Group #15765927 — subgroups

Subgroups — #15765927

Order 3328.

588 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 131 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	#13119865	C₂	1	1	yes	maximal, characteristic, complemented
2	#13115764	C₂	1	2	yes	maximal
3	#13112719	C₂	1	1	yes	maximal, characteristic, complemented
4	#13112676	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1957	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
7	C₂×#88142	—	2	2	no	—
8	C₂×C₁₃×#102	—	2	2	no	—
9	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₁₃×#384	C₂²	1	1	yes	characteristic
11	C₂×#88072	—	2	2	no	—
12	C₂×#88072	—	2	2	no	—
13	#11718640	—	2	2	no	—
14	#11718634	—	2	2	no	—
15	C₄×C₄⋊Dic₁₃	C₂²	1	2	yes	—
16	C₂×C₄⋊#1055	C₂²	1	2	yes	—
17	C₂²×D₄×C₁₃	—	2	1	no	—
18	C₂²×D₄×C₁₃	—	2	2	no	—
19	C₂²×Dic₂₆	—	2	2	no	—
20	C₂²×C₈×C₁₃	—	2	1	no	—
21	C₁₃×#127	—	2	1	no	—
22	C₁₃×#127	—	2	2	no	—
23	C₁₃×#127	Q₈	1	2	yes	complemented
24	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
25	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
26	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
27	C₂×C₄⋊Dic₁₃	D₄	1	2	yes	—
28	C₂×C₄⋊Dic₁₃	D₄	1	2	yes	—
29	C₂×#6101	—	2	4	no	—
30	C₂×C₄×Dic₁₃	—	2	2	no	—
31	C₂²×#1055	—	2	2	no	—
32	#88142	—	4	4	no	—
33	#88142	—	4	4	no	—
34	C₁₃×#102	—	4	4	no	—
35	C₄×C₈×C₁₃	—	2	2	no	—
36	#88072	—	4	4	no	—
37	#88072	—	4	4	no	—
38	#88071	—	2	2	no	—
39	#88071	—	2	2	no	—
40	C₄⋊#1055	—	2	2	no	—
41	C₄⋊#1055	—	2	2	no	—
42	#10348	—	13	1	no	maximal, Sylow
43	C₂⁴×C₁₃	—	4	1	no	—
44	C₂×D₄×C₁₃	—	2	4	no	—
45	C₂×D₄×C₁₃	—	2	2	no	—
46	C₂×D₄×C₁₃	—	4	2	no	—
47	C₂×D₄×C₁₃	—	4	2	no	—
48	C₂×D₄×C₁₃	—	4	2	no	—
49	C₂×D₄×C₁₃	—	4	1	no	—
50	C₂×D₄×C₁₃	—	4	2	no	—
51	C₂×D₄×C₁₃	—	4	2	no	—
52	C₂×D₄×C₁₃	—	4	2	no	—
53	C₂×D₄×C₁₃	—	4	2	no	—
54	C₂²×C₄×C₁₃	—	2	2	no	—
55	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
56	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
57	C₂²×Dic₁₃	—	2	2	no	—
58	C₂²×Dic₁₃	—	2	2	no	—
59	C₂×Dic₂₆	—	4	8	no	—
60	C₂×Dic₂₆	—	8	2	no	—
61	C₂×C₈×C₁₃	—	2	2	no	—
62	C₂×C₈×C₁₃	—	4	1	no	—
63	C₂×C₈×C₁₃	—	4	1	no	—
64	C₁₃×C₄⋊C₄	—	4	2	no	—
65	C₁₃×C₄⋊C₄	—	4	2	no	—
66	C₁₃×C₄⋊C₄	—	4	2	no	—
67	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
68	C₄²×C₁₃	#41	1	1	yes	characteristic
69	C₄²×C₁₃	#41	1	2	yes	—
70	C₄⋊Dic₁₃	—	2	2	no	—
71	C₄⋊Dic₁₃	—	2	2	no	—
72	C₄⋊Dic₁₃	D₈	1	4	yes	—
73	C₄⋊Dic₁₃	SD₁₆	1	4	yes	—
74	#6101	—	4	8	no	—
75	C₄×Dic₁₃	—	4	2	no	—
76	C₄×Dic₁₃	—	4	2	no	—
77	C₂×#1055	—	4	2	no	—
78	C₂×#1055	—	4	2	no	—
79	C₂×#1055	—	4	2	no	—
80	#2551	—	13	1	no	—
81	#1982	—	13	2	no	—
82	#1957	D₁₃	1	1	yes	characteristic
83	#1296	—	13	1	no	—
84	#1279	—	13	2	no	—
85	C₂³×C₁₃	—	4	2	no	—
86	C₂³×C₁₃	—	8	2	no	—
87	C₂³×C₁₃	—	8	2	no	—
88	C₂³×C₁₃	—	8	1	no	—
89	C₂³×C₁₃	—	8	1	no	—
90	C₂³×C₁₃	#120	1	1	yes	characteristic
91	D₄×C₁₃	—	4	4	no	—
92	D₄×C₁₃	—	4	4	no	—
93	D₄×C₁₃	—	4	4	no	—
94	D₄×C₁₃	—	8	2	no	—
95	D₄×C₁₃	—	8	2	no	—
96	D₄×C₁₃	—	8	2	no	—
97	C₂×C₄×C₁₃	—	2	1	no	—
98	C₂×C₄×C₁₃	—	2	1	no	—
99	C₂×C₄×C₁₃	—	4	4	no	—
100	C₂×C₄×C₁₃	—	4	2	no	—
101	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
102	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
103	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
104	C₂×C₄×C₁₃	#124	1	2	yes	—
105	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
106	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
107	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
108	C₂×C₄×C₁₃	#137	1	2	yes	—
109	C₂×Dic₁₃	—	2	4	no	—
110	C₂×Dic₁₃	—	2	4	no	—
111	C₂×Dic₁₃	—	4	2	no	—
112	C₂×Dic₁₃	—	4	2	no	—
113	C₂×Dic₁₃	—	4	2	no	—
114	C₂×Dic₁₃	—	4	2	no	—
115	Dic₂₆	—	8	8	no	—
116	C₈×C₁₃	—	4	2	no	—
117	#1055	—	8	2	no	—
118	C₂×C₄⋊Q₈	—	26	2	no	—
119	C₂×#127	C₂×D₁₃	1	1	yes	characteristic
120	C₂×C₄⋊C₈	—	13	2	no	—
121	C₂×#102	—	2	2	no	—
122	C₂×#102	—	26	2	no	—
123	C₂×#102	—	26	2	no	—
124	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
125	#395	—	26	2	no	—
126	#389	—	26	2	no	—
127	#384	C₂×D₁₃	1	1	yes	characteristic
128	C₄×C₄⋊C₄	—	13	2	no	—
129	C₂²×C₁₃	—	8	4	no	—
130	C₂²×C₁₃	—	8	2	no	—
131	C₂²×C₁₃	—	16	1	no	—
132	C₂²×C₁₃	—	16	1	no	—
133	C₂²×C₁₃	—	16	2	no	—
134	C₂²×C₁₃	#393	1	1	yes	characteristic
135	C₂²×C₁₃	#447	1	2	yes	—
136	C₂²×C₁₃	#448	1	2	yes	—
137	C₂²×C₁₃	#453	1	1	yes	characteristic
138	C₂²×C₁₃	#454	1	1	yes	characteristic
139	C₄×C₁₃	—	2	1	no	—
140	C₄×C₁₃	—	2	1	no	—
141	C₄×C₁₃	—	8	2	no	—
142	C₄×C₁₃	#474	1	2	yes	—
143	C₄×C₁₃	#476	1	2	yes	—
144	C₄×C₁₃	#486	1	2	yes	—
145	C₄×C₁₃	#489	1	2	yes	—
146	Dic₁₃	—	4	4	no	—
147	Dic₁₃	—	4	4	no	—
148	C₂²×Q₈	—	26	2	no	—
149	C₂²×D₄	—	2	2	no	—
150	C₂²×D₄	—	2	1	no	—
151	C₂²×C₈	—	2	1	no	—
152	C₂²×C₈	—	26	2	no	—
153	C₄⋊Q₈	—	52	4	no	—
154	C₄⋊Q₈	—	52	4	no	—
155	#127	—	2	1	no	—
156	#127	—	2	2	no	—
157	#127	Dic₂₆	1	2	yes	complemented
158	C₂×C₄⋊C₄	—	2	2	no	—
159	C₂×C₄⋊C₄	—	13	2	no	—
160	C₂×C₄⋊C₄	—	13	2	no	—
161	C₂×C₄⋊C₄	—	26	4	no	—
162	C₂×C₄⋊C₄	C₂²⋊D₁₃	1	2	yes	—
163	C₂×C₄²	—	26	2	no	—
164	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
165	C₄⋊C₈	—	26	2	no	—
166	C₄⋊C₈	—	26	2	no	—
167	#102	—	4	4	no	—
168	#102	—	52	4	no	—
169	#102	—	52	4	no	—
170	C₄×C₈	—	2	2	no	—
171	#95	—	26	2	no	—
172	#95	—	26	2	no	—
173	C₂×C₁₃	—	16	2	no	—
174	C₂×C₁₃	#1619	1	1	yes	characteristic
175	C₂×C₁₃	#1623	1	1	yes	characteristic
176	C₂×C₁₃	#1627	1	2	yes	—
177	C₂×C₁₃	#2023	1	2	yes	—
178	C₂×C₁₃	#2027	1	1	yes	characteristic
179	C₂⁴	—	4	1	no	—
180	C₂×Q₈	—	52	8	no	—
181	C₂×Q₈	—	104	2	no	—
182	C₂×D₄	—	2	4	no	—
183	C₂×D₄	—	2	2	no	—
184	C₂×D₄	—	4	2	no	—
185	C₂×D₄	—	4	2	no	—
186	C₂×D₄	—	4	2	no	—
187	C₂×D₄	—	4	2	no	—
188	C₂×D₄	—	4	2	no	—
189	C₂×D₄	—	4	2	no	—
190	C₂×D₄	—	4	2	no	—
191	C₂×D₄	—	4	1	no	—
192	C₂²×C₄	—	2	2	no	—
193	C₂²×C₄	—	26	2	no	—
194	C₂²×C₄	—	26	2	no	—
195	C₂²×C₄	D₄×D₁₃	1	2	yes	—
196	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
197	C₂×C₈	—	2	2	no	—
198	C₂×C₈	—	4	1	no	—
199	C₂×C₈	—	4	1	no	—
200	C₂×C₈	—	52	2	no	—
201	C₂×C₈	—	52	2	no	—
202	C₂×C₈	—	52	2	no	—
203	C₄⋊C₄	—	4	2	no	—
204	C₄⋊C₄	—	4	2	no	—
205	C₄⋊C₄	—	4	2	no	—
206	C₄⋊C₄	—	13	4	no	—
207	C₄⋊C₄	—	13	4	no	—
208	C₄⋊C₄	—	26	2	no	—
209	C₄⋊C₄	—	26	2	no	—
210	C₄⋊C₄	—	52	8	no	—
211	C₄²	—	52	2	no	—
212	C₄²	—	52	2	no	—
213	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
214	C₄²	#6127	1	1	yes	characteristic
215	C₄²	#6129	1	2	yes	—
216	C₁₃	#10348	1	1	yes	characteristic, complemented, Sylow
217	C₂³	—	4	2	no	—
218	C₂³	—	8	1	no	—
219	C₂³	—	8	1	no	—
220	C₂³	—	8	2	no	—
221	C₂³	—	8	2	no	—
222	C₂³	#88191	1	1	yes	characteristic
223	Q₈	—	104	8	no	—
224	D₄	—	4	4	no	—
225	D₄	—	4	4	no	—
226	D₄	—	4	4	no	—
227	D₄	—	8	2	no	—
228	D₄	—	8	2	no	—
229	D₄	—	8	2	no	—
230	C₂×C₄	—	2	1	no	—
231	C₂×C₄	—	2	1	no	—
232	C₂×C₄	—	4	2	no	—
233	C₂×C₄	—	4	4	no	—
234	C₂×C₄	—	26	4	no	—
235	C₂×C₄	—	26	4	no	—
236	C₂×C₄	—	52	2	no	—
237	C₂×C₄	—	52	2	no	—
238	C₂×C₄	—	52	2	no	—
239	C₂×C₄	—	52	2	no	—
240	C₂×C₄	#88132	1	2	yes	—
241	C₂×C₄	#88139	1	2	yes	—
242	C₂×C₄	D₈×D₁₃	1	2	yes	—
243	C₂×C₄	#88165	1	2	yes	—
244	C₂×C₄	SD₁₆×D₁₃	1	2	yes	—
245	C₂×C₄	#88169	1	2	yes	—
246	C₂×C₄	#88178	1	1	yes	characteristic
247	C₂×C₄	#88190	1	1	yes	characteristic
248	C₈	—	4	2	no	—
249	C₈	—	104	2	no	—
250	C₂²	—	8	4	no	—
251	C₂²	—	8	2	no	—
252	C₂²	—	16	1	no	—
253	C₂²	—	16	1	no	—
254	C₂²	—	16	2	no	—
255	C₂²	#11718608	1	1	yes	characteristic
256	C₂²	#11718723	1	1	yes	characteristic
257	C₂²	#11718738	1	1	yes	characteristic
258	C₂²	#11718817	1	2	yes	—
259	C₂²	#11718831	1	2	yes	—
260	C₄	—	2	1	no	—
261	C₄	—	2	1	no	—
262	C₄	—	8	2	no	—
263	C₄	—	52	4	no	—
264	C₄	—	52	4	no	—
265	C₄	#11718420	1	2	yes	—
266	C₄	#11718421	1	2	yes	—
267	C₄	#11718422	1	2	yes	—
268	C₄	#11718426	1	2	yes	—
269	C₂	—	16	2	no	—
270	C₂	#13113888	1	1	yes	characteristic
271	C₂	#13113912	1	1	yes	characteristic
272	C₂	#13113936	1	2	yes	—
273	C₂	#13115970	1	2	yes	—
274	C₂	#13115992	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13119865

C₂

yes

maximal, characteristic, complemented

#13115764

C₂

yes

maximal

#13112719

C₂

yes

maximal, characteristic, complemented

#13112676

C₂

yes

maximal, complemented

C₁₃×#1957

C₂

yes

maximal, characteristic

C₂×C₁₃×#127

C₂²

yes

characteristic

C₂×#88142

—

C₂×C₁₃×#102

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₁₃×#384

C₂²

yes

—

—

—

—

C₄×C₄⋊Dic₁₃

C₂²

yes

—

C₂×C₄⋊#1055

C₂²

yes

—

C₂²×D₄×C₁₃

—

C₂²×D₄×C₁₃

—

C₂²×Dic₂₆

—

C₂²×C₈×C₁₃

—

C₁₃×#127

—

C₁₃×#127

—

C₁₃×#127

Q₈

yes

complemented

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

D₄

yes

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₃

D₄

yes

—

C₂×C₄⋊Dic₁₃

D₄

yes

—

C₂×#6101

—

C₂×C₄×Dic₁₃

—

C₂²×#1055

—

#88142

—

#88142

—

C₁₃×#102

—

C₄×C₈×C₁₃

—

—

—

—

—

—

—

—

C₂⁴×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×Dic₁₃

—

C₂²×Dic₁₃

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

C₂×Q₈

yes

C₄²×C₁₃

yes

C₄²×C₁₃

yes

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

D₈

yes

—

C₄⋊Dic₁₃

SD₁₆

yes

—

#6101

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

—

—

—

—

—

D₁₃

yes

characteristic

#1296

—

#1279

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

#120

yes

characteristic

D₄×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

100

C₂×C₄×C₁₃

—

101

C₂×C₄×C₁₃

C₂²⋊Q₈

yes

characteristic

102

C₂×C₄×C₁₃

C₂²⋊Q₈

yes

—

103

C₂×C₄×C₁₃

#124

yes

characteristic

104

C₂×C₄×C₁₃

#124

yes

—

105

C₂×C₄×C₁₃

C₂×D₈

yes

—

106

C₂×C₄×C₁₃

C₂×SD₁₆

yes

—

107

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

—

108

C₂×C₄×C₁₃

#137

yes

—

109

C₂×Dic₁₃

—

110

C₂×Dic₁₃

—

111

C₂×Dic₁₃

—

112

C₂×Dic₁₃

—

113

C₂×Dic₁₃

—

114

C₂×Dic₁₃

—

115

Dic₂₆

—

116

C₈×C₁₃

—

117

#1055

—

118

C₂×C₄⋊Q₈

—

119

C₂×#127

C₂×D₁₃

yes

characteristic

120

C₂×C₄⋊C₈

—

121

C₂×#102

—

122

C₂×#102

—

123

C₂×#102

—

124

C₂×C₄×C₈

C₂×D₁₃

yes

characteristic

125

#395

—

126

#389

—

127

#384

C₂×D₁₃

yes

characteristic

128

C₄×C₄⋊C₄

—

129

C₂²×C₁₃

—

130

C₂²×C₁₃

—

131

C₂²×C₁₃

—

132

C₂²×C₁₃

—

133

C₂²×C₁₃

—

134

C₂²×C₁₃

#393

yes

characteristic

135

C₂²×C₁₃

#447

yes

—

136

C₂²×C₁₃

#448

yes

—

137

C₂²×C₁₃

#453

yes

characteristic

138

C₂²×C₁₃

#454

yes

characteristic

139

C₄×C₁₃

—

140

C₄×C₁₃

—

141

C₄×C₁₃

—

142

C₄×C₁₃

#474

yes

—

143

C₄×C₁₃

#476

yes

—

144

C₄×C₁₃

#486

yes

—

145

C₄×C₁₃

#489

yes

—

146

Dic₁₃

—

147

Dic₁₃

—

148

C₂²×Q₈

—

149

C₂²×D₄

—

150

C₂²×D₄

—

151

C₂²×C₈

—

152

C₂²×C₈

—

153

C₄⋊Q₈

—

154

C₄⋊Q₈

—

155

#127

—

156

#127

—

157

#127

Dic₂₆

yes

complemented

158

C₂×C₄⋊C₄

—

159

C₂×C₄⋊C₄

—

160

C₂×C₄⋊C₄

—

161

C₂×C₄⋊C₄

—

162

C₂×C₄⋊C₄

C₂²⋊D₁₃

yes

—

163

C₂×C₄²

—

164

C₂×C₄²

C₂²×D₁₃

yes

characteristic

165

C₄⋊C₈

—

166

C₄⋊C₈

—

167

#102

—

168

#102

—

169

#102

—

170

C₄×C₈

—

171

#95

—

172

#95

—

173

C₂×C₁₃

—

174

C₂×C₁₃

#1619

yes

characteristic

175

C₂×C₁₃

#1623

yes

characteristic

176

C₂×C₁₃

#1627

yes

—

177

C₂×C₁₃

#2023

yes

—

178

C₂×C₁₃

#2027

yes

characteristic

179

C₂⁴

—

180

C₂×Q₈

—

181

C₂×Q₈

—

104

—

182

C₂×D₄

—

183

C₂×D₄

—

184

C₂×D₄

—

185

C₂×D₄

—

186

C₂×D₄

—

187

C₂×D₄

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂×D₄

—

191

C₂×D₄

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

D₄×D₁₃

yes

—

196

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₄²

—

212

C₄²

—

213

C₄²

C₂×Dic₂₆

yes

characteristic

214

C₄²

#6127

yes

characteristic

215

C₄²

#6129

yes

—

216

C₁₃

#10348

yes

characteristic, complemented, Sylow

217

C₂³

—

218

C₂³

—

219

C₂³

—

220

C₂³

—

221

C₂³

—

222

C₂³

#88191

yes

characteristic

223

Q₈

—

104

—

224

D₄

—

225

D₄

—

226

D₄

—

227

D₄

—

228

D₄

—

229

D₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

#88132

yes

—

241

C₂×C₄

#88139

yes

—

242

C₂×C₄

D₈×D₁₃

yes

—

243

C₂×C₄

#88165

yes

—

244

C₂×C₄

SD₁₆×D₁₃

yes

—

245

C₂×C₄

#88169

yes

—

246

C₂×C₄

#88178

yes

characteristic

247

C₂×C₄

#88190

yes

characteristic

248

C₈

—

249

C₈

—

104

—

250

C₂²

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

—

255

C₂²

#11718608

yes

characteristic

256

C₂²

#11718723

yes

characteristic

257

C₂²

#11718738

yes

characteristic

258

C₂²

#11718817

yes

—

259

C₂²

#11718831

yes

—

260

C₄

—

261

C₄

—

262

C₄

—

263

C₄

—

264

C₄

—

265

C₄

#11718420

yes

—

266

C₄

#11718421

yes

—

267

C₄

#11718422

yes

—

268

C₄

#11718426

yes

—

269

C₂

—

270

C₂

#13113888

yes

characteristic

271

C₂

#13113912

yes

characteristic

272

C₂

#13113936

yes

—

273

C₂

#13115970

yes

—

274

C₂

#13115992

yes

characteristic

	subgroup	G/H
center	C₂³	#88191
commutator, cosocle	C₂×C₄²×C₁₃	C₂³
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1957	C₂
socle	C₂³×C₁₃	#120
prime radical	C₂×C₁₃×#127	C₂²
hypercenter	#1957	D₁₃
hypocenter	C₁₃	#10348
LCS	G ▷ C₂×C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1957

subgroup

G/H

center

C₂³

#88191

commutator, cosocle

C₂×C₄²×C₁₃

C₂³

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₁₃×#1957

C₂

socle

C₂³×C₁₃

#120

prime radical

C₂×C₁₃×#127

C₂²

D₁₃

C₁₃

G ▷ C₂×C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1957

N	H ≅ G/N	type
1. #13119865	C₂	semidirect
3. #13112719	C₂	semidirect
4. #13112676	C₂	semidirect
23. C₁₃×#127	Q₈	semidirect
157. #127	Dic₂₆	semidirect
216. C₁₃	#10348	semidirect

H ≅ G/N

type

1. #13119865

C₂

semidirect

3. #13112719

C₂

semidirect

4. #13112676

C₂

semidirect

23. C₁₃×#127

Q₈

semidirect

157. #127

Dic₂₆

semidirect

216. C₁₃

#10348

semidirect

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

subgroup	index
#13119865	2
#13115764	2
#13112719	2
#13112676	2
C₁₃×#1957	2
#10348	13

subgroup

index

C₁₃×#1957

Subgroups — #15765927

Conjugacy classes of subgroups

Complements

Maximal subgroups