Group #15696861 — subgroups

Subgroups — C₁₃×#10522 #15696861

Order 3328.

402 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 114 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	C₁₃×#3249	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1994	C₂	1	2	yes	maximal
3	C₁₃×#1842	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1550	C₂	1	2	yes	maximal
5	C₁₃×#1292	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#533	C₂²	1	2	yes	—
7	C₁₃×#477	—	2	2	no	—
8	C₁₃×#467	—	2	2	no	—
9	C₁₃×#462	—	2	2	no	—
10	C₁₃×#423	C₂²	1	2	yes	—
11	C₂×C₁₃×C₄⋊C₈	—	2	2	no	—
12	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₄³×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#339	—	2	2	no	—
16	C₁₃×#339	—	2	2	no	—
17	C₁₃×#333	—	2	2	no	—
18	C₁₃×#332	—	2	2	no	—
19	C₂×C₁₃×Q₁₆	—	2	2	no	—
20	C₂×C₁₃×M₁₆	—	2	2	no	—
21	C₂²×C₈×C₁₃	—	2	1	no	—
22	C₂²×C₈×C₁₃	D₄	1	2	yes	—
23	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
24	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
25	C₁₃×#125	—	2	2	no	—
26	C₁₃×C₂²⋊Q₈	—	2	2	no	—
27	C₁₃×C₂²⋊Q₈	—	2	2	no	—
28	C₄×Q₈×C₁₃	—	2	2	no	—
29	C₄×Q₈×C₁₃	—	2	2	no	—
30	C₁₃×#117	—	2	2	no	—
31	C₂×C₄²×C₁₃	—	2	1	no	—
32	C₂×C₄²×C₁₃	—	2	1	no	—
33	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
36	C₁₃×#107	—	2	2	no	—
37	C₁₃×C₄⋊C₈	—	2	2	no	—
38	C₁₃×C₄⋊C₈	—	2	2	no	—
39	C₁₃×C₄⋊C₈	—	2	2	no	—
40	C₁₃×C₄⋊C₈	—	2	2	no	—
41	C₁₃×C₄⋊C₈	—	4	4	no	—
42	C₁₃×#103	—	2	4	no	—
43	#10522	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×Q₈×C₁₃	—	2	2	no	—
45	C₂×Q₈×C₁₃	—	2	2	no	—
46	C₂²×C₄×C₁₃	—	2	1	no	—
47	C₂²×C₄×C₁₃	—	2	1	no	—
48	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
51	C₁₃×Q₁₆	—	8	2	no	—
52	C₁₃×M₁₆	—	4	2	no	—
53	C₁₃×M₁₆	—	4	2	no	—
54	C₂×C₈×C₁₃	—	2	2	no	—
55	C₂×C₈×C₁₃	—	4	2	no	—
56	C₂×C₈×C₁₃	—	4	2	no	—
57	C₂×C₈×C₁₃	—	4	1	no	—
58	C₂×C₈×C₁₃	—	4	2	no	—
59	C₁₃×C₄⋊C₄	—	2	2	no	—
60	C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₁₃×C₄⋊C₄	—	2	2	no	—
63	C₁₃×C₄⋊C₄	—	4	2	no	—
64	C₁₃×C₄⋊C₄	—	4	2	no	—
65	C₁₃×C₂²⋊C₄	—	4	2	no	—
66	C₄²×C₁₃	—	2	2	no	—
67	C₄²×C₁₃	—	2	2	no	—
68	C₄²×C₁₃	—	2	1	no	—
69	C₄²×C₁₃	—	2	2	no	—
70	C₄²×C₁₃	—	4	2	no	—
71	C₄²×C₁₃	—	4	2	no	—
72	C₄²×C₁₃	Q₁₆	1	2	yes	complemented
73	C₄²×C₁₃	C₂×D₄	1	2	yes	—
74	C₄²×C₁₃	#41	1	2	yes	—
75	#3249	C₂×C₁₃	1	1	yes	characteristic
76	#1994	C₂×C₁₃	1	2	yes	—
77	#1842	C₂×C₁₃	1	1	yes	characteristic
78	#1550	C₂×C₁₃	1	2	yes	—
79	#1292	C₂×C₁₃	1	1	yes	characteristic
80	C₂³×C₁₃	#121	1	1	yes	characteristic
81	Q₈×C₁₃	—	4	2	no	—
82	Q₈×C₁₃	—	4	2	no	—
83	Q₈×C₁₃	—	8	2	no	—
84	C₂×C₄×C₁₃	—	2	2	no	—
85	C₂×C₄×C₁₃	—	2	2	no	—
86	C₂×C₄×C₁₃	—	2	2	no	—
87	C₂×C₄×C₁₃	—	2	1	no	—
88	C₂×C₄×C₁₃	—	2	1	no	—
89	C₂×C₄×C₁₃	—	2	2	no	—
90	C₂×C₄×C₁₃	—	4	1	no	—
91	C₂×C₄×C₁₃	—	4	1	no	—
92	C₂×C₄×C₁₃	—	4	1	no	—
93	C₂×C₄×C₁₃	—	4	2	no	—
94	C₂×C₄×C₁₃	—	4	2	no	—
95	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
96	C₂×C₄×C₁₃	#121	1	2	yes	—
97	C₂×C₄×C₁₃	#123	1	2	yes	—
98	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
99	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
100	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
101	C₂×C₄×C₁₃	#137	1	2	yes	—
102	C₈×C₁₃	—	4	2	no	—
103	C₈×C₁₃	—	8	1	no	—
104	C₈×C₁₃	—	8	2	no	—
105	#533	C₂²×C₁₃	1	2	yes	—
106	#477	—	2	2	no	—
107	#467	—	2	2	no	—
108	#462	—	2	2	no	—
109	#423	C₂²×C₁₃	1	2	yes	—
110	C₂×C₄⋊C₈	—	2	2	no	—
111	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
112	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
113	C₄³	C₂²×C₁₃	1	1	yes	characteristic
114	#339	—	2	2	no	—
115	#339	—	2	2	no	—
116	#333	—	2	2	no	—
117	#332	—	2	2	no	—
118	C₂²×C₁₃	—	2	1	no	—
119	C₂²×C₁₃	—	2	1	no	—
120	C₂²×C₁₃	#394	1	1	yes	characteristic
121	C₂²×C₁₃	#467	1	1	yes	characteristic
122	C₂²×C₁₃	#470	1	1	yes	characteristic
123	C₄×C₁₃	—	2	4	no	—
124	C₄×C₁₃	—	2	2	no	—
125	C₄×C₁₃	—	2	1	no	—
126	C₄×C₁₃	—	4	2	no	—
127	C₄×C₁₃	—	8	2	no	—
128	C₄×C₁₃	—	8	2	no	—
129	C₄×C₁₃	#453	1	1	yes	characteristic
130	C₄×C₁₃	#456	1	1	yes	characteristic
131	C₄×C₁₃	#462	1	2	yes	—
132	C₄×C₁₃	#464	1	2	yes	—
133	C₂×Q₁₆	—	2	2	no	—
134	C₂×M₁₆	—	2	2	no	—
135	C₂²×C₈	—	2	1	no	—
136	C₂²×C₈	D₄×C₁₃	1	2	yes	—
137	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
138	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
139	#125	—	2	2	no	—
140	C₂²⋊Q₈	—	2	2	no	—
141	C₂²⋊Q₈	—	2	2	no	—
142	C₄×Q₈	—	2	2	no	—
143	C₄×Q₈	—	2	2	no	—
144	#117	—	2	2	no	—
145	C₂×C₄²	—	2	1	no	—
146	C₂×C₄²	—	2	1	no	—
147	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
148	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
149	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
150	#107	—	2	2	no	—
151	C₄⋊C₈	—	2	2	no	—
152	C₄⋊C₈	—	2	2	no	—
153	C₄⋊C₈	—	2	2	no	—
154	C₄⋊C₈	—	2	2	no	—
155	C₄⋊C₈	—	4	4	no	—
156	#103	—	2	4	no	—
157	C₂×C₁₃	—	2	1	no	—
158	C₂×C₁₃	—	2	1	no	—
159	C₂×C₁₃	#2039	1	1	yes	characteristic
160	C₂×C₁₃	#2050	1	1	yes	characteristic
161	C₂×C₁₃	#2056	1	1	yes	characteristic
162	C₂×Q₈	—	2	2	no	—
163	C₂×Q₈	—	2	2	no	—
164	C₂²×C₄	—	2	1	no	—
165	C₂²×C₄	—	2	1	no	—
166	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
167	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
168	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
169	Q₁₆	—	8	2	no	—
170	M₁₆	—	4	2	no	—
171	M₁₆	—	4	2	no	—
172	C₂×C₈	—	2	2	no	—
173	C₂×C₈	—	4	2	no	—
174	C₂×C₈	—	4	2	no	—
175	C₂×C₈	—	4	1	no	—
176	C₂×C₈	—	4	2	no	—
177	C₄⋊C₄	—	2	2	no	—
178	C₄⋊C₄	—	2	2	no	—
179	C₄⋊C₄	—	2	2	no	—
180	C₄⋊C₄	—	2	2	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₄⋊C₄	—	4	2	no	—
183	C₂²⋊C₄	—	4	2	no	—
184	C₄²	—	2	2	no	—
185	C₄²	—	2	2	no	—
186	C₄²	—	2	1	no	—
187	C₄²	—	2	2	no	—
188	C₄²	—	4	2	no	—
189	C₄²	—	4	2	no	—
190	C₄²	C₁₃×Q₁₆	1	2	yes	complemented
191	C₄²	C₂×D₄×C₁₃	1	2	yes	—
192	C₄²	C₁₃×#41	1	2	yes	—
193	C₁₃	#10522	1	1	yes	characteristic, direct product factor, Sylow
194	C₂³	C₁₃×#121	1	1	yes	characteristic
195	Q₈	—	4	2	no	—
196	Q₈	—	4	2	no	—
197	Q₈	—	8	2	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	2	1	no	—
202	C₂×C₄	—	2	1	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	4	1	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
210	C₂×C₄	C₁₃×#121	1	2	yes	—
211	C₂×C₄	C₁₃×#123	1	2	yes	—
212	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
213	C₂×C₄	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
214	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
215	C₂×C₄	C₁₃×#137	1	2	yes	—
216	C₈	—	4	2	no	—
217	C₈	—	8	1	no	—
218	C₈	—	8	2	no	—
219	C₂²	—	2	1	no	—
220	C₂²	—	2	1	no	—
221	C₂²	C₁₃×#394	1	1	yes	characteristic
222	C₂²	C₁₃×#467	1	1	yes	characteristic
223	C₂²	C₁₃×#470	1	1	yes	characteristic
224	C₄	—	2	4	no	—
225	C₄	—	2	1	no	—
226	C₄	—	2	2	no	—
227	C₄	—	4	2	no	—
228	C₄	—	8	2	no	—
229	C₄	—	8	2	no	—
230	C₄	C₁₃×#453	1	1	yes	characteristic
231	C₄	C₁₃×#456	1	1	yes	characteristic
232	C₄	C₁₃×#462	1	2	yes	—
233	C₄	C₁₃×#464	1	2	yes	—
234	C₂	—	2	1	no	—
235	C₂	—	2	1	no	—
236	C₂	C₁₃×#2039	1	1	yes	characteristic
237	C₂	C₁₃×#2050	1	1	yes	characteristic
238	C₂	C₁₃×#2056	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#3249

C₂

yes

maximal, characteristic

C₁₃×#1994

C₂

yes

maximal

C₁₃×#1842

C₂

yes

maximal, characteristic

C₁₃×#1550

C₂

yes

maximal

C₁₃×#1292

C₂

yes

maximal, characteristic

C₁₃×#533

C₂²

yes

—

C₁₃×#477

—

C₁₃×#467

—

C₁₃×#462

—

C₁₃×#423

C₂²

yes

—

C₂×C₁₃×C₄⋊C₈

—

C₂×C₁₃×C₄⋊C₈

C₂²

yes

characteristic

C₂×C₁₃×C₄⋊C₈

C₂²

yes

characteristic

C₄³×C₁₃

C₂²

yes

characteristic

C₁₃×#339

—

C₁₃×#339

—

C₁₃×#333

—

C₁₃×#332

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×M₁₆

—

C₂²×C₈×C₁₃

—

C₂²×C₈×C₁₃

D₄

yes

—

C₁₃×C₄⋊Q₈

D₄

yes

—

C₁₃×C₄⋊Q₈

D₄

yes

—

C₁₃×#125

—

C₁₃×C₂²⋊Q₈

—

C₁₃×C₂²⋊Q₈

—

C₄×Q₈×C₁₃

—

C₄×Q₈×C₁₃

—

C₁₃×#117

—

C₂×C₄²×C₁₃

—

C₂×C₄²×C₁₃

—

C₂×C₄²×C₁₃

D₄

yes

characteristic

C₂×C₄²×C₁₃

D₄

yes

characteristic

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₁₃×#107

—

C₁₃×C₄⋊C₈

—

C₁₃×C₄⋊C₈

—

C₁₃×C₄⋊C₈

—

C₁₃×C₄⋊C₈

—

C₁₃×C₄⋊C₈

—

C₁₃×#103

—

#10522

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃

#41

yes

characteristic

C₁₃×Q₁₆

—

C₁₃×M₁₆

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₂²⋊C₄

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

Q₁₆

yes

complemented

C₄²×C₁₃

C₂×D₄

yes

—

C₄²×C₁₃

#41

yes

—

#3249

C₂×C₁₃

yes

characteristic

#1994

C₂×C₁₃

yes

—

#1842

C₂×C₁₃

yes

characteristic

#1550

C₂×C₁₃

yes

—

#1292

C₂×C₁₃

yes

characteristic

C₂³×C₁₃

#121

yes

characteristic

Q₈×C₁₃

—

Q₈×C₁₃

—

Q₈×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

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#120

yes

characteristic

C₂×C₄×C₁₃

#121

yes

—

C₂×C₄×C₁₃

#123

yes

—

C₂×C₄×C₁₃

#124

yes

characteristic

C₂×C₄×C₁₃

C₂×Q₁₆

yes

characteristic

100

C₂×C₄×C₁₃

#135

yes

characteristic

101

C₂×C₄×C₁₃

#137

yes

—

102

C₈×C₁₃

—

103

C₈×C₁₃

—

104

C₈×C₁₃

—

105

#533

C₂²×C₁₃

yes

—

106

#477

—

107

#467

—

108

#462

—

109

#423

C₂²×C₁₃

yes

—

110

C₂×C₄⋊C₈

—

111

C₂×C₄⋊C₈

C₂²×C₁₃

yes

characteristic

112

C₂×C₄⋊C₈

C₂²×C₁₃

yes

characteristic

113

C₄³

C₂²×C₁₃

yes

characteristic

114

#339

—

115

#339

—

116

#333

—

117

#332

—

118

C₂²×C₁₃

—

119

C₂²×C₁₃

—

120

C₂²×C₁₃

#394

yes

characteristic

121

C₂²×C₁₃

#467

yes

characteristic

122

C₂²×C₁₃

#470

yes

characteristic

123

C₄×C₁₃

—

124

C₄×C₁₃

—

125

C₄×C₁₃

—

126

C₄×C₁₃

—

127

C₄×C₁₃

—

128

C₄×C₁₃

—

129

C₄×C₁₃

#453

yes

characteristic

130

C₄×C₁₃

#456

yes

characteristic

131

C₄×C₁₃

#462

yes

—

132

C₄×C₁₃

#464

yes

—

133

C₂×Q₁₆

—

134

C₂×M₁₆

—

135

C₂²×C₈

—

136

C₂²×C₈

D₄×C₁₃

yes

—

137

C₄⋊Q₈

D₄×C₁₃

yes

—

138

C₄⋊Q₈

D₄×C₁₃

yes

—

139

#125

—

140

C₂²⋊Q₈

—

141

C₂²⋊Q₈

—

142

C₄×Q₈

—

143

C₄×Q₈

—

144

#117

—

145

C₂×C₄²

—

146

C₂×C₄²

—

147

C₂×C₄²

D₄×C₁₃

yes

characteristic

148

C₂×C₄²

D₄×C₁₃

yes

characteristic

149

C₂×C₄²

C₂³×C₁₃

yes

characteristic

150

#107

—

151

C₄⋊C₈

—

152

C₄⋊C₈

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

#103

—

157

C₂×C₁₃

—

158

C₂×C₁₃

—

159

C₂×C₁₃

#2039

yes

characteristic

160

C₂×C₁₃

#2050

yes

characteristic

161

C₂×C₁₃

#2056

yes

characteristic

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂²×C₄

—

165

C₂²×C₄

—

166

C₂²×C₄

C₂×D₄×C₁₃

yes

characteristic

167

C₂²×C₄

C₂×D₄×C₁₃

yes

characteristic

168

C₂²×C₄

C₁₃×#41

yes

characteristic

169

Q₁₆

—

170

M₁₆

—

171

M₁₆

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₂²⋊C₄

—

184

C₄²

—

185

C₄²

—

186

C₄²

—

187

C₄²

—

188

C₄²

—

189

C₄²

—

190

C₄²

C₁₃×Q₁₆

yes

complemented

191

C₄²

C₂×D₄×C₁₃

yes

—

192

C₄²

C₁₃×#41

yes

—

193

C₁₃

#10522

yes

characteristic, direct product factor, Sylow

194

C₂³

C₁₃×#121

yes

characteristic

195

Q₈

—

196

Q₈

—

197

Q₈

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

C₁₃×#120

yes

characteristic

210

C₂×C₄

C₁₃×#121

yes

—

211

C₂×C₄

C₁₃×#123

yes

—

212

C₂×C₄

C₁₃×#124

yes

characteristic

213

C₂×C₄

C₂×C₁₃×Q₁₆

yes

characteristic

214

C₂×C₄

C₁₃×#135

yes

characteristic

215

C₂×C₄

C₁₃×#137

yes

—

216

C₈

—

217

C₈

—

218

C₈

—

219

C₂²

—

220

C₂²

—

221

C₂²

C₁₃×#394

yes

characteristic

222

C₂²

C₁₃×#467

yes

characteristic

223

C₂²

C₁₃×#470

yes

characteristic

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

C₁₃×#453

yes

characteristic

231

C₄

C₁₃×#456

yes

characteristic

232

C₄

C₁₃×#462

yes

—

233

C₄

C₁₃×#464

yes

—

234

C₂

—

235

C₂

—

236

C₂

C₁₃×#2039

yes

characteristic

237

C₂

C₁₃×#2050

yes

characteristic

238

C₂

C₁₃×#2056

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	#394
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂³×C₁₃	#121
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₃

#394

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₁₃

prime radical

C₂³×C₁₃

#121

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

N	H ≅ G/N	type
43. #10522	C₁₃	direct (N × H)
72. C₄²×C₁₃	Q₁₆	semidirect
190. C₄²	C₁₃×Q₁₆	semidirect
193. C₁₃	#10522	direct (N × H)

H ≅ G/N

type

43. #10522

C₁₃

direct (N × H)

72. C₄²×C₁₃

Q₁₆

semidirect

190. C₄²

C₁₃×Q₁₆

semidirect

193. C₁₃

#10522

direct (N × H)

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

subgroup	index
C₁₃×#3249	2
C₁₃×#1994	2
C₁₃×#1842	2
C₁₃×#1550	2
C₁₃×#1292	2
#10522	13

subgroup

index

C₁₃×#3249

C₁₃×#1994

C₁₃×#1842

C₁₃×#1550

C₁₃×#1292

#10522

Subgroups — C₁₃×#10522 #15696861

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#10522 #15696861

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10522 #15696861