Group #34190887 — subgroups

Subgroups — #34190887

Order 20224.

562 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 139 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	C₂×#19098850	C₂	1	2	yes	maximal
2	#23764194	C₂	1	1	yes	maximal, characteristic
3	C₂×#19098312	C₂	1	2	yes	maximal, complemented
4	#23761235	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#500×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₃₁₆	C₂²	1	1	yes	characteristic
7	#19098850	—	2	4	no	—
8	#19098850	—	2	4	no	—
9	C₂×#14579092	—	2	2	no	—
10	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
12	C₂×#14579081	—	2	2	no	—
13	C₂×(C₂×D₇₉)⋊C₈	—	2	2	no	—
14	#19098312	—	2	4	no	—
15	C₂×C₄⋊Q₈×C₇₉	C₂²	1	2	yes	—
16	#500×C₇₉	—	2	4	no	—
17	C₂×#107×C₇₉	—	2	2	no	—
18	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
19	C₂²×D₃₁₆	D₄	1	1	yes	characteristic
20	C₂²×C₄×D₇₉	—	2	1	no	—
21	C₂²×C₇₉⋊C₈	—	2	2	no	—
22	C₂²×C₇₉⋊C₈	—	2	1	no	—
23	C₄×D₃₁₆	—	2	2	no	—
24	C₄×D₃₁₆	—	2	2	no	—
25	C₂×C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
26	C₂×(C₂×D₇₉)⋊C₄	—	2	1	no	—
27	#14579092	—	2	8	no	—
28	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
29	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
30	C₄⋊(C₇₉⋊C₈)	D₄	1	4	yes	—
31	#14579081	—	2	8	no	—
32	(C₂×D₇₉)⋊C₈	—	4	4	no	—
33	C₂²×Q₈×C₇₉	—	2	2	no	—
34	C₂²×C₈×C₇₉	D₄	1	2	yes	—
35	C₄⋊Q₈×C₇₉	—	2	2	no	—
36	C₄⋊Q₈×C₇₉	—	2	2	no	—
37	C₄⋊Q₈×C₇₉	—	2	2	no	—
38	C₄⋊Q₈×C₇₉	D₄	1	4	yes	—
39	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
40	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
41	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
42	#107×C₇₉	—	2	8	no	—
43	C₄×C₈×C₇₉	—	2	2	no	—
44	C₂³×D₇₉	—	2	1	no	—
45	C₂×D₃₁₆	—	2	2	no	—
46	C₂×D₃₁₆	—	2	1	no	—
47	C₂×D₃₁₆	—	2	2	no	—
48	C₂×D₃₁₆	Q₁₆	1	2	yes	—
49	C₂²×Dic₇₉	—	2	1	no	—
50	C₂×C₄×D₇₉	—	4	1	no	—
51	C₂×C₄×D₇₉	—	4	1	no	—
52	C₂×C₄×D₇₉	—	4	2	no	—
53	C₂×C₄×D₇₉	—	4	2	no	—
54	C₂×C₇₉⋊C₈	—	2	4	no	—
55	C₂×C₇₉⋊C₈	—	4	1	no	—
56	C₂×C₇₉⋊C₈	—	4	2	no	—
57	C₂×C₇₉⋊C₈	—	4	2	no	—
58	C₂×C₇₉⋊C₈	—	4	2	no	—
59	C₄⋊Dic₇₉	—	2	2	no	—
60	(C₂×D₇₉)⋊C₄	—	4	2	no	—
61	C₂×Q₈×C₇₉	—	2	4	no	—
62	C₂×Q₈×C₇₉	—	4	2	no	—
63	C₂×Q₈×C₇₉	—	8	4	no	—
64	C₂²×C₄×C₇₉	—	4	2	no	—
65	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
68	C₂×C₈×C₇₉	—	2	2	no	—
69	C₂×C₈×C₇₉	—	2	2	no	—
70	C₂×C₈×C₇₉	SD₁₆	1	4	yes	—
71	C₄⋊C₄×C₇₉	—	2	4	no	—
72	C₄⋊C₄×C₇₉	—	2	4	no	—
73	C₄⋊C₄×C₇₉	—	4	2	no	—
74	C₄⋊C₄×C₇₉	—	4	2	no	—
75	C₄²×C₇₉	C₂×D₄	1	2	yes	—
76	C₄²×C₇₉	C₂×D₄	1	2	yes	—
77	C₂³×C₇₉	#121	1	1	yes	characteristic
78	C₂²×D₇₉	—	2	2	no	—
79	C₂²×D₇₉	—	4	1	no	—
80	C₂²×D₇₉	—	4	2	no	—
81	C₂²×D₇₉	—	4	1	no	—
82	C₂²×D₇₉	—	4	2	no	—
83	Q₈×C₇₉	—	8	4	no	—
84	Q₈×C₇₉	—	8	4	no	—
85	C₂×C₄×C₇₉	—	2	2	no	—
86	C₂×C₄×C₇₉	—	4	4	no	—
87	C₂×C₄×C₇₉	—	8	4	no	—
88	C₂×C₄×C₇₉	#120	1	2	yes	—
89	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
90	C₂×C₄×C₇₉	#121	1	2	yes	—
91	C₂×C₄×C₇₉	#127	1	1	yes	characteristic
92	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
93	C₂×C₄×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
94	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
95	C₂×C₄×C₇₉	#137	1	2	yes	—
96	C₂×C₄×C₇₉	#137	1	2	yes	—
97	C₂×Dic₇₉	—	4	1	no	—
98	C₂×Dic₇₉	—	4	2	no	—
99	D₃₁₆	—	2	4	no	—
100	D₃₁₆	—	4	2	no	—
101	C₄×D₇₉	—	8	2	no	—
102	C₄×D₇₉	—	8	1	no	—
103	C₄×D₇₉	—	8	1	no	—
104	C₈×C₇₉	—	2	4	no	—
105	C₇₉⋊C₈	—	4	4	no	—
106	C₇₉⋊C₈	—	8	1	no	—
107	C₂²×C₇₉	#392	1	1	yes	characteristic
108	C₂²×C₇₉	#461	1	2	yes	—
109	C₂²×C₇₉	#467	1	1	yes	characteristic
110	C₂²×C₇₉	#470	1	1	yes	characteristic
111	C₂²×C₇₉	#472	1	2	yes	—
112	C₂×D₇₉	—	4	4	no	—
113	C₂×D₇₉	—	4	2	no	—
114	C₂×D₇₉	—	8	2	no	—
115	C₂×D₇₉	—	8	1	no	—
116	C₂×D₇₉	—	8	1	no	—
117	C₄×C₇₉	—	2	2	no	—
118	C₄×C₇₉	—	8	4	no	—
119	C₄×C₇₉	#448	1	2	yes	—
120	C₄×C₇₉	#451	1	2	yes	—
121	C₄×C₇₉	#452	1	2	yes	—
122	C₄×C₇₉	#492	1	1	yes	characteristic
123	C₄×C₇₉	#497	1	1	yes	characteristic
124	Dic₇₉	—	8	1	no	—
125	#10278	—	79	1	no	maximal, Sylow
126	C₂×C₇₉	#1675	1	2	yes	—
127	C₂×C₇₉	#1695	1	2	yes	—
128	C₂×C₇₉	#2001	1	1	yes	characteristic
129	C₂×C₇₉	#2013	1	1	yes	characteristic
130	C₂×C₇₉	#2018	1	1	yes	characteristic
131	D₇₉	—	8	2	no	—
132	C₂×#500	D₇₉	1	1	yes	characteristic, complemented
133	C₂×#476	—	79	2	no	—
134	#1954	—	79	1	no	—
135	C₂×#333	—	79	2	no	—
136	#1277	—	79	1	no	—
137	C₇₉	#10278	1	1	yes	characteristic, complemented, Sylow
138	C₂×C₄⋊Q₈	C₂×D₇₉	1	2	yes	—
139	C₂×C₄×D₄	—	79	1	no	—
140	#500	—	2	4	no	—
141	#476	—	158	4	no	—
142	#476	—	158	4	no	—
143	C₂×#107	—	2	2	no	—
144	C₂×#106	—	158	2	no	—
145	C₂×C₄⋊C₈	—	79	2	no	—
146	C₂×C₄⋊C₈	—	79	1	no	—
147	C₂×#102	—	158	2	no	—
148	C₂×C₂²⋊C₈	—	158	2	no	—
149	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
150	#333	—	158	4	no	—
151	C₂²×Q₈	—	2	2	no	—
152	C₂²×D₄	—	79	1	no	—
153	C₂³×C₄	—	158	1	no	—
154	C₂²×C₈	—	158	1	no	—
155	C₂²×C₈	—	158	2	no	—
156	C₂²×C₈	C₂²⋊D₇₉	1	2	yes	—
157	C₄⋊Q₈	—	2	2	no	—
158	C₄⋊Q₈	—	2	2	no	—
159	C₄⋊Q₈	—	2	2	no	—
160	C₄⋊Q₈	C₂²⋊D₇₉	1	4	yes	—
161	C₄×D₄	—	158	2	no	—
162	C₄×D₄	—	158	2	no	—
163	C₂×C₄⋊C₄	—	2	2	no	—
164	C₂×C₄⋊C₄	—	2	2	no	—
165	C₂×C₄⋊C₄	—	79	1	no	—
166	C₂×C₂²⋊C₄	—	158	1	no	—
167	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
168	#107	—	2	8	no	—
169	#106	—	158	8	no	—
170	C₄⋊C₈	—	79	4	no	—
171	C₄⋊C₈	—	158	2	no	—
172	C₄⋊C₈	—	158	2	no	—
173	#102	—	158	8	no	—
174	C₂²⋊C₈	—	316	4	no	—
175	C₄×C₈	—	2	2	no	—
176	C₂⁴	—	158	1	no	—
177	C₂×Q₈	—	2	4	no	—
178	C₂×Q₈	—	4	2	no	—
179	C₂×Q₈	—	8	4	no	—
180	C₂×D₄	—	79	2	no	—
181	C₂×D₄	—	158	2	no	—
182	C₂×D₄	—	158	1	no	—
183	C₂×D₄	—	158	2	no	—
184	C₂²×C₄	—	4	2	no	—
185	C₂²×C₄	—	316	1	no	—
186	C₂²×C₄	—	316	1	no	—
187	C₂²×C₄	—	316	2	no	—
188	C₂²×C₄	—	316	2	no	—
189	C₂²×C₄	—	158	1	no	—
190	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
191	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
192	C₂²×C₄	#11929623	1	1	yes	characteristic
193	C₂×C₈	—	2	2	no	—
194	C₂×C₈	—	2	2	no	—
195	C₂×C₈	—	316	2	no	—
196	C₂×C₈	—	316	2	no	—
197	C₂×C₈	—	316	1	no	—
198	C₂×C₈	—	316	2	no	—
199	C₂×C₈	—	158	4	no	—
200	C₂×C₈	#11929611	1	4	yes	—
201	C₄⋊C₄	—	2	4	no	—
202	C₄⋊C₄	—	2	4	no	—
203	C₄⋊C₄	—	4	2	no	—
204	C₄⋊C₄	—	4	2	no	—
205	C₄⋊C₄	—	158	2	no	—
206	C₂²⋊C₄	—	316	2	no	—
207	C₄²	D₄×D₇₉	1	2	yes	—
208	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
209	C₂³	—	316	1	no	—
210	C₂³	—	316	2	no	—
211	C₂³	—	316	1	no	—
212	C₂³	—	316	2	no	—
213	C₂³	—	158	2	no	—
214	C₂³	#14579132	1	1	yes	characteristic
215	Q₈	—	8	4	no	—
216	Q₈	—	8	4	no	—
217	D₄	—	316	2	no	—
218	D₄	—	158	4	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	4	4	no	—
221	C₂×C₄	—	8	4	no	—
222	C₂×C₄	—	316	1	no	—
223	C₂×C₄	—	316	2	no	—
224	C₂×C₄	—	632	1	no	—
225	C₂×C₄	—	632	1	no	—
226	C₂×C₄	—	632	2	no	—
227	C₂×C₄	#14579129	1	2	yes	—
228	C₂×C₄	#14579130	1	1	yes	characteristic
229	C₂×C₄	#14579133	1	2	yes	—
230	C₂×C₄	#14579157	1	1	yes	characteristic
231	C₂×C₄	C₂×#11929611	1	2	yes	—
232	C₂×C₄	Q₁₆×D₇₉	1	1	yes	characteristic
233	C₂×C₄	#14579184	1	1	yes	characteristic
234	C₂×C₄	#14579192	1	2	yes	—
235	C₂×C₄	#14579193	1	2	yes	—
236	C₈	—	2	4	no	—
237	C₈	—	316	4	no	—
238	C₈	—	632	1	no	—
239	C₂²	—	316	4	no	—
240	C₂²	—	316	2	no	—
241	C₂²	—	632	1	no	—
242	C₂²	—	632	1	no	—
243	C₂²	—	632	2	no	—
244	C₂²	#19098471	1	1	yes	characteristic
245	C₂²	#19098765	1	2	yes	—
246	C₂²	#19098801	1	1	yes	characteristic
247	C₂²	#19098818	1	1	yes	characteristic
248	C₂²	#19098830	1	2	yes	—
249	C₄	—	2	2	no	—
250	C₄	—	8	4	no	—
251	C₄	—	632	1	no	—
252	C₄	#19098702	1	2	yes	—
253	C₄	#19098717	1	2	yes	—
254	C₄	#19098724	1	2	yes	—
255	C₄	#19098937	1	1	yes	characteristic
256	C₄	#19098955	1	1	yes	characteristic
257	C₂	—	632	2	no	—
258	C₂	#23762796	1	2	yes	—
259	C₂	#23762920	1	2	yes	—
260	C₂	#23764407	1	1	yes	characteristic
261	C₂	#23764483	1	1	yes	characteristic
262	C₂	#23764507	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19098850

C₂

yes

maximal

#23764194

C₂

yes

maximal, characteristic

C₂×#19098312

C₂

yes

maximal, complemented

#23761235

C₂

yes

maximal, characteristic, complemented

C₂×#500×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×C₄×D₃₁₆

C₂²

yes

—

—

—

C₂×C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

C₂×C₄⋊(C₇₉⋊C₈)

C₂²

yes

—

C₂×#14579081

—

C₂×(C₂×D₇₉)⋊C₈

—

#19098312

—

C₂×C₄⋊Q₈×C₇₉

C₂²

yes

—

#500×C₇₉

—

C₂×#107×C₇₉

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂²×D₃₁₆

D₄

yes

characteristic

C₂²×C₄×D₇₉

—

C₂²×C₇₉⋊C₈

—

C₂²×C₇₉⋊C₈

—

C₄×D₃₁₆

—

C₄×D₃₁₆

—

C₂×C₄⋊Dic₇₉

D₄

yes

characteristic

C₂×(C₂×D₇₉)⋊C₄

—

#14579092

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

D₄

yes

—

#14579081

—

(C₂×D₇₉)⋊C₈

—

C₂²×Q₈×C₇₉

—

C₂²×C₈×C₇₉

D₄

yes

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

D₄

yes

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

#107×C₇₉

—

C₄×C₈×C₇₉

—

C₂³×D₇₉

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

Q₁₆

yes

—

C₂²×Dic₇₉

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

(C₂×D₇₉)⋊C₄

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

#41

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

SD₁₆

yes

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

C₂×D₄

yes

—

C₄²×C₇₉

C₂×D₄

yes

—

C₂³×C₇₉

#121

yes

characteristic

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂²×D₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

#120

yes

—

C₂×C₄×C₇₉

#120

yes

characteristic

C₂×C₄×C₇₉

#121

yes

—

C₂×C₄×C₇₉

#127

yes

characteristic

C₂×C₄×C₇₉

C₂×SD₁₆

yes

—

C₂×C₄×C₇₉

C₂×Q₁₆

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

—

C₂×C₄×C₇₉

#137

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

D₃₁₆

—

100

D₃₁₆

—

101

C₄×D₇₉

—

102

C₄×D₇₉

—

103

C₄×D₇₉

—

104

C₈×C₇₉

—

105

C₇₉⋊C₈

—

106

C₇₉⋊C₈

—

107

C₂²×C₇₉

#392

yes

characteristic

108

C₂²×C₇₉

#461

yes

—

109

C₂²×C₇₉

#467

yes

characteristic

110

C₂²×C₇₉

#470

yes

characteristic

111

C₂²×C₇₉

#472

yes

—

112

C₂×D₇₉

—

113

C₂×D₇₉

—

114

C₂×D₇₉

—

115

C₂×D₇₉

—

116

C₂×D₇₉

—

117

C₄×C₇₉

—

118

C₄×C₇₉

—

119

C₄×C₇₉

#448

yes

—

120

C₄×C₇₉

#451

yes

—

121

C₄×C₇₉

#452

yes

—

122

C₄×C₇₉

#492

yes

characteristic

123

C₄×C₇₉

#497

yes

characteristic

124

Dic₇₉

—

125

#10278

—

maximal, Sylow

126

C₂×C₇₉

#1675

yes

—

127

C₂×C₇₉

#1695

yes

—

128

C₂×C₇₉

#2001

yes

characteristic

129

C₂×C₇₉

#2013

yes

characteristic

130

C₂×C₇₉

#2018

yes

characteristic

131

D₇₉

—

132

C₂×#500

D₇₉

yes

characteristic, complemented

133

C₂×#476

—

134

#1954

—

135

C₂×#333

—

136

#1277

—

137

C₇₉

#10278

yes

characteristic, complemented, Sylow

138

C₂×C₄⋊Q₈

C₂×D₇₉

yes

—

139

C₂×C₄×D₄

—

140

#500

—

141

#476

—

158

—

142

#476

—

158

—

143

C₂×#107

—

144

C₂×#106

—

158

—

145

C₂×C₄⋊C₈

—

146

C₂×C₄⋊C₈

—

147

C₂×#102

—

158

—

148

C₂×C₂²⋊C₈

—

158

—

149

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

150

#333

—

158

—

151

C₂²×Q₈

—

152

C₂²×D₄

—

153

C₂³×C₄

—

158

—

154

C₂²×C₈

—

158

—

155

C₂²×C₈

—

158

—

156

C₂²×C₈

C₂²⋊D₇₉

yes

—

157

C₄⋊Q₈

—

158

C₄⋊Q₈

—

159

C₄⋊Q₈

—

160

C₄⋊Q₈

C₂²⋊D₇₉

yes

—

161

C₄×D₄

—

158

—

162

C₄×D₄

—

158

—

163

C₂×C₄⋊C₄

—

164

C₂×C₄⋊C₄

—

165

C₂×C₄⋊C₄

—

166

C₂×C₂²⋊C₄

—

158

—

167

C₂×C₄²

C₂²×D₇₉

yes

characteristic

168

#107

—

169

#106

—

158

—

170

C₄⋊C₈

—

171

C₄⋊C₈

—

158

—

172

C₄⋊C₈

—

158

—

173

#102

—

158

—

174

C₂²⋊C₈

—

316

—

175

C₄×C₈

—

176

C₂⁴

—

158

—

177

C₂×Q₈

—

178

C₂×Q₈

—

179

C₂×Q₈

—

180

C₂×D₄

—

181

C₂×D₄

—

158

—

182

C₂×D₄

—

158

—

183

C₂×D₄

—

158

—

184

C₂²×C₄

—

185

C₂²×C₄

—

316

—

186

C₂²×C₄

—

316

—

187

C₂²×C₄

—

316

—

188

C₂²×C₄

—

316

—

189

C₂²×C₄

—

158

—

190

C₂²×C₄

D₄×D₇₉

yes

characteristic

191

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

192

C₂²×C₄

#11929623

yes

characteristic

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

316

—

196

C₂×C₈

—

316

—

197

C₂×C₈

—

316

—

198

C₂×C₈

—

316

—

199

C₂×C₈

—

158

—

200

C₂×C₈

#11929611

yes

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

158

—

206

C₂²⋊C₄

—

316

—

207

C₄²

D₄×D₇₉

yes

—

208

C₄²

C₂×C₂²⋊D₇₉

yes

—

209

C₂³

—

316

—

210

C₂³

—

316

—

211

C₂³

—

316

—

212

C₂³

—

316

—

213

C₂³

—

158

—

214

C₂³

#14579132

yes

characteristic

215

Q₈

—

216

Q₈

—

217

D₄

—

316

—

218

D₄

—

158

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

316

—

223

C₂×C₄

—

316

—

224

C₂×C₄

—

632

—

225

C₂×C₄

—

632

—

226

C₂×C₄

—

632

—

227

C₂×C₄

#14579129

yes

—

228

C₂×C₄

#14579130

yes

characteristic

229

C₂×C₄

#14579133

yes

—

230

C₂×C₄

#14579157

yes

characteristic

231

C₂×C₄

C₂×#11929611

yes

—

232

C₂×C₄

Q₁₆×D₇₉

yes

characteristic

233

C₂×C₄

#14579184

yes

characteristic

234

C₂×C₄

#14579192

yes

—

235

C₂×C₄

#14579193

yes

—

236

C₈

—

237

C₈

—

316

—

238

C₈

—

632

—

239

C₂²

—

316

—

240

C₂²

—

316

—

241

C₂²

—

632

—

242

C₂²

—

632

—

243

C₂²

—

632

—

244

C₂²

#19098471

yes

characteristic

245

C₂²

#19098765

yes

—

246

C₂²

#19098801

yes

characteristic

247

C₂²

#19098818

yes

characteristic

248

C₂²

#19098830

yes

—

249

C₄

—

250

C₄

—

251

C₄

—

632

—

252

C₄

#19098702

yes

—

253

C₄

#19098717

yes

—

254

C₄

#19098724

yes

—

255

C₄

#19098937

yes

characteristic

256

C₄

#19098955

yes

characteristic

257

C₂

—

632

—

258

C₂

#23762796

yes

—

259

C₂

#23762920

yes

—

260

C₂

#23764407

yes

characteristic

261

C₂

#23764483

yes

characteristic

262

C₂

#23764507

yes

characteristic

	subgroup	G/H
center	C₂³	#14579132
commutator, cosocle	C₂×C₄²×C₇₉	C₂³
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₂×#500×C₇₉	C₂
socle	C₂³×C₇₉	#121
prime radical	C₂²×D₃₁₆	D₄
hypercenter	C₂×#500	D₇₉
hypocenter	C₇₉	#10278
LCS	G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#500

subgroup

G/H

center

C₂³

#14579132

commutator, cosocle

C₂×C₄²×C₇₉

C₂³

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₂×#500×C₇₉

C₂

socle

C₂³×C₇₉

#121

prime radical

C₂²×D₃₁₆

D₄

D₇₉

C₇₉

G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#500

N	H ≅ G/N	type
3. C₂×#19098312	C₂	semidirect
4. #23761235	C₂	semidirect
5. C₂×#500×C₇₉	C₂	semidirect
132. C₂×#500	D₇₉	semidirect
137. C₇₉	#10278	semidirect

H ≅ G/N

type

3. C₂×#19098312

C₂

semidirect

4. #23761235

C₂

semidirect

5. C₂×#500×C₇₉

C₂

semidirect

132. C₂×#500

D₇₉

semidirect

137. C₇₉

#10278

semidirect

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

subgroup	index
C₂×#19098850	2
#23764194	2
C₂×#19098312	2
#23761235	2
C₂×#500×C₇₉	2
#10278	79

subgroup

index

C₂×#500×C₇₉

Subgroups — #34190887

Conjugacy classes of subgroups

Complements

Maximal subgroups