Group #23764716 — subgroups

Subgroups — #23764716

Order 10112.

324 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 85 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	C₂²×#11929612	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#14579086	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098468	C₂	1	1	yes	maximal, characteristic, complemented
5	#19098466	C₂	1	1	yes	maximal, characteristic
6	#19098325	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#102×C₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₁₅₈	C₂²	1	1	yes	characteristic
9	C₂×#11929612	—	2	2	no	—
10	C₂×#11929612	—	2	2	no	—
11	C₂×#11929612	—	2	2	no	—
12	C₂²×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Dic₇₉	—	2	1	no	—
15	C₂×C₂²⋊Dic₇₉	—	2	1	no	—
16	C₂×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
17	Dic₇₉⋊C₈	—	2	2	no	—
18	#14579086	—	2	2	no	—
19	C₇₉⋊#95	—	2	1	no	—
20	C₇₉⋊#95	—	2	1	no	—
21	C₂²×D₄×C₇₉	C₂²	1	1	yes	characteristic
22	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
24	#102×C₇₉	—	2	2	no	—
25	C₂×Dic₁₅₈	—	2	1	no	—
26	C₂×Dic₁₅₈	—	2	1	no	—
27	C₂×Dic₁₅₈	—	2	1	no	—
28	C₂×Dic₁₅₈	—	2	1	no	—
29	C₂×Dic₁₅₈	—	2	1	no	—
30	C₂×Dic₁₅₈	D₄	1	2	yes	—
31	C₂²×Dic₇₉	—	2	1	no	—
32	C₂²×Dic₇₉	—	2	1	no	—
33	C₂²×Dic₇₉	D₄	1	1	yes	characteristic
34	C₂²×Dic₇₉	D₄	1	1	yes	characteristic
35	#11929612	—	2	8	no	—
36	C₂×C₇₉⋊C₈	—	2	1	no	—
37	C₂×C₇₉⋊C₈	—	2	1	no	—
38	C₂×C₇₉⋊C₈	D₄	1	2	yes	—
39	C₄⋊Dic₇₉	—	2	1	no	—
40	C₄⋊Dic₇₉	—	2	1	no	—
41	C₂²⋊Dic₇₉	—	4	2	no	—
42	C₂²⋊Dic₇₉	—	4	2	no	—
43	C₄×Dic₇₉	—	2	1	no	—
44	C₄×Dic₇₉	—	2	1	no	—
45	C₂⁴×C₇₉	—	2	1	no	—
46	C₂×D₄×C₇₉	—	2	1	no	—
47	C₂×D₄×C₇₉	—	2	1	no	—
48	C₂×D₄×C₇₉	—	2	1	no	—
49	C₂×D₄×C₇₉	—	2	1	no	—
50	C₂×D₄×C₇₉	—	2	1	no	—
51	C₂×D₄×C₇₉	D₄	1	2	yes	—
52	C₂²×C₄×C₇₉	—	2	1	no	—
53	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
54	C₂×C₈×C₇₉	—	2	1	no	—
55	C₂×C₈×C₇₉	—	2	1	no	—
56	C₂×C₈×C₇₉	—	2	1	no	—
57	C₄⋊C₄×C₇₉	—	2	1	no	—
58	C₄⋊C₄×C₇₉	—	2	1	no	—
59	C₂³×C₇₉	—	2	2	no	—
60	C₂³×C₇₉	—	4	1	no	—
61	C₂³×C₇₉	—	4	1	no	—
62	C₂³×C₇₉	—	4	1	no	—
63	C₂³×C₇₉	—	4	1	no	—
64	C₂³×C₇₉	—	4	1	no	—
65	C₂³×C₇₉	—	4	1	no	—
66	C₂³×C₇₉	C₂×D₄	1	1	yes	characteristic
67	D₄×C₇₉	—	2	2	no	—
68	D₄×C₇₉	—	2	2	no	—
69	D₄×C₇₉	—	4	1	no	—
70	D₄×C₇₉	—	4	1	no	—
71	C₂×C₄×C₇₉	—	4	1	no	—
72	C₂×C₄×C₇₉	—	4	1	no	—
73	C₂×C₄×C₇₉	—	4	1	no	—
74	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
75	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
76	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
77	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
78	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
79	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
80	C₂×Dic₇₉	—	2	1	no	—
81	C₂×Dic₇₉	—	2	1	no	—
82	C₂×Dic₇₉	—	2	1	no	—
83	C₂×Dic₇₉	—	2	2	no	—
84	C₂×Dic₇₉	—	2	1	no	—
85	C₂×Dic₇₉	—	2	1	no	—
86	C₂×Dic₇₉	—	4	1	no	—
87	C₂×Dic₇₉	—	4	1	no	—
88	C₂×Dic₇₉	—	4	1	no	—
89	C₂×Dic₇₉	—	4	1	no	—
90	C₂×Dic₇₉	—	4	1	no	—
91	C₂×Dic₇₉	SD₁₆	1	2	yes	complemented
92	Dic₁₅₈	—	2	2	no	—
93	Dic₁₅₈	—	2	2	no	—
94	Dic₁₅₈	—	4	1	no	—
95	Dic₁₅₈	—	4	1	no	—
96	C₈×C₇₉	—	4	1	no	—
97	C₇₉⋊C₈	—	2	2	no	—
98	C₂²×C₇₉	—	4	2	no	—
99	C₂²×C₇₉	—	4	2	no	—
100	C₂²×C₇₉	—	4	2	no	—
101	C₂²×C₇₉	—	8	1	no	—
102	C₂²×C₇₉	—	8	1	no	—
103	C₂²×C₇₉	—	8	1	no	—
104	C₂²×C₇₉	—	8	1	no	—
105	C₂²×C₇₉	#121	1	1	yes	characteristic
106	C₂²×C₇₉	#121	1	1	yes	characteristic
107	C₂²×C₇₉	#121	1	1	yes	characteristic
108	C₂²×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
109	C₂²×C₇₉	#135	1	1	yes	characteristic
110	C₂²×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
111	C₂²×C₇₉	#137	1	1	yes	characteristic
112	C₄×C₇₉	—	8	1	no	—
113	C₄×C₇₉	#120	1	1	yes	characteristic
114	C₄×C₇₉	#123	1	1	yes	characteristic
115	C₄×C₇₉	#123	1	1	yes	characteristic
116	C₄×C₇₉	#124	1	1	yes	characteristic
117	Dic₇₉	—	2	2	no	—
118	Dic₇₉	—	4	2	no	—
119	Dic₇₉	—	4	1	no	—
120	Dic₇₉	—	8	1	no	—
121	C₂×C₇₉	—	8	2	no	—
122	C₂×C₇₉	#394	1	1	yes	characteristic
123	C₂×C₇₉	#460	1	1	yes	characteristic
124	C₂×C₇₉	#461	1	1	yes	characteristic
125	C₂×C₇₉	#463	1	1	yes	characteristic
126	C₂×C₇₉	#464	1	1	yes	characteristic
127	C₂×C₇₉	#465	1	1	yes	characteristic
128	C₂×C₇₉	#468	1	1	yes	characteristic
129	#2055	—	79	1	no	maximal, Sylow
130	C₇₉	#2055	1	1	yes	characteristic, complemented, Sylow
131	C₂²×SD₁₆	—	79	1	no	—
132	C₂×C₄⋊C₈	—	79	1	no	—
133	C₂×#103	—	79	1	no	—
134	C₂×#102	D₇₉	1	1	yes	characteristic
135	#391	—	79	1	no	—
136	#390	—	79	1	no	—
137	#340	—	79	1	no	—
138	C₂²×Q₈	—	79	1	no	—
139	C₂²×D₄	C₂×D₇₉	1	1	yes	characteristic
140	C₂×SD₁₆	—	158	2	no	—
141	C₂×SD₁₆	—	158	2	no	—
142	C₂×SD₁₆	—	158	2	no	—
143	C₂²×C₈	—	79	1	no	—
144	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
145	C₂×C₄⋊C₄	—	79	1	no	—
146	C₂×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
147	C₂×C₂²⋊C₄	—	158	1	no	—
148	C₂×C₂²⋊C₄	—	158	1	no	—
149	C₂×C₄²	—	79	1	no	—
150	C₄⋊C₈	—	158	2	no	—
151	#103	—	158	2	no	—
152	#102	—	2	2	no	—
153	#95	—	158	1	no	—
154	#95	—	158	1	no	—
155	C₂⁴	—	2	1	no	—
156	C₂×Q₈	—	79	2	no	—
157	C₂×Q₈	—	158	1	no	—
158	C₂×Q₈	—	158	1	no	—
159	C₂×Q₈	—	158	1	no	—
160	C₂×Q₈	—	158	1	no	—
161	C₂×Q₈	—	158	1	no	—
162	C₂×D₄	—	2	1	no	—
163	C₂×D₄	—	2	1	no	—
164	C₂×D₄	—	2	1	no	—
165	C₂×D₄	—	2	1	no	—
166	C₂×D₄	—	2	1	no	—
167	C₂×D₄	C₂²⋊D₇₉	1	2	yes	—
168	C₂²×C₄	—	2	1	no	—
169	C₂²×C₄	—	79	1	no	—
170	C₂²×C₄	—	79	1	no	—
171	C₂²×C₄	—	158	1	no	—
172	C₂²×C₄	—	158	1	no	—
173	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
174	SD₁₆	—	158	8	no	—
175	C₂×C₈	—	2	1	no	—
176	C₂×C₈	—	2	1	no	—
177	C₂×C₈	—	2	1	no	—
178	C₂×C₈	—	79	2	no	—
179	C₂×C₈	—	158	1	no	—
180	C₂×C₈	—	158	1	no	—
181	C₄⋊C₄	—	2	1	no	—
182	C₄⋊C₄	—	2	1	no	—
183	C₄⋊C₄	—	158	1	no	—
184	C₄⋊C₄	—	158	1	no	—
185	C₂²⋊C₄	—	316	2	no	—
186	C₂²⋊C₄	—	316	2	no	—
187	C₄²	—	158	1	no	—
188	C₄²	—	158	1	no	—
189	C₂³	—	2	2	no	—
190	C₂³	—	4	1	no	—
191	C₂³	—	4	1	no	—
192	C₂³	—	4	1	no	—
193	C₂³	—	4	1	no	—
194	C₂³	—	4	1	no	—
195	C₂³	—	4	1	no	—
196	C₂³	D₄×D₇₉	1	1	yes	characteristic
197	Q₈	—	316	1	no	—
198	Q₈	—	316	1	no	—
199	Q₈	—	158	2	no	—
200	Q₈	—	158	2	no	—
201	D₄	—	2	2	no	—
202	D₄	—	2	2	no	—
203	D₄	—	4	1	no	—
204	D₄	—	4	1	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	4	1	no	—
208	C₂×C₄	—	316	1	no	—
209	C₂×C₄	—	316	1	no	—
210	C₂×C₄	—	316	1	no	—
211	C₂×C₄	—	316	1	no	—
212	C₂×C₄	—	316	1	no	—
213	C₂×C₄	—	79	2	no	—
214	C₂×C₄	—	158	1	no	—
215	C₂×C₄	—	158	2	no	—
216	C₂×C₄	—	158	1	no	—
217	C₂×C₄	—	158	1	no	—
218	C₂×C₄	—	158	1	no	—
219	C₂×C₄	—	158	1	no	—
220	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
221	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
222	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
223	C₂×C₄	#11929623	1	1	yes	characteristic
224	C₂×C₄	#11929624	1	1	yes	characteristic
225	C₂×C₄	#11929624	1	1	yes	characteristic
226	C₈	—	4	1	no	—
227	C₈	—	158	2	no	—
228	C₂²	—	4	2	no	—
229	C₂²	—	4	2	no	—
230	C₂²	—	4	2	no	—
231	C₂²	—	8	1	no	—
232	C₂²	—	8	1	no	—
233	C₂²	—	8	1	no	—
234	C₂²	—	8	1	no	—
235	C₂²	#14579133	1	1	yes	characteristic
236	C₂²	#14579134	1	1	yes	characteristic
237	C₂²	#14579134	1	1	yes	characteristic
238	C₂²	SD₁₆×D₇₉	1	1	yes	characteristic
239	C₂²	#14579180	1	1	yes	characteristic
240	C₂²	#14579185	1	1	yes	characteristic
241	C₂²	#14579190	1	1	yes	characteristic
242	C₄	—	8	1	no	—
243	C₄	—	316	2	no	—
244	C₄	—	316	1	no	—
245	C₄	—	632	1	no	—
246	C₄	—	158	2	no	—
247	C₄	#14579129	1	1	yes	characteristic
248	C₄	#14579143	1	1	yes	characteristic
249	C₄	#14579144	1	1	yes	characteristic
250	C₄	#14579147	1	1	yes	characteristic
251	C₂	—	8	2	no	—
252	C₂	#19098478	1	1	yes	characteristic
253	C₂	#19098762	1	1	yes	characteristic
254	C₂	#19098766	1	1	yes	characteristic
255	C₂	#19098776	1	1	yes	characteristic
256	C₂	#19098784	1	1	yes	characteristic
257	C₂	#19098791	1	1	yes	characteristic
258	C₂	#19098808	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#11929612

C₂

yes

maximal, characteristic

C₂×Dic₇₉⋊C₈

C₂

yes

maximal, characteristic, complemented

C₂×#14579086

C₂

yes

maximal, characteristic, complemented

#19098468

C₂

yes

maximal, characteristic, complemented

#19098466

C₂

yes

maximal, characteristic

#19098325

C₂

yes

maximal, characteristic, complemented

C₂×#102×C₇₉

C₂

yes

maximal, characteristic

C₂²×Dic₁₅₈

C₂²

yes

—

—

—

C₂²×C₇₉⋊C₈

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₉

C₂²

yes

characteristic

C₂×C₂²⋊Dic₇₉

—

C₂×C₂²⋊Dic₇₉

—

C₂×C₄×Dic₇₉

C₂²

yes

characteristic

Dic₇₉⋊C₈

—

#14579086

—

C₇₉⋊#95

—

C₇₉⋊#95

—

C₂²×D₄×C₇₉

C₂²

yes

characteristic

C₂²×C₈×C₇₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₉

C₂²

yes

characteristic

#102×C₇₉

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

D₄

yes

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

D₄

yes

characteristic

C₂²×Dic₇₉

D₄

yes

characteristic

#11929612

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

D₄

yes

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂²⋊Dic₇₉

—

C₂²⋊Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂⁴×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

D₄

yes

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

C₂×D₄

yes

characteristic

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

SD₁₆

yes

complemented

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

100

C₂²×C₇₉

—

101

C₂²×C₇₉

—

102

C₂²×C₇₉

—

103

C₂²×C₇₉

—

104

C₂²×C₇₉

—

105

C₂²×C₇₉

#121

yes

characteristic

106

C₂²×C₇₉

#121

yes

characteristic

107

C₂²×C₇₉

#121

yes

characteristic

108

C₂²×C₇₉

C₂×SD₁₆

yes

characteristic

109

C₂²×C₇₉

#135

yes

characteristic

110

C₂²×C₇₉

AGL(1,ℤ/8)

yes

characteristic

111

C₂²×C₇₉

#137

yes

characteristic

112

C₄×C₇₉

—

113

C₄×C₇₉

#120

yes

characteristic

114

C₄×C₇₉

#123

yes

characteristic

115

C₄×C₇₉

#123

yes

characteristic

116

C₄×C₇₉

#124

yes

characteristic

117

Dic₇₉

—

118

Dic₇₉

—

119

Dic₇₉

—

120

Dic₇₉

—

121

C₂×C₇₉

—

122

C₂×C₇₉

#394

yes

characteristic

123

C₂×C₇₉

#460

yes

characteristic

124

C₂×C₇₉

#461

yes

characteristic

125

C₂×C₇₉

#463

yes

characteristic

126

C₂×C₇₉

#464

yes

characteristic

127

C₂×C₇₉

#465

yes

characteristic

128

C₂×C₇₉

yes

129

—

130

C₇₉

#2055

yes

characteristic, complemented, Sylow

131

C₂²×SD₁₆

—

132

C₂×C₄⋊C₈

—

133

C₂×#103

—

134

C₂×#102

D₇₉

yes

characteristic

135

#391

—

136

#390

—

137

#340

—

138

C₂²×Q₈

—

139

C₂²×D₄

C₂×D₇₉

yes

characteristic

140

C₂×SD₁₆

—

158

—

141

C₂×SD₁₆

—

158

—

142

C₂×SD₁₆

—

158

—

143

C₂²×C₈

—

144

C₂²×C₈

C₂×D₇₉

yes

characteristic

145

C₂×C₄⋊C₄

—

146

C₂×C₄⋊C₄

C₂×D₇₉

yes

characteristic

147

C₂×C₂²⋊C₄

—

158

—

148

C₂×C₂²⋊C₄

—

158

—

149

C₂×C₄²

—

150

C₄⋊C₈

—

158

—

151

#103

—

158

—

152

#102

—

153

#95

—

158

—

154

#95

—

158

—

155

C₂⁴

—

156

C₂×Q₈

—

157

C₂×Q₈

—

158

—

158

C₂×Q₈

—

158

—

159

C₂×Q₈

—

158

—

160

C₂×Q₈

—

158

—

161

C₂×Q₈

—

158

—

162

C₂×D₄

—

163

C₂×D₄

—

164

C₂×D₄

—

165

C₂×D₄

—

166

C₂×D₄

—

167

C₂×D₄

C₂²⋊D₇₉

yes

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

—

158

—

172

C₂²×C₄

—

158

—

173

C₂²×C₄

C₂²×D₇₉

yes

characteristic

174

SD₁₆

—

158

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

158

—

180

C₂×C₈

—

158

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

158

—

184

C₄⋊C₄

—

158

—

185

C₂²⋊C₄

—

316

—

186

C₂²⋊C₄

—

316

—

187

C₄²

—

158

—

188

C₄²

—

158

—

189

C₂³

—

190

C₂³

—

191

C₂³

—

192

C₂³

—

193

C₂³

—

194

C₂³

—

195

C₂³

—

196

C₂³

D₄×D₇₉

yes

characteristic

197

Q₈

—

316

—

198

Q₈

—

316

—

199

Q₈

—

158

—

200

Q₈

—

158

—

201

D₄

—

202

D₄

—

203

D₄

—

204

D₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

316

—

209

C₂×C₄

—

316

—

210

C₂×C₄

—

316

—

211

C₂×C₄

—

316

—

212

C₂×C₄

—

316

—

213

C₂×C₄

—

214

C₂×C₄

—

158

—

215

C₂×C₄

—

158

—

216

C₂×C₄

—

158

—

217

C₂×C₄

—

158

—

218

C₂×C₄

—

158

—

219

C₂×C₄

—

158

—

220

C₂×C₄

D₄×D₇₉

yes

characteristic

221

C₂×C₄

D₄×D₇₉

yes

characteristic

222

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

223

C₂×C₄

#11929623

yes

characteristic

224

C₂×C₄

#11929624

yes

characteristic

225

C₂×C₄

#11929624

yes

characteristic

226

C₈

—

227

C₈

—

158

—

228

C₂²

—

229

C₂²

—

230

C₂²

—

231

C₂²

—

232

C₂²

—

233

C₂²

—

234

C₂²

—

235

C₂²

#14579133

yes

characteristic

236

C₂²

#14579134

yes

characteristic

237

C₂²

#14579134

yes

characteristic

238

C₂²

SD₁₆×D₇₉

yes

characteristic

239

C₂²

#14579180

yes

characteristic

240

C₂²

#14579185

yes

characteristic

241

C₂²

#14579190

yes

characteristic

242

C₄

—

243

C₄

—

316

—

244

C₄

—

316

—

245

C₄

—

632

—

246

C₄

—

158

—

247

C₄

#14579129

yes

characteristic

248

C₄

#14579143

yes

characteristic

249

C₄

#14579144

yes

characteristic

250

C₄

#14579147

yes

characteristic

251

C₂

—

252

C₂

#19098478

yes

characteristic

253

C₂

#19098762

yes

characteristic

254

C₂

#19098766

yes

characteristic

255

C₂

#19098776

yes

characteristic

256

C₂

#19098784

yes

characteristic

257

C₂

#19098791

yes

characteristic

258

C₂

#19098808

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₇₉
commutator, cosocle	C₂²×C₄×C₇₉	C₂³
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	C₂×#102×C₇₉	C₂
socle	C₂³×C₇₉	C₂×D₄
prime radical	C₂²×D₄×C₇₉	C₂²
hypercenter	C₂×#102	D₇₉
hypocenter	C₇₉	#2055
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#102

subgroup

G/H

center

C₂³

D₄×D₇₉

commutator, cosocle

C₂²×C₄×C₇₉

C₂³

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

C₂×#102×C₇₉

C₂

socle

C₂³×C₇₉

C₂×D₄

prime radical

C₂²×D₄×C₇₉

C₂²

D₇₉

C₇₉

G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#102

N	H ≅ G/N	type
2. C₂×Dic₇₉⋊C₈	C₂	semidirect
3. C₂×#14579086	C₂	semidirect
4. #19098468	C₂	semidirect
6. #19098325	C₂	semidirect
91. C₂×Dic₇₉	SD₁₆	semidirect
130. C₇₉	#2055	semidirect

H ≅ G/N

type

2. C₂×Dic₇₉⋊C₈

C₂

semidirect

3. C₂×#14579086

C₂

semidirect

4. #19098468

C₂

semidirect

6. #19098325

C₂

semidirect

91. C₂×Dic₇₉

SD₁₆

semidirect

130. C₇₉

#2055

semidirect

Subgroups — #23764716

Conjugacy classes of subgroups

Complements