Group #23774581 — subgroups

Subgroups — #23774581

Order 10112.

332 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 121 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	#19099120	C₂	1	1	yes	maximal, characteristic, complemented
2	#19099097	C₂	1	1	yes	maximal, characteristic
3	#19098965	C₂	1	2	yes	maximal, complemented
4	#19098918	C₂	1	2	yes	maximal, complemented
5	#19098905	C₂	1	2	yes	maximal, complemented
6	#19098888	C₂	1	2	yes	maximal
7	#19098859	C₂	1	1	yes	maximal, characteristic, complemented
8	#19098854	C₂	1	1	yes	maximal, characteristic, complemented
9	#19098849	C₂	1	1	yes	maximal, characteristic, complemented
10	#19098844	C₂	1	1	yes	maximal, characteristic, complemented
11	#431×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#14579161	C₂²	1	1	yes	characteristic
13	#14579161	C₂²	1	1	yes	characteristic
14	#14579155	—	2	1	no	—
15	#14579153	C₂²	1	2	yes	—
16	#14579153	C₂²	1	1	yes	characteristic
17	#14579149	C₂²	1	1	yes	characteristic
18	#14579144	—	2	1	no	—
19	#14579140	—	2	1	no	—
20	#14579140	—	2	1	no	—
21	#14579140	C₂²	1	1	yes	characteristic
22	#14579135	C₂²	1	1	yes	characteristic
23	C₄×Dic₁₅₈	—	2	1	no	—
24	C₄×Dic₁₅₈	—	2	1	no	—
25	C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
26	C₄×D₃₁₆	C₂²	1	1	yes	characteristic
27	C₄×C₂²⋊D₇₉	—	2	1	no	—
28	#14579120	C₂²	1	2	yes	—
29	#14579118	—	2	1	no	—
30	#14579095	C₂²	1	2	yes	—
31	#14579095	C₂²	1	2	yes	—
32	#14579093	C₂²	1	2	yes	—
33	#14579093	C₂²	1	2	yes	—
34	#14579086	C₂²	1	2	yes	—
35	#14579086	C₂²	1	2	yes	—
36	#14579083	C₂²	1	2	yes	—
37	#14579083	C₂²	1	2	yes	—
38	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
39	C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
40	C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
41	C₂²⋊C₈×C₇₉	C₂²	1	2	yes	—
42	C₄×C₈×C₇₉	C₂²	1	2	yes	—
43	C₂×Dic₁₅₈	—	2	1	no	—
44	C₂×Dic₁₅₈	—	2	1	no	—
45	C₂×Dic₁₅₈	C₂³	1	1	yes	characteristic
46	C₂×D₃₁₆	C₂³	1	1	yes	characteristic
47	C₂×C₂²⋊D₇₉	—	2	1	no	—
48	C₂×C₄×D₇₉	—	2	1	no	—
49	C₄⋊Dic₇₉	—	2	1	no	—
50	C₄⋊Dic₇₉	—	2	1	no	—
51	C₄⋊Dic₇₉	C₂³	1	2	yes	—
52	C₄⋊Dic₇₉	C₂³	1	2	yes	—
53	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
54	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
55	Dic₇₉⋊C₄	—	2	1	no	—
56	Dic₇₉⋊C₄	—	2	1	no	—
57	Dic₇₉⋊C₄	—	2	1	no	—
58	Dic₇₉⋊C₄	—	2	2	no	—
59	Dic₇₉⋊C₄	—	2	2	no	—
60	Dic₇₉⋊C₄	—	2	1	no	—
61	C₂²⋊Dic₇₉	—	2	2	no	—
62	C₂²⋊Dic₇₉	—	2	1	no	—
63	(C₂×D₇₉)⋊C₄	—	2	1	no	—
64	(C₂×D₇₉)⋊C₄	—	2	1	no	—
65	(C₂×D₇₉)⋊C₄	—	2	1	no	—
66	(C₂×D₇₉)⋊C₄	—	2	1	no	—
67	C₄×Dic₇₉	—	2	1	no	—
68	C₄×Dic₇₉	—	2	2	no	—
69	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
70	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
71	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
72	C₂×C₈×C₇₉	C₂³	1	2	yes	—
73	C₂×C₈×C₇₉	C₂³	1	2	yes	—
74	C₄²×C₇₉	D₄	1	1	yes	characteristic
75	C₄²×C₇₉	D₄	1	1	yes	characteristic
76	C₄²×C₇₉	C₂³	1	1	yes	characteristic
77	C₄²×C₇₉	C₂³	1	1	yes	characteristic
78	C₂³×C₇₉	C₂×D₄	1	1	yes	characteristic
79	C₂²×D₇₉	—	2	1	no	—
80	C₂×C₄×C₇₉	—	2	2	no	—
81	C₂×C₄×C₇₉	—	2	1	no	—
82	C₂×C₄×C₇₉	—	2	1	no	—
83	C₂×C₄×C₇₉	—	4	1	no	—
84	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
85	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
86	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
87	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
88	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
89	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
90	C₂²⋊D₇₉	—	4	2	no	—
91	C₂×Dic₇₉	—	2	1	no	—
92	C₂×Dic₇₉	—	2	1	no	—
93	C₂×Dic₇₉	—	2	2	no	—
94	C₂×Dic₇₉	—	2	2	no	—
95	C₂×Dic₇₉	—	2	1	no	—
96	D₃₁₆	—	2	1	no	—
97	D₃₁₆	—	2	1	no	—
98	C₄×D₇₉	—	4	2	no	—
99	Dic₁₅₈	—	2	1	no	—
100	Dic₁₅₈	—	2	1	no	—
101	Dic₁₅₈	—	4	2	no	—
102	Dic₁₅₈	—	4	2	no	—
103	C₈×C₇₉	—	2	2	no	—
104	C₈×C₇₉	—	2	2	no	—
105	C₂²×C₇₉	—	2	1	no	—
106	C₂²×C₇₉	—	2	1	no	—
107	C₂²×C₇₉	—	2	1	no	—
108	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
109	C₂×D₇₉	—	4	1	no	—
110	C₂×D₇₉	—	4	1	no	—
111	C₂×D₇₉	—	4	1	no	—
112	C₄×C₇₉	—	2	1	no	—
113	C₄×C₇₉	—	2	1	no	—
114	C₄×C₇₉	—	2	1	no	—
115	C₄×C₇₉	—	2	1	no	—
116	C₄×C₇₉	#135	1	2	yes	—
117	C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
118	C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
119	Dic₇₉	—	4	1	no	—
120	Dic₇₉	—	4	2	no	—
121	Dic₇₉	—	4	1	no	—
122	Dic₇₉	—	4	1	no	—
123	Dic₇₉	—	4	2	no	—
124	C₂×C₇₉	—	4	1	no	—
125	C₂×C₇₉	#536	1	1	yes	characteristic
126	C₂×C₇₉	C₂×#135	1	1	yes	characteristic
127	C₂×C₇₉	#575	1	1	yes	characteristic
128	D₇₉	—	8	1	no	—
129	#3233	—	79	1	no	maximal, Sylow
130	C₇₉	#3233	1	1	yes	characteristic, complemented, Sylow
131	#533	—	79	1	no	—
132	#529	—	79	1	no	—
133	#499	—	79	2	no	—
134	#488	—	79	2	no	—
135	#485	—	79	2	no	—
136	#482	—	79	2	no	—
137	#477	—	79	1	no	—
138	#476	—	79	1	no	—
139	#475	—	79	1	no	—
140	#474	—	79	1	no	—
141	#431	D₇₉	1	1	yes	characteristic, complemented
142	C₄⋊Q₈	—	79	1	no	—
143	C₄⋊Q₈	—	79	1	no	—
144	#126	—	158	1	no	—
145	#125	—	79	1	no	—
146	#125	—	79	2	no	—
147	#124	—	79	1	no	—
148	#123	—	158	1	no	—
149	C₂²⋊Q₈	—	79	1	no	—
150	C₂²⋊Q₈	—	158	1	no	—
151	C₂²⋊Q₈	—	158	1	no	—
152	#121	—	79	1	no	—
153	C₄×Q₈	—	79	1	no	—
154	C₄×Q₈	—	158	1	no	—
155	C₄×Q₈	—	158	1	no	—
156	C₄×D₄	—	79	1	no	—
157	C₄×D₄	—	158	1	no	—
158	#117	—	79	2	no	—
159	#117	—	158	1	no	—
160	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
161	#107	—	79	2	no	—
162	#107	—	79	2	no	—
163	#106	—	79	2	no	—
164	#106	—	79	2	no	—
165	C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
166	C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
167	#103	—	79	2	no	—
168	#103	—	79	2	no	—
169	#102	—	79	2	no	—
170	#102	—	79	2	no	—
171	C₂²⋊C₈	C₂×D₇₉	1	2	yes	—
172	C₄×C₈	C₂×D₇₉	1	2	yes	—
173	C₂×Q₈	—	79	1	no	—
174	C₂×Q₈	—	158	1	no	—
175	C₂×Q₈	—	158	1	no	—
176	C₂×D₄	—	79	1	no	—
177	C₂×D₄	—	158	1	no	—
178	C₂²×C₄	—	158	1	no	—
179	C₂²×C₄	D₃₁₆	1	1	yes	characteristic
180	C₂²×C₄	D₃₁₆	1	1	yes	characteristic
181	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
182	C₂×C₈	C₂²×D₇₉	1	2	yes	—
183	C₂×C₈	C₂²×D₇₉	1	2	yes	—
184	C₄⋊C₄	—	79	2	no	—
185	C₄⋊C₄	—	79	2	no	—
186	C₄⋊C₄	—	79	1	no	—
187	C₄⋊C₄	—	79	1	no	—
188	C₄⋊C₄	—	158	1	no	—
189	C₄⋊C₄	—	158	1	no	—
190	C₄⋊C₄	—	158	1	no	—
191	C₄⋊C₄	—	158	1	no	—
192	C₄⋊C₄	—	158	2	no	—
193	C₄⋊C₄	—	158	2	no	—
194	C₄⋊C₄	—	158	1	no	—
195	C₄⋊C₄	—	158	1	no	—
196	C₂²⋊C₄	—	158	2	no	—
197	C₂²⋊C₄	—	158	1	no	—
198	C₂²⋊C₄	—	158	1	no	—
199	C₂²⋊C₄	—	158	1	no	—
200	C₂²⋊C₄	—	158	1	no	—
201	C₂²⋊C₄	—	158	1	no	—
202	C₄²	—	158	2	no	—
203	C₄²	—	158	1	no	—
204	C₄²	D₃₁₆	1	1	yes	characteristic
205	C₄²	D₃₁₆	1	1	yes	characteristic
206	C₄²	C₂²×D₇₉	1	1	yes	characteristic
207	C₄²	C₂²×D₇₉	1	1	yes	characteristic
208	C₂³	—	158	1	no	—
209	C₂³	C₂×D₃₁₆	1	1	yes	characteristic
210	Q₈	—	316	2	no	—
211	Q₈	—	316	2	no	—
212	Q₈	—	158	1	no	—
213	Q₈	—	158	1	no	—
214	D₄	—	316	2	no	—
215	D₄	—	158	1	no	—
216	D₄	—	158	1	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	4	1	no	—
221	C₂×C₄	—	316	2	no	—
222	C₂×C₄	—	158	1	no	—
223	C₂×C₄	—	158	1	no	—
224	C₂×C₄	—	158	2	no	—
225	C₂×C₄	—	158	2	no	—
226	C₂×C₄	—	158	1	no	—
227	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
228	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
229	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
230	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
231	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
232	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
233	C₈	—	2	2	no	—
234	C₈	—	2	2	no	—
235	C₂²	—	2	1	no	—
236	C₂²	—	2	1	no	—
237	C₂²	—	2	1	no	—
238	C₂²	—	316	1	no	—
239	C₂²	—	316	1	no	—
240	C₂²	—	316	1	no	—
241	C₂²	C₂²×D₃₁₆	1	1	yes	characteristic
242	C₄	—	2	1	no	—
243	C₄	—	2	1	no	—
244	C₄	—	2	1	no	—
245	C₄	—	2	1	no	—
246	C₄	—	316	1	no	—
247	C₄	—	316	1	no	—
248	C₄	—	316	2	no	—
249	C₄	—	316	1	no	—
250	C₄	—	316	2	no	—
251	C₄	#14579183	1	2	yes	—
252	C₄	#14579208	1	1	yes	characteristic
253	C₄	#14579208	1	1	yes	characteristic
254	C₂	—	4	1	no	—
255	C₂	—	632	1	no	—
256	C₂	#19099139	1	1	yes	characteristic
257	C₂	C₂×#14579183	1	1	yes	characteristic
258	C₂	#19099363	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19099120

C₂

yes

maximal, characteristic, complemented

#19099097

C₂

yes

maximal, characteristic

#19098965

C₂

yes

maximal, complemented

#19098918

C₂

yes

maximal, complemented

#19098905

C₂

yes

maximal, complemented

#19098888

C₂

yes

maximal

#19098859

C₂

yes

maximal, characteristic, complemented

#19098854

C₂

yes

maximal, characteristic, complemented

#19098849

C₂

yes

maximal, characteristic, complemented

#19098844

C₂

yes

maximal, characteristic, complemented

#431×C₇₉

C₂

yes

maximal, characteristic, complemented

#14579161

C₂²

yes

characteristic

#14579161

C₂²

yes

characteristic

#14579155

—

#14579153

C₂²

yes

—

#14579153

C₂²

yes

characteristic

#14579149

C₂²

yes

—

—

—

C₂²

yes

characteristic

#14579135

C₂²

yes

characteristic

C₄×Dic₁₅₈

—

C₄×Dic₁₅₈

—

C₄×Dic₁₅₈

C₂²

yes

characteristic

C₄×D₃₁₆

C₂²

yes

characteristic

C₄×C₂²⋊D₇₉

—

#14579120

C₂²

yes

—

#14579118

—

#14579095

C₂²

yes

—

#14579095

C₂²

yes

—

#14579093

C₂²

yes

—

#14579093

C₂²

yes

—

#14579086

C₂²

yes

—

#14579086

C₂²

yes

—

#14579083

C₂²

yes

—

#14579083

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₄⋊C₈×C₇₉

C₂²

yes

characteristic

C₄⋊C₈×C₇₉

C₂²

yes

characteristic

C₂²⋊C₈×C₇₉

C₂²

yes

—

C₄×C₈×C₇₉

C₂²

yes

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

C₂³

yes

characteristic

C₂×D₃₁₆

C₂³

yes

characteristic

C₂×C₂²⋊D₇₉

—

C₂×C₄×D₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

C₂³

yes

—

C₄⋊Dic₇₉

C₂³

yes

—

C₄⋊Dic₇₉

C₂³

yes

characteristic

C₄⋊Dic₇₉

C₂³

yes

characteristic

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₂²⋊Dic₇₉

—

C₂²⋊Dic₇₉

—

(C₂×D₇₉)⋊C₄

—

(C₂×D₇₉)⋊C₄

—

(C₂×D₇₉)⋊C₄

—

(C₂×D₇₉)⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

D₄

yes

characteristic

C₂²×C₄×C₇₉

D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₂×C₈×C₇₉

C₂³

yes

—

C₂×C₈×C₇₉

C₂³

yes

—

C₄²×C₇₉

D₄

yes

characteristic

C₄²×C₇₉

D₄

yes

characteristic

C₄²×C₇₉

C₂³

yes

characteristic

C₄²×C₇₉

C₂³

yes

characteristic

C₂³×C₇₉

C₂×D₄

yes

characteristic

C₂²×D₇₉

—

C₂×C₄×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

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂⁴

yes

characteristic

C₂²⋊D₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

D₃₁₆

—

D₃₁₆

—

C₄×D₇₉

—

Dic₁₅₈

—

100

Dic₁₅₈

—

101

Dic₁₅₈

—

102

Dic₁₅₈

—

103

C₈×C₇₉

—

104

C₈×C₇₉

—

105

C₂²×C₇₉

—

106

C₂²×C₇₉

—

107

C₂²×C₇₉

—

108

C₂²×C₇₉

C₂²×D₄

yes

characteristic

109

C₂×D₇₉

—

110

C₂×D₇₉

—

111

C₂×D₇₉

—

112

C₄×C₇₉

—

113

C₄×C₇₉

—

114

C₄×C₇₉

—

115

C₄×C₇₉

—

116

C₄×C₇₉

#135

yes

—

117

C₄×C₇₉

2₋¹⁺⁴

yes

characteristic

118

C₄×C₇₉

2₋¹⁺⁴

yes

characteristic

119

Dic₇₉

—

120

Dic₇₉

—

121

Dic₇₉

—

122

Dic₇₉

—

123

Dic₇₉

—

124

C₂×C₇₉

—

125

C₂×C₇₉

#536

yes

characteristic

126

C₂×C₇₉

C₂×#135

yes

characteristic

127

C₂×C₇₉

#575

yes

characteristic

128

D₇₉

—

129

#3233

—

maximal, Sylow

130

C₇₉

#3233

yes

characteristic, complemented, Sylow

131

#533

—

132

#529

—

133

#499

—

134

#488

—

135

#485

—

136

#482

—

137

#477

—

138

#476

—

139

#475

—

140

#474

—

141

#431

D₇₉

yes

characteristic, complemented

142

C₄⋊Q₈

—

143

C₄⋊Q₈

—

144

#126

—

158

—

145

#125

—

146

#125

—

147

#124

—

148

#123

—

158

—

149

C₂²⋊Q₈

—

150

C₂²⋊Q₈

—

158

—

151

C₂²⋊Q₈

—

158

—

152

#121

—

153

C₄×Q₈

—

154

C₄×Q₈

—

158

—

155

C₄×Q₈

—

158

—

156

C₄×D₄

—

157

C₄×D₄

—

158

—

158

#117

—

159

#117

—

158

—

160

C₂×C₄²

C₂×D₇₉

yes

characteristic

161

#107

—

162

#107

—

163

#106

—

164

#106

—

165

C₄⋊C₈

C₂×D₇₉

yes

characteristic

166

C₄⋊C₈

C₂×D₇₉

yes

characteristic

167

#103

—

168

#103

—

169

#102

—

170

#102

—

171

C₂²⋊C₈

C₂×D₇₉

yes

—

172

C₄×C₈

C₂×D₇₉

yes

—

173

C₂×Q₈

—

174

C₂×Q₈

—

158

—

175

C₂×Q₈

—

158

—

176

C₂×D₄

—

177

C₂×D₄

—

158

—

178

C₂²×C₄

—

158

—

179

C₂²×C₄

D₃₁₆

yes

characteristic

180

C₂²×C₄

D₃₁₆

yes

characteristic

181

C₂²×C₄

C₂²×D₇₉

yes

characteristic

182

C₂×C₈

C₂²×D₇₉

yes

—

183

C₂×C₈

C₂²×D₇₉

yes

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

158

—

189

C₄⋊C₄

—

158

—

190

C₄⋊C₄

—

158

—

191

C₄⋊C₄

—

158

—

192

C₄⋊C₄

—

158

—

193

C₄⋊C₄

—

158

—

194

C₄⋊C₄

—

158

—

195

C₄⋊C₄

—

158

—

196

C₂²⋊C₄

—

158

—

197

C₂²⋊C₄

—

158

—

198

C₂²⋊C₄

—

158

—

199

C₂²⋊C₄

—

158

—

200

C₂²⋊C₄

—

158

—

201

C₂²⋊C₄

—

158

—

202

C₄²

—

158

—

203

C₄²

—

158

—

204

C₄²

D₃₁₆

yes

characteristic

205

C₄²

D₃₁₆

yes

characteristic

206

C₄²

C₂²×D₇₉

yes

characteristic

207

C₄²

C₂²×D₇₉

yes

characteristic

208

C₂³

—

158

—

209

C₂³

C₂×D₃₁₆

yes

characteristic

210

Q₈

—

316

—

211

Q₈

—

316

—

212

Q₈

—

158

—

213

Q₈

—

158

—

214

D₄

—

316

—

215

D₄

—

158

—

216

D₄

—

158

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

316

—

222

C₂×C₄

—

158

—

223

C₂×C₄

—

158

—

224

C₂×C₄

—

158

—

225

C₂×C₄

—

158

—

226

C₂×C₄

—

158

—

227

C₂×C₄

C₂×D₃₁₆

yes

characteristic

228

C₂×C₄

C₂×D₃₁₆

yes

characteristic

229

C₂×C₄

C₂×D₃₁₆

yes

characteristic

230

C₂×C₄

C₂×D₃₁₆

yes

characteristic

231

C₂×C₄

C₂×D₃₁₆

yes

characteristic

232

C₂×C₄

C₂³×D₇₉

yes

characteristic

233

C₈

—

234

C₈

—

235

C₂²

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

316

—

239

C₂²

—

316

—

240

C₂²

—

316

—

241

C₂²

C₂²×D₃₁₆

yes

characteristic

242

C₄

—

243

C₄

—

244

C₄

—

245

C₄

—

246

C₄

—

316

—

247

C₄

—

316

—

248

C₄

—

316

—

249

C₄

—

316

—

250

C₄

—

316

—

251

C₄

#14579183

yes

—

252

C₄

#14579208

yes

characteristic

253

C₄

#14579208

yes

characteristic

254

C₂

—

255

C₂

—

632

—

256

C₂

#19099139

yes

characteristic

257

C₂

C₂×#14579183

yes

characteristic

258

C₂

#19099363

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×D₃₁₆
commutator, cosocle	C₂×C₄×C₇₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₇₉
Fitting	#431×C₇₉	C₂
socle	C₂²×C₇₉	C₂²×D₄
prime radical	#14579135	C₂²
hypercenter	#431	D₇₉
hypocenter	C₇₉	#3233
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #431

subgroup

G/H

center

C₂²

C₂²×D₃₁₆

commutator, cosocle

C₂×C₄×C₇₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₇₉

Fitting

#431×C₇₉

C₂

socle

C₂²×C₇₉

C₂²×D₄

C₂²

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #431

N	H ≅ G/N	type
1. #19099120	C₂	semidirect
3. #19098965	C₂	semidirect
4. #19098918	C₂	semidirect
5. #19098905	C₂	semidirect
7. #19098859	C₂	semidirect
8. #19098854	C₂	semidirect
9. #19098849	C₂	semidirect
10. #19098844	C₂	semidirect
11. #431×C₇₉	C₂	semidirect
130. C₇₉	#3233	semidirect
141. #431	D₇₉	semidirect

H ≅ G/N

type

1. #19099120

C₂

semidirect

3. #19098965

C₂

semidirect

4. #19098918

C₂

semidirect

5. #19098905

C₂

semidirect

7. #19098859

C₂

semidirect

8. #19098854

C₂

semidirect

9. #19098849

C₂

semidirect

10. #19098844

C₂

semidirect

11. #431×C₇₉

C₂

semidirect

130. C₇₉

#3233

semidirect

141. #431

D₇₉

semidirect

Subgroups — #23774581

Conjugacy classes of subgroups

Complements