Group #15699652 — subgroups

Subgroups — C₁₃×#13313 #15699652

Order 3328.

556 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 118 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	C₂²×C₁₃×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#472	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#361	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2113	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1381	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
7	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
8	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×D₁₆	—	2	4	no	—
10	C₂×C₁₃×D₁₆	—	2	2	no	—
11	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
12	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
13	C₁₃×#472	—	2	4	no	—
14	C₁₃×#472	—	2	4	no	—
15	C₂×C₁₃×#108	C₂²	1	2	yes	—
16	C₂×C₁₃×#100	—	2	2	no	—
17	C₁₃×#361	—	2	4	no	—
18	C₁₃×C₂²⋊C₁₆	—	2	2	no	—
19	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
20	C₂²×D₄×C₁₃	—	2	2	no	—
21	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
22	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
23	C₂×C₁₃×SD₁₆	—	4	2	no	—
24	C₂×C₁₃×D₈	—	2	2	no	—
25	C₂×C₁₃×D₈	—	2	2	no	—
26	C₂×C₁₃×D₈	—	2	2	no	—
27	C₂×C₁₃×D₈	—	2	2	no	—
28	C₂×C₁₃×D₈	—	2	2	no	—
29	C₂×C₁₃×D₈	—	4	2	no	—
30	C₂×C₁₃×D₈	D₄	1	4	yes	—
31	C₁₃×#131	—	2	2	no	—
32	C₁₃×#131	—	2	2	no	—
33	C₂×C₁₃×M₁₆	—	2	1	no	—
34	C₂×C₁₃×M₁₆	—	2	2	no	—
35	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₁₃	—	2	1	no	—
37	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
38	C₁₃×D₁₆	—	2	8	no	—
39	C₁₃×M₃₂	—	2	2	no	—
40	C₂×C₁₃×C₁₆	—	2	2	no	—
41	C₂×C₁₃×C₁₆	—	2	1	no	—
42	C₂×C₁₃×C₁₆	D₄	1	2	yes	—
43	C₁₃×#108	—	2	2	no	—
44	C₁₃×#108	D₄	1	4	yes	—
45	C₁₃×#100	—	2	8	no	—
46	#13313	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	C₂⁴×C₁₃	—	4	2	no	—
48	C₁₃×#41	—	2	2	no	—
49	C₁₃×#41	—	2	2	no	—
50	C₂×Q₈×C₁₃	D₈	1	1	yes	characteristic
51	C₂×D₄×C₁₃	—	2	1	no	—
52	C₂×D₄×C₁₃	—	2	4	no	—
53	C₂×D₄×C₁₃	—	4	2	no	—
54	C₂×D₄×C₁₃	—	4	2	no	—
55	C₂×D₄×C₁₃	—	4	2	no	—
56	C₂×D₄×C₁₃	—	4	2	no	—
57	C₂×D₄×C₁₃	—	4	2	no	—
58	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
59	C₂²×C₄×C₁₃	—	2	1	no	—
60	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
61	C₁₃×SD₁₆	—	4	8	no	—
62	C₁₃×D₈	—	2	4	no	—
63	C₁₃×D₈	—	2	4	no	—
64	C₁₃×D₈	—	4	8	no	—
65	C₁₃×D₈	—	4	2	no	—
66	C₁₃×D₈	—	4	2	no	—
67	C₁₃×M₁₆	—	2	2	no	—
68	C₁₃×M₁₆	—	2	4	no	—
69	C₁₃×M₁₆	—	4	2	no	—
70	C₁₃×M₁₆	—	4	2	no	—
71	C₂×C₈×C₁₃	—	2	1	no	—
72	C₂×C₈×C₁₃	—	4	2	no	—
73	C₂×C₈×C₁₃	—	4	1	no	—
74	C₂×C₈×C₁₃	—	4	1	no	—
75	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
76	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
77	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
78	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
79	C₁₃×C₁₆	—	2	2	no	—
80	C₁₃×C₁₆	—	4	1	no	—
81	C₂²×D₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
82	C₂×#472	C₂×C₁₃	1	2	yes	complemented
83	C₂×#361	C₂×C₁₃	1	2	yes	complemented
84	#2113	C₂×C₁₃	1	1	yes	characteristic, complemented
85	#1381	C₂×C₁₃	1	1	yes	characteristic, complemented
86	C₂³×C₁₃	—	2	1	no	—
87	C₂³×C₁₃	—	4	4	no	—
88	C₂³×C₁₃	—	8	2	no	—
89	C₂³×C₁₃	—	8	2	no	—
90	C₂³×C₁₃	—	16	4	no	—
91	C₂³×C₁₃	#135	1	1	yes	characteristic
92	Q₈×C₁₃	—	2	2	no	—
93	D₄×C₁₃	—	2	2	no	—
94	D₄×C₁₃	—	4	2	no	—
95	D₄×C₁₃	—	4	4	no	—
96	D₄×C₁₃	—	4	4	no	—
97	D₄×C₁₃	—	8	2	no	—
98	D₄×C₁₃	—	8	2	no	—
99	C₂×C₄×C₁₃	—	2	1	no	—
100	C₂×C₄×C₁₃	—	4	1	no	—
101	C₂×C₄×C₁₃	—	4	1	no	—
102	C₂×C₄×C₁₃	#120	1	2	yes	—
103	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
104	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
105	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
106	C₈×C₁₃	—	4	1	no	—
107	C₈×C₁₃	—	4	4	no	—
108	C₈×C₁₃	#120	1	1	yes	characteristic
109	C₈×C₁₃	#121	1	2	yes	—
110	C₈×C₁₃	#127	1	1	yes	characteristic
111	C₂×AGL(1,ℤ/8)	—	2	2	no	—
112	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
113	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
114	C₂×D₁₆	—	2	4	no	—
115	C₂×D₁₆	—	2	2	no	—
116	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
117	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
118	#472	—	2	4	no	—
119	#472	—	2	4	no	—
120	C₂×#108	C₂²×C₁₃	1	2	yes	—
121	C₂×#100	—	2	2	no	—
122	#361	—	2	4	no	—
123	C₂²⋊C₁₆	—	2	2	no	—
124	C₂²×C₁₃	—	2	2	no	—
125	C₂²×C₁₃	—	4	2	no	—
126	C₂²×C₁₃	—	4	1	no	—
127	C₂²×C₁₃	—	8	4	no	—
128	C₂²×C₁₃	—	16	4	no	—
129	C₂²×C₁₃	—	16	4	no	—
130	C₂²×C₁₃	—	16	4	no	—
131	C₂²×C₁₃	#449	1	2	yes	—
132	C₂²×C₁₃	#466	1	1	yes	characteristic
133	C₄×C₁₃	—	4	1	no	—
134	C₄×C₁₃	#392	1	1	yes	characteristic
135	C₄×C₁₃	#447	1	2	yes	—
136	C₄×C₁₃	#469	1	1	yes	characteristic
137	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
138	C₂²×D₄	—	2	2	no	—
139	AGL(1,ℤ/8)	—	2	8	no	—
140	AGL(1,ℤ/8)	—	4	4	no	—
141	C₂×SD₁₆	—	4	2	no	—
142	C₂×D₈	—	2	2	no	—
143	C₂×D₈	—	2	2	no	—
144	C₂×D₈	—	2	2	no	—
145	C₂×D₈	—	2	2	no	—
146	C₂×D₈	—	2	2	no	—
147	C₂×D₈	—	4	2	no	—
148	C₂×D₈	D₄×C₁₃	1	4	yes	—
149	#131	—	2	2	no	—
150	#131	—	2	2	no	—
151	C₂×M₁₆	—	2	1	no	—
152	C₂×M₁₆	—	2	2	no	—
153	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
154	C₂²×C₈	—	2	1	no	—
155	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
156	D₁₆	—	2	8	no	—
157	M₃₂	—	2	2	no	—
158	C₂×C₁₆	—	2	2	no	—
159	C₂×C₁₆	—	2	1	no	—
160	C₂×C₁₆	D₄×C₁₃	1	2	yes	—
161	#108	—	2	2	no	—
162	#108	D₄×C₁₃	1	4	yes	—
163	#100	—	2	8	no	—
164	C₂×C₁₃	—	2	2	no	—
165	C₂×C₁₃	—	8	1	no	—
166	C₂×C₁₃	—	16	4	no	—
167	C₂×C₁₃	#1999	1	1	yes	characteristic
168	C₂×C₁₃	#2221	1	2	yes	—
169	C₂⁴	—	4	2	no	—
170	#41	—	2	2	no	—
171	#41	—	2	2	no	—
172	C₂×Q₈	C₁₃×D₈	1	1	yes	characteristic
173	C₂×D₄	—	2	1	no	—
174	C₂×D₄	—	2	4	no	—
175	C₂×D₄	—	4	2	no	—
176	C₂×D₄	—	4	2	no	—
177	C₂×D₄	—	4	2	no	—
178	C₂×D₄	—	4	2	no	—
179	C₂×D₄	—	4	2	no	—
180	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
181	C₂²×C₄	—	2	1	no	—
182	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
183	SD₁₆	—	4	8	no	—
184	D₈	—	2	4	no	—
185	D₈	—	2	4	no	—
186	D₈	—	4	8	no	—
187	D₈	—	4	2	no	—
188	D₈	—	4	2	no	—
189	M₁₆	—	2	2	no	—
190	M₁₆	—	2	4	no	—
191	M₁₆	—	4	2	no	—
192	M₁₆	—	4	2	no	—
193	C₂×C₈	—	2	1	no	—
194	C₂×C₈	—	4	2	no	—
195	C₂×C₈	—	4	1	no	—
196	C₂×C₈	—	4	1	no	—
197	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
198	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
199	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
200	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
201	C₁₆	—	2	2	no	—
202	C₁₆	—	4	1	no	—
203	C₁₃	#13313	1	1	yes	characteristic, direct product factor, Sylow
204	C₂³	—	2	1	no	—
205	C₂³	—	4	4	no	—
206	C₂³	—	8	2	no	—
207	C₂³	—	8	2	no	—
208	C₂³	—	16	4	no	—
209	C₂³	C₁₃×#135	1	1	yes	characteristic
210	Q₈	—	2	2	no	—
211	D₄	—	2	2	no	—
212	D₄	—	4	2	no	—
213	D₄	—	4	4	no	—
214	D₄	—	4	4	no	—
215	D₄	—	8	2	no	—
216	D₄	—	8	2	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	4	1	no	—
219	C₂×C₄	—	4	1	no	—
220	C₂×C₄	C₁₃×#120	1	2	yes	—
221	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
222	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
223	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
224	C₈	—	4	1	no	—
225	C₈	—	4	4	no	—
226	C₈	C₁₃×#120	1	1	yes	characteristic
227	C₈	C₁₃×#121	1	2	yes	—
228	C₈	C₁₃×#127	1	1	yes	characteristic
229	C₂²	—	2	2	no	—
230	C₂²	—	4	1	no	—
231	C₂²	—	4	2	no	—
232	C₂²	—	8	4	no	—
233	C₂²	—	16	4	no	—
234	C₂²	—	16	4	no	—
235	C₂²	—	16	4	no	—
236	C₂²	C₁₃×#449	1	2	yes	—
237	C₂²	C₁₃×#466	1	1	yes	characteristic
238	C₄	—	4	1	no	—
239	C₄	C₁₃×#392	1	1	yes	characteristic
240	C₄	C₁₃×#447	1	2	yes	—
241	C₄	C₁₃×#469	1	1	yes	characteristic
242	C₂	—	2	2	no	—
243	C₂	—	8	1	no	—
244	C₂	—	16	4	no	—
245	C₂	C₁₃×#1999	1	1	yes	characteristic
246	C₂	C₁₃×#2221	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₁₃×D₁₆

C₂

yes

maximal, characteristic, complemented

C₂×C₁₃×#472

C₂

yes

maximal, complemented

C₂×C₁₃×#361

C₂

yes

maximal, complemented

C₁₃×#2113

C₂

yes

maximal, characteristic, complemented

C₁₃×#1381

C₂

yes

maximal, characteristic, complemented

C₂×C₁₃×AGL(1,ℤ/8)

—

C₂²×C₁₃×D₈

C₂²

yes

—

C₂×C₁₃×#131

C₂²

yes

characteristic

C₂×C₁₃×D₁₆

—

C₂×C₁₃×D₁₆

—

C₂×C₁₃×M₃₂

C₂²

yes

characteristic

C₂²×C₁₃×C₁₆

C₂²

yes

characteristic

C₁₃×#472

—

C₁₃×#472

—

C₂×C₁₃×#108

C₂²

yes

—

C₂×C₁₃×#100

—

C₁₃×#361

—

C₁₃×C₂²⋊C₁₆

—

C₂×C₁₃×#41

D₄

yes

characteristic

C₂²×D₄×C₁₃

—

C₁₃×AGL(1,ℤ/8)

—

C₁₃×AGL(1,ℤ/8)

—

C₂×C₁₃×SD₁₆

—

C₂×C₁₃×D₈

—

C₂×C₁₃×D₈

—

C₂×C₁₃×D₈

—

C₂×C₁₃×D₈

—

C₂×C₁₃×D₈

—

C₂×C₁₃×D₈

—

C₂×C₁₃×D₈

D₄

yes

—

C₁₃×#131

—

C₁₃×#131

—

C₂×C₁₃×M₁₆

—

C₂×C₁₃×M₁₆

—

C₂×C₁₃×M₁₆

D₄

yes

characteristic

C₂²×C₈×C₁₃

—

C₂²×C₈×C₁₃

C₂³

yes

characteristic

C₁₃×D₁₆

—

C₁₃×M₃₂

—

C₂×C₁₃×C₁₆

—

C₂×C₁₃×C₁₆

—

C₂×C₁₃×C₁₆

D₄

yes

—

C₁₃×#108

—

C₁₃×#108

D₄

yes

—

C₁₃×#100

—

#13313

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂⁴×C₁₃

—

C₁₃×#41

—

C₁₃×#41

—

C₂×Q₈×C₁₃

D₈

yes

characteristic

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

D₈

yes

characteristic

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₁₃×SD₁₆

—

C₁₃×D₈

—

C₁₃×D₈

—

C₁₃×D₈

—

C₁₃×D₈

—

C₁₃×D₈

—

C₁₃×M₁₆

—

C₁₃×M₁₆

—

C₁₃×M₁₆

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

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

C₁₃×C₁₆

—

C₁₃×C₁₆

—

C₂²×D₁₆

C₂×C₁₃

yes

characteristic, complemented

C₂×#472

C₂×C₁₃

yes

complemented

C₂×#361

C₂×C₁₃

yes

complemented

#2113

C₂×C₁₃

yes

characteristic, complemented

#1381

C₂×C₁₃

yes

characteristic, complemented

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

#135

yes

characteristic

Q₈×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

C₂×C₄×C₁₃

—

100

C₂×C₄×C₁₃

—

101

C₂×C₄×C₁₃

—

102

C₂×C₄×C₁₃

#120

yes

—

103

C₂×C₄×C₁₃

#121

yes

characteristic

104

C₂×C₄×C₁₃

C₂×D₈

yes

characteristic

105

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

—

106

C₈×C₁₃

—

107

C₈×C₁₃

—

108

C₈×C₁₃

#120

yes

characteristic

109

C₈×C₁₃

#121

yes

—

110

C₈×C₁₃

#127

yes

characteristic

111

C₂×AGL(1,ℤ/8)

—

112

C₂²×D₈

C₂²×C₁₃

yes

—

113

C₂×#131

C₂²×C₁₃

yes

characteristic

114

C₂×D₁₆

—

115

C₂×D₁₆

—

116

C₂×M₃₂

C₂²×C₁₃

yes

characteristic

117

C₂²×C₁₆

C₂²×C₁₃

yes

characteristic

118

#472

—

119

#472

—

120

C₂×#108

C₂²×C₁₃

yes

—

121

C₂×#100

—

122

#361

—

123

C₂²⋊C₁₆

—

124

C₂²×C₁₃

—

125

C₂²×C₁₃

—

126

C₂²×C₁₃

—

127

C₂²×C₁₃

—

128

C₂²×C₁₃

—

129

C₂²×C₁₃

—

130

C₂²×C₁₃

—

131

C₂²×C₁₃

#449

yes

—

132

C₂²×C₁₃

#466

yes

characteristic

133

C₄×C₁₃

—

134

C₄×C₁₃

#392

yes

characteristic

135

C₄×C₁₃

#447

yes

—

136

C₄×C₁₃

#469

yes

characteristic

137

C₂×#41

D₄×C₁₃

yes

characteristic

138

C₂²×D₄

—

139

AGL(1,ℤ/8)

—

140

AGL(1,ℤ/8)

—

141

C₂×SD₁₆

—

142

C₂×D₈

—

143

C₂×D₈

—

144

C₂×D₈

—

145

C₂×D₈

—

146

C₂×D₈

—

147

C₂×D₈

—

148

C₂×D₈

D₄×C₁₃

yes

—

149

#131

—

150

#131

—

151

C₂×M₁₆

—

152

C₂×M₁₆

—

153

C₂×M₁₆

D₄×C₁₃

yes

characteristic

154

C₂²×C₈

—

155

C₂²×C₈

C₂³×C₁₃

yes

characteristic

156

D₁₆

—

157

M₃₂

—

158

C₂×C₁₆

—

159

C₂×C₁₆

—

160

C₂×C₁₆

D₄×C₁₃

yes

—

161

#108

—

162

#108

D₄×C₁₃

yes

—

163

#100

—

164

C₂×C₁₃

—

165

C₂×C₁₃

—

166

C₂×C₁₃

—

167

C₂×C₁₃

#1999

yes

characteristic

168

C₂×C₁₃

#2221

yes

—

169

C₂⁴

—

170

#41

—

171

#41

—

172

C₂×Q₈

C₁₃×D₈

yes

characteristic

173

C₂×D₄

—

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂×D₄

—

179

C₂×D₄

—

180

C₂×D₄

C₁₃×D₈

yes

characteristic

181

C₂²×C₄

—

182

C₂²×C₄

C₂×D₄×C₁₃

yes

characteristic

183

SD₁₆

—

184

D₈

—

185

D₈

—

186

D₈

—

187

D₈

—

188

D₈

—

189

M₁₆

—

190

M₁₆

—

191

M₁₆

—

192

M₁₆

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

C₂×D₄×C₁₃

yes

—

198

C₂×C₈

C₂×D₄×C₁₃

yes

characteristic

199

C₂×C₈

C₂×D₄×C₁₃

yes

—

200

C₂×C₈

C₁₃×#41

yes

characteristic

201

C₁₆

—

202

C₁₆

—

203

C₁₃

#13313

yes

characteristic, direct product factor, Sylow

204

C₂³

—

205

C₂³

—

206

C₂³

—

207

C₂³

—

208

C₂³

—

209

C₂³

C₁₃×#135

yes

characteristic

210

Q₈

—

211

D₄

—

212

D₄

—

213

D₄

—

214

D₄

—

215

D₄

—

216

D₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

C₁₃×#120

yes

—

221

C₂×C₄

C₁₃×#121

yes

characteristic

222

C₂×C₄

C₂×C₁₃×D₈

yes

characteristic

223

C₂×C₄

C₁₃×AGL(1,ℤ/8)

yes

—

224

C₈

—

225

C₈

—

226

C₈

C₁₃×#120

yes

characteristic

227

C₈

C₁₃×#121

yes

—

228

C₈

C₁₃×#127

yes

characteristic

229

C₂²

—

230

C₂²

—

231

C₂²

—

232

C₂²

—

233

C₂²

—

234

C₂²

—

235

C₂²

—

236

C₂²

C₁₃×#449

yes

—

237

C₂²

C₁₃×#466

yes

characteristic

238

C₄

—

239

C₄

C₁₃×#392

yes

characteristic

240

C₄

C₁₃×#447

yes

—

241

C₄

C₁₃×#469

yes

characteristic

242

C₂

—

243

C₂

—

244

C₂

—

245

C₂

C₁₃×#1999

yes

characteristic

246

C₂

C₁₃×#2221

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₃	#466
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#131 ◁ G

subgroup

G/H

center, socle

C₂²×C₁₃

#466

commutator, Frattini, cosocle

C₂²×C₈

C₂³×C₁₃

LCS

G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#131 ◁ G

N	H ≅ G/N	type
1. C₂²×C₁₃×D₁₆	C₂	semidirect
2. C₂×C₁₃×#472	C₂	semidirect
3. C₂×C₁₃×#361	C₂	semidirect
4. C₁₃×#2113	C₂	semidirect
5. C₁₃×#1381	C₂	semidirect
46. #13313	C₁₃	direct (N × H)
81. C₂²×D₁₆	C₂×C₁₃	semidirect
82. C₂×#472	C₂×C₁₃	semidirect
83. C₂×#361	C₂×C₁₃	semidirect
84. #2113	C₂×C₁₃	semidirect
85. #1381	C₂×C₁₃	semidirect
203. C₁₃	#13313	direct (N × H)

H ≅ G/N

type

1. C₂²×C₁₃×D₁₆

C₂

semidirect

2. C₂×C₁₃×#472

C₂

semidirect

3. C₂×C₁₃×#361

C₂

semidirect

4. C₁₃×#2113

C₂

semidirect

5. C₁₃×#1381

C₂

semidirect

46. #13313

C₁₃

direct (N × H)

81. C₂²×D₁₆

C₂×C₁₃

semidirect

82. C₂×#472

C₂×C₁₃

semidirect

83. C₂×#361

C₂×C₁₃

semidirect

84. #2113

C₂×C₁₃

semidirect

85. #1381

C₂×C₁₃

semidirect

203. C₁₃

#13313

direct (N × H)

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

subgroup	index
C₂²×C₁₃×D₁₆	2
C₂×C₁₃×#472	2
C₂×C₁₃×#361	2
C₁₃×#2113	2
C₁₃×#1381	2
#13313	13

subgroup

index

C₂²×C₁₃×D₁₆

C₂×C₁₃×#472

C₂×C₁₃×#361

C₁₃×#2113

C₁₃×#1381

#13313

Subgroups — C₁₃×#13313 #15699652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#13313 #15699652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13313 #15699652