Group #15750894 — subgroups

Subgroups — #15750894

Order 3328.

684 conjugacy classes of subgroups; only the 207 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 207 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	C₄×C₄⋊#1055	C₂	1	2	yes	maximal, complemented
2	#13112657	C₂	1	4	yes	maximal, complemented
3	C₄×C₁₃×#127	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#127	C₄	1	1	yes	characteristic
5	C₂×C₄×D₄×C₁₃	—	2	2	no	—
6	C₂×C₄×D₄×C₁₃	C₄	1	2	yes	—
7	C₁₃×#390	—	2	2	no	—
8	C₁₃×#390	C₂²	1	2	yes	—
9	C₁₃×#384	C₄	1	1	yes	characteristic
10	C₄³×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊#1055	—	2	2	no	—
12	C₂×C₄×#1055	—	2	2	no	—
13	#11718116	C₂²	1	4	yes	—
14	C₂²×D₄×C₁₃	—	2	2	no	—
15	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
16	C₂³×C₄×C₁₃	—	2	2	no	—
17	C₁₃×#127	—	2	2	no	—
18	C₁₃×#127	C₈	1	4	yes	complemented
19	C₄×D₄×C₁₃	—	4	4	no	—
20	C₄×D₄×C₁₃	—	4	4	no	—
21	C₄×D₄×C₁₃	—	4	4	no	—
22	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
23	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
24	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
25	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
26	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₃	D₄	1	2	yes	—
29	C₂×C₄²×C₁₃	D₄	1	2	yes	—
30	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
31	C₂²×#1055	—	2	4	no	—
32	C₄⋊#1055	—	2	8	no	—
33	C₄×#1055	—	4	4	no	—
34	#7569	—	13	1	no	maximal, Sylow
35	C₂⁴×C₁₃	—	2	2	no	—
36	C₂×D₄×C₁₃	—	2	8	no	—
37	C₂×D₄×C₁₃	—	2	2	no	—
38	C₂×D₄×C₁₃	—	4	2	no	—
39	C₂×D₄×C₁₃	—	4	2	no	—
40	C₂×D₄×C₁₃	—	4	4	no	—
41	C₂×D₄×C₁₃	—	4	4	no	—
42	C₂×D₄×C₁₃	C₂×C₈	1	4	yes	—
43	C₂²×C₄×C₁₃	—	2	2	no	—
44	C₂²×C₄×C₁₃	—	4	4	no	—
45	C₂²×C₄×C₁₃	—	4	8	no	—
46	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
48	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
51	C₁₃×C₄⋊C₄	—	4	2	no	—
52	C₁₃×C₄⋊C₄	—	4	4	no	—
53	C₁₃×C₂²⋊C₄	—	4	4	no	—
54	C₁₃×C₂²⋊C₄	—	4	4	no	—
55	C₁₃×C₂²⋊C₄	—	4	4	no	—
56	C₄²×C₁₃	—	2	2	no	—
57	C₄²×C₁₃	—	2	4	no	—
58	C₄²×C₁₃	—	4	1	no	—
59	C₄²×C₁₃	C₂×C₈	1	2	yes	—
60	C₄²×C₁₃	M₁₆	1	2	yes	—
61	C₄²×C₁₃	D₈	1	4	yes	—
62	C₄²×C₁₃	SD₁₆	1	4	yes	—
63	C₂×#1055	—	2	8	no	—
64	C₂×#1055	—	4	4	no	—
65	C₂×#1055	—	4	4	no	—
66	C₄×#127	D₁₃	1	1	yes	characteristic
67	C₄×C₄⋊C₈	—	13	2	no	—
68	#1270	—	13	4	no	—
69	C₂³×C₁₃	—	2	4	no	—
70	C₂³×C₁₃	—	4	2	no	—
71	C₂³×C₁₃	—	4	2	no	—
72	C₂³×C₁₃	—	4	4	no	—
73	C₂³×C₁₃	—	4	4	no	—
74	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
75	D₄×C₁₃	—	4	4	no	—
76	D₄×C₁₃	—	4	4	no	—
77	D₄×C₁₃	—	4	16	no	—
78	C₂×C₄×C₁₃	—	2	2	no	—
79	C₂×C₄×C₁₃	—	2	1	no	—
80	C₂×C₄×C₁₃	—	2	1	no	—
81	C₂×C₄×C₁₃	—	2	2	no	—
82	C₂×C₄×C₁₃	—	2	1	no	—
83	C₂×C₄×C₁₃	—	2	2	no	—
84	C₂×C₄×C₁₃	—	4	2	no	—
85	C₂×C₄×C₁₃	—	4	4	no	—
86	C₂×C₄×C₁₃	—	8	8	no	—
87	C₂×C₄×C₁₃	C₂²⋊C₈	1	4	yes	—
88	C₂×C₄×C₁₃	#100	1	2	yes	—
89	C₂×C₄×C₁₃	#102	1	4	yes	—
90	C₂×C₄×C₁₃	#102	1	4	yes	—
91	C₂×C₄×C₁₃	#104	1	4	yes	—
92	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
93	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
94	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
95	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
96	#1055	—	4	8	no	—
97	C₂×#127	Dic₁₃	1	1	yes	characteristic
98	C₂×C₄×D₄	—	2	2	no	—
99	C₂×C₄×D₄	Dic₁₃	1	2	yes	—
100	C₂×C₄⋊C₈	—	26	2	no	—
101	C₂×C₄×C₈	—	26	2	no	—
102	#390	—	2	2	no	—
103	#390	C₂×D₁₃	1	2	yes	—
104	#384	Dic₁₃	1	1	yes	characteristic
105	C₄³	C₂×D₁₃	1	1	yes	characteristic
106	#336	—	13	4	no	—
107	C₂²×C₁₃	—	4	4	no	—
108	C₂²×C₁₃	—	4	8	no	—
109	C₂²×C₁₃	—	8	2	no	—
110	C₂²×C₁₃	—	8	4	no	—
111	C₂²×C₁₃	—	8	2	no	—
112	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
113	C₂²×C₁₃	#410	1	1	yes	characteristic
114	C₂²×C₁₃	C₂×#100	1	1	yes	characteristic
115	C₂²×C₁₃	C₂×#102	1	2	yes	—
116	C₂²×C₁₃	C₂×#104	1	2	yes	—
117	C₄×C₁₃	—	2	1	no	—
118	C₄×C₁₃	—	2	1	no	—
119	C₄×C₁₃	—	2	2	no	—
120	C₄×C₁₃	—	2	2	no	—
121	C₄×C₁₃	—	4	1	no	—
122	C₄×C₁₃	—	8	2	no	—
123	C₄×C₁₃	D₄⋊C₈	1	8	yes	—
124	C₄×C₁₃	#331	1	4	yes	—
125	C₂²×D₄	—	2	2	no	—
126	C₂²×D₄	C₂×Dic₁₃	1	2	yes	—
127	C₂³×C₄	—	2	2	no	—
128	C₂²×C₈	—	26	4	no	—
129	#127	—	2	2	no	—
130	#127	#1055	1	4	yes	complemented
131	C₄×D₄	—	4	4	no	—
132	C₄×D₄	—	4	4	no	—
133	C₄×D₄	—	4	4	no	—
134	C₂×C₄⋊C₄	—	2	2	no	—
135	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
136	C₂×C₂²⋊C₄	—	2	2	no	—
137	C₂×C₂²⋊C₄	—	2	4	no	—
138	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
139	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
140	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
141	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
142	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
143	C₄⋊C₈	—	26	8	no	—
144	C₄×C₈	—	52	4	no	—
145	C₂×C₁₃	—	8	4	no	—
146	C₂×C₁₃	#1460	1	1	yes	characteristic
147	C₂×C₁₃	C₂×D₄⋊C₈	1	2	yes	—
148	C₂×C₁₃	#1502	1	2	yes	—
149	C₂×C₁₃	#1525	1	1	yes	characteristic
150	C₂×C₁₃	C₂×#331	1	1	yes	characteristic
151	C₂⁴	—	2	2	no	—
152	C₂×D₄	—	2	8	no	—
153	C₂×D₄	—	2	2	no	—
154	C₂×D₄	—	4	2	no	—
155	C₂×D₄	—	4	2	no	—
156	C₂×D₄	—	4	4	no	—
157	C₂×D₄	—	4	4	no	—
158	C₂×D₄	C₂×#1055	1	4	yes	—
159	C₂²×C₄	—	2	2	no	—
160	C₂²×C₄	—	4	8	no	—
161	C₂²×C₄	—	4	4	no	—
162	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
163	C₂²×C₄	C₂²⋊Dic₁₃	1	2	yes	—
164	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
165	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
166	C₂²×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
167	C₂×C₈	—	26	8	no	—
168	C₂×C₈	—	52	4	no	—
169	C₂×C₈	—	52	4	no	—
170	C₄⋊C₄	—	4	2	no	—
171	C₄⋊C₄	—	4	4	no	—
172	C₂²⋊C₄	—	4	4	no	—
173	C₂²⋊C₄	—	4	4	no	—
174	C₂²⋊C₄	—	4	4	no	—
175	C₄²	—	2	2	no	—
176	C₄²	—	2	4	no	—
177	C₄²	—	4	1	no	—
178	C₄²	C₂×#1055	1	2	yes	—
179	C₄²	#6099	1	2	yes	—
180	C₄²	#6104	1	4	yes	—
181	C₄²	#6105	1	4	yes	—
182	C₁₃	#7569	1	1	yes	characteristic, complemented, Sylow
183	C₂³	—	2	4	no	—
184	C₂³	—	4	4	no	—
185	C₂³	—	4	2	no	—
186	C₂³	—	4	4	no	—
187	C₂³	—	4	2	no	—
188	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
189	D₄	—	4	4	no	—
190	D₄	—	4	4	no	—
191	D₄	—	4	16	no	—
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	1	no	—
196	C₂×C₄	—	2	1	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	4	4	no	—
199	C₂×C₄	—	4	2	no	—
200	C₂×C₄	—	8	8	no	—
201	C₂×C₄	C₂²⋊#1055	1	4	yes	—
202	C₂×C₄	#88072	1	4	yes	—
203	C₂×C₄	#88072	1	4	yes	—
204	C₂×C₄	#88073	1	2	yes	—
205	C₂×C₄	#88077	1	4	yes	—
206	C₂×C₄	C₂²×#1055	1	1	yes	characteristic
207	C₂×C₄	C₂×#6099	1	1	yes	characteristic
208	C₂×C₄	C₂×#6104	1	2	yes	—
209	C₂×C₄	C₂×#6105	1	2	yes	—
210	C₈	—	52	8	no	—
211	C₂²	—	4	4	no	—
212	C₂²	—	4	8	no	—
213	C₂²	—	8	2	no	—
214	C₂²	—	8	2	no	—
215	C₂²	—	8	4	no	—
216	C₂²	C₂×C₂²⋊#1055	1	1	yes	characteristic
217	C₂²	C₂×#88072	1	2	yes	—
218	C₂²	C₂×#88073	1	1	yes	characteristic
219	C₂²	C₂×#88077	1	2	yes	—
220	C₂²	#11718901	1	1	yes	characteristic
221	C₄	—	2	1	no	—
222	C₄	—	2	1	no	—
223	C₄	—	2	2	no	—
224	C₄	—	2	2	no	—
225	C₄	—	4	1	no	—
226	C₄	—	8	2	no	—
227	C₄	D₄⋊#1055	1	8	yes	—
228	C₄	#11718136	1	4	yes	—
229	C₂	—	8	4	no	—
230	C₂	#13113157	1	1	yes	characteristic
231	C₂	C₂×D₄⋊#1055	1	2	yes	—
232	C₂	#13113331	1	2	yes	—
233	C₂	#13113428	1	1	yes	characteristic
234	C₂	C₂×#11718136	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×C₄⋊#1055

C₂

yes

maximal, complemented

#13112657

C₂

yes

maximal, complemented

C₄×C₁₃×#127

C₂

yes

maximal, characteristic

C₂×C₁₃×#127

C₄

yes

characteristic

C₂×C₄×D₄×C₁₃

—

C₂×C₄×D₄×C₁₃

C₄

yes

—

C₁₃×#390

—

C₁₃×#390

C₂²

yes

—

C₁₃×#384

C₄

yes

characteristic

C₄³×C₁₃

C₂²

yes

characteristic

C₂×C₄⋊#1055

—

C₂×C₄×#1055

—

#11718116

C₂²

yes

—

C₂²×D₄×C₁₃

—

C₂²×D₄×C₁₃

C₂×C₄

yes

—

C₂³×C₄×C₁₃

—

C₁₃×#127

—

C₁₃×#127

C₈

yes

complemented

C₄×D₄×C₁₃

—

C₄×D₄×C₁₃

—

C₄×D₄×C₁₃

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

C₂×C₄

yes

—

C₂×C₁₃×C₂²⋊C₄

—

C₂×C₁₃×C₂²⋊C₄

—

C₂×C₄²×C₁₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₃

D₄

yes

—

C₂×C₄²×C₁₃

D₄

yes

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₂²×#1055

—

—

—

—

C₂⁴×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

C₂×C₈

yes

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₂²⋊C₄

—

C₁₃×C₂²⋊C₄

—

C₁₃×C₂²⋊C₄

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

C₂×C₈

yes

—

C₄²×C₁₃

M₁₆

yes

—

C₄²×C₁₃

D₈

yes

—

C₄²×C₁₃

SD₁₆

yes

—

—

—

—

D₁₃

yes

characteristic

C₄×C₄⋊C₈

—

#1270

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

D₄×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²⋊C₈

yes

—

C₂×C₄×C₁₃

#100

yes

—

C₂×C₄×C₁₃

#102

yes

—

C₂×C₄×C₁₃

#102

yes

—

C₂×C₄×C₁₃

#104

yes

—

C₂×C₄×C₁₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₃

C₂×M₁₆

yes

characteristic

C₂×C₄×C₁₃

C₂×D₈

yes

—

C₂×C₄×C₁₃

C₂×SD₁₆

yes

—

#1055

—

C₂×#127

Dic₁₃

yes

characteristic

C₂×C₄×D₄

—

C₂×C₄×D₄

Dic₁₃

yes

—

100

C₂×C₄⋊C₈

—

101

C₂×C₄×C₈

—

102

#390

—

103

#390

C₂×D₁₃

yes

—

104

#384

Dic₁₃

yes

characteristic

105

C₄³

C₂×D₁₃

yes

characteristic

106

#336

—

107

C₂²×C₁₃

—

108

C₂²×C₁₃

—

109

C₂²×C₁₃

—

110

C₂²×C₁₃

—

111

C₂²×C₁₃

—

112

C₂²×C₁₃

C₂×C₂²⋊C₈

yes

characteristic

113

C₂²×C₁₃

#410

yes

characteristic

114

C₂²×C₁₃

C₂×#100

yes

characteristic

115

C₂²×C₁₃

C₂×#102

yes

—

116

C₂²×C₁₃

C₂×#104

yes

—

117

C₄×C₁₃

—

118

C₄×C₁₃

—

119

C₄×C₁₃

—

120

C₄×C₁₃

—

121

C₄×C₁₃

—

122

C₄×C₁₃

—

123

C₄×C₁₃

D₄⋊C₈

yes

—

124

C₄×C₁₃

#331

yes

—

125

C₂²×D₄

—

126

C₂²×D₄

C₂×Dic₁₃

yes

—

127

C₂³×C₄

—

128

C₂²×C₈

—

129

#127

—

130

#127

#1055

yes

complemented

131

C₄×D₄

—

132

C₄×D₄

—

133

C₄×D₄

—

134

C₂×C₄⋊C₄

—

135

C₂×C₄⋊C₄

C₂×Dic₁₃

yes

—

136

C₂×C₂²⋊C₄

—

137

C₂×C₂²⋊C₄

—

138

C₂×C₄²

C₂×Dic₁₃

yes

characteristic

139

C₂×C₄²

C₂×Dic₁₃

yes

characteristic

140

C₂×C₄²

C₂²⋊D₁₃

yes

—

141

C₂×C₄²

C₂²⋊D₁₃

yes

—

142

C₂×C₄²

C₂²×D₁₃

yes

characteristic

143

C₄⋊C₈

—

144

C₄×C₈

—

145

C₂×C₁₃

—

146

C₂×C₁₃

#1460

yes

characteristic

147

C₂×C₁₃

C₂×D₄⋊C₈

yes

—

148

C₂×C₁₃

#1502

yes

—

149

C₂×C₁₃

#1525

yes

characteristic

150

C₂×C₁₃

C₂×#331

yes

characteristic

151

C₂⁴

—

152

C₂×D₄

—

153

C₂×D₄

—

154

C₂×D₄

—

155

C₂×D₄

—

156

C₂×D₄

—

157

C₂×D₄

—

158

C₂×D₄

C₂×#1055

yes

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

C₂²⋊Dic₁₃

yes

characteristic

163

C₂²×C₄

C₂²⋊Dic₁₃

yes

—

164

C₂²×C₄

C₂²⋊Dic₁₃

yes

characteristic

165

C₂²×C₄

C₂²×Dic₁₃

yes

characteristic

166

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

—

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₂²⋊C₄

—

173

C₂²⋊C₄

—

174

C₂²⋊C₄

—

175

C₄²

—

176

C₄²

—

177

C₄²

—

178

C₄²

C₂×#1055

yes

—

179

C₄²

#6099

yes

—

180

C₄²

#6104

yes

—

181

C₄²

#6105

yes

—

182

C₁₃

#7569

yes

characteristic, complemented, Sylow

183

C₂³

—

184

C₂³

—

185

C₂³

—

186

C₂³

—

187

C₂³

—

188

C₂³

C₂×C₂²⋊Dic₁₃

yes

characteristic

189

D₄

—

190

D₄

—

191

D₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

C₂²⋊#1055

yes

—

202

C₂×C₄

#88072

yes

—

203

C₂×C₄

#88072

yes

—

204

C₂×C₄

#88073

yes

—

205

C₂×C₄

#88077

yes

—

206

C₂×C₄

C₂²×#1055

yes

characteristic

207

C₂×C₄

C₂×#6099

yes

characteristic

208

C₂×C₄

C₂×#6104

yes

—

209

C₂×C₄

C₂×#6105

yes

—

210

C₈

—

211

C₂²

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

C₂×C₂²⋊#1055

yes

characteristic

217

C₂²

C₂×#88072

yes

—

218

C₂²

C₂×#88073

yes

characteristic

219

C₂²

C₂×#88077

yes

—

220

C₂²

#11718901

yes

characteristic

221

C₄

—

222

C₄

—

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

D₄⋊#1055

yes

—

228

C₄

#11718136

yes

—

229

C₂

—

230

C₂

#13113157

yes

characteristic

231

C₂

C₂×D₄⋊#1055

yes

—

232

C₂

#13113331

yes

—

233

C₂

#13113428

yes

characteristic

234

C₂

C₂×#11718136

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²⋊Dic₁₃
commutator	C₂×C₄×C₁₃	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₄×C₁₃×#127	C₂
socle	C₂³×C₁₃	C₂×C₂²⋊C₄
prime radical	C₂×C₁₃×#127	C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	C₄×#127	D₁₃
hypocenter	C₁₃	#7569
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×#127

subgroup

G/H

center

C₂²×C₄

C₂²⋊Dic₁₃

commutator

C₂×C₄×C₁₃

C₂²×C₈

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₄×C₁₃×#127

C₂

socle

C₂³×C₁₃

C₂×C₂²⋊C₄

prime radical

C₂×C₁₃×#127

C₄

cosocle

C₂×C₄²×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×#127

N	H ≅ G/N	type
1. C₄×C₄⋊#1055	C₂	semidirect
2. #13112657	C₂	semidirect
18. C₁₃×#127	C₈	semidirect
130. #127	#1055	semidirect
182. C₁₃	#7569	semidirect

H ≅ G/N

type

1. C₄×C₄⋊#1055

C₂

semidirect

2. #13112657

C₂

semidirect

18. C₁₃×#127

C₈

semidirect

130. #127

#1055

semidirect

182. C₁₃

#7569

semidirect

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

subgroup	index
C₄×C₄⋊#1055	2
#13112657	2
C₄×C₁₃×#127	2
#7569	13

subgroup

index

C₄×C₄⋊#1055

#13112657

C₄×C₁₃×#127

#7569

Subgroups — #15750894

Conjugacy classes of subgroups

Complements

Maximal subgroups