Group #15695730 — subgroups

Subgroups — C₁₃×#9391 #15695730

Order 3328.

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

normal subgroups only

This group has 538 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×#2972	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2563	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1800	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1548	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1303	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
7	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
8	C₈×D₄×C₁₃	—	2	4	no	—
9	C₁₃×#431	C₂²	1	2	yes	—
10	C₁₃×#423	C₂²	1	2	yes	—
11	C₂×C₁₃×#100	—	2	1	no	—
12	C₂×C₁₃×C₂²⋊C₈	—	2	2	no	—
13	C₁₃×#393	C₄	1	4	yes	—
14	C₁₃×#390	—	2	1	no	—
15	C₁₃×#382	—	2	1	no	—
16	C₁₃×#380	—	2	2	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×D₄×C₁₃	D₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₃	D₄	1	2	yes	—
23	C₂×C₁₃×M₁₆	—	2	2	no	—
24	C₂²×C₈×C₁₃	—	2	4	no	—
25	C₁₃×C₄⋊Q₈	—	2	2	no	—
26	C₁₃×C₄⋊Q₈	—	2	2	no	—
27	C₄×D₄×C₁₃	—	2	2	no	—
28	C₄×D₄×C₁₃	—	2	2	no	—
29	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
30	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
31	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
32	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
33	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
34	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
35	C₂×C₄²×C₁₃	—	2	1	no	—
36	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
37	C₁₃×C₄⋊C₈	—	2	2	no	—
38	C₁₃×C₄⋊C₈	—	2	2	no	—
39	C₁₃×C₄⋊C₈	D₄	1	4	yes	—
40	C₁₃×#100	—	4	2	no	—
41	C₁₃×C₂²⋊C₈	—	2	4	no	—
42	C₁₃×C₂²⋊C₈	—	2	2	no	—
43	C₄×C₈×C₁₃	—	2	2	no	—
44	C₁₃×#95	—	2	4	no	—
45	C₁₃×#95	C₂×C₄	1	2	yes	—
46	#9391	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	C₂⁴×C₁₃	C₂²⋊C₄	1	2	yes	—
48	C₂×Q₈×C₁₃	—	2	4	no	—
49	C₂×Q₈×C₁₃	—	8	2	no	—
50	C₂×D₄×C₁₃	—	2	2	no	—
51	C₂×D₄×C₁₃	—	2	2	no	—
52	C₂×D₄×C₁₃	SD₁₆	1	2	yes	—
53	C₂×D₄×C₁₃	Q₁₆	1	2	yes	—
54	C₂²×C₄×C₁₃	—	2	2	no	—
55	C₂²×C₄×C₁₃	—	2	2	no	—
56	C₂²×C₄×C₁₃	—	2	2	no	—
57	C₂²×C₄×C₁₃	—	2	2	no	—
58	C₂²×C₄×C₁₃	—	4	4	no	—
59	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
60	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
63	C₁₃×M₁₆	—	4	2	no	—
64	C₁₃×M₁₆	—	4	2	no	—
65	C₂×C₈×C₁₃	—	2	4	no	—
66	C₂×C₈×C₁₃	—	4	2	no	—
67	C₂×C₈×C₁₃	—	8	4	no	—
68	C₁₃×C₄⋊C₄	—	2	2	no	—
69	C₁₃×C₄⋊C₄	—	4	2	no	—
70	C₁₃×C₄⋊C₄	—	4	1	no	—
71	C₁₃×C₄⋊C₄	—	4	2	no	—
72	C₁₃×C₄⋊C₄	—	4	1	no	—
73	C₁₃×C₂²⋊C₄	—	2	4	no	—
74	C₁₃×C₂²⋊C₄	—	8	4	no	—
75	C₄²×C₁₃	—	4	2	no	—
76	C₄²×C₁₃	C₂×D₄	1	2	yes	—
77	C₄²×C₁₃	#41	1	2	yes	—
78	#2972	C₂×C₁₃	1	1	yes	characteristic
79	#2563	C₂×C₁₃	1	1	yes	characteristic
80	#1800	C₂×C₁₃	1	1	yes	characteristic
81	#1548	C₂×C₁₃	1	2	yes	complemented
82	#1303	C₂×C₁₃	1	2	yes	complemented
83	C₂³×C₁₃	—	2	2	no	—
84	C₂³×C₁₃	—	2	2	no	—
85	C₂³×C₁₃	—	4	2	no	—
86	C₂³×C₁₃	—	4	2	no	—
87	C₂³×C₁₃	#103	1	4	yes	—
88	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
89	Q₈×C₁₃	—	8	4	no	—
90	D₄×C₁₃	—	2	4	no	—
91	D₄×C₁₃	—	2	4	no	—
92	C₂×C₄×C₁₃	—	2	2	no	—
93	C₂×C₄×C₁₃	—	2	2	no	—
94	C₂×C₄×C₁₃	—	4	1	no	—
95	C₂×C₄×C₁₃	—	4	4	no	—
96	C₂×C₄×C₁₃	—	4	2	no	—
97	C₂×C₄×C₁₃	—	4	2	no	—
98	C₂×C₄×C₁₃	—	4	4	no	—
99	C₂×C₄×C₁₃	—	4	2	no	—
100	C₂×C₄×C₁₃	—	4	2	no	—
101	C₂×C₄×C₁₃	—	4	2	no	—
102	C₂×C₄×C₁₃	—	8	2	no	—
103	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
104	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
105	C₂×C₄×C₁₃	#121	1	2	yes	—
106	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
107	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
108	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
109	C₂×C₄×C₁₃	#135	1	2	yes	—
110	C₈×C₁₃	—	4	4	no	—
111	C₈×C₁₃	—	8	2	no	—
112	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
113	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
114	C₈×D₄	—	2	4	no	—
115	#431	C₂²×C₁₃	1	2	yes	—
116	#423	C₂²×C₁₃	1	2	yes	—
117	C₂×#100	—	2	1	no	—
118	C₂×C₂²⋊C₈	—	2	2	no	—
119	#393	C₄×C₁₃	1	4	yes	—
120	#390	—	2	1	no	—
121	#382	—	2	1	no	—
122	#380	—	2	2	no	—
123	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
124	#343	—	2	1	no	—
125	#333	—	2	4	no	—
126	C₂²×C₁₃	—	2	1	no	—
127	C₂²×C₁₃	—	2	1	no	—
128	C₂²×C₁₃	—	2	4	no	—
129	C₂²×C₁₃	—	4	4	no	—
130	C₂²×C₁₃	—	4	2	no	—
131	C₂²×C₁₃	—	4	2	no	—
132	C₂²×C₁₃	—	8	2	no	—
133	C₂²×C₁₃	#386	1	1	yes	characteristic
134	C₂²×C₁₃	C₂×#103	1	1	yes	characteristic
135	C₂²×C₁₃	#416	1	1	yes	characteristic
136	C₄×C₁₃	—	2	1	no	—
137	C₄×C₁₃	—	2	2	no	—
138	C₄×C₁₃	—	4	2	no	—
139	C₄×C₁₃	—	8	2	no	—
140	C₄×C₁₃	—	8	2	no	—
141	C₄×C₁₃	#455	1	2	yes	—
142	C₄×C₁₃	#465	1	2	yes	—
143	C₄×C₁₃	#467	1	2	yes	—
144	C₂²×Q₈	C₂×C₄×C₁₃	1	2	yes	—
145	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
146	C₂³×C₄	D₄×C₁₃	1	2	yes	—
147	C₂×M₁₆	—	2	2	no	—
148	C₂²×C₈	—	2	4	no	—
149	C₄⋊Q₈	—	2	2	no	—
150	C₄⋊Q₈	—	2	2	no	—
151	C₄×D₄	—	2	2	no	—
152	C₄×D₄	—	2	2	no	—
153	C₂×C₄⋊C₄	—	2	1	no	—
154	C₂×C₄⋊C₄	—	2	1	no	—
155	C₂×C₄⋊C₄	—	2	1	no	—
156	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
157	C₂×C₂²⋊C₄	—	2	4	no	—
158	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
159	C₂×C₄²	—	2	1	no	—
160	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
161	C₄⋊C₈	—	2	2	no	—
162	C₄⋊C₈	—	2	2	no	—
163	C₄⋊C₈	D₄×C₁₃	1	4	yes	—
164	#100	—	4	2	no	—
165	C₂²⋊C₈	—	2	4	no	—
166	C₂²⋊C₈	—	2	2	no	—
167	C₄×C₈	—	2	2	no	—
168	#95	—	2	4	no	—
169	#95	C₂×C₄×C₁₃	1	2	yes	—
170	C₂×C₁₃	—	2	1	no	—
171	C₂×C₁₃	—	2	1	no	—
172	C₂×C₁₃	—	4	4	no	—
173	C₂×C₁₃	#1885	1	1	yes	characteristic
174	C₂×C₁₃	#1892	1	1	yes	characteristic
175	C₂×C₁₃	#1914	1	1	yes	characteristic
176	C₂⁴	C₁₃×C₂²⋊C₄	1	2	yes	—
177	C₂×Q₈	—	2	4	no	—
178	C₂×Q₈	—	8	2	no	—
179	C₂×D₄	—	2	2	no	—
180	C₂×D₄	—	2	2	no	—
181	C₂×D₄	C₁₃×SD₁₆	1	2	yes	—
182	C₂×D₄	C₁₃×Q₁₆	1	2	yes	—
183	C₂²×C₄	—	2	2	no	—
184	C₂²×C₄	—	2	2	no	—
185	C₂²×C₄	—	2	2	no	—
186	C₂²×C₄	—	2	2	no	—
187	C₂²×C₄	—	4	4	no	—
188	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
189	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
190	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
191	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
192	M₁₆	—	4	2	no	—
193	M₁₆	—	4	2	no	—
194	C₂×C₈	—	2	4	no	—
195	C₂×C₈	—	4	2	no	—
196	C₂×C₈	—	8	4	no	—
197	C₄⋊C₄	—	2	2	no	—
198	C₄⋊C₄	—	4	2	no	—
199	C₄⋊C₄	—	4	1	no	—
200	C₄⋊C₄	—	4	2	no	—
201	C₄⋊C₄	—	4	1	no	—
202	C₂²⋊C₄	—	2	4	no	—
203	C₂²⋊C₄	—	8	4	no	—
204	C₄²	—	4	2	no	—
205	C₄²	C₂×D₄×C₁₃	1	2	yes	—
206	C₄²	C₁₃×#41	1	2	yes	—
207	C₁₃	#9391	1	1	yes	characteristic, direct product factor, Sylow
208	C₂³	—	2	2	no	—
209	C₂³	—	2	2	no	—
210	C₂³	—	4	2	no	—
211	C₂³	—	4	2	no	—
212	C₂³	C₁₃×#103	1	4	yes	—
213	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
214	Q₈	—	8	4	no	—
215	D₄	—	2	4	no	—
216	D₄	—	2	4	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	2	no	—
219	C₂×C₄	—	4	1	no	—
220	C₂×C₄	—	4	4	no	—
221	C₂×C₄	—	4	2	no	—
222	C₂×C₄	—	4	2	no	—
223	C₂×C₄	—	4	4	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	—	4	2	no	—
226	C₂×C₄	—	4	2	no	—
227	C₂×C₄	—	8	2	no	—
228	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
229	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
230	C₂×C₄	C₁₃×#121	1	2	yes	—
231	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
232	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
233	C₂×C₄	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
234	C₂×C₄	C₁₃×#135	1	2	yes	—
235	C₈	—	4	4	no	—
236	C₈	—	8	2	no	—
237	C₂²	—	2	1	no	—
238	C₂²	—	2	1	no	—
239	C₂²	—	2	4	no	—
240	C₂²	—	4	4	no	—
241	C₂²	—	4	2	no	—
242	C₂²	—	4	2	no	—
243	C₂²	—	8	2	no	—
244	C₂²	C₁₃×#386	1	1	yes	characteristic
245	C₂²	C₂×C₁₃×#103	1	1	yes	characteristic
246	C₂²	C₁₃×#416	1	1	yes	characteristic
247	C₄	—	2	1	no	—
248	C₄	—	2	2	no	—
249	C₄	—	4	2	no	—
250	C₄	—	8	2	no	—
251	C₄	—	8	2	no	—
252	C₄	C₁₃×#455	1	2	yes	—
253	C₄	C₁₃×#465	1	2	yes	—
254	C₄	C₁₃×#467	1	2	yes	—
255	C₂	—	2	1	no	—
256	C₂	—	2	1	no	—
257	C₂	—	4	4	no	—
258	C₂	C₁₃×#1885	1	1	yes	characteristic
259	C₂	C₁₃×#1892	1	1	yes	characteristic
260	C₂	C₁₃×#1914	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#2972

C₂

yes

maximal, characteristic

C₁₃×#2563

C₂

yes

maximal, characteristic

C₁₃×#1800

C₂

yes

maximal, characteristic

C₁₃×#1548

C₂

yes

maximal, complemented

C₁₃×#1303

C₂

yes

maximal, complemented

C₂×C₁₃×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₄×D₄×C₁₃

C₂²

yes

characteristic

C₈×D₄×C₁₃

—

C₁₃×#431

C₂²

yes

—

C₁₃×#423

C₂²

yes

—

C₂×C₁₃×#100

—

C₂×C₁₃×C₂²⋊C₈

—

C₁₃×#393

C₄

yes

—

C₁₃×#390

—

C₁₃×#382

—

C₁₃×#380

—

C₄×C₁₃×C₄⋊C₄

C₂²

yes

characteristic

C₁₃×#343

—

C₁₃×#333

—

C₂²×Q₈×C₁₃

C₂×C₄

yes

—

C₂²×D₄×C₁₃

D₄

yes

characteristic

C₂³×C₄×C₁₃

D₄

yes

—

C₂×C₁₃×M₁₆

—

C₂²×C₈×C₁₃

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

—

C₄×D₄×C₁₃

—

C₄×D₄×C₁₃

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

D₄

yes

characteristic

C₂×C₁₃×C₂²⋊C₄

—

C₂×C₁₃×C₂²⋊C₄

C₂×C₄

yes

—

C₂×C₄²×C₁₃

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₁₃×C₄⋊C₈

—

C₁₃×C₄⋊C₈

—

C₁₃×C₄⋊C₈

D₄

yes

—

C₁₃×#100

—

C₁₃×C₂²⋊C₈

—

C₁₃×C₂²⋊C₈

—

C₄×C₈×C₁₃

—

C₁₃×#95

—

C₁₃×#95

C₂×C₄

yes

—

#9391

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂⁴×C₁₃

C₂²⋊C₄

yes

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

SD₁₆

yes

—

C₂×D₄×C₁₃

Q₁₆

yes

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

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

—

C₂×C₈×C₁₃

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₂²⋊C₄

—

C₁₃×C₂²⋊C₄

—

C₄²×C₁₃

—

C₄²×C₁₃

C₂×D₄

yes

—

C₄²×C₁₃

#41

yes

—

#2972

C₂×C₁₃

yes

characteristic

#2563

C₂×C₁₃

yes

characteristic

#1800

C₂×C₁₃

yes

characteristic

#1548

C₂×C₁₃

yes

complemented

#1303

C₂×C₁₃

yes

complemented

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

#103

yes

—

C₂³×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₁₃

—

D₄×C₁₃

—

D₄×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

—

100

C₂×C₄×C₁₃

—

101

C₂×C₄×C₁₃

—

102

C₂×C₄×C₁₃

—

103

C₂×C₄×C₁₃

C₄×D₄

yes

—

104

C₂×C₄×C₁₃

#120

yes

characteristic

105

C₂×C₄×C₁₃

#121

yes

—

106

C₂×C₄×C₁₃

#123

yes

characteristic

107

C₂×C₄×C₁₃

C₂×SD₁₆

yes

characteristic

108

C₂×C₄×C₁₃

C₂×Q₁₆

yes

characteristic

109

C₂×C₄×C₁₃

#135

yes

—

110

C₈×C₁₃

—

111

C₈×C₁₃

—

112

C₂×C₄⋊Q₈

C₂²×C₁₃

yes

characteristic

113

C₂×C₄×D₄

C₂²×C₁₃

yes

characteristic

114

C₈×D₄

—

115

#431

C₂²×C₁₃

yes

—

116

#423

C₂²×C₁₃

yes

—

117

C₂×#100

—

118

C₂×C₂²⋊C₈

—

119

#393

C₄×C₁₃

yes

—

120

#390

—

121

#382

—

122

#380

—

123

C₄×C₄⋊C₄

C₂²×C₁₃

yes

characteristic

124

#343

—

125

#333

—

126

C₂²×C₁₃

—

127

C₂²×C₁₃

—

128

C₂²×C₁₃

—

129

C₂²×C₁₃

—

130

C₂²×C₁₃

—

131

C₂²×C₁₃

—

132

C₂²×C₁₃

—

133

C₂²×C₁₃

#386

yes

characteristic

134

C₂²×C₁₃

C₂×#103

yes

characteristic

135

C₂²×C₁₃

#416

yes

characteristic

136

C₄×C₁₃

—

137

C₄×C₁₃

—

138

C₄×C₁₃

—

139

C₄×C₁₃

—

140

C₄×C₁₃

—

141

C₄×C₁₃

#455

yes

—

142

C₄×C₁₃

#465

yes

—

143

C₄×C₁₃

#467

yes

—

144

C₂²×Q₈

C₂×C₄×C₁₃

yes

—

145

C₂²×D₄

D₄×C₁₃

yes

characteristic

146

C₂³×C₄

D₄×C₁₃

yes

—

147

C₂×M₁₆

—

148

C₂²×C₈

—

149

C₄⋊Q₈

—

150

C₄⋊Q₈

—

151

C₄×D₄

—

152

C₄×D₄

—

153

C₂×C₄⋊C₄

—

154

C₂×C₄⋊C₄

—

155

C₂×C₄⋊C₄

—

156

C₂×C₄⋊C₄

D₄×C₁₃

yes

characteristic

157

C₂×C₂²⋊C₄

—

158

C₂×C₂²⋊C₄

C₂×C₄×C₁₃

yes

—

159

C₂×C₄²

—

160

C₂×C₄²

C₂³×C₁₃

yes

characteristic

161

C₄⋊C₈

—

162

C₄⋊C₈

—

163

C₄⋊C₈

D₄×C₁₃

yes

—

164

#100

—

165

C₂²⋊C₈

—

166

C₂²⋊C₈

—

167

C₄×C₈

—

168

#95

—

169

#95

C₂×C₄×C₁₃

yes

—

170

C₂×C₁₃

—

171

C₂×C₁₃

—

172

C₂×C₁₃

—

173

C₂×C₁₃

#1885

yes

characteristic

174

C₂×C₁₃

#1892

yes

characteristic

175

C₂×C₁₃

#1914

yes

characteristic

176

C₂⁴

C₁₃×C₂²⋊C₄

yes

—

177

C₂×Q₈

—

178

C₂×Q₈

—

179

C₂×D₄

—

180

C₂×D₄

—

181

C₂×D₄

C₁₃×SD₁₆

yes

—

182

C₂×D₄

C₁₃×Q₁₆

yes

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

—

188

C₂²×C₄

C₁₃×C₂²⋊C₄

yes

—

189

C₂²×C₄

C₂²×C₄×C₁₃

yes

characteristic

190

C₂²×C₄

C₂×D₄×C₁₃

yes

characteristic

191

C₂²×C₄

C₂×D₄×C₁₃

yes

characteristic

192

M₁₆

—

193

M₁₆

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄⋊C₄

—

201

C₄⋊C₄

—

202

C₂²⋊C₄

—

203

C₂²⋊C₄

—

204

C₄²

—

205

C₄²

C₂×D₄×C₁₃

yes

—

206

C₄²

C₁₃×#41

yes

—

207

C₁₃

#9391

yes

characteristic, direct product factor, Sylow

208

C₂³

—

209

C₂³

—

210

C₂³

—

211

C₂³

—

212

C₂³

C₁₃×#103

yes

—

213

C₂³

C₂×C₁₃×C₂²⋊C₄

yes

characteristic

214

Q₈

—

215

D₄

—

216

D₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

C₄×D₄×C₁₃

yes

—

229

C₂×C₄

C₁₃×#120

yes

characteristic

230

C₂×C₄

C₁₃×#121

yes

—

231

C₂×C₄

C₁₃×#123

yes

characteristic

232

C₂×C₄

C₂×C₁₃×SD₁₆

yes

characteristic

233

C₂×C₄

C₂×C₁₃×Q₁₆

yes

characteristic

234

C₂×C₄

C₁₃×#135

yes

—

235

C₈

—

236

C₈

—

237

C₂²

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

C₁₃×#386

yes

characteristic

245

C₂²

C₂×C₁₃×#103

yes

characteristic

246

C₂²

C₁₃×#416

yes

characteristic

247

C₄

—

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

C₁₃×#455

yes

—

253

C₄

C₁₃×#465

yes

—

254

C₄

C₁₃×#467

yes

—

255

C₂

—

256

C₂

—

257

C₂

—

258

C₂

C₁₃×#1885

yes

characteristic

259

C₂

C₁₃×#1892

yes

characteristic

260

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	C₂²×D₄×C₁₃	D₄
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

C₂²×D₄×C₁₃

D₄

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

N	H ≅ G/N	type
4. C₁₃×#1548	C₂	semidirect
5. C₁₃×#1303	C₂	semidirect
46. #9391	C₁₃	direct (N × H)
81. #1548	C₂×C₁₃	semidirect
82. #1303	C₂×C₁₃	semidirect
207. C₁₃	#9391	direct (N × H)

H ≅ G/N

type

4. C₁₃×#1548

C₂

semidirect

5. C₁₃×#1303

C₂

semidirect

46. #9391

C₁₃

direct (N × H)

81. #1548

C₂×C₁₃

semidirect

82. #1303

C₂×C₁₃

semidirect

207. C₁₃

#9391

direct (N × H)

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

subgroup	index
C₁₃×#2972	2
C₁₃×#2563	2
C₁₃×#1800	2
C₁₃×#1548	2
C₁₃×#1303	2
#9391	13

subgroup

index

C₁₃×#2972

C₁₃×#2563

C₁₃×#1800

C₁₃×#1548

C₁₃×#1303

#9391

Subgroups — C₁₃×#9391 #15695730

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#9391 #15695730

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#9391 #15695730