Group #15695731 — subgroups

Subgroups — C₁₃×#9392 #15695731

Order 3328.

486 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 154 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×#2982	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2567	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1801	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1548	C₂	1	2	yes	maximal
5	C₁₃×#1303	C₂	1	2	yes	maximal
6	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
7	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₈×Q₈×C₁₃	—	2	4	no	—
9	C₁₃×#431	—	2	2	no	—
10	C₁₃×#431	C₂²	1	2	yes	—
11	C₁₃×#423	C₂²	1	2	yes	—
12	C₂×C₁₃×#101	—	2	1	no	—
13	C₁₃×#395	C₄	1	4	yes	—
14	C₁₃×#391	—	2	1	no	—
15	C₁₃×#389	—	2	2	no	—
16	C₁₃×#384	—	2	1	no	—
17	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₁₃×#343	—	2	1	no	—
19	C₁₃×#333	—	2	4	no	—
20	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	—
21	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
22	C₂×C₁₃×M₁₆	—	2	2	no	—
23	C₁₃×C₄⋊Q₈	—	2	2	no	—
24	C₁₃×C₄⋊Q₈	—	2	2	no	—
25	C₄×Q₈×C₁₃	—	2	2	no	—
26	C₄×Q₈×C₁₃	—	2	2	no	—
27	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
28	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
29	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
30	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
31	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
32	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₃	—	2	1	no	—
34	C₂×C₄²×C₁₃	D₄	1	2	yes	—
35	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
36	C₁₃×C₄⋊C₈	—	2	4	no	—
37	C₁₃×C₄⋊C₈	—	2	2	no	—
38	C₁₃×C₄⋊C₈	—	2	2	no	—
39	C₁₃×C₄⋊C₈	D₄	1	4	yes	—
40	C₁₃×#101	—	4	2	no	—
41	C₁₃×C₂²⋊C₈	—	2	2	no	—
42	C₄×C₈×C₁₃	—	2	4	no	—
43	C₄×C₈×C₁₃	—	2	2	no	—
44	C₁₃×#95	—	2	4	no	—
45	C₁₃×#95	C₂×C₄	1	2	yes	—
46	#9392	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	C₂×Q₈×C₁₃	—	2	2	no	—
48	C₂×Q₈×C₁₃	—	2	2	no	—
49	C₂×Q₈×C₁₃	—	2	4	no	—
50	C₂×Q₈×C₁₃	—	8	2	no	—
51	C₂×Q₈×C₁₃	SD₁₆	1	2	yes	—
52	C₂×Q₈×C₁₃	Q₁₆	1	2	yes	—
53	C₂²×C₄×C₁₃	—	2	2	no	—
54	C₂²×C₄×C₁₃	—	2	2	no	—
55	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
56	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
57	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
60	C₁₃×M₁₆	—	4	2	no	—
61	C₁₃×M₁₆	—	4	2	no	—
62	C₂×C₈×C₁₃	—	2	4	no	—
63	C₂×C₈×C₁₃	—	4	2	no	—
64	C₁₃×C₄⋊C₄	—	2	4	no	—
65	C₁₃×C₄⋊C₄	—	2	4	no	—
66	C₁₃×C₄⋊C₄	—	2	2	no	—
67	C₁₃×C₄⋊C₄	—	4	1	no	—
68	C₁₃×C₄⋊C₄	—	4	2	no	—
69	C₁₃×C₄⋊C₄	—	4	1	no	—
70	C₁₃×C₄⋊C₄	—	8	4	no	—
71	C₄²×C₁₃	—	2	2	no	—
72	C₄²×C₁₃	—	2	2	no	—
73	C₄²×C₁₃	—	4	2	no	—
74	C₄²×C₁₃	C₂×D₄	1	2	yes	—
75	C₄²×C₁₃	#41	1	2	yes	—
76	#2982	C₂×C₁₃	1	1	yes	characteristic
77	#2567	C₂×C₁₃	1	1	yes	characteristic
78	#1801	C₂×C₁₃	1	1	yes	characteristic
79	#1548	C₂×C₁₃	1	2	yes	—
80	#1303	C₂×C₁₃	1	2	yes	—
81	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	Q₈×C₁₃	—	2	4	no	—
83	Q₈×C₁₃	—	2	4	no	—
84	Q₈×C₁₃	—	8	4	no	—
85	C₂×C₄×C₁₃	—	2	2	no	—
86	C₂×C₄×C₁₃	—	2	2	no	—
87	C₂×C₄×C₁₃	—	2	2	no	—
88	C₂×C₄×C₁₃	—	2	4	no	—
89	C₂×C₄×C₁₃	—	2	2	no	—
90	C₂×C₄×C₁₃	—	4	1	no	—
91	C₂×C₄×C₁₃	—	4	2	no	—
92	C₂×C₄×C₁₃	—	4	2	no	—
93	C₂×C₄×C₁₃	—	4	2	no	—
94	C₂×C₄×C₁₃	—	4	4	no	—
95	C₂×C₄×C₁₃	—	4	2	no	—
96	C₂×C₄×C₁₃	#103	1	4	yes	—
97	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
98	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
99	C₂×C₄×C₁₃	#121	1	2	yes	—
100	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
101	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
102	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
103	C₂×C₄×C₁₃	#135	1	2	yes	—
104	C₈×C₁₃	—	4	4	no	—
105	C₈×C₁₃	—	8	2	no	—
106	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
107	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
108	C₈×Q₈	—	2	4	no	—
109	#431	—	2	2	no	—
110	#431	C₂²×C₁₃	1	2	yes	—
111	#423	C₂²×C₁₃	1	2	yes	—
112	C₂×#101	—	2	1	no	—
113	#395	C₄×C₁₃	1	4	yes	—
114	#391	—	2	1	no	—
115	#389	—	2	2	no	—
116	#384	—	2	1	no	—
117	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
118	#343	—	2	1	no	—
119	#333	—	2	4	no	—
120	C₂²×C₁₃	—	2	1	no	—
121	C₂²×C₁₃	—	2	1	no	—
122	C₂²×C₁₃	#386	1	1	yes	characteristic
123	C₂²×C₁₃	C₂×#103	1	1	yes	characteristic
124	C₂²×C₁₃	#416	1	1	yes	characteristic
125	C₄×C₁₃	—	2	1	no	—
126	C₄×C₁₃	—	2	4	no	—
127	C₄×C₁₃	—	2	2	no	—
128	C₄×C₁₃	—	4	4	no	—
129	C₄×C₁₃	—	4	2	no	—
130	C₄×C₁₃	—	8	2	no	—
131	C₄×C₁₃	#456	1	2	yes	—
132	C₄×C₁₃	#465	1	2	yes	—
133	C₄×C₁₃	#467	1	2	yes	—
134	C₂²×Q₈	C₂×C₄×C₁₃	1	2	yes	—
135	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
136	C₂×M₁₆	—	2	2	no	—
137	C₄⋊Q₈	—	2	2	no	—
138	C₄⋊Q₈	—	2	2	no	—
139	C₄×Q₈	—	2	2	no	—
140	C₄×Q₈	—	2	2	no	—
141	C₂×C₄⋊C₄	—	2	1	no	—
142	C₂×C₄⋊C₄	—	2	1	no	—
143	C₂×C₄⋊C₄	—	2	1	no	—
144	C₂×C₄⋊C₄	—	2	4	no	—
145	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
146	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
147	C₂×C₄²	—	2	1	no	—
148	C₂×C₄²	D₄×C₁₃	1	2	yes	—
149	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
150	C₄⋊C₈	—	2	4	no	—
151	C₄⋊C₈	—	2	2	no	—
152	C₄⋊C₈	—	2	2	no	—
153	C₄⋊C₈	D₄×C₁₃	1	4	yes	—
154	#101	—	4	2	no	—
155	C₂²⋊C₈	—	2	2	no	—
156	C₄×C₈	—	2	4	no	—
157	C₄×C₈	—	2	2	no	—
158	#95	—	2	4	no	—
159	#95	C₂×C₄×C₁₃	1	2	yes	—
160	C₂×C₁₃	—	2	1	no	—
161	C₂×C₁₃	—	2	1	no	—
162	C₂×C₁₃	#1886	1	1	yes	characteristic
163	C₂×C₁₃	#1892	1	1	yes	characteristic
164	C₂×C₁₃	#1914	1	1	yes	characteristic
165	C₂×Q₈	—	2	2	no	—
166	C₂×Q₈	—	2	2	no	—
167	C₂×Q₈	—	2	4	no	—
168	C₂×Q₈	—	8	2	no	—
169	C₂×Q₈	C₁₃×SD₁₆	1	2	yes	—
170	C₂×Q₈	C₁₃×Q₁₆	1	2	yes	—
171	C₂²×C₄	—	2	2	no	—
172	C₂²×C₄	—	2	2	no	—
173	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
174	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
175	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
176	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
177	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
178	M₁₆	—	4	2	no	—
179	M₁₆	—	4	2	no	—
180	C₂×C₈	—	2	4	no	—
181	C₂×C₈	—	4	2	no	—
182	C₄⋊C₄	—	2	4	no	—
183	C₄⋊C₄	—	2	4	no	—
184	C₄⋊C₄	—	2	2	no	—
185	C₄⋊C₄	—	4	1	no	—
186	C₄⋊C₄	—	4	2	no	—
187	C₄⋊C₄	—	4	1	no	—
188	C₄⋊C₄	—	8	4	no	—
189	C₄²	—	2	2	no	—
190	C₄²	—	2	2	no	—
191	C₄²	—	4	2	no	—
192	C₄²	C₂×D₄×C₁₃	1	2	yes	—
193	C₄²	C₁₃×#41	1	2	yes	—
194	C₁₃	#9392	1	1	yes	characteristic, direct product factor, Sylow
195	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
196	Q₈	—	2	4	no	—
197	Q₈	—	2	4	no	—
198	Q₈	—	8	4	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	4	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	4	1	no	—
205	C₂×C₄	—	4	2	no	—
206	C₂×C₄	—	4	2	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	—	4	4	no	—
209	C₂×C₄	—	4	2	no	—
210	C₂×C₄	C₁₃×#103	1	4	yes	—
211	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
212	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
213	C₂×C₄	C₁₃×#121	1	2	yes	—
214	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
215	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
216	C₂×C₄	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
217	C₂×C₄	C₁₃×#135	1	2	yes	—
218	C₈	—	4	4	no	—
219	C₈	—	8	2	no	—
220	C₂²	—	2	1	no	—
221	C₂²	—	2	1	no	—
222	C₂²	C₁₃×#386	1	1	yes	characteristic
223	C₂²	C₂×C₁₃×#103	1	1	yes	characteristic
224	C₂²	C₁₃×#416	1	1	yes	characteristic
225	C₄	—	2	1	no	—
226	C₄	—	2	4	no	—
227	C₄	—	2	2	no	—
228	C₄	—	4	4	no	—
229	C₄	—	4	2	no	—
230	C₄	—	8	2	no	—
231	C₄	C₁₃×#456	1	2	yes	—
232	C₄	C₁₃×#465	1	2	yes	—
233	C₄	C₁₃×#467	1	2	yes	—
234	C₂	—	2	1	no	—
235	C₂	—	2	1	no	—
236	C₂	C₁₃×#1886	1	1	yes	characteristic
237	C₂	C₁₃×#1892	1	1	yes	characteristic
238	C₂	C₁₃×#1914	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#2982

C₂

yes

maximal, characteristic

C₁₃×#2567

C₂

yes

maximal, characteristic

C₁₃×#1801

C₂

yes

maximal, characteristic

C₁₃×#1548

C₂

yes

maximal

C₁₃×#1303

C₂

yes

maximal

C₂×C₁₃×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₄×Q₈×C₁₃

C₂²

yes

characteristic

C₈×Q₈×C₁₃

—

C₁₃×#431

—

C₁₃×#431

C₂²

yes

—

C₁₃×#423

C₂²

yes

—

C₂×C₁₃×#101

—

C₁₃×#395

C₄

yes

—

C₁₃×#391

—

C₁₃×#389

—

C₁₃×#384

—

C₄×C₁₃×C₄⋊C₄

C₂²

yes

characteristic

C₁₃×#343

—

C₁₃×#333

—

C₂²×Q₈×C₁₃

C₂×C₄

yes

—

C₂²×Q₈×C₁₃

D₄

yes

characteristic

C₂×C₁₃×M₁₆

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

—

C₄×Q₈×C₁₃

—

C₄×Q₈×C₁₃

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

C₂×C₄

yes

—

C₂×C₁₃×C₄⋊C₄

D₄

yes

characteristic

C₂×C₄²×C₁₃

—

C₂×C₄²×C₁₃

D₄

yes

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₁₃×C₄⋊C₈

—

C₁₃×C₄⋊C₈

—

C₁₃×C₄⋊C₈

—

C₁₃×C₄⋊C₈

D₄

yes

—

C₁₃×#101

—

C₁₃×C₂²⋊C₈

—

C₄×C₈×C₁₃

—

C₄×C₈×C₁₃

—

C₁₃×#95

—

C₁₃×#95

C₂×C₄

yes

—

#9392

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

SD₁₆

yes

—

C₂×Q₈×C₁₃

Q₁₆

yes

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₁₃×M₁₆

—

C₁₃×M₁₆

—

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

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

C₂×D₄

yes

—

C₄²×C₁₃

#41

yes

—

#2982

C₂×C₁₃

yes

characteristic

#2567

C₂×C₁₃

yes

characteristic

#1801

C₂×C₁₃

yes

characteristic

#1548

C₂×C₁₃

yes

—

#1303

C₂×C₁₃

yes

—

C₂³×C₁₃

C₂×C₂²⋊C₄

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

#103

yes

—

C₂×C₄×C₁₃

C₄×D₄

yes

—

C₂×C₄×C₁₃

#120

yes

characteristic

C₂×C₄×C₁₃

#121

yes

—

100

C₂×C₄×C₁₃

#123

yes

characteristic

101

C₂×C₄×C₁₃

C₂×SD₁₆

yes

characteristic

102

C₂×C₄×C₁₃

C₂×Q₁₆

yes

characteristic

103

C₂×C₄×C₁₃

#135

yes

—

104

C₈×C₁₃

—

105

C₈×C₁₃

—

106

C₂×C₄⋊Q₈

C₂²×C₁₃

yes

characteristic

107

C₂×C₄×Q₈

C₂²×C₁₃

yes

characteristic

108

C₈×Q₈

—

109

#431

—

110

#431

C₂²×C₁₃

yes

—

111

#423

C₂²×C₁₃

yes

—

112

C₂×#101

—

113

#395

C₄×C₁₃

yes

—

114

#391

—

115

#389

—

116

#384

—

117

C₄×C₄⋊C₄

C₂²×C₁₃

yes

characteristic

118

#343

—

119

#333

—

120

C₂²×C₁₃

—

121

C₂²×C₁₃

—

122

C₂²×C₁₃

#386

yes

characteristic

123

C₂²×C₁₃

C₂×#103

yes

characteristic

124

C₂²×C₁₃

#416

yes

characteristic

125

C₄×C₁₃

—

126

C₄×C₁₃

—

127

C₄×C₁₃

—

128

C₄×C₁₃

—

129

C₄×C₁₃

—

130

C₄×C₁₃

—

131

C₄×C₁₃

#456

yes

—

132

C₄×C₁₃

#465

yes

—

133

C₄×C₁₃

#467

yes

—

134

C₂²×Q₈

C₂×C₄×C₁₃

yes

—

135

C₂²×Q₈

D₄×C₁₃

yes

characteristic

136

C₂×M₁₆

—

137

C₄⋊Q₈

—

138

C₄⋊Q₈

—

139

C₄×Q₈

—

140

C₄×Q₈

—

141

C₂×C₄⋊C₄

—

142

C₂×C₄⋊C₄

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

—

145

C₂×C₄⋊C₄

C₂×C₄×C₁₃

yes

—

146

C₂×C₄⋊C₄

D₄×C₁₃

yes

characteristic

147

C₂×C₄²

—

148

C₂×C₄²

D₄×C₁₃

yes

—

149

C₂×C₄²

C₂³×C₁₃

yes

characteristic

150

C₄⋊C₈

—

151

C₄⋊C₈

—

152

C₄⋊C₈

—

153

C₄⋊C₈

D₄×C₁₃

yes

—

154

#101

—

155

C₂²⋊C₈

—

156

C₄×C₈

—

157

C₄×C₈

—

158

#95

—

159

#95

C₂×C₄×C₁₃

yes

—

160

C₂×C₁₃

—

161

C₂×C₁₃

—

162

C₂×C₁₃

#1886

yes

characteristic

163

C₂×C₁₃

#1892

yes

characteristic

164

C₂×C₁₃

#1914

yes

characteristic

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

C₁₃×SD₁₆

yes

—

170

C₂×Q₈

C₁₃×Q₁₆

yes

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

C₁₃×C₂²⋊C₄

yes

—

174

C₂²×C₄

C₁₃×C₂²⋊C₄

yes

—

175

C₂²×C₄

C₂²×C₄×C₁₃

yes

characteristic

176

C₂²×C₄

C₂×D₄×C₁₃

yes

characteristic

177

C₂²×C₄

C₂×D₄×C₁₃

yes

characteristic

178

M₁₆

—

179

M₁₆

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄²

—

190

C₄²

—

191

C₄²

—

192

C₄²

C₂×D₄×C₁₃

yes

—

193

C₄²

C₁₃×#41

yes

—

194

C₁₃

#9392

yes

characteristic, direct product factor, Sylow

195

C₂³

C₂×C₁₃×C₂²⋊C₄

yes

characteristic

196

Q₈

—

197

Q₈

—

198

Q₈

—

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

—

210

C₂×C₄

C₁₃×#103

yes

—

211

C₂×C₄

C₄×D₄×C₁₃

yes

—

212

C₂×C₄

C₁₃×#120

yes

characteristic

213

C₂×C₄

C₁₃×#121

yes

—

214

C₂×C₄

C₁₃×#123

yes

characteristic

215

C₂×C₄

C₂×C₁₃×SD₁₆

yes

characteristic

216

C₂×C₄

C₂×C₁₃×Q₁₆

yes

characteristic

217

C₂×C₄

C₁₃×#135

yes

—

218

C₈

—

219

C₈

—

220

C₂²

—

221

C₂²

—

222

C₂²

C₁₃×#386

yes

characteristic

223

C₂²

C₂×C₁₃×#103

yes

characteristic

224

C₂²

C₁₃×#416

yes

characteristic

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

C₁₃×#456

yes

—

232

C₄

C₁₃×#465

yes

—

233

C₄

C₁₃×#467

yes

—

234

C₂

—

235

C₂

—

236

C₂

C₁₃×#1886

yes

characteristic

237

C₂

C₁₃×#1892

yes

characteristic

238

C₂

C₁₃×#1914

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂³×C₁₃	C₂×C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₃

#386

commutator

C₂²×C₄

C₂²×C₄×C₁₃

Frattini, cosocle

C₂×C₄²

C₂³×C₁₃

prime radical

C₂³×C₁₃

C₂×C₂²⋊C₄

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

N	H ≅ G/N	type
46. #9392	C₁₃	direct (N × H)
194. C₁₃	#9392	direct (N × H)

H ≅ G/N

type

46. #9392

C₁₃

direct (N × H)

194. C₁₃

#9392

direct (N × H)

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

subgroup	index
C₁₃×#2982	2
C₁₃×#2567	2
C₁₃×#1801	2
C₁₃×#1548	2
C₁₃×#1303	2
#9392	13

subgroup

index

C₁₃×#2982

C₁₃×#2567

C₁₃×#1801

C₁₃×#1548

C₁₃×#1303

#9392

Subgroups — C₁₃×#9392 #15695731

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#9392 #15695731

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#9392 #15695731