Subgroups — C₂×#95×Dic₇₉ #34209337

Order 20224.

4462 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×Dic₇₉	C₂	1	3	yes	maximal
2	C₂²×C₇₉⋊#95	C₂	1	3	yes	maximal
3	#95×Dic₇₉	C₂	1	8	yes	maximal, direct product factor
4	C₂²×#95×C₇₉	C₂	1	1	yes	maximal, characteristic
5	C₂⁴×Dic₇₉	C₂²	1	3	yes	—
6	C₂⁴×Dic₇₉	C₂²	1	1	yes	characteristic
7	C₂²×C₄×Dic₇₉	—	2	24	no	—
8	C₂²×C₄×Dic₇₉	C₄	1	24	yes	complemented
9	C₂²×C₄×Dic₇₉	C₂²	1	12	yes	—
10	C₂×C₇₉⋊#95	C₄	1	24	yes	complemented
11	C₂×C₇₉⋊#95	C₂²	1	12	yes	—
12	C₂⁴×C₄×C₇₉	C₂²	1	3	yes	—
13	C₂×#95×C₇₉	C₄	1	8	yes	complemented
14	C₂×#95×C₇₉	C₂²	1	4	yes	—
15	C₂³×Dic₇₉	—	2	12	no	—
16	C₂³×Dic₇₉	—	2	6	no	—
17	C₂³×Dic₇₉	—	2	6	no	—
18	C₂³×Dic₇₉	C₂×C₄	1	24	yes	—
19	C₂³×Dic₇₉	C₂×C₄	1	12	yes	—
20	C₂³×Dic₇₉	C₂×C₄	1	12	yes	—
21	C₂³×Dic₇₉	D₄	1	12	yes	—
22	C₂³×Dic₇₉	Q₈	1	4	yes	—
23	C₂³×Dic₇₉	C₂³	1	6	yes	—
24	C₂³×Dic₇₉	C₂³	1	2	yes	—
25	C₂×C₄×Dic₇₉	—	2	96	no	—
26	C₂×C₄×Dic₇₉	—	2	48	no	—
27	C₂×C₄×Dic₇₉	C₂×C₄	1	48	yes	complemented
28	C₇₉⋊#95	C₂×C₄	1	48	yes	complemented
29	C₂⁵×C₇₉	C₂³	1	1	yes	characteristic
30	C₂³×C₄×C₇₉	—	2	12	no	—
31	C₂³×C₄×C₇₉	—	2	12	no	—
32	C₂³×C₄×C₇₉	C₂×C₄	1	12	yes	—
33	C₂³×C₄×C₇₉	C₂×C₄	1	12	yes	—
34	C₂³×C₄×C₇₉	C₂×C₄	1	12	yes	—
35	C₂³×C₄×C₇₉	C₂³	1	6	yes	—
36	#95×C₇₉	C₂×C₄	1	16	yes	complemented
37	C₂²×Dic₇₉	—	2	24	no	—
38	C₂²×Dic₇₉	—	2	24	no	—
39	C₂²×Dic₇₉	—	2	48	no	—
40	C₂²×Dic₇₉	—	2	48	no	—
41	C₂²×Dic₇₉	—	2	12	no	—
42	C₂²×Dic₇₉	—	2	6	no	—
43	C₂²×Dic₇₉	—	2	6	no	—
44	C₂²×Dic₇₉	C₄²	1	16	yes	—
45	C₂²×Dic₇₉	C₄²	1	48	yes	complemented
46	C₂²×Dic₇₉	C₂²⋊C₄	1	48	yes	—
47	C₂²×Dic₇₉	C₄⋊C₄	1	48	yes	—
48	C₂²×Dic₇₉	C₂²×C₄	1	24	yes	—
49	C₂²×Dic₇₉	C₂²×C₄	1	12	yes	—
50	C₂²×Dic₇₉	C₂²×C₄	1	12	yes	—
51	C₂²×Dic₇₉	C₂×D₄	1	12	yes	—
52	C₂²×Dic₇₉	C₂×Q₈	1	4	yes	—
53	C₄×Dic₇₉	—	2	96	no	—
54	C₂⁴×C₇₉	C₂²×C₄	1	6	yes	—
55	C₂⁴×C₇₉	C₂²×C₄	1	6	yes	—
56	C₂⁴×C₇₉	C₂²×C₄	1	2	yes	—
57	C₂⁴×C₇₉	C₂×D₄	1	6	yes	—
58	C₂⁴×C₇₉	C₂×Q₈	1	2	yes	—
59	C₂⁴×C₇₉	#41	1	6	yes	—
60	C₂⁴×C₇₉	#41	1	2	yes	—
61	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
62	C₂²×C₄×C₇₉	—	2	24	no	—
63	C₂²×C₄×C₇₉	—	2	24	no	—
64	C₂²×C₄×C₇₉	—	2	48	no	—
65	C₂²×C₄×C₇₉	—	2	48	no	—
66	C₂²×C₄×C₇₉	—	2	12	no	—
67	C₂²×C₄×C₇₉	—	2	12	no	—
68	C₂²×C₄×C₇₉	C₄²	1	48	yes	complemented
69	C₂²×C₄×C₇₉	C₂²×C₄	1	12	yes	—
70	C₂²×C₄×C₇₉	C₂²×C₄	1	12	yes	—
71	C₂²×C₄×C₇₉	C₂²×C₄	1	12	yes	—
72	C₂³×C₇₉	C₂×C₄²	1	4	yes	—
73	C₂³×C₇₉	C₂×C₄²	1	12	yes	—
74	C₂³×C₇₉	C₂×C₄²	1	12	yes	—
75	C₂³×C₇₉	C₂×C₂²⋊C₄	1	12	yes	—
76	C₂³×C₇₉	C₂×C₄⋊C₄	1	12	yes	—
77	C₂³×C₇₉	#117	1	12	yes	—
78	C₂³×C₇₉	#117	1	12	yes	—
79	C₂³×C₇₉	C₄×D₄	1	24	yes	—
80	C₂³×C₇₉	C₄×D₄	1	12	yes	—
81	C₂³×C₇₉	C₄×D₄	1	12	yes	—
82	C₂³×C₇₉	C₄×Q₈	1	12	yes	—
83	C₂³×C₇₉	C₄×Q₈	1	4	yes	—
84	C₂³×C₇₉	C₂³×C₄	1	3	yes	—
85	C₂³×C₇₉	C₂³×C₄	1	3	yes	—
86	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
87	C₂³×C₇₉	C₂²×D₄	1	3	yes	—
88	C₂³×C₇₉	C₂²×Q₈	1	1	yes	characteristic
89	C₂³×C₇₉	C₂×#41	1	3	yes	—
90	C₂³×C₇₉	C₂×#41	1	1	yes	characteristic
91	C₂×C₄×C₇₉	—	2	12	no	—
92	C₂×C₄×C₇₉	—	2	12	no	—
93	C₂×C₄×C₇₉	—	2	24	no	—
94	C₂×C₄×C₇₉	—	2	24	no	—
95	C₂×C₄×C₇₉	—	2	96	no	—
96	C₂×C₄×C₇₉	C₂×C₄²	1	24	yes	complemented
97	C₂×Dic₇₉	—	2	12	no	—
98	C₂×Dic₇₉	—	2	12	no	—
99	C₂×Dic₇₉	—	2	24	no	—
100	C₂×Dic₇₉	—	2	24	no	—
101	C₂×Dic₇₉	—	2	96	no	—
102	C₂×Dic₇₉	#95	1	64	yes	direct product factor
103	C₂×Dic₇₉	C₂×C₄²	1	8	yes	—
104	C₂×Dic₇₉	C₂×C₄²	1	24	yes	complemented
105	C₂×Dic₇₉	C₂×C₂²⋊C₄	1	24	yes	—
106	C₂×Dic₇₉	C₂×C₄⋊C₄	1	24	yes	—
107	C₂²×C₇₉	C₄³	1	8	yes	—
108	C₂²×C₇₉	C₂×#95	1	8	yes	—
109	C₂²×C₇₉	#376	1	8	yes	—
110	C₂²×C₇₉	C₄×C₂²⋊C₄	1	24	yes	—
111	C₂²×C₇₉	C₄×C₂²⋊C₄	1	24	yes	—
112	C₂²×C₇₉	C₄×C₄⋊C₄	1	24	yes	—
113	C₂²×C₇₉	C₄×C₄⋊C₄	1	24	yes	—
114	C₂²×C₇₉	C₂²×C₄²	1	1	yes	characteristic
115	C₂²×C₇₉	C₂²×C₄²	1	3	yes	—
116	C₂²×C₇₉	C₂²×C₄²	1	3	yes	—
117	C₂²×C₇₉	C₂²×C₂²⋊C₄	1	3	yes	—
118	C₂²×C₇₉	C₂²×C₄⋊C₄	1	3	yes	—
119	C₂²×C₇₉	C₂×#117	1	3	yes	—
120	C₂²×C₇₉	C₂×#117	1	3	yes	—
121	C₂²×C₇₉	C₂×C₄×D₄	1	6	yes	—
122	C₂²×C₇₉	C₂×C₄×D₄	1	3	yes	—
123	C₂²×C₇₉	C₂×C₄×D₄	1	3	yes	—
124	C₂²×C₇₉	C₂×C₄×Q₈	1	3	yes	—
125	C₂²×C₇₉	C₂×C₄×Q₈	1	1	yes	characteristic
126	C₄×C₇₉	—	2	24	no	—
127	Dic₇₉	—	2	24	no	—
128	Dic₇₉	C₂×#95	1	16	yes	direct product factor
129	C₂×C₄×#95	—	79	1	no	maximal, Sylow
130	C₂×C₇₉	C₄×#95	1	16	yes	complemented
131	C₂×C₇₉	C₂×C₄³	1	1	yes	characteristic
132	C₂×C₇₉	C₂²×#95	1	1	yes	characteristic
133	C₂×C₇₉	C₂×#376	1	1	yes	characteristic
134	C₂×C₇₉	C₂×C₄×C₂²⋊C₄	1	3	yes	—
135	C₂×C₇₉	C₂×C₄×C₂²⋊C₄	1	3	yes	—
136	C₂×C₇₉	C₂×C₄×C₄⋊C₄	1	3	yes	—
137	C₂×C₇₉	C₂×C₄×C₄⋊C₄	1	3	yes	—
138	C₂³×C₄²	—	79	3	no	—
139	C₂²×#95	—	79	3	no	—
140	C₂²×#95	D₇₉	1	1	yes	characteristic
141	C₄×#95	—	79	8	no	—
142	C₇₉	C₂×C₄×#95	1	1	yes	characteristic, complemented, Sylow
143	C₂⁴×C₄	—	79	1	no	—
144	C₂⁴×C₄	—	79	3	no	—
145	C₂⁴×C₄	C₂×D₇₉	1	3	yes	—
146	C₂²×C₄²	—	79	12	no	—
147	C₂²×C₄²	—	79	24	no	—
148	C₂²×C₄²	—	158	24	no	—
149	C₂×#95	—	79	12	no	—
150	C₂×#95	—	79	24	no	—
151	C₂×#95	Dic₇₉	1	8	yes	direct product factor
152	C₂×#95	C₂×D₇₉	1	4	yes	—
153	C₂⁵	C₂²×D₇₉	1	1	yes	characteristic
154	C₂³×C₄	—	2	12	no	—
155	C₂³×C₄	—	2	12	no	—
156	C₂³×C₄	—	79	12	no	—
157	C₂³×C₄	—	79	12	no	—
158	C₂³×C₄	—	79	4	no	—
159	C₂³×C₄	—	79	2	no	—
160	C₂³×C₄	—	79	24	no	—
161	C₂³×C₄	—	79	12	no	—
162	C₂³×C₄	—	79	6	no	—
163	C₂³×C₄	—	158	12	no	—
164	C₂³×C₄	—	158	6	no	—
165	C₂³×C₄	—	158	6	no	—
166	C₂³×C₄	C₄×D₇₉	1	12	yes	—
167	C₂³×C₄	C₄×D₇₉	1	12	yes	—
168	C₂³×C₄	C₂×Dic₇₉	1	12	yes	—
169	C₂³×C₄	C₂²×D₇₉	1	6	yes	—
170	C₂×C₄²	—	79	48	no	—
171	C₂×C₄²	—	158	96	no	—
172	C₂×C₄²	—	158	48	no	—
173	#95	—	79	48	no	—
174	#95	C₂×Dic₇₉	1	16	yes	direct product factor
175	C₂⁴	C₂×C₄×D₇₉	1	6	yes	—
176	C₂⁴	C₂×C₄×D₇₉	1	6	yes	—
177	C₂⁴	C₂²×Dic₇₉	1	2	yes	—
178	C₂⁴	D₄×D₇₉	1	6	yes	—
179	C₂⁴	Q₈×D₇₉	1	2	yes	—
180	C₂⁴	#11929623	1	6	yes	—
181	C₂⁴	#11929625	1	2	yes	—
182	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
183	C₂²×C₄	—	2	12	no	—
184	C₂²×C₄	—	2	24	no	—
185	C₂²×C₄	—	2	24	no	—
186	C₂²×C₄	—	2	48	no	—
187	C₂²×C₄	—	2	48	no	—
188	C₂²×C₄	—	2	12	no	—
189	C₂²×C₄	—	79	4	no	—
190	C₂²×C₄	—	79	16	no	—
191	C₂²×C₄	—	79	48	no	—
192	C₂²×C₄	—	79	48	no	—
193	C₂²×C₄	—	79	12	no	—
194	C₂²×C₄	—	79	12	no	—
195	C₂²×C₄	—	79	48	no	—
196	C₂²×C₄	—	79	24	no	—
197	C₂²×C₄	—	79	12	no	—
198	C₂²×C₄	—	158	6	no	—
199	C₂²×C₄	—	158	6	no	—
200	C₂²×C₄	—	158	24	no	—
201	C₂²×C₄	—	158	24	no	—
202	C₂²×C₄	—	158	48	no	—
203	C₂²×C₄	—	158	48	no	—
204	C₂²×C₄	—	158	12	no	—
205	C₂²×C₄	C₄×Dic₇₉	1	48	yes	complemented
206	C₂²×C₄	C₂×C₄×D₇₉	1	12	yes	—
207	C₂²×C₄	C₂×C₄×D₇₉	1	12	yes	—
208	C₂²×C₄	C₂²×Dic₇₉	1	12	yes	—
209	C₄²	—	158	96	no	—
210	C₂³	C₄²×D₇₉	1	4	yes	—
211	C₂³	C₄²×D₇₉	1	12	yes	—
212	C₂³	C₂×C₄×Dic₇₉	1	12	yes	—
213	C₂³	C₂²⋊C₄×D₇₉	1	12	yes	—
214	C₂³	C₄⋊C₄×D₇₉	1	12	yes	—
215	C₂³	#14579117	1	12	yes	—
216	C₂³	#14579119	1	12	yes	—
217	C₂³	(C₂²⋊D₇₉)⋊C₄	1	24	yes	—
218	C₂³	#14579123	1	12	yes	—
219	C₂³	D₄×Dic₇₉	1	12	yes	—
220	C₂³	#14579126	1	12	yes	—
221	C₂³	Q₈×Dic₇₉	1	4	yes	—
222	C₂³	C₂²×C₄×D₇₉	1	3	yes	—
223	C₂³	C₂²×C₄×D₇₉	1	3	yes	—
224	C₂³	C₂³×Dic₇₉	1	1	yes	characteristic
225	C₂³	C₂×D₄×D₇₉	1	3	yes	—
226	C₂³	C₂×Q₈×D₇₉	1	1	yes	characteristic
227	C₂³	C₂×#11929623	1	3	yes	—
228	C₂³	C₂×#11929625	1	1	yes	characteristic
229	C₂×C₄	—	2	96	no	—
230	C₂×C₄	—	2	12	no	—
231	C₂×C₄	—	2	12	no	—
232	C₂×C₄	—	2	24	no	—
233	C₂×C₄	—	2	24	no	—
234	C₂×C₄	—	79	64	no	—
235	C₂×C₄	—	79	8	no	—
236	C₂×C₄	—	79	24	no	—
237	C₂×C₄	—	79	24	no	—
238	C₂×C₄	—	79	24	no	—
239	C₂×C₄	—	158	96	no	—
240	C₂×C₄	—	158	12	no	—
241	C₂×C₄	—	158	12	no	—
242	C₂×C₄	—	158	24	no	—
243	C₂×C₄	—	158	24	no	—
244	C₂×C₄	C₂×C₄×Dic₇₉	1	24	yes	complemented
245	C₂²	C₄²×Dic₇₉	1	8	yes	—
246	C₂²	#95×D₇₉	1	8	yes	—
247	C₂²	#19098408	1	8	yes	—
248	C₂²	#19098410	1	24	yes	—
249	C₂²	C₂²⋊C₄×Dic₇₉	1	24	yes	—
250	C₂²	#19098414	1	24	yes	—
251	C₂²	C₄⋊C₄×Dic₇₉	1	24	yes	—
252	C₂²	C₂×C₄²×D₇₉	1	1	yes	characteristic
253	C₂²	C₂×C₄²×D₇₉	1	3	yes	—
254	C₂²	C₂²×C₄×Dic₇₉	1	3	yes	—
255	C₂²	C₂×C₂²⋊C₄×D₇₉	1	3	yes	—
256	C₂²	C₂×C₄⋊C₄×D₇₉	1	3	yes	—
257	C₂²	C₂×#14579117	1	3	yes	—
258	C₂²	C₂×#14579119	1	3	yes	—
259	C₂²	C₂×(C₂²⋊D₇₉)⋊C₄	1	6	yes	—
260	C₂²	C₂×#14579123	1	3	yes	—
261	C₂²	C₂×D₄×Dic₇₉	1	3	yes	—
262	C₂²	C₂×#14579126	1	3	yes	—
263	C₂²	C₂×Q₈×Dic₇₉	1	1	yes	characteristic
264	C₄	—	2	24	no	—
265	C₄	—	79	16	no	—
266	C₄	—	158	24	no	—
267	C₂	#95×Dic₇₉	1	16	yes	direct product factor
268	C₂	C₂×C₄²×Dic₇₉	1	1	yes	characteristic
269	C₂	C₂×#95×D₇₉	1	1	yes	characteristic
270	C₂	C₂×#19098408	1	1	yes	characteristic
271	C₂	C₂×#19098410	1	3	yes	—
272	C₂	C₂×C₂²⋊C₄×Dic₇₉	1	3	yes	—
273	C₂	C₂×#19098414	1	3	yes	—
274	C₂	C₂×C₄⋊C₄×Dic₇₉	1	3	yes	—

	subgroup	G/H
center	C₂⁵	C₂²×D₇₉
commutator	C₂×C₇₉	C₂×C₄³
Frattini	C₂⁴	C₂³×D₇₉
Fitting	C₂²×#95×C₇₉	C₂
socle, prime radical	C₂⁵×C₇₉	C₂³
cosocle	C₂⁴×C₇₉	C₂⁴
hypercenter	C₂²×#95	D₇₉
hypocenter	C₇₉	C₂×C₄×#95
LCS	G ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂⁵ ◁ C₂²×#95

Complements

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

N	H ≅ G/N	type
3. #95×Dic₇₉	C₂	direct (N × H)
8. C₂²×C₄×Dic₇₉	C₄	semidirect
10. C₂×C₇₉⋊#95	C₄	semidirect
13. C₂×#95×C₇₉	C₄	semidirect
27. C₂×C₄×Dic₇₉	C₂×C₄	semidirect
28. C₇₉⋊#95	C₂×C₄	semidirect
36. #95×C₇₉	C₂×C₄	semidirect
45. C₂²×Dic₇₉	C₄²	semidirect
68. C₂²×C₄×C₇₉	C₄²	semidirect
96. C₂×C₄×C₇₉	C₂×C₄²	semidirect
102. C₂×Dic₇₉	#95	direct (N × H)
104. C₂×Dic₇₉	C₂×C₄²	semidirect
128. Dic₇₉	C₂×#95	direct (N × H)
130. C₂×C₇₉	C₄×#95	semidirect
142. C₇₉	C₂×C₄×#95	semidirect
151. C₂×#95	Dic₇₉	direct (N × H)
174. #95	C₂×Dic₇₉	direct (N × H)
205. C₂²×C₄	C₄×Dic₇₉	semidirect
244. C₂×C₄	C₂×C₄×Dic₇₉	semidirect
267. C₂	#95×Dic₇₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄×Dic₇₉	2
C₂²×C₇₉⋊#95	2
#95×Dic₇₉	2
C₂²×#95×C₇₉	2
C₂×C₄×#95	79

Subgroups — C2×#95×Dic79 #34209337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#95×Dic₇₉ #34209337