇₉	C₂²	1	16	yes	complemented
43	C₂×#14579072	C₂²	1	1	yes	characteristic, complemented
44	C₂×#14579071	C₂²	1	1	yes	characteristic, complemented
45	C₂×#14579071	C₂²	1	1	yes	characteristic, complemented
46	#97×D₇₉	C₂²	1	8	yes	complemented
47	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	complemented
49	#442×C₇₉	C₂²	1	8	yes	complemented
50	C₂×#106×C₇₉	C₂²	1	1	yes	characteristic, complemented
51	C₂×#102×C₇₉	C₂²	1	2	yes	complemented
52	C₂×#97×C₇₉	C₂²	1	1	yes	characteristic, complemented
53	C₂⁴×D₇₉	—	2	2	no	—
54	C₂²×D₃₁₆	C₂³	1	2	yes	—
55	C₂²×C₂²⋊D₇₉	—	2	2	no	—
56	C₂×D₄×D₇₉	—	2	4	no	—
57	C₂×D₄×D₇₉	—	2	8	no	—
58	C₂×D₄×D₇₉	C₂×C₄	1	16	yes	complemented
59	C₂×D₄×D₇₉	C₂³	1	8	yes	—
60	C₂³×Dic₇₉	—	2	2	no	—
61	C₂²×C₄×D₇₉	—	2	2	no	—
62	C₂²×C₄×D₇₉	—	2	2	no	—
63	C₂²×C₄×D₇₉	—	2	2	no	—
64	C₂²×C₄×D₇₉	—	2	16	no	—
65	C₂²×C₄×D₇₉	—	4	16	no	—
66	C₂²×C₄×D₇₉	D₄	1	2	yes	—
67	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
68	C₂×D₆₃₂	C₂×C₄	1	8	yes	complemented
69	C₂×D₆₃₂	C₂³	1	4	yes	—
70	C₂×#11929609	C₂×C₄	1	16	yes	complemented
71	C₂×#11929609	C₂³	1	8	yes	—
72	D₈×D₇₉	C₂×C₄	1	64	yes	complemented
73	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
75	C₂×C₈×D₇₉	—	2	4	no	—
76	C₂×C₈×D₇₉	C₂×C₄	1	8	yes	complemented
77	C₂×C₈×D₇₉	C₂³	1	4	yes	—
78	C₂×C₈×D₇₉	C₂³	1	4	yes	—
79	C₄×D₃₁₆	—	2	4	no	—
80	C₄×D₃₁₆	C₂³	1	8	yes	complemented
81	D₄×Dic₇₉	—	2	4	no	—
82	D₄×Dic₇₉	C₂³	1	8	yes	complemented
83	#14579123	—	2	4	no	—
84	#14579123	C₂³	1	8	yes	complemented
85	C₄×C₂²⋊D₇₉	—	2	16	no	—
86	(C₂²⋊D₇₉)⋊C₄	—	2	16	no	—
87	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
88	C₂×Dic₇₉⋊C₄	—	2	2	no	—
89	C₄⋊C₄×D₇₉	—	2	4	no	—
90	C₄⋊C₄×D₇₉	C₂³	1	8	yes	—
91	C₂×C₂²⋊Dic₇₉	—	2	2	no	—
92	C₂×(C₂×D₇₉)⋊C₄	—	2	2	no	—
93	C₂×(C₂×D₇₉)⋊C₄	—	2	2	no	—
94	C₂²⋊C₄×D₇₉	—	2	16	no	—
95	C₂×C₄×Dic₇₉	D₄	1	2	yes	—
96	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
97	C₄²×D₇₉	D₄	1	4	yes	—
98	C₄²×D₇₉	C₂³	1	4	yes	—
99	#14579093	C₂³	1	4	yes	complemented
100	#14579092	C₂³	1	8	yes	complemented
101	#14579083	C₂³	1	8	yes	complemented
102	#14579082	C₂³	1	8	yes	complemented
103	#14579081	C₂³	1	8	yes	complemented
104	#14579072	C₂³	1	4	yes	complemented
105	#14579071	C₂³	1	4	yes	complemented
106	#14579071	C₂³	1	4	yes	complemented
107	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
108	C₂³×C₄×C₇₉	—	2	2	no	—
109	C₂×D₈×C₇₉	C₂×C₄	1	8	yes	complemented
110	C₂×D₈×C₇₉	C₂³	1	4	yes	—
111	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
113	C₄×D₄×C₇₉	—	2	4	no	—
114	C₄×D₄×C₇₉	C₂³	1	8	yes	complemented
115	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
116	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
117	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
118	#106×C₇₉	C₂³	1	4	yes	complemented
119	#102×C₇₉	C₂³	1	8	yes	complemented
120	#97×C₇₉	C₂³	1	4	yes	complemented
121	C₂³×D₇₉	—	2	2	no	—
122	C₂³×D₇₉	—	2	16	no	—
123	C₂³×D₇₉	—	2	8	no	—
124	C₂³×D₇₉	—	4	8	no	—
125	C₂³×D₇₉	—	4	8	no	—
126	C₂³×D₇₉	C₂×D₄	1	1	yes	characteristic
127	C₂×D₃₁₆	—	2	2	no	—
128	C₂×D₃₁₆	—	2	4	no	—
129	C₂×D₃₁₆	C₂²×C₄	1	8	yes	complemented
130	C₂×D₃₁₆	C₂⁴	1	4	yes	—
131	C₂×C₂²⋊D₇₉	—	2	16	no	—
132	C₂×C₂²⋊D₇₉	—	2	8	no	—
133	D₄×D₇₉	—	2	32	no	—
134	D₄×D₇₉	—	2	16	no	—
135	D₄×D₇₉	C₂²×C₄	1	32	yes	complemented
136	C₂²×Dic₇₉	—	2	8	no	—
137	C₂²×Dic₇₉	—	2	2	no	—
138	C₂²×Dic₇₉	—	4	8	no	—
139	C₂²×Dic₇₉	C₂×D₄	1	2	yes	—
140	C₂²×Dic₇₉	C₂×D₄	1	1	yes	characteristic
141	C₂×C₄×D₇₉	—	2	8	no	—
142	C₂×C₄×D₇₉	—	2	8	no	—
143	C₂×C₄×D₇₉	—	2	8	no	—
144	C₂×C₄×D₇₉	—	2	8	no	—
145	C₂×C₄×D₇₉	—	4	8	no	—
146	C₂×C₄×D₇₉	—	4	64	no	—
147	C₂×C₄×D₇₉	—	4	8	no	—
148	C₂×C₄×D₇₉	—	4	8	no	—
149	C₂×C₄×D₇₉	C₂²×C₄	1	4	yes	—
150	C₂×C₄×D₇₉	C₂×D₄	1	8	yes	—
151	C₂×C₄×D₇₉	C₂×D₄	1	2	yes	—
152	C₂×C₄×D₇₉	#41	1	4	yes	—
153	C₂×C₄×D₇₉	C₂⁴	1	2	yes	—
154	D₆₃₂	C₂²×C₄	1	16	yes	complemented
155	#11929609	C₂²×C₄	1	32	yes	complemented
156	C₂×C₇₉⋊C₈	—	2	2	no	—
157	C₂×C₇₉⋊C₈	C₂²×C₄	1	4	yes	complemented
158	C₂×C₇₉⋊C₈	C₂⁴	1	2	yes	—
159	C₂×C₇₉⋊C₈	C₂⁴	1	2	yes	—
160	C₈×D₇₉	—	2	8	no	—
161	C₈×D₇₉	C₂²×C₄	1	16	yes	complemented
162	C₄⋊Dic₇₉	—	2	2	no	—
163	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
164	Dic₇₉⋊C₄	—	2	8	no	—
165	C₂²⋊Dic₇₉	—	2	8	no	—
166	(C₂×D₇₉)⋊C₄	—	2	8	no	—
167	(C₂×D₇₉)⋊C₄	—	2	8	no	—
168	C₄×Dic₇₉	C₂×D₄	1	2	yes	—
169	C₄×Dic₇₉	C₂×D₄	1	8	yes	—
170	C₄×Dic₇₉	C₂⁴	1	2	yes	—
171	C₂⁴×C₇₉	—	2	2	no	—
172	C₂×D₄×C₇₉	—	2	2	no	—
173	C₂×D₄×C₇₉	—	2	4	no	—
174	C₂×D₄×C₇₉	C₂²×C₄	1	8	yes	complemented
175	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
176	C₂²×C₄×C₇₉	—	2	2	no	—
177	C₂²×C₄×C₇₉	—	2	8	no	—
178	C₂²×C₄×C₇₉	—	4	8	no	—
179	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
180	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
181	D₈×C₇₉	C₂²×C₄	1	16	yes	complemented
182	C₂×C₈×C₇₉	—	2	2	no	—
183	C₂×C₈×C₇₉	C₂²×C₄	1	4	yes	complemented
184	C₂×C₈×C₇₉	C₂⁴	1	2	yes	—
185	C₂×C₈×C₇₉	C₂⁴	1	2	yes	—
186	C₄⋊C₄×C₇₉	—	2	2	no	—
187	C₄⋊C₄×C₇₉	C₂⁴	1	4	yes	—
188	C₂²⋊C₄×C₇₉	—	2	8	no	—
189	C₄²×C₇₉	C₂×D₄	1	2	yes	—
190	C₄²×C₇₉	C₂⁴	1	2	yes	—
191	C₂³×C₇₉	—	2	8	no	—
192	C₂³×C₇₉	—	2	4	no	—
193	C₂³×C₇₉	—	4	4	no	—
194	C₂³×C₇₉	—	4	4	no	—
195	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
196	C₂²×D₇₉	—	2	8	no	—
197	C₂²×D₇₉	—	2	4	no	—
198	C₂²×D₇₉	—	2	32	no	—
199	C₂²×D₇₉	—	4	4	no	—
200	C₂²×D₇₉	—	4	4	no	—
201	C₂²×D₇₉	—	4	16	no	—
202	C₂²×D₇₉	—	4	16	no	—
203	C₂²×D₇₉	—	4	64	no	—
204	C₂²×D₇₉	C₄×D₄	1	4	yes	—
205	C₂²×D₇₉	AGL(1,ℤ/8)	1	8	yes	—
206	C₂²×D₇₉	C₂²×D₄	1	2	yes	—
207	D₄×C₇₉	—	2	8	no	—
208	D₄×C₇₉	—	2	4	no	—
209	D₄×C₇₉	C₂³×C₄	1	8	yes	complemented
210	C₂×C₄×C₇₉	—	2	4	no	—
211	C₂×C₄×C₇₉	—	2	4	no	—
212	C₂×C₄×C₇₉	—	4	16	no	—
213	C₂×C₄×C₇₉	—	4	4	no	—
214	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
215	C₂×C₄×C₇₉	C₂²×D₄	1	4	yes	—
216	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
218	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
219	C₂²⋊D₇₉	—	2	32	no	—
220	C₂×Dic₇₉	—	2	4	no	—
221	C₂×Dic₇₉	—	2	4	no	—
222	C₂×Dic₇₉	—	4	16	no	—
223	C₂×Dic₇₉	—	4	4	no	—
224	C₂×Dic₇₉	C₄×D₄	1	4	yes	—
225	C₂×Dic₇₉	C₂²×D₄	1	4	yes	—
226	C₂×Dic₇₉	C₂²×D₄	1	2	yes	—
227	D₃₁₆	—	2	8	no	—
228	D₃₁₆	—	2	4	no	—
229	D₃₁₆	C₂³×C₄	1	8	yes	complemented
230	C₄×D₇₉	—	2	16	no	—
231	C₄×D₇₉	—	4	16	no	—
232	C₄×D₇₉	—	4	16	no	—
233	C₄×D₇₉	—	4	16	no	—
234	C₄×D₇₉	C₄×D₄	1	8	yes	—
235	C₄×D₇₉	C₂³×C₄	1	4	yes	—
236	C₄×D₇₉	C₂×#41	1	4	yes	—
237	C₈×C₇₉	—	2	2	no	—
238	C₈×C₇₉	C₂³×C₄	1	4	yes	complemented
239	C₇₉⋊C₈	—	2	2	no	—
240	C₇₉⋊C₈	C₂³×C₄	1	4	yes	complemented
241	C₂²×C₇₉	—	2	8	no	—
242	C₂²×C₇₉	—	4	16	no	—
243	C₂²×C₇₉	—	4	4	no	—
244	C₂²×C₇₉	—	4	4	no	—
245	C₂²×C₇₉	C₂×C₄×D₄	1	2	yes	—
246	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	4	yes	—
247	C₂²×C₇₉	C₂³×D₄	1	1	yes	characteristic
248	C₂×D₇₉	—	2	8	no	—
249	C₂×D₇₉	—	4	16	no	—
250	C₂×D₇₉	—	4	4	no	—
251	C₂×D₇₉	—	4	4	no	—
252	C₂×D₇₉	—	4	64	no	—
253	C₂×D₇₉	#442	1	16	yes	direct product factor
254	C₂×D₇₉	C₂×C₄×D₄	1	4	yes	—
255	C₂×D₇₉	C₂×AGL(1,ℤ/8)	1	8	yes	—
256	C₄×C₇₉	—	2	4	no	—
257	C₄×C₇₉	—	4	4	no	—
258	C₄×C₇₉	C₂×C₄×D₄	1	2	yes	—
259	C₄×C₇₉	C₂⁴×C₄	1	1	yes	characteristic
260	C₄×C₇₉	C₂²×#41	1	1	yes	characteristic
261	Dic₇₉	—	2	4	no	—
262	Dic₇₉	—	4	4	no	—
263	Dic₇₉	C₂×C₄×D₄	1	4	yes	—
264	C₂²×#442	—	79	1	no	maximal, Sylow
265	C₂×C₇₉	—	4	8	no	—
266	C₂×C₇₉	C₂×#442	1	4	yes	complemented
267	C₂×C₇₉	C₂²×C₄×D₄	1	1	yes	characteristic
268	C₂×C₇₉	C₂²×AGL(1,ℤ/8)	1	2	yes	—
269	D₇₉	—	4	8	no	—
270	D₇₉	C₂×#442	1	8	yes	direct product factor
271	C₂³×D₈	—	79	1	no	—
272	C₂²×C₄×D₄	—	79	2	no	—
273	C₂×#442	—	79	16	no	—
274	C₂×#442	—	79	1	no	—
275	C₂×#442	—	79	2	no	—
276	C₂×#442	—	79	1	no	—
277	C₂×#442	—	79	1	no	—
278	C₂×#442	—	79	2	no	—
279	C₂×#442	D₇₉	1	1	yes	characteristic, direct product factor
280	C₂²×#106	—	79	1	no	—
281	C₂²×#102	—	79	2	no	—
282	C₂²×#97	—	79	1	no	—
283	C₇₉	C₂²×#442	1	1	yes	characteristic, complemented, Sylow
284	C₂³×D₄	—	79	2	no	—
285	C₂⁴×C₄	—	158	2	no	—
286	C₂²×D₈	—	79	2	no	—
287	C₂²×D₈	—	79	8	no	—
288	C₂²×D₈	—	79	16	no	—
289	C₂²×D₈	—	79	1	no	—
290	C₂²×D₈	C₂×D₇₉	1	1	yes	characteristic
291	C₂³×C₈	—	79	1	no	—
292	C₂³×C₈	—	79	1	no	—
293	C₂×C₄×D₄	—	79	2	no	—
294	C₂×C₄×D₄	—	79	16	no	—
295	C₂×C₄×D₄	—	79	2	no	—
296	C₂×C₄×D₄	—	79	2	no	—
297	C₂×C₄×D₄	—	158	2	no	—
298	C₂×C₄×D₄	—	158	8	no	—
299	C₂×C₄×D₄	—	158	2	no	—
300	C₂×C₄×D₄	C₂×D₇₉	1	2	yes	complemented
301	C₂²×C₄⋊C₄	—	79	2	no	—
302	C₂²×C₂²⋊C₄	—	158	2	no	—
303	C₂²×C₄²	—	79	1	no	—
304	#442	—	79	8	no	—
305	#442	—	79	16	no	—
306	#442	—	79	8	no	—
307	#442	—	79	16	no	—
308	#442	—	79	8	no	—
309	#442	C₂×D₇₉	1	8	yes	direct product factor
310	C₂×#106	—	79	1	no	—
311	C₂×#106	—	79	2	no	—
312	C₂×#106	—	79	8	no	—
313	C₂×#106	C₂×D₇₉	1	1	yes	characteristic, complemented
314	C₂×#102	—	79	2	no	—
315	C₂×#102	—	79	2	no	—
316	C₂×#102	—	79	2	no	—
317	C₂×#102	—	79	16	no	—
318	C₂×#102	C₂×D₇₉	1	2	yes	complemented
319	C₂×#97	—	79	1	no	—
320	C₂×#97	—	79	1	no	—
321	C₂×#97	—	79	1	no	—
322	C₂×#97	—	79	8	no	—
323	C₂×#97	C₂×D₇₉	1	1	yes	characteristic, complemented
324	C₂⁵	—	158	2	no	—
325	C₂²×D₄	—	79	16	no	—
326	C₂²×D₄	—	79	8	no	—
327	C₂²×D₄	—	79	2	no	—
328	C₂²×D₄	—	158	4	no	—
329	C₂²×D₄	—	158	8	no	—
330	C₂²×D₄	—	158	2	no	—
331	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
332	C₂³×C₄	—	2	2	no	—
333	C₂³×C₄	—	316	16	no	—
334	C₂³×C₄	—	79	1	no	—
335	C₂³×C₄	—	79	2	no	—
336	C₂³×C₄	—	158	2	no	—
337	C₂³×C₄	—	158	16	no	—
338	C₂³×C₄	—	158	2	no	—
339	C₂³×C₄	—	158	2	no	—
340	C₂³×C₄	—	158	2	no	—
341	C₂×D₈	—	79	16	no	—
342	C₂×D₈	—	79	8	no	—
343	C₂×D₈	—	79	64	no	—
344	C₂×D₈	—	79	8	no	—
345	C₂×D₈	—	79	4	no	—
346	C₂×D₈	C₄×D₇₉	1	8	yes	complemented
347	C₂×D₈	C₂²×D₇₉	1	4	yes	—
348	C₂²×C₈	—	79	1	no	—
349	C₂²×C₈	—	79	8	no	—
350	C₂²×C₈	—	79	4	no	—
351	C₂²×C₈	—	79	1	no	—
352	C₂²×C₈	—	79	4	no	—
353	C₂²×C₈	—	158	4	no	—
354	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
355	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
356	C₄×D₄	—	2	4	no	—
357	C₄×D₄	—	79	8	no	—
358	C₄×D₄	—	79	8	no	—
359	C₄×D₄	—	79	8	no	—
360	C₄×D₄	—	158	16	no	—
361	C₄×D₄	—	158	4	no	—
362	C₄×D₄	—	158	16	no	—
363	C₄×D₄	—	158	4	no	—
364	C₄×D₄	—	158	4	no	—
365	C₄×D₄	C₂²×D₇₉	1	8	yes	complemented
366	C₂×C₄⋊C₄	—	79	2	no	—
367	C₂×C₄⋊C₄	—	79	8	no	—
368	C₂×C₄⋊C₄	—	158	4	no	—
369	C₂×C₄⋊C₄	—	158	2	no	—
370	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
371	C₂×C₂²⋊C₄	—	2	2	no	—
372	C₂×C₂²⋊C₄	—	158	16	no	—
373	C₂×C₂²⋊C₄	—	158	2	no	—
374	C₂×C₂²⋊C₄	—	158	2	no	—
375	C₂×C₂²⋊C₄	—	158	2	no	—
376	C₂×C₄²	—	79	2	no	—
377	C₂×C₄²	—	79	1	no	—
378	C₂×C₄²	—	79	4	no	—
379	C₂×C₄²	—	79	4	no	—
380	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
381	#106	—	79	4	no	—
382	#106	—	79	8	no	—
383	#106	C₂²×D₇₉	1	4	yes	complemented
384	#102	—	79	8	no	—
385	#102	—	79	8	no	—
386	#102	—	79	8	no	—
387	#102	C₂²×D₇₉	1	8	yes	complemented
388	#97	—	79	4	no	—
389	#97	—	79	4	no	—
390	#97	—	79	4	no	—
391	#97	C₂²×D₇₉	1	4	yes	complemented
392	C₂⁴	—	2	2	no	—
393	C₂⁴	—	316	8	no	—
394	C₂⁴	—	316	8	no	—
395	C₂⁴	—	79	1	no	—
396	C₂⁴	—	158	8	no	—
397	C₂⁴	—	158	16	no	—
398	C₂⁴	—	158	2	no	—
399	C₂×D₄	—	2	4	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	79	32	no	—
402	C₂×D₄	—	79	4	no	—
403	C₂×D₄	—	79	8	no	—
404	C₂×D₄	—	158	32	no	—
405	C₂×D₄	—	158	16	no	—
406	C₂×D₄	—	158	8	no	—
407	C₂×D₄	—	158	16	no	—
408	C₂×D₄	—	158	4	no	—
409	C₂×D₄	—	158	2	no	—
410	C₂×D₄	C₂×C₄×D₇₉	1	8	yes	complemented
411	C₂×D₄	C₂³×D₇₉	1	4	yes	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	8	no	—
414	C₂²×C₄	—	4	8	no	—
415	C₂²×C₄	—	316	8	no	—
416	C₂²×C₄	—	316	8	no	—
417	C₂²×C₄	—	316	64	no	—
418	C₂²×C₄	—	316	8	no	—
419	C₂²×C₄	—	316	8	no	—
420	C₂²×C₄	—	79	1	no	—
421	C₂²×C₄	—	79	4	no	—
422	C₂²×C₄	—	79	2	no	—
423	C₂²×C₄	—	79	4	no	—
424	C₂²×C₄	—	79	2	no	—
425	C₂²×C₄	—	79	2	no	—
426	C₂²×C₄	—	79	8	no	—
427	C₂²×C₄	—	158	8	no	—
428	C₂²×C₄	—	158	8	no	—
429	C₂²×C₄	—	158	8	no	—
430	C₂²×C₄	—	158	8	no	—
431	C₂²×C₄	—	158	2	no	—
432	C₂²×C₄	—	158	8	no	—
433	C₂²×C₄	D₄×D₇₉	1	2	yes	—
434	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
435	D₈	—	79	32	no	—
436	D₈	—	79	16	no	—
437	D₈	C₂×C₄×D₇₉	1	16	yes	complemented
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	79	2	no	—
440	C₂×C₈	—	79	4	no	—
441	C₂×C₈	—	79	16	no	—
442	C₂×C₈	—	79	2	no	—
443	C₂×C₈	—	158	8	no	—
444	C₂×C₈	—	158	2	no	—
445	C₂×C₈	C₂×C₄×D₇₉	1	4	yes	complemented
446	C₂×C₈	C₂³×D₇₉	1	2	yes	—
447	C₂×C₈	C₂³×D₇₉	1	2	yes	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	79	4	no	—
450	C₄⋊C₄	—	158	8	no	—
451	C₄⋊C₄	—	158	2	no	—
452	C₄⋊C₄	C₂³×D₇₉	1	4	yes	—
453	C₂²⋊C₄	—	2	8	no	—
454	C₂²⋊C₄	—	158	8	no	—
455	C₂²⋊C₄	—	158	8	no	—
456	C₂²⋊C₄	—	158	8	no	—
457	C₄²	—	79	2	no	—
458	C₄²	—	79	8	no	—
459	C₄²	—	79	2	no	—
460	C₄²	D₄×D₇₉	1	2	yes	—
461	C₄²	C₂³×D₇₉	1	2	yes	—
462	C₂³	—	2	8	no	—
463	C₂³	—	2	4	no	—
464	C₂³	—	4	4	no	—
465	C₂³	—	4	4	no	—
466	C₂³	—	316	16	no	—
467	C₂³	—	316	64	no	—
468	C₂³	—	316	16	no	—
469	C₂³	—	316	4	no	—
470	C₂³	—	316	4	no	—
471	C₂³	—	79	4	no	—
472	C₂³	—	79	8	no	—
473	C₂³	—	79	2	no	—
474	C₂³	—	158	32	no	—
475	C₂³	—	158	8	no	—
476	C₂³	—	158	4	no	—
477	C₂³	C₂×D₄×D₇₉	1	1	yes	characteristic
478	D₄	—	2	8	no	—
479	D₄	—	2	4	no	—
480	D₄	—	79	8	no	—
481	D₄	—	158	32	no	—
482	D₄	—	158	8	no	—
483	D₄	—	158	4	no	—
484	D₄	C₂²×C₄×D₇₉	1	8	yes	complemented
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	4	16	no	—
488	C₂×C₄	—	4	4	no	—
489	C₂×C₄	—	316	16	no	—
490	C₂×C₄	—	316	16	no	—
491	C₂×C₄	—	316	16	no	—
492	C₂×C₄	—	316	4	no	—
493	C₂×C₄	—	316	16	no	—
494	C₂×C₄	—	79	4	no	—
495	C₂×C₄	—	79	2	no	—
496	C₂×C₄	—	79	8	no	—
497	C₂×C₄	—	79	4	no	—
498	C₂×C₄	—	79	4	no	—
499	C₂×C₄	—	79	4	no	—
500	C₂×C₄	—	158	16	no	—
501	C₂×C₄	—	158	4	no	—
502	C₂×C₄	—	158	4	no	—
503	C₂×C₄	C₂²×C₄×D₇₉	1	2	yes	—
504	C₂×C₄	C₂×D₄×D₇₉	1	4	yes	—
505	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
506	C₂×C₄	#41×D₇₉	1	2	yes	—
507	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
508	C₈	—	2	2	no	—
509	C₈	—	79	4	no	—
510	C₈	—	158	2	no	—
511	C₈	C₂²×C₄×D₇₉	1	4	yes	complemented
512	C₂²	—	2	8	no	—
513	C₂²	—	4	16	no	—
514	C₂²	—	4	4	no	—
515	C₂²	—	4	4	no	—
516	C₂²	—	316	64	no	—
517	C₂²	—	316	16	no	—
518	C₂²	—	316	4	no	—
519	C₂²	—	316	4	no	—
520	C₂²	—	79	16	no	—
521	C₂²	—	79	4	no	—
522	C₂²	—	79	8	no	—
523	C₂²	—	158	8	no	—
524	C₂²	C₄×D₄×D₇₉	1	2	yes	—
525	C₂²	AGL(1,ℤ/8)×D₇₉	1	4	yes	—
526	C₂²	C₂²×D₄×D₇₉	1	1	yes	characteristic
527	C₄	—	2	4	no	—
528	C₄	—	4	4	no	—
529	C₄	—	316	4	no	—
530	C₄	—	79	4	no	—
531	C₄	—	158	4	no	—
532	C₄	C₄×D₄×D₇₉	1	2	yes	—
533	C₄	C₂³×C₄×D₇₉	1	1	yes	characteristic
534	C₄	C₂×#41×D₇₉	1	1	yes	characteristic
535	C₂	—	4	8	no	—
536	C₂	—	316	8	no	—
537	C₂	—	79	8	no	—
538	C₂	#442×D₇₉	1	4	yes	direct product factor
539	C₂	C₂×C₄×D₄×D₇₉	1	1	yes	characteristic
540	C₂	C₂×AGL(1,ℤ/8)×D₇₉	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₇₉
commutator	C₄×C₇₉	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₇₉
Fitting	C₂×#442×C₇₉	C₂
socle	C₂³×C₇₉	C₂²×D₄
prime radical	C₂²×D₈×D₇₉	C₂
cosocle	C₂×C₄×C₇₉	C₂⁵
hypercenter	C₂×#442	D₇₉
hypocenter	C₇₉	C₂²×#442
LCS	G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#442

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×D₄×D₇₉	C₂	semidirect
3. C₂×#19098676	C₂	semidirect
4. C₂×#19098675	C₂	semidirect
5. C₂×#19098674	C₂	semidirect
6. C₂×#19098673	C₂	semidirect
7. C₂×#19098672	C₂	semidirect
8. #442×D₇₉	C₂	direct (N × H)
9. C₂×#106×D₇₉	C₂	semidirect
10. C₂×#102×D₇₉	C₂	semidirect
11. C₂×#97×D₇₉	C₂	semidirect
12. C₂×#442×C₇₉	C₂	semidirect
17. C₂×D₈×D₇₉	C₄	semidirect
21. C₂×C₄×D₃₁₆	C₂²	semidirect
22. C₂×D₄×Dic₇₉	C₂²	semidirect
23. C₂×#14579123	C₂²	semidirect
27. C₄×D₄×D₇₉	C₂²	semidirect
31. #19098676	C₂²	semidirect
32. #19098675	C₂²	semidirect
33. #19098674	C₂²	semidirect
34. #19098673	C₂²	semidirect
35. #19098672	C₂²	semidirect
36. C₂×#14579093	C₂²	semidirect
37. C₂×#14579092	C₂²	semidirect
38. #106×D₇₉	C₂²	semidirect
39. C₂×#14579083	C₂²	semidirect
40. C₂×#14579082	C₂²	semidirect
41. C₂×#14579081	C₂²	semidirect
42. #102×D₇₉	C₂²	semidirect
43. C₂×#14579072	C₂²	semidirect
44. C₂×#14579071	C₂²	semidirect
45. C₂×#14579071	C₂²	semidirect
46. #97×D₇₉	C₂²	semidirect
48. C₂×C₄×D₄×C₇₉	C₂²	semidirect
49. #442×C₇₉	C₂²	semidirect
50. C₂×#106×C₇₉	C₂²	semidirect
51. C₂×#102×C₇₉	C₂²	semidirect
52. C₂×#97×C₇₉	C₂²	semidirect
58. C₂×D₄×D₇₉	C₂×C₄	semidirect
68. C₂×D₆₃₂	C₂×C₄	semidirect
70. C₂×#11929609	C₂×C₄	semidirect
72. D₈×D₇₉	C₂×C₄	semidirect
76. C₂×C₈×D₇₉	C₂×C₄	semidirect
80. C₄×D₃₁₆	C₂³	semidirect
82. D₄×Dic₇₉	C₂³	semidirect
84. #14579123	C₂³	semidirect
99. #14579093	C₂³	semidirect
100. #14579092	C₂³	semidirect
101. #14579083	C₂³	semidirect
102. #14579082	C₂³	semidirect
103. #14579081	C₂³	semidirect
104. #14579072	C₂³	semidirect
105. #14579071	C₂³	semidirect
106. #14579071	C₂³	semidirect
109. C₂×D₈×C₇₉	C₂×C₄	semidirect
114. C₄×D₄×C₇₉	C₂³	semidirect
118. #106×C₇₉	C₂³	semidirect
119. #102×C₇₉	C₂³	semidirect
120. #97×C₇₉	C₂³	semidirect
129. C₂×D₃₁₆	C₂²×C₄	semidirect
135. D₄×D₇₉	C₂²×C₄	semidirect
154. D₆₃₂	C₂²×C₄	semidirect
155. #11929609	C₂²×C₄	semidirect
157. C₂×C₇₉⋊C₈	C₂²×C₄	semidirect
161. C₈×D₇₉	C₂²×C₄	semidirect
174. C₂×D₄×C₇₉	C₂²×C₄	semidirect
181. D₈×C₇₉	C₂²×C₄	semidirect
183. C₂×C₈×C₇₉	C₂²×C₄	semidirect
209. D₄×C₇₉	C₂³×C₄	semidirect
229. D₃₁₆	C₂³×C₄	semidirect
238. C₈×C₇₉	C₂³×C₄	semidirect
240. C₇₉⋊C₈	C₂³×C₄	semidirect
253. C₂×D₇₉	#442	direct (N × H)
266. C₂×C₇₉	C₂×#442	semidirect
270. D₇₉	C₂×#442	direct (N × H)
279. C₂×#442	D₇₉	direct (N × H)
283. C₇₉	C₂²×#442	semidirect
300. C₂×C₄×D₄	C₂×D₇₉	semidirect
309. #442	C₂×D₇₉	direct (N × H)
313. C₂×#106	C₂×D₇₉	semidirect
318. C₂×#102	C₂×D₇₉	semidirect
323. C₂×#97	C₂×D₇₉	semidirect
346. C₂×D₈	C₄×D₇₉	semidirect
365. C₄×D₄	C₂²×D₇₉	semidirect
383. #106	C₂²×D₇₉	semidirect
387. #102	C₂²×D₇₉	semidirect
391. #97	C₂²×D₇₉	semidirect
410. C₂×D₄	C₂×C₄×D₇₉	semidirect
437. D₈	C₂×C₄×D₇₉	semidirect
445. C₂×C₈	C₂×C₄×D₇₉	semidirect
484. D₄	C₂²×C₄×D₇₉	semidirect
511. C₈	C₂²×C₄×D₇₉	semidirect
538. C₂	#442×D₇₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×D₈×D₇₉	2
C₂×C₄×D₄×D₇₉	2
C₂×#19098676	2
C₂×#19098675	2
C₂×#19098674	2
C₂×#19098673	2
C₂×#19098672	2
#442×D₇₉	2
C₂×#106×D₇₉	2
C₂×#102×D₇₉	2
C₂×#97×D₇₉	2
C₂×#442×C₇₉	2
C₂²×#442	79

Subgroups — C2×#442×D79 #35152310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#442×D₇₉ #35152310