Group #15781625 — subgroups

Subgroups — #15781625

Order 3328.

566 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 117 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×#11718849	C₂	1	2	yes	maximal
2	C₂×#11718156	C₂	1	2	yes	maximal, complemented
3	C₂×#11718099	C₂	1	1	yes	maximal, characteristic
4	#13112928	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₁₃×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
7	C₂×#88200	—	2	2	no	—
8	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×Q₃₂	—	2	4	no	—
10	C₂×C₁₃×Q₃₂	—	2	2	no	—
11	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
12	C₂×#88075	—	2	2	no	—
13	#11718849	—	2	4	no	—
14	#11718849	—	2	4	no	—
15	C₂×#88058	C₂²	1	2	yes	—
16	C₂²×#6090	C₂²	1	1	yes	characteristic
17	#11718156	—	2	4	no	—
18	#11718099	—	2	2	no	—
19	C₂²×Q₈×C₁₃	—	2	2	no	—
20	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
21	C₂×C₁₃×Q₁₆	—	2	2	no	—
22	C₂×C₁₃×Q₁₆	—	2	2	no	—
23	C₂×C₁₃×Q₁₆	—	2	2	no	—
24	C₂×C₁₃×Q₁₆	—	2	2	no	—
25	C₂×C₁₃×Q₁₆	—	2	2	no	—
26	C₂×C₁₃×Q₁₆	D₄	1	4	yes	—
27	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
28	#88200	—	2	8	no	—
29	#88200	—	4	4	no	—
30	C₂×#6103	—	4	2	no	—
31	C₂×C₄⋊Dic₁₃	—	2	2	no	—
32	C₂×#6101	—	4	2	no	—
33	C₂²×#1055	D₄	1	1	yes	characteristic
34	C₂×C₈×D₁₃	—	2	2	no	—
35	C₂×C₈×D₁₃	—	2	2	no	—
36	C₂×C₈×D₁₃	—	2	1	no	—
37	C₂×C₈×D₁₃	—	2	1	no	—
38	C₁₃×Q₃₂	—	2	8	no	—
39	C₂×C₁₃×C₁₆	—	2	2	no	—
40	C₂×C₁₃×C₁₆	D₄	1	2	yes	—
41	#88075	—	2	8	no	—
42	#88058	—	2	2	no	—
43	#88058	D₄	1	4	yes	—
44	C₂×#6090	—	2	2	no	—
45	C₂×#6090	—	2	1	no	—
46	#13306	—	13	1	no	maximal, Sylow
47	C₂³×D₁₃	D₈	1	1	yes	characteristic
48	C₂×Q₈×C₁₃	—	2	4	no	—
49	C₂×Q₈×C₁₃	—	4	2	no	—
50	C₂×Q₈×C₁₃	—	4	2	no	—
51	C₂×Q₈×C₁₃	—	4	2	no	—
52	C₂×Q₈×C₁₃	—	4	2	no	—
53	C₂×Q₈×C₁₃	—	4	2	no	—
54	C₂²×C₄×C₁₃	—	4	2	no	—
55	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
56	C₂²×Dic₁₃	—	4	2	no	—
57	C₂²×Dic₁₃	D₈	1	1	yes	characteristic
58	C₂×C₄×D₁₃	—	2	2	no	—
59	C₂×C₄×D₁₃	—	2	1	no	—
60	C₂×C₄×D₁₃	—	2	1	no	—
61	C₂×C₄×D₁₃	—	2	2	no	—
62	C₁₃×Q₁₆	—	2	4	no	—
63	C₁₃×Q₁₆	—	2	4	no	—
64	C₁₃×Q₁₆	—	4	2	no	—
65	C₁₃×Q₁₆	—	4	2	no	—
66	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
67	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
68	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
69	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
70	#6103	—	4	8	no	—
71	C₄⋊Dic₁₃	—	2	4	no	—
72	C₄⋊Dic₁₃	—	4	2	no	—
73	#6101	—	4	8	no	—
74	C₂×#1055	—	2	2	no	—
75	C₂×#1055	—	2	1	no	—
76	C₈×D₁₃	—	4	1	no	—
77	C₈×D₁₃	—	4	2	no	—
78	C₈×D₁₃	—	4	1	no	—
79	C₁₃×C₁₆	—	2	2	no	—
80	#6090	—	4	1	no	—
81	C₂²×Q₃₂	D₁₃	1	1	yes	characteristic, complemented
82	C₂×#467	—	13	2	no	—
83	C₂×#358	—	13	2	no	—
84	C₂×C₂²⋊C₁₆	—	13	1	no	—
85	#1380	—	13	1	no	—
86	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
87	C₂²×D₁₃	—	2	2	no	—
88	C₂²×D₁₃	—	2	1	no	—
89	C₂²×D₁₃	—	2	1	no	—
90	C₂²×D₁₃	—	2	2	no	—
91	C₂²×D₁₃	Q₃₂	1	2	yes	complemented
92	Q₈×C₁₃	—	4	4	no	—
93	Q₈×C₁₃	—	4	4	no	—
94	Q₈×C₁₃	—	8	2	no	—
95	Q₈×C₁₃	—	8	2	no	—
96	C₂×C₄×C₁₃	—	4	4	no	—
97	C₂×C₄×C₁₃	—	8	2	no	—
98	C₂×C₄×C₁₃	—	8	2	no	—
99	C₂×C₄×C₁₃	#120	1	2	yes	—
100	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
101	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
102	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
103	C₂×Dic₁₃	—	2	2	no	—
104	C₂×Dic₁₃	—	2	1	no	—
105	C₂×Dic₁₃	—	4	4	no	—
106	C₂×Dic₁₃	—	8	2	no	—
107	C₂×Dic₁₃	—	8	2	no	—
108	C₄×D₁₃	—	4	1	no	—
109	C₄×D₁₃	—	4	2	no	—
110	C₄×D₁₃	—	4	1	no	—
111	C₈×C₁₃	#120	1	1	yes	characteristic
112	C₈×C₁₃	#121	1	2	yes	—
113	C₈×C₁₃	#127	1	1	yes	characteristic
114	#1055	—	4	1	no	—
115	C₂²×Q₁₆	C₂×D₁₃	1	2	yes	—
116	C₂³×C₈	—	13	1	no	—
117	C₂×C₂²⋊Q₈	—	26	2	no	—
118	C₂×Q₃₂	—	2	4	no	—
119	C₂×Q₃₂	—	2	2	no	—
120	C₂²×C₁₆	—	13	1	no	—
121	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
122	#467	—	26	4	no	—
123	#467	—	26	4	no	—
124	C₂×#107	—	13	2	no	—
125	C₂×#103	—	26	2	no	—
126	#358	—	26	4	no	—
127	C₂²⋊C₁₆	—	26	2	no	—
128	C₂²×C₁₃	#447	1	2	yes	—
129	C₂²×C₁₃	#466	1	1	yes	characteristic
130	C₂²×C₁₃	C₂×Q₃₂	1	1	yes	characteristic
131	C₂²×C₁₃	#508	1	1	yes	characteristic
132	C₂²×C₁₃	#510	1	2	yes	—
133	C₂×D₁₃	—	2	4	no	—
134	C₂×D₁₃	—	2	2	no	—
135	C₂×D₁₃	—	4	2	no	—
136	C₂×D₁₃	—	4	1	no	—
137	C₂×D₁₃	—	4	1	no	—
138	C₄×C₁₃	—	8	4	no	—
139	C₄×C₁₃	#392	1	1	yes	characteristic
140	C₄×C₁₃	#449	1	2	yes	—
141	C₄×C₁₃	#469	1	1	yes	characteristic
142	Dic₁₃	—	4	1	no	—
143	Dic₁₃	—	8	4	no	—
144	C₂²×Q₈	—	2	2	no	—
145	C₂³×C₄	—	13	1	no	—
146	C₂×Q₁₆	—	2	2	no	—
147	C₂×Q₁₆	—	2	2	no	—
148	C₂×Q₁₆	—	2	2	no	—
149	C₂×Q₁₆	—	2	2	no	—
150	C₂×Q₁₆	—	2	2	no	—
151	C₂×Q₁₆	C₂²⋊D₁₃	1	4	yes	—
152	C₂²×C₈	—	13	1	no	—
153	C₂²×C₈	—	26	2	no	—
154	C₂²×C₈	—	26	1	no	—
155	C₂²×C₈	—	26	1	no	—
156	C₂²×C₈	—	26	2	no	—
157	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
158	C₂²⋊Q₈	—	26	8	no	—
159	C₂²⋊Q₈	—	52	4	no	—
160	C₂×C₄⋊C₄	—	26	2	no	—
161	C₂×C₄⋊C₄	—	52	2	no	—
162	C₂×C₂²⋊C₄	—	52	2	no	—
163	Q₃₂	—	2	8	no	—
164	C₂×C₁₆	—	2	2	no	—
165	C₂×C₁₆	—	26	2	no	—
166	C₂×C₁₆	—	26	1	no	—
167	C₂×C₁₆	C₂²⋊D₁₃	1	2	yes	—
168	#107	—	13	4	no	—
169	#107	—	26	2	no	—
170	#103	—	26	8	no	—
171	C₂×C₁₃	#1999	1	1	yes	characteristic
172	C₂×C₁₃	#2188	1	2	yes	—
173	C₂×C₁₃	#2189	1	2	yes	—
174	C₂×C₁₃	#2216	1	1	yes	characteristic
175	C₂×C₁₃	#2219	1	1	yes	characteristic
176	D₁₃	—	4	2	no	—
177	C₂⁴	—	13	1	no	—
178	C₂×Q₈	—	2	4	no	—
179	C₂×Q₈	—	4	2	no	—
180	C₂×Q₈	—	4	2	no	—
181	C₂×Q₈	—	4	2	no	—
182	C₂×Q₈	—	4	2	no	—
183	C₂×Q₈	—	4	2	no	—
184	C₂²×C₄	—	4	2	no	—
185	C₂²×C₄	—	13	1	no	—
186	C₂²×C₄	—	26	2	no	—
187	C₂²×C₄	—	26	1	no	—
188	C₂²×C₄	—	26	2	no	—
189	C₂²×C₄	—	26	1	no	—
190	C₂²×C₄	—	52	2	no	—
191	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
192	Q₁₆	—	2	4	no	—
193	Q₁₆	—	2	4	no	—
194	Q₁₆	—	4	2	no	—
195	Q₁₆	—	4	2	no	—
196	C₂×C₈	—	26	2	no	—
197	C₂×C₈	—	26	1	no	—
198	C₂×C₈	—	52	2	no	—
199	C₂×C₈	—	52	1	no	—
200	C₂×C₈	—	52	1	no	—
201	C₂×C₈	D₄×D₁₃	1	2	yes	—
202	C₂×C₈	#6129	1	1	yes	characteristic
203	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
204	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
205	C₄⋊C₄	—	26	4	no	—
206	C₄⋊C₄	—	52	8	no	—
207	C₄⋊C₄	—	52	2	no	—
208	C₂²⋊C₄	—	52	8	no	—
209	C₁₆	—	2	2	no	—
210	C₁₆	—	52	1	no	—
211	C₁₃	#13306	1	1	yes	characteristic, complemented, Sylow
212	C₂³	—	13	2	no	—
213	C₂³	—	26	2	no	—
214	C₂³	—	26	1	no	—
215	C₂³	—	26	2	no	—
216	C₂³	—	26	1	no	—
217	C₂³	D₈×D₁₃	1	1	yes	characteristic
218	Q₈	—	4	4	no	—
219	Q₈	—	4	4	no	—
220	Q₈	—	8	2	no	—
221	Q₈	—	8	2	no	—
222	C₂×C₄	—	4	4	no	—
223	C₂×C₄	—	8	2	no	—
224	C₂×C₄	—	8	2	no	—
225	C₂×C₄	—	26	2	no	—
226	C₂×C₄	—	26	1	no	—
227	C₂×C₄	—	52	2	no	—
228	C₂×C₄	—	52	1	no	—
229	C₂×C₄	—	52	1	no	—
230	C₂×C₄	—	52	4	no	—
231	C₂×C₄	—	104	2	no	—
232	C₂×C₄	—	104	2	no	—
233	C₂×C₄	#88165	1	2	yes	—
234	C₂×C₄	#88166	1	1	yes	characteristic
235	C₂×C₄	#88191	1	2	yes	—
236	C₂×C₄	#88192	1	1	yes	characteristic
237	C₈	—	52	1	no	—
238	C₈	#88193	1	2	yes	—
239	C₈	#88194	1	1	yes	characteristic
240	C₈	#88207	1	1	yes	characteristic
241	C₂²	—	26	4	no	—
242	C₂²	—	26	2	no	—
243	C₂²	—	52	1	no	—
244	C₂²	—	52	2	no	—
245	C₂²	—	52	1	no	—
246	C₂²	D₁₃×Q₃₂	1	1	yes	characteristic
247	C₂²	#11718579	1	2	yes	—
248	C₂²	#11718580	1	1	yes	characteristic
249	C₂²	#11718817	1	2	yes	—
250	C₂²	#11718818	1	1	yes	characteristic
251	C₄	—	8	4	no	—
252	C₄	—	52	1	no	—
253	C₄	—	104	4	no	—
254	C₄	#11718819	1	2	yes	—
255	C₄	#11718820	1	1	yes	characteristic
256	C₄	#11718884	1	1	yes	characteristic
257	C₂	—	52	2	no	—
258	C₂	#13115831	1	1	yes	characteristic
259	C₂	#13116768	1	2	yes	—
260	C₂	#13116775	1	2	yes	—
261	C₂	#13116924	1	1	yes	characteristic
262	C₂	#13116941	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11718849

C₂

yes

maximal

C₂×#11718156

C₂

yes

maximal, complemented

C₂×#11718099

C₂

yes

maximal, characteristic

#13112928

C₂

yes

maximal, characteristic, complemented

C₂²×C₁₃×Q₃₂

C₂

yes

maximal, characteristic, complemented

C₂²×C₁₃×Q₁₆

C₂²

yes

—

C₂×#88200

—

C₂²×C₈×D₁₃

C₂²

yes

characteristic

C₂×C₁₃×Q₃₂

—

C₂×C₁₃×Q₃₂

—

C₂²×C₁₃×C₁₆

C₂²

yes

—

—

—

C₂²

yes

—

C₂²×#6090

C₂²

yes

characteristic

#11718156

—

#11718099

—

C₂²×Q₈×C₁₃

—

C₂²×C₄×D₁₃

D₄

yes

characteristic

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

D₄

yes

—

C₂²×C₈×C₁₃

C₂³

yes

—

—

—

C₂×C₄⋊Dic₁₃

—

C₂×#6101

—

C₂²×#1055

D₄

yes

characteristic

C₂×C₈×D₁₃

—

C₂×C₈×D₁₃

—

C₂×C₈×D₁₃

—

C₂×C₈×D₁₃

—

C₁₃×Q₃₂

—

C₂×C₁₃×C₁₆

—

C₂×C₁₃×C₁₆

D₄

yes

—

#88075

—

#88058

—

#88058

D₄

yes

—

—

—

—

C₂³×D₁₃

D₈

yes

characteristic

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×Dic₁₃

—

C₂²×Dic₁₃

D₈

yes

characteristic

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

—

C₁₃×Q₁₆

—

C₁₃×Q₁₆

—

C₁₃×Q₁₆

—

C₁₃×Q₁₆

—

C₂×C₈×C₁₃

C₂×D₄

yes

—

C₂×C₈×C₁₃

C₂×D₄

yes

characteristic

C₂×C₈×C₁₃

C₂×D₄

yes

—

C₂×C₈×C₁₃

#41

yes

characteristic

#6103

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

#6101

—

C₂×#1055

—

C₂×#1055

—

C₈×D₁₃

—

C₈×D₁₃

—

C₈×D₁₃

—

C₁₃×C₁₆

—

#6090

—

C₂²×Q₃₂

D₁₃

yes

characteristic, complemented

C₂×#467

—

C₂×#358

—

C₂×C₂²⋊C₁₆

—

#1380

—

C₂³×C₁₃

C₂×D₈

yes

characteristic

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

Q₃₂

yes

complemented

Q₈×C₁₃

—

Q₈×C₁₃

—

Q₈×C₁₃

—

Q₈×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#120

yes

—

100

C₂×C₄×C₁₃

#121

yes

characteristic

101

C₂×C₄×C₁₃

#135

yes

characteristic

102

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

—

103

C₂×Dic₁₃

—

104

C₂×Dic₁₃

—

105

C₂×Dic₁₃

—

106

C₂×Dic₁₃

—

107

C₂×Dic₁₃

—

108

C₄×D₁₃

—

109

C₄×D₁₃

—

110

C₄×D₁₃

—

111

C₈×C₁₃

#120

yes

characteristic

112

C₈×C₁₃

#121

yes

—

113

C₈×C₁₃

#127

yes

characteristic

114

#1055

—

115

C₂²×Q₁₆

C₂×D₁₃

yes

—

116

C₂³×C₈

—

117

C₂×C₂²⋊Q₈

—

118

C₂×Q₃₂

—

119

C₂×Q₃₂

—

120

C₂²×C₁₆

—

121

C₂²×C₁₆

C₂×D₁₃

yes

characteristic

122

#467

—

123

#467

—

124

C₂×#107

—

125

C₂×#103

—

126

#358

—

127

C₂²⋊C₁₆

—

128

C₂²×C₁₃

#447

yes

—

129

C₂²×C₁₃

#466

yes

characteristic

130

C₂²×C₁₃

C₂×Q₃₂

yes

characteristic

131

C₂²×C₁₃

#508

yes

characteristic

132

C₂²×C₁₃

#510

yes

—

133

C₂×D₁₃

—

134

C₂×D₁₃

—

135

C₂×D₁₃

—

136

C₂×D₁₃

—

137

C₂×D₁₃

—

138

C₄×C₁₃

—

139

C₄×C₁₃

#392

yes

characteristic

140

C₄×C₁₃

#449

yes

—

141

C₄×C₁₃

#469

yes

characteristic

142

Dic₁₃

—

143

Dic₁₃

—

144

C₂²×Q₈

—

145

C₂³×C₄

—

146

C₂×Q₁₆

—

147

C₂×Q₁₆

—

148

C₂×Q₁₆

—

149

C₂×Q₁₆

—

150

C₂×Q₁₆

—

151

C₂×Q₁₆

C₂²⋊D₁₃

yes

—

152

C₂²×C₈

—

153

C₂²×C₈

—

154

C₂²×C₈

—

155

C₂²×C₈

—

156

C₂²×C₈

—

157

C₂²×C₈

C₂²×D₁₃

yes

characteristic

158

C₂²⋊Q₈

—

159

C₂²⋊Q₈

—

160

C₂×C₄⋊C₄

—

161

C₂×C₄⋊C₄

—

162

C₂×C₂²⋊C₄

—

163

Q₃₂

—

164

C₂×C₁₆

—

165

C₂×C₁₆

—

166

C₂×C₁₆

—

167

C₂×C₁₆

C₂²⋊D₁₃

yes

—

168

#107

—

169

#107

—

170

#103

—

171

C₂×C₁₃

#1999

yes

characteristic

172

C₂×C₁₃

#2188

yes

—

173

C₂×C₁₃

#2189

yes

—

174

C₂×C₁₃

#2216

yes

characteristic

175

C₂×C₁₃

#2219

yes

characteristic

176

D₁₃

—

177

C₂⁴

—

178

C₂×Q₈

—

179

C₂×Q₈

—

180

C₂×Q₈

—

181

C₂×Q₈

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

—

188

C₂²×C₄

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂²×C₄

D₄×D₁₃

yes

characteristic

192

Q₁₆

—

193

Q₁₆

—

194

Q₁₆

—

195

Q₁₆

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

D₄×D₁₃

yes

—

202

C₂×C₈

#6129

yes

characteristic

203

C₂×C₈

C₂×C₂²⋊D₁₃

yes

—

204

C₂×C₈

C₂×C₂²⋊D₁₃

yes

characteristic

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₂²⋊C₄

—

209

C₁₆

—

210

C₁₆

—

211

C₁₃

#13306

yes

characteristic, complemented, Sylow

212

C₂³

—

213

C₂³

—

214

C₂³

—

215

C₂³

—

216

C₂³

—

217

C₂³

D₈×D₁₃

yes

characteristic

218

Q₈

—

219

Q₈

—

220

Q₈

—

221

Q₈

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

104

—

232

C₂×C₄

—

104

—

233

C₂×C₄

#88165

yes

—

234

C₂×C₄

#88166

yes

characteristic

235

C₂×C₄

#88191

yes

—

236

C₂×C₄

#88192

yes

characteristic

237

C₈

—

238

C₈

#88193

yes

—

239

C₈

#88194

yes

characteristic

240

C₈

#88207

yes

characteristic

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

—

245

C₂²

—

246

C₂²

D₁₃×Q₃₂

yes

characteristic

247

C₂²

#11718579

yes

—

248

C₂²

#11718580

yes

characteristic

249

C₂²

#11718817

yes

—

250

C₂²

#11718818

yes

characteristic

251

C₄

—

252

C₄

—

253

C₄

—

104

—

254

C₄

#11718819

yes

—

255

C₄

#11718820

yes

characteristic

256

C₄

#11718884

yes

characteristic

257

C₂

—

258

C₂

#13115831

yes

characteristic

259

C₂

#13116768

yes

—

260

C₂

#13116775

yes

—

261

C₂

#13116924

yes

characteristic

262

C₂

#13116941

yes

characteristic

	subgroup	G/H
center	C₂³	D₈×D₁₃
commutator, cosocle	C₂²×C₈×C₁₃	C₂³
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₂²×C₁₃×Q₃₂	C₂
socle	C₂³×C₁₃	C₂×D₈
prime radical	C₂³×D₁₃	D₈
hypercenter	C₂²×Q₃₂	D₁₃
hypocenter	C₁₃	#13306
LCS	G ▷ C₂²×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

subgroup

G/H

center

C₂³

D₈×D₁₃

commutator, cosocle

C₂²×C₈×C₁₃

C₂³

Frattini

C₂²×C₈

C₂²×D₁₃

Fitting

C₂²×C₁₃×Q₃₂

C₂

socle

C₂³×C₁₃

C₂×D₈

prime radical

C₂³×D₁₃

D₈

hypercenter

C₂²×Q₃₂

D₁₃

hypocenter

C₁₃

#13306

LCS

G ▷ C₂²×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

N	H ≅ G/N	type
2. C₂×#11718156	C₂	semidirect
4. #13112928	C₂	semidirect
5. C₂²×C₁₃×Q₃₂	C₂	semidirect
81. C₂²×Q₃₂	D₁₃	semidirect
91. C₂²×D₁₃	Q₃₂	semidirect
211. C₁₃	#13306	semidirect

H ≅ G/N

type

2. C₂×#11718156

C₂

semidirect

4. #13112928

C₂

semidirect

5. C₂²×C₁₃×Q₃₂

C₂

semidirect

81. C₂²×Q₃₂

D₁₃

semidirect

91. C₂²×D₁₃

Q₃₂

semidirect

211. C₁₃

#13306

semidirect

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

subgroup	index
C₂×#11718849	2
C₂×#11718156	2
C₂×#11718099	2
#13112928	2
C₂²×C₁₃×Q₃₂	2
#13306	13

subgroup

index

C₂²×C₁₃×Q₃₂

Subgroups — #15781625

Conjugacy classes of subgroups

Complements

Maximal subgroups