Group #15696691 — subgroups

Subgroups — C₁₃×#10352 #15696691

Order 3328.

416 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 138 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×#2571	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1987	C₂	1	2	yes	maximal
3	C₁₃×#1956	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1296	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1279	C₂	1	2	yes	maximal
6	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
8	C₂×C₁₃×#103	—	2	2	no	—
9	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₁₃×#400	—	2	2	no	—
11	C₁₃×#389	—	2	2	no	—
12	C₁₃×#384	C₂²	1	1	yes	characteristic
13	C₁₃×#382	—	2	2	no	—
14	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
15	C₁₃×#340	—	2	2	no	—
16	C₁₃×#340	—	2	2	no	—
17	C₂²×Q₈×C₁₃	—	2	1	no	—
18	C₂²×C₈×C₁₃	—	2	1	no	—
19	C₂²×C₈×C₁₃	—	2	2	no	—
20	C₁₃×C₄⋊Q₈	—	2	2	no	—
21	C₁₃×C₄⋊Q₈	—	2	1	no	—
22	C₁₃×C₄⋊Q₈	Q₈	1	2	yes	—
23	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
24	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
25	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
26	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
27	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
28	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
29	C₂×C₄²×C₁₃	—	2	2	no	—
30	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
31	C₁₃×C₄⋊C₈	—	2	2	no	—
32	C₁₃×C₄⋊C₈	—	2	2	no	—
33	C₁₃×#103	—	4	4	no	—
34	C₄×C₈×C₁₃	—	2	2	no	—
35	C₁₃×#95	—	2	2	no	—
36	C₁₃×#95	—	2	4	no	—
37	C₁₃×#95	—	2	2	no	—
38	#10352	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂×Q₈×C₁₃	—	2	2	no	—
40	C₂×Q₈×C₁₃	—	4	2	no	—
41	C₂×Q₈×C₁₃	—	4	2	no	—
42	C₂×Q₈×C₁₃	—	4	1	no	—
43	C₂²×C₄×C₁₃	—	2	2	no	—
44	C₂²×C₄×C₁₃	—	2	2	no	—
45	C₂²×C₄×C₁₃	—	2	2	no	—
46	C₂²×C₄×C₁₃	—	4	1	no	—
47	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
49	C₂×C₈×C₁₃	—	2	2	no	—
50	C₂×C₈×C₁₃	—	4	1	no	—
51	C₂×C₈×C₁₃	—	4	1	no	—
52	C₂×C₈×C₁₃	—	4	2	no	—
53	C₂×C₈×C₁₃	—	4	2	no	—
54	C₂×C₈×C₁₃	—	4	2	no	—
55	C₁₃×C₄⋊C₄	—	2	4	no	—
56	C₁₃×C₄⋊C₄	—	2	2	no	—
57	C₁₃×C₄⋊C₄	—	2	2	no	—
58	C₁₃×C₄⋊C₄	—	2	2	no	—
59	C₁₃×C₄⋊C₄	—	2	2	no	—
60	C₁₃×C₄⋊C₄	—	4	2	no	—
61	C₁₃×C₄⋊C₄	—	4	2	no	—
62	C₁₃×C₄⋊C₄	—	4	2	no	—
63	C₁₃×C₄⋊C₄	—	4	2	no	—
64	C₁₃×C₄⋊C₄	—	8	2	no	—
65	C₄²×C₁₃	—	4	2	no	—
66	C₄²×C₁₃	—	4	2	no	—
67	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
68	C₄²×C₁₃	#41	1	2	yes	—
69	C₄²×C₁₃	#41	1	1	yes	characteristic
70	#2571	C₂×C₁₃	1	1	yes	characteristic
71	#1987	C₂×C₁₃	1	2	yes	—
72	#1956	C₂×C₁₃	1	1	yes	characteristic
73	#1296	C₂×C₁₃	1	1	yes	characteristic
74	#1279	C₂×C₁₃	1	2	yes	—
75	C₂³×C₁₃	#120	1	1	yes	characteristic
76	Q₈×C₁₃	—	4	4	no	—
77	Q₈×C₁₃	—	8	2	no	—
78	C₂×C₄×C₁₃	—	2	1	no	—
79	C₂×C₄×C₁₃	—	2	1	no	—
80	C₂×C₄×C₁₃	—	4	2	no	—
81	C₂×C₄×C₁₃	—	4	2	no	—
82	C₂×C₄×C₁₃	—	4	2	no	—
83	C₂×C₄×C₁₃	—	4	2	no	—
84	C₂×C₄×C₁₃	—	4	2	no	—
85	C₂×C₄×C₁₃	—	4	4	no	—
86	C₂×C₄×C₁₃	—	4	2	no	—
87	C₂×C₄×C₁₃	—	4	2	no	—
88	C₂×C₄×C₁₃	—	4	2	no	—
89	C₂×C₄×C₁₃	—	8	1	no	—
90	C₂×C₄×C₁₃	—	8	1	no	—
91	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
92	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
93	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
94	C₂×C₄×C₁₃	#124	1	2	yes	—
95	C₂×C₄×C₁₃	#135	1	2	yes	—
96	C₂×C₄×C₁₃	#135	1	2	yes	—
97	C₂×C₄×C₁₃	#137	1	2	yes	—
98	C₂×C₄×C₁₃	#137	1	2	yes	—
99	C₈×C₁₃	—	4	2	no	—
100	C₈×C₁₃	—	8	2	no	—
101	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
102	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
103	C₂×#103	—	2	2	no	—
104	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
105	#400	—	2	2	no	—
106	#389	—	2	2	no	—
107	#384	C₂²×C₁₃	1	1	yes	characteristic
108	#382	—	2	2	no	—
109	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
110	#340	—	2	2	no	—
111	#340	—	2	2	no	—
112	C₂²×C₁₃	#393	1	1	yes	characteristic
113	C₂²×C₁₃	#452	1	2	yes	—
114	C₂²×C₁₃	#452	1	2	yes	—
115	C₂²×C₁₃	#453	1	1	yes	characteristic
116	C₂²×C₁₃	#454	1	1	yes	characteristic
117	C₄×C₁₃	—	2	1	no	—
118	C₄×C₁₃	—	2	1	no	—
119	C₄×C₁₃	—	8	2	no	—
120	C₄×C₁₃	—	8	2	no	—
121	C₄×C₁₃	—	8	2	no	—
122	C₄×C₁₃	—	8	2	no	—
123	C₄×C₁₃	#479	1	2	yes	—
124	C₄×C₁₃	#479	1	2	yes	—
125	C₄×C₁₃	#488	1	2	yes	—
126	C₄×C₁₃	#491	1	2	yes	—
127	C₂²×Q₈	—	2	1	no	—
128	C₂²×C₈	—	2	1	no	—
129	C₂²×C₈	—	2	2	no	—
130	C₄⋊Q₈	—	2	2	no	—
131	C₄⋊Q₈	—	2	1	no	—
132	C₄⋊Q₈	Q₈×C₁₃	1	2	yes	—
133	C₂×C₄⋊C₄	—	2	2	no	—
134	C₂×C₄⋊C₄	—	2	2	no	—
135	C₂×C₄⋊C₄	—	2	2	no	—
136	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
137	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
138	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
139	C₂×C₄²	—	2	2	no	—
140	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
141	C₄⋊C₈	—	2	2	no	—
142	C₄⋊C₈	—	2	2	no	—
143	#103	—	4	4	no	—
144	C₄×C₈	—	2	2	no	—
145	#95	—	2	2	no	—
146	#95	—	2	4	no	—
147	#95	—	2	2	no	—
148	C₂×C₁₃	#1630	1	1	yes	characteristic
149	C₂×C₁₃	#1634	1	1	yes	characteristic
150	C₂×C₁₃	#1638	1	2	yes	—
151	C₂×C₁₃	#2026	1	2	yes	—
152	C₂×C₁₃	#2027	1	1	yes	characteristic
153	C₂×Q₈	—	2	2	no	—
154	C₂×Q₈	—	4	2	no	—
155	C₂×Q₈	—	4	2	no	—
156	C₂×Q₈	—	4	1	no	—
157	C₂²×C₄	—	2	2	no	—
158	C₂²×C₄	—	2	2	no	—
159	C₂²×C₄	—	2	2	no	—
160	C₂²×C₄	—	4	1	no	—
161	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
162	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
163	C₂×C₈	—	2	2	no	—
164	C₂×C₈	—	4	1	no	—
165	C₂×C₈	—	4	1	no	—
166	C₂×C₈	—	4	2	no	—
167	C₂×C₈	—	4	2	no	—
168	C₂×C₈	—	4	2	no	—
169	C₄⋊C₄	—	2	4	no	—
170	C₄⋊C₄	—	2	2	no	—
171	C₄⋊C₄	—	2	2	no	—
172	C₄⋊C₄	—	2	2	no	—
173	C₄⋊C₄	—	2	2	no	—
174	C₄⋊C₄	—	4	2	no	—
175	C₄⋊C₄	—	4	2	no	—
176	C₄⋊C₄	—	4	2	no	—
177	C₄⋊C₄	—	4	2	no	—
178	C₄⋊C₄	—	8	2	no	—
179	C₄²	—	4	2	no	—
180	C₄²	—	4	2	no	—
181	C₄²	C₂×Q₈×C₁₃	1	1	yes	characteristic
182	C₄²	C₁₃×#41	1	2	yes	—
183	C₄²	C₁₃×#41	1	1	yes	characteristic
184	C₁₃	#10352	1	1	yes	characteristic, direct product factor, Sylow
185	C₂³	C₁₃×#120	1	1	yes	characteristic
186	Q₈	—	4	4	no	—
187	Q₈	—	8	2	no	—
188	C₂×C₄	—	2	1	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	4	2	no	—
191	C₂×C₄	—	4	2	no	—
192	C₂×C₄	—	4	2	no	—
193	C₂×C₄	—	4	2	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	—	4	4	no	—
196	C₂×C₄	—	4	2	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	—	8	1	no	—
200	C₂×C₄	—	8	1	no	—
201	C₂×C₄	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
202	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
203	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
204	C₂×C₄	C₁₃×#124	1	2	yes	—
205	C₂×C₄	C₁₃×#135	1	2	yes	—
206	C₂×C₄	C₁₃×#135	1	2	yes	—
207	C₂×C₄	C₁₃×#137	1	2	yes	—
208	C₂×C₄	C₁₃×#137	1	2	yes	—
209	C₈	—	4	2	no	—
210	C₈	—	8	2	no	—
211	C₂²	C₁₃×#393	1	1	yes	characteristic
212	C₂²	C₁₃×#452	1	2	yes	—
213	C₂²	C₁₃×#452	1	2	yes	—
214	C₂²	C₁₃×#453	1	1	yes	characteristic
215	C₂²	C₁₃×#454	1	1	yes	characteristic
216	C₄	—	2	1	no	—
217	C₄	—	2	1	no	—
218	C₄	—	8	2	no	—
219	C₄	—	8	2	no	—
220	C₄	—	8	2	no	—
221	C₄	—	8	2	no	—
222	C₄	C₁₃×#479	1	2	yes	—
223	C₄	C₁₃×#479	1	2	yes	—
224	C₄	C₁₃×#488	1	2	yes	—
225	C₄	C₁₃×#491	1	2	yes	—
226	C₂	C₁₃×#1630	1	1	yes	characteristic
227	C₂	C₁₃×#1634	1	1	yes	characteristic
228	C₂	C₁₃×#1638	1	2	yes	—
229	C₂	C₁₃×#2026	1	2	yes	—
230	C₂	C₁₃×#2027	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#2571

C₂

yes

maximal, characteristic

C₁₃×#1987

C₂

yes

maximal

C₁₃×#1956

C₂

yes

maximal, characteristic

C₁₃×#1296

C₂

yes

maximal, characteristic

C₁₃×#1279

C₂

yes

maximal

C₂×C₁₃×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₁₃×C₄⋊C₈

C₂²

yes

—

C₂×C₁₃×#103

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₁₃×#400

—

C₁₃×#389

—

C₁₃×#384

C₂²

yes

characteristic

C₁₃×#382

—

C₄×C₁₃×C₄⋊C₄

C₂²

yes

—

C₁₃×#340

—

C₁₃×#340

—

C₂²×Q₈×C₁₃

—

C₂²×C₈×C₁₃

—

C₂²×C₈×C₁₃

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

Q₈

yes

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

D₄

yes

—

C₂×C₁₃×C₄⋊C₄

D₄

yes

—

C₂×C₁₃×C₄⋊C₄

D₄

yes

—

C₂×C₄²×C₁₃

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₁₃×C₄⋊C₈

—

C₁₃×C₄⋊C₈

—

C₁₃×#103

—

C₄×C₈×C₁₃

—

C₁₃×#95

—

C₁₃×#95

—

C₁₃×#95

—

#10352

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂×C₈×C₁₃

—

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×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

C₂×Q₈

yes

characteristic

C₄²×C₁₃

#41

yes

—

C₄²×C₁₃

#41

yes

characteristic

#2571

C₂×C₁₃

yes

characteristic

#1987

C₂×C₁₃

yes

—

#1956

C₂×C₁₃

yes

characteristic

#1296

C₂×C₁₃

yes

characteristic

#1279

C₂×C₁₃

yes

—

C₂³×C₁₃

#120

yes

characteristic

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

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₃

#124

yes

characteristic

C₂×C₄×C₁₃

#124

yes

—

C₂×C₄×C₁₃

#135

yes

—

C₂×C₄×C₁₃

#135

yes

—

C₂×C₄×C₁₃

#137

yes

—

C₂×C₄×C₁₃

#137

yes

—

C₈×C₁₃

—

100

C₈×C₁₃

—

101

C₂×C₄⋊Q₈

C₂²×C₁₃

yes

characteristic

102

C₂×C₄⋊C₈

C₂²×C₁₃

yes

—

103

C₂×#103

—

104

C₂×C₄×C₈

C₂²×C₁₃

yes

characteristic

105

#400

—

106

#389

—

107

#384

C₂²×C₁₃

yes

characteristic

108

#382

—

109

C₄×C₄⋊C₄

C₂²×C₁₃

yes

—

110

#340

—

111

#340

—

112

C₂²×C₁₃

#393

yes

characteristic

113

C₂²×C₁₃

#452

yes

—

114

C₂²×C₁₃

#452

yes

—

115

C₂²×C₁₃

#453

yes

characteristic

116

C₂²×C₁₃

#454

yes

characteristic

117

C₄×C₁₃

—

118

C₄×C₁₃

—

119

C₄×C₁₃

—

120

C₄×C₁₃

—

121

C₄×C₁₃

—

122

C₄×C₁₃

—

123

C₄×C₁₃

#479

yes

—

124

C₄×C₁₃

#479

yes

—

125

C₄×C₁₃

#488

yes

—

126

C₄×C₁₃

#491

yes

—

127

C₂²×Q₈

—

128

C₂²×C₈

—

129

C₂²×C₈

—

130

C₄⋊Q₈

—

131

C₄⋊Q₈

—

132

C₄⋊Q₈

Q₈×C₁₃

yes

—

133

C₂×C₄⋊C₄

—

134

C₂×C₄⋊C₄

—

135

C₂×C₄⋊C₄

—

136

C₂×C₄⋊C₄

D₄×C₁₃

yes

—

137

C₂×C₄⋊C₄

D₄×C₁₃

yes

—

138

C₂×C₄⋊C₄

D₄×C₁₃

yes

—

139

C₂×C₄²

—

140

C₂×C₄²

C₂³×C₁₃

yes

characteristic

141

C₄⋊C₈

—

142

C₄⋊C₈

—

143

#103

—

144

C₄×C₈

—

145

#95

—

146

#95

—

147

#95

—

148

C₂×C₁₃

#1630

yes

characteristic

149

C₂×C₁₃

#1634

yes

characteristic

150

C₂×C₁₃

#1638

yes

—

151

C₂×C₁₃

#2026

yes

—

152

C₂×C₁₃

#2027

yes

characteristic

153

C₂×Q₈

—

154

C₂×Q₈

—

155

C₂×Q₈

—

156

C₂×Q₈

—

157

C₂²×C₄

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

C₂×D₄×C₁₃

yes

characteristic

162

C₂²×C₄

C₂×D₄×C₁₃

yes

—

163

C₂×C₈

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄²

—

180

C₄²

—

181

C₄²

C₂×Q₈×C₁₃

yes

characteristic

182

C₄²

C₁₃×#41

yes

—

183

C₄²

C₁₃×#41

yes

characteristic

184

C₁₃

#10352

yes

characteristic, direct product factor, Sylow

185

C₂³

C₁₃×#120

yes

characteristic

186

Q₈

—

187

Q₈

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

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

C₁₃×C₂²⋊Q₈

yes

characteristic

202

C₂×C₄

C₁₃×C₂²⋊Q₈

yes

—

203

C₂×C₄

C₁₃×#124

yes

characteristic

204

C₂×C₄

C₁₃×#124

yes

—

205

C₂×C₄

C₁₃×#135

yes

—

206

C₂×C₄

C₁₃×#135

yes

—

207

C₂×C₄

C₁₃×#137

yes

—

208

C₂×C₄

C₁₃×#137

yes

—

209

C₈

—

210

C₈

—

211

C₂²

C₁₃×#393

yes

characteristic

212

C₂²

C₁₃×#452

yes

—

213

C₂²

C₁₃×#452

yes

—

214

C₂²

C₁₃×#453

yes

characteristic

215

C₂²

C₁₃×#454

yes

characteristic

216

C₄

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

C₁₃×#479

yes

—

223

C₄

C₁₃×#479

yes

—

224

C₄

C₁₃×#488

yes

—

225

C₄

C₁₃×#491

yes

—

226

C₂

C₁₃×#1630

yes

characteristic

227

C₂

C₁₃×#1634

yes

characteristic

228

C₂

C₁₃×#1638

yes

—

229

C₂

C₁₃×#2026

yes

—

230

C₂

C₁₃×#2027

yes

characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₁₃

#120

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₁₃

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

N	H ≅ G/N	type
38. #10352	C₁₃	direct (N × H)
184. C₁₃	#10352	direct (N × H)

H ≅ G/N

type

38. #10352

C₁₃

direct (N × H)

184. C₁₃

#10352

direct (N × H)

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

subgroup	index
C₁₃×#2571	2
C₁₃×#1987	2
C₁₃×#1956	2
C₁₃×#1296	2
C₁₃×#1279	2
#10352	13

subgroup

index

C₁₃×#2571

C₁₃×#1987

C₁₃×#1956

C₁₃×#1296

C₁₃×#1279

#10352

Subgroups — C₁₃×#10352 #15696691

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#10352 #15696691

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10352 #15696691