Group #34182133 — subgroups

Subgroups — #34182133

Order 20224.

482 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 155 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23772424	C₂	1	1	yes	maximal, characteristic
2	#23764195	C₂	1	1	yes	maximal, characteristic
3	#23762152	C₂	1	2	yes	maximal, complemented
4	#23761238	C₂	1	2	yes	maximal, complemented
5	C₄×#100×C₇₉	C₂	1	1	yes	maximal, characteristic
6	D₄×C₇₉⋊C₈	—	2	2	no	—
7	D₄×C₇₉⋊C₈	—	2	2	no	—
8	#19098616	C₂²	1	2	yes	—
9	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
10	C₂×C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
11	C₂×C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
12	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
13	#19098316	—	2	2	no	—
14	#19098314	—	2	2	no	—
15	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
16	C₂×#100×C₇₉	C₄	1	1	yes	characteristic
17	C₂×#100×C₇₉	C₄	1	1	yes	characteristic
18	C₄×M₁₆×C₇₉	C₂²	1	2	yes	—
19	#343×C₇₉	C₄	1	2	yes	—
20	C₂²×C₇₉⋊C₈	—	2	1	no	—
21	C₂²×C₇₉⋊C₈	—	2	2	no	—
22	C₂²×C₇₉⋊C₈	—	2	2	no	—
23	C₂²×C₇₉⋊C₈	—	2	1	no	—
24	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
25	C₄⋊(C₇₉⋊C₈)	D₄	1	2	yes	—
26	C₄⋊(C₇₉⋊C₈)	D₄	1	2	yes	—
27	C₂²⋊(C₇₉⋊C₈)	—	2	4	no	—
28	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
29	C₂²⋊(C₇₉⋊C₈)	—	4	4	no	—
30	C₄×C₇₉⋊C₈	—	2	2	no	—
31	C₄×C₇₉⋊C₈	—	2	2	no	—
32	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₇₉	D₄	1	2	yes	—
34	C₂×M₁₆×C₇₉	C₂×C₄	1	2	yes	—
35	C₂×M₁₆×C₇₉	C₂×C₄	1	2	yes	—
36	C₄×D₄×C₇₉	—	2	2	no	—
37	C₄×D₄×C₇₉	—	2	2	no	—
38	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₂²⋊C₄×C₇₉	Q₈	1	2	yes	—
40	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
41	#100×C₇₉	—	2	2	no	—
42	#100×C₇₉	C₈	1	4	yes	complemented
43	#97×C₇₉	—	2	2	no	—
44	C₄×C₈×C₇₉	—	2	2	no	—
45	C₂×C₇₉⋊C₈	—	2	2	no	—
46	C₂×C₇₉⋊C₈	—	2	2	no	—
47	C₂×C₇₉⋊C₈	—	2	2	no	—
48	C₂×C₇₉⋊C₈	—	4	1	no	—
49	C₂×C₇₉⋊C₈	—	4	2	no	—
50	C₂×C₇₉⋊C₈	—	4	1	no	—
51	C₂×C₇₉⋊C₈	—	4	1	no	—
52	C₂×C₇₉⋊C₈	—	8	2	no	—
53	C₂×C₇₉⋊C₈	—	8	2	no	—
54	C₂⁴×C₇₉	C₄⋊C₄	1	2	yes	—
55	C₂×D₄×C₇₉	—	2	2	no	—
56	C₂×D₄×C₇₉	—	2	2	no	—
57	C₂×D₄×C₇₉	C₂×C₈	1	2	yes	—
58	C₂×D₄×C₇₉	M₁₆	1	2	yes	—
59	C₂²×C₄×C₇₉	—	2	2	no	—
60	C₂²×C₄×C₇₉	—	2	2	no	—
61	C₂²×C₄×C₇₉	—	4	2	no	—
62	C₂²×C₄×C₇₉	—	4	2	no	—
63	C₂²×C₄×C₇₉	C₄⋊C₄	1	2	yes	—
64	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
67	M₁₆×C₇₉	—	2	2	no	—
68	M₁₆×C₇₉	—	2	2	no	—
69	M₁₆×C₇₉	—	2	2	no	—
70	M₁₆×C₇₉	C₂×C₈	1	4	yes	complemented
71	C₂×C₈×C₇₉	—	2	2	no	—
72	C₂×C₈×C₇₉	—	2	2	no	—
73	C₄⋊C₄×C₇₉	—	2	2	no	—
74	C₂²⋊C₄×C₇₉	—	2	4	no	—
75	C₄²×C₇₉	C₂×D₄	1	2	yes	—
76	C₄²×C₇₉	#41	1	2	yes	—
77	C₂³×C₇₉	—	2	2	no	—
78	C₂³×C₇₉	—	2	2	no	—
79	C₂³×C₇₉	—	4	2	no	—
80	C₂³×C₇₉	—	4	2	no	—
81	C₂³×C₇₉	C₄⋊C₈	1	4	yes	—
82	C₂³×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
83	D₄×C₇₉	—	2	4	no	—
84	D₄×C₇₉	—	2	4	no	—
85	C₂×C₄×C₇₉	—	2	1	no	—
86	C₂×C₄×C₇₉	—	2	1	no	—
87	C₂×C₄×C₇₉	—	2	2	no	—
88	C₂×C₄×C₇₉	—	4	1	no	—
89	C₂×C₄×C₇₉	—	4	2	no	—
90	C₂×C₄×C₇₉	—	4	2	no	—
91	C₂×C₄×C₇₉	—	4	2	no	—
92	C₂×C₄×C₇₉	—	8	2	no	—
93	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
94	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
95	C₂×C₄×C₇₉	C₂²⋊Q₈	1	2	yes	—
96	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
97	C₂×C₄×C₇₉	C₂²×C₈	1	1	yes	characteristic
98	C₂×C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
99	C₂×C₄×C₇₉	#131	1	2	yes	—
100	C₈×C₇₉	—	2	4	no	—
101	C₈×C₇₉	—	4	2	no	—
102	C₇₉⋊C₈	—	4	2	no	—
103	C₇₉⋊C₈	—	4	2	no	—
104	C₇₉⋊C₈	—	4	2	no	—
105	C₇₉⋊C₈	—	8	1	no	—
106	C₂²×C₇₉	—	2	1	no	—
107	C₂²×C₇₉	—	2	1	no	—
108	C₂²×C₇₉	—	2	4	no	—
109	C₂²×C₇₉	—	4	4	no	—
110	C₂²×C₇₉	—	4	2	no	—
111	C₂²×C₇₉	—	4	2	no	—
112	C₂²×C₇₉	—	8	2	no	—
113	C₂²×C₇₉	#385	1	1	yes	characteristic
114	C₂²×C₇₉	C₂×C₄⋊C₈	1	1	yes	characteristic
115	C₂²×C₇₉	#424	1	1	yes	characteristic
116	C₄×C₇₉	—	2	1	no	—
117	C₄×C₇₉	—	2	2	no	—
118	C₄×C₇₉	—	4	2	no	—
119	C₄×C₇₉	C₈×D₄	1	2	yes	—
120	C₄×C₇₉	#435	1	2	yes	—
121	C₄×C₇₉	#453	1	1	yes	characteristic
122	C₄×C₇₉	#455	1	1	yes	characteristic
123	#8835	—	79	1	no	maximal, Sylow
124	C₂×C₇₉	—	2	1	no	—
125	C₂×C₇₉	—	2	1	no	—
126	C₂×C₇₉	—	4	4	no	—
127	C₂×C₇₉	#1850	1	1	yes	characteristic
128	C₂×C₇₉	#1856	1	1	yes	characteristic
129	C₂×C₇₉	#1858	1	1	yes	characteristic
130	#2972	—	79	1	no	—
131	#1954	—	79	1	no	—
132	C₄×#100	D₇₉	1	1	yes	characteristic
133	#1565	—	79	2	no	—
134	#1278	—	79	2	no	—
135	C₇₉	#8835	1	1	yes	characteristic, complemented, Sylow
136	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
137	C₈×D₄	—	158	2	no	—
138	C₈×D₄	—	158	2	no	—
139	#431	—	79	2	no	—
140	C₂×C₄⋊C₈	—	79	1	no	—
141	C₂×#100	Dic₇₉	1	1	yes	characteristic
142	C₂×#100	Dic₇₉	1	1	yes	characteristic
143	C₂×C₂²⋊C₈	—	158	2	no	—
144	C₂×C₂²⋊C₈	—	158	2	no	—
145	C₄×M₁₆	C₂×D₇₉	1	2	yes	—
146	C₂×C₄×C₈	—	79	1	no	—
147	#343	Dic₇₉	1	2	yes	—
148	#335	—	158	2	no	—
149	#334	—	158	2	no	—
150	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
151	C₂³×C₄	D₃₁₆	1	2	yes	—
152	C₂×M₁₆	C₂×Dic₇₉	1	2	yes	—
153	C₂×M₁₆	C₂×Dic₇₉	1	2	yes	—
154	C₂²×C₈	—	158	1	no	—
155	C₂²×C₈	—	158	1	no	—
156	C₂²×C₈	—	158	2	no	—
157	C₂²×C₈	—	158	2	no	—
158	C₄×D₄	—	2	2	no	—
159	C₄×D₄	—	2	2	no	—
160	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
161	C₂×C₂²⋊C₄	Dic₁₅₈	1	2	yes	—
162	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
163	C₄⋊C₈	—	79	2	no	—
164	C₄⋊C₈	—	79	2	no	—
165	C₄⋊C₈	—	158	2	no	—
166	#100	—	2	2	no	—
167	#100	C₇₉⋊C₈	1	4	yes	complemented
168	C₂²⋊C₈	—	316	4	no	—
169	C₂²⋊C₈	—	158	4	no	—
170	C₂²⋊C₈	—	158	2	no	—
171	#97	—	2	2	no	—
172	C₄×C₈	—	2	2	no	—
173	C₄×C₈	—	158	2	no	—
174	C₄×C₈	—	158	2	no	—
175	C₂⁴	C₄⋊Dic₇₉	1	2	yes	—
176	C₂×D₄	—	2	2	no	—
177	C₂×D₄	—	2	2	no	—
178	C₂×D₄	C₂×C₇₉⋊C₈	1	2	yes	—
179	C₂×D₄	#11929608	1	2	yes	—
180	C₂²×C₄	—	2	2	no	—
181	C₂²×C₄	—	2	2	no	—
182	C₂²×C₄	—	4	2	no	—
183	C₂²×C₄	—	4	2	no	—
184	C₂²×C₄	C₄⋊Dic₇₉	1	2	yes	—
185	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
186	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
187	C₂²×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
188	M₁₆	—	2	2	no	—
189	M₁₆	—	2	2	no	—
190	M₁₆	—	2	2	no	—
191	M₁₆	C₂×C₇₉⋊C₈	1	4	yes	complemented
192	C₂×C₈	—	2	2	no	—
193	C₂×C₈	—	2	2	no	—
194	C₂×C₈	—	316	1	no	—
195	C₂×C₈	—	316	1	no	—
196	C₂×C₈	—	316	2	no	—
197	C₂×C₈	—	316	1	no	—
198	C₂×C₈	—	632	2	no	—
199	C₂×C₈	—	632	2	no	—
200	C₂×C₈	—	158	2	no	—
201	C₂×C₈	—	158	2	no	—
202	C₂×C₈	—	158	2	no	—
203	C₄⋊C₄	—	2	2	no	—
204	C₂²⋊C₄	—	2	4	no	—
205	C₄²	D₄×D₇₉	1	2	yes	—
206	C₄²	#11929623	1	2	yes	—
207	C₂³	—	2	2	no	—
208	C₂³	—	2	2	no	—
209	C₂³	—	4	2	no	—
210	C₂³	—	4	2	no	—
211	C₂³	C₄⋊(C₇₉⋊C₈)	1	4	yes	—
212	C₂³	C₂×C₄⋊Dic₇₉	1	1	yes	characteristic
213	D₄	—	2	4	no	—
214	D₄	—	2	4	no	—
215	C₂×C₄	—	2	1	no	—
216	C₂×C₄	—	2	1	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	4	1	no	—
219	C₂×C₄	—	4	2	no	—
220	C₂×C₄	—	4	2	no	—
221	C₂×C₄	—	4	2	no	—
222	C₂×C₄	—	8	2	no	—
223	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
224	C₂×C₄	#14579131	1	1	yes	characteristic
225	C₂×C₄	#14579138	1	2	yes	—
226	C₂×C₄	#14579145	1	1	yes	characteristic
227	C₂×C₄	C₂²×C₇₉⋊C₈	1	1	yes	characteristic
228	C₂×C₄	C₂×#11929608	1	1	yes	characteristic
229	C₂×C₄	#14579168	1	2	yes	—
230	C₈	—	2	4	no	—
231	C₈	—	4	2	no	—
232	C₈	—	316	2	no	—
233	C₈	—	316	2	no	—
234	C₈	—	316	2	no	—
235	C₈	—	632	1	no	—
236	C₂²	—	2	1	no	—
237	C₂²	—	2	1	no	—
238	C₂²	—	2	4	no	—
239	C₂²	—	4	4	no	—
240	C₂²	—	4	2	no	—
241	C₂²	—	4	2	no	—
242	C₂²	—	8	2	no	—
243	C₂²	#19098438	1	1	yes	characteristic
244	C₂²	C₂×C₄⋊(C₇₉⋊C₈)	1	1	yes	characteristic
245	C₂²	#19098590	1	1	yes	characteristic
246	C₄	—	2	1	no	—
247	C₄	—	2	2	no	—
248	C₄	—	4	2	no	—
249	C₄	D₄×C₇₉⋊C₈	1	2	yes	—
250	C₄	#19098635	1	2	yes	—
251	C₄	#19098733	1	1	yes	characteristic
252	C₄	#19098743	1	1	yes	characteristic
253	C₂	—	2	1	no	—
254	C₂	—	2	1	no	—
255	C₂	—	4	4	no	—
256	C₂	#23763580	1	1	yes	characteristic
257	C₂	#23763612	1	1	yes	characteristic
258	C₂	#23763622	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23772424

C₂

yes

maximal, characteristic

#23764195

C₂

yes

maximal, characteristic

#23762152

C₂

yes

maximal, complemented

#23761238

C₂

yes

maximal, complemented

C₄×#100×C₇₉

C₂

yes

maximal, characteristic

D₄×C₇₉⋊C₈

—

D₄×C₇₉⋊C₈

—

#19098616

C₂²

yes

—

C₂×C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

C₂×C₂²⋊(C₇₉⋊C₈)

—

C₂×C₂²⋊(C₇₉⋊C₈)

—

C₂×C₄×C₇₉⋊C₈

C₂²

yes

characteristic

#19098316

—

#19098314

—

C₂×C₄×D₄×C₇₉

C₂²

yes

characteristic

C₂×#100×C₇₉

C₄

yes

characteristic

C₂×#100×C₇₉

C₄

yes

characteristic

C₄×M₁₆×C₇₉

C₂²

yes

—

#343×C₇₉

C₄

yes

—

C₂²×C₇₉⋊C₈

—

C₂²×C₇₉⋊C₈

—

C₂²×C₇₉⋊C₈

—

C₂²×C₇₉⋊C₈

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

D₄

yes

—

C₄⋊(C₇₉⋊C₈)

D₄

yes

—

C₂²⋊(C₇₉⋊C₈)

—

C₂²⋊(C₇₉⋊C₈)

—

C₂²⋊(C₇₉⋊C₈)

—

C₄×C₇₉⋊C₈

—

C₄×C₇₉⋊C₈

—

C₂²×D₄×C₇₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₇₉

D₄

yes

—

C₂×M₁₆×C₇₉

C₂×C₄

yes

—

C₂×M₁₆×C₇₉

C₂×C₄

yes

—

C₄×D₄×C₇₉

—

C₄×D₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

C₂×C₄

yes

characteristic

C₂×C₂²⋊C₄×C₇₉

Q₈

yes

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

#100×C₇₉

—

#100×C₇₉

C₈

yes

complemented

#97×C₇₉

—

C₄×C₈×C₇₉

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂⁴×C₇₉

C₄⋊C₄

yes

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

C₂×C₈

yes

—

C₂×D₄×C₇₉

M₁₆

yes

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₄⋊C₄

yes

—

C₂²×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×Q₈

yes

characteristic

M₁₆×C₇₉

—

M₁₆×C₇₉

—

M₁₆×C₇₉

—

M₁₆×C₇₉

C₂×C₈

yes

complemented

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₄⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

C₂×D₄

yes

—

C₄²×C₇₉

#41

yes

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

C₄⋊C₈

yes

—

C₂³×C₇₉

C₂×C₄⋊C₄

yes

characteristic

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₄×D₄

yes

—

C₂×C₄×C₇₉

#120

yes

characteristic

C₂×C₄×C₇₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₇₉

#123

yes

characteristic

C₂×C₄×C₇₉

C₂²×C₈

yes

characteristic

C₂×C₄×C₇₉

C₂×M₁₆

yes

characteristic

C₂×C₄×C₇₉

#131

yes

—

100

C₈×C₇₉

—

101

C₈×C₇₉

—

102

C₇₉⋊C₈

—

103

C₇₉⋊C₈

—

104

C₇₉⋊C₈

—

105

C₇₉⋊C₈

—

106

C₂²×C₇₉

—

107

C₂²×C₇₉

—

108

C₂²×C₇₉

—

109

C₂²×C₇₉

—

110

C₂²×C₇₉

—

111

C₂²×C₇₉

—

112

C₂²×C₇₉

—

113

C₂²×C₇₉

#385

yes

characteristic

114

C₂²×C₇₉

C₂×C₄⋊C₈

yes

characteristic

115

C₂²×C₇₉

#424

yes

characteristic

116

C₄×C₇₉

—

117

C₄×C₇₉

—

118

C₄×C₇₉

—

119

C₄×C₇₉

C₈×D₄

yes

—

120

C₄×C₇₉

#435

yes

—

121

C₄×C₇₉

#453

yes

characteristic

122

C₄×C₇₉

yes

123

—

124

C₂×C₇₉

—

125

C₂×C₇₉

—

126

C₂×C₇₉

—

127

C₂×C₇₉

#1850

yes

characteristic

128

C₂×C₇₉

#1856

yes

characteristic

129

C₂×C₇₉

#1858

yes

characteristic

130

#2972

—

131

#1954

—

132

C₄×#100

D₇₉

yes

characteristic

133

#1565

—

134

#1278

—

135

C₇₉

#8835

yes

characteristic, complemented, Sylow

136

C₂×C₄×D₄

C₂×D₇₉

yes

characteristic

137

C₈×D₄

—

158

—

138

C₈×D₄

—

158

—

139

#431

—

140

C₂×C₄⋊C₈

—

141

C₂×#100

Dic₇₉

yes

characteristic

142

C₂×#100

Dic₇₉

yes

characteristic

143

C₂×C₂²⋊C₈

—

158

—

144

C₂×C₂²⋊C₈

—

158

—

145

C₄×M₁₆

C₂×D₇₉

yes

—

146

C₂×C₄×C₈

—

147

#343

Dic₇₉

yes

—

148

#335

—

158

—

149

#334

—

158

—

150

C₂²×D₄

C₂×Dic₇₉

yes

characteristic

151

C₂³×C₄

D₃₁₆

yes

—

152

C₂×M₁₆

C₂×Dic₇₉

yes

—

153

C₂×M₁₆

C₂×Dic₇₉

yes

—

154

C₂²×C₈

—

158

—

155

C₂²×C₈

—

158

—

156

C₂²×C₈

—

158

—

157

C₂²×C₈

—

158

—

158

C₄×D₄

—

159

C₄×D₄

—

160

C₂×C₄⋊C₄

C₂×Dic₇₉

yes

characteristic

161

C₂×C₂²⋊C₄

Dic₁₅₈

yes

—

162

C₂×C₄²

C₂²×D₇₉

yes

characteristic

163

C₄⋊C₈

—

164

C₄⋊C₈

—

165

C₄⋊C₈

—

158

—

166

#100

—

167

#100

C₇₉⋊C₈

yes

complemented

168

C₂²⋊C₈

—

316

—

169

C₂²⋊C₈

—

158

—

170

C₂²⋊C₈

—

158

—

171

#97

—

172

C₄×C₈

—

173

C₄×C₈

—

158

—

174

C₄×C₈

—

158

—

175

C₂⁴

C₄⋊Dic₇₉

yes

—

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂×D₄

C₂×C₇₉⋊C₈

yes

—

179

C₂×D₄

#11929608

yes

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

C₄⋊Dic₇₉

yes

—

185

C₂²×C₄

C₂²×Dic₇₉

yes

characteristic

186

C₂²×C₄

C₂×D₃₁₆

yes

characteristic

187

C₂²×C₄

C₂×Dic₁₅₈

yes

characteristic

188

M₁₆

—

189

M₁₆

—

190

M₁₆

—

191

M₁₆

C₂×C₇₉⋊C₈

yes

complemented

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

316

—

195

C₂×C₈

—

316

—

196

C₂×C₈

—

316

—

197

C₂×C₈

—

316

—

198

C₂×C₈

—

632

—

199

C₂×C₈

—

632

—

200

C₂×C₈

—

158

—

201

C₂×C₈

—

158

—

202

C₂×C₈

—

158

—

203

C₄⋊C₄

—

204

C₂²⋊C₄

—

205

C₄²

D₄×D₇₉

yes

—

206

C₄²

#11929623

yes

—

207

C₂³

—

208

C₂³

—

209

C₂³

—

210

C₂³

—

211

C₂³

C₄⋊(C₇₉⋊C₈)

yes

—

212

C₂³

C₂×C₄⋊Dic₇₉

yes

characteristic

213

D₄

—

214

D₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

D₄×Dic₇₉

yes

—

224

C₂×C₄

#14579131

yes

characteristic

225

C₂×C₄

#14579138

yes

—

226

C₂×C₄

#14579145

yes

characteristic

227

C₂×C₄

C₂²×C₇₉⋊C₈

yes

characteristic

228

C₂×C₄

C₂×#11929608

yes

characteristic

229

C₂×C₄

#14579168

yes

—

230

C₈

—

231

C₈

—

232

C₈

—

316

—

233

C₈

—

316

—

234

C₈

—

316

—

235

C₈

—

632

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

242

C₂²

—

243

C₂²

#19098438

yes

characteristic

244

C₂²

C₂×C₄⋊(C₇₉⋊C₈)

yes

characteristic

245

C₂²

#19098590

yes

characteristic

246

C₄

—

247

C₄

—

248

C₄

—

249

C₄

D₄×C₇₉⋊C₈

yes

—

250

C₄

#19098635

yes

—

251

C₄

#19098733

yes

characteristic

252

C₄

#19098743

yes

characteristic

253

C₂

—

254

C₂

—

255

C₂

—

256

C₂

#23763580

yes

characteristic

257

C₂

#23763612

yes

characteristic

258

C₂

#23763622

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14579131
commutator	C₂×C₄×C₇₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₄×#100×C₇₉	C₂
socle	C₂²×C₇₉	#385
prime radical	C₂²×D₄×C₇₉	C₂×C₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	C₄×#100	D₇₉
hypocenter	C₇₉	#8835
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#100

subgroup

G/H

center

C₂×C₄

#14579131

commutator

C₂×C₄×C₇₉

C₂²×C₈

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₄×#100×C₇₉

C₂

socle

C₂²×C₇₉

#385

prime radical

C₂²×D₄×C₇₉

C₂×C₄

cosocle

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#100

N	H ≅ G/N	type
3. #23762152	C₂	semidirect
4. #23761238	C₂	semidirect
42. #100×C₇₉	C₈	semidirect
70. M₁₆×C₇₉	C₂×C₈	semidirect
135. C₇₉	#8835	semidirect
167. #100	C₇₉⋊C₈	semidirect
191. M₁₆	C₂×C₇₉⋊C₈	semidirect

H ≅ G/N

type

3. #23762152

C₂

semidirect

4. #23761238

C₂

semidirect

42. #100×C₇₉

C₈

semidirect

70. M₁₆×C₇₉

C₂×C₈

semidirect

135. C₇₉

#8835

semidirect

167. #100

C₇₉⋊C₈

semidirect

191. M₁₆

C₂×C₇₉⋊C₈

semidirect

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

subgroup	index
#23772424	2
#23764195	2
#23762152	2
#23761238	2
C₄×#100×C₇₉	2
#8835	79

subgroup

index

C₄×#100×C₇₉

Subgroups — #34182133

Conjugacy classes of subgroups

Complements

Maximal subgroups