Group #15695738 — subgroups

Subgroups — C₁₃×#9399 #15695738

Order 3328.

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

normal subgroups only

This group has 514 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×#2975	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	C₁₃×#436	—	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	C₁₃×#407	—	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	4	no	—
24	C₂×C₁₃×M₁₆	—	2	2	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	#9399	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	1	no	—
52	C₂×D₄×C₁₃	—	2	2	no	—
53	C₂×D₄×C₁₃	—	2	1	no	—
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	C₁₃×M₁₆	—	8	4	no	—
66	C₂×C₈×C₁₃	—	2	4	no	—
67	C₂×C₈×C₁₃	—	4	2	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	1	no	—
76	C₄²×C₁₃	—	4	1	no	—
77	C₄²×C₁₃	C₂×D₄	1	2	yes	—
78	C₄²×C₁₃	#41	1	2	yes	—
79	#2975	C₂×C₁₃	1	1	yes	characteristic
80	#2563	C₂×C₁₃	1	1	yes	characteristic
81	#1800	C₂×C₁₃	1	1	yes	characteristic
82	#1548	C₂×C₁₃	1	2	yes	complemented
83	#1303	C₂×C₁₃	1	2	yes	complemented
84	C₂³×C₁₃	—	2	2	no	—
85	C₂³×C₁₃	—	2	2	no	—
86	C₂³×C₁₃	—	2	2	no	—
87	C₂³×C₁₃	—	4	2	no	—
88	C₂³×C₁₃	—	4	2	no	—
89	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
90	Q₈×C₁₃	—	8	4	no	—
91	D₄×C₁₃	—	4	2	no	—
92	D₄×C₁₃	—	4	2	no	—
93	C₂×C₄×C₁₃	—	2	2	no	—
94	C₂×C₄×C₁₃	—	2	2	no	—
95	C₂×C₄×C₁₃	—	4	1	no	—
96	C₂×C₄×C₁₃	—	4	4	no	—
97	C₂×C₄×C₁₃	—	4	2	no	—
98	C₂×C₄×C₁₃	—	4	2	no	—
99	C₂×C₄×C₁₃	—	4	4	no	—
100	C₂×C₄×C₁₃	—	4	2	no	—
101	C₂×C₄×C₁₃	—	4	2	no	—
102	C₂×C₄×C₁₃	—	4	2	no	—
103	C₂×C₄×C₁₃	—	8	2	no	—
104	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
105	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
106	C₂×C₄×C₁₃	#121	1	2	yes	—
107	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
108	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
109	C₂×C₄×C₁₃	#137	1	2	yes	—
110	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
111	C₈×C₁₃	—	4	4	no	—
112	C₈×C₁₃	—	8	2	no	—
113	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
114	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
115	#436	—	2	4	no	—
116	#431	C₂²×C₁₃	1	2	yes	—
117	#423	C₂²×C₁₃	1	2	yes	—
118	C₂×#100	—	2	1	no	—
119	#407	—	2	2	no	—
120	#393	C₄×C₁₃	1	4	yes	—
121	#390	—	2	1	no	—
122	#382	—	2	1	no	—
123	#380	—	2	2	no	—
124	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
125	#343	—	2	1	no	—
126	#333	—	2	4	no	—
127	C₂²×C₁₃	—	2	1	no	—
128	C₂²×C₁₃	—	2	1	no	—
129	C₂²×C₁₃	—	4	4	no	—
130	C₂²×C₁₃	—	4	2	no	—
131	C₂²×C₁₃	—	4	2	no	—
132	C₂²×C₁₃	—	4	2	no	—
133	C₂²×C₁₃	—	8	2	no	—
134	C₂²×C₁₃	#386	1	1	yes	characteristic
135	C₂²×C₁₃	#417	1	1	yes	characteristic
136	C₂²×C₁₃	#419	1	1	yes	characteristic
137	C₄×C₁₃	—	2	1	no	—
138	C₄×C₁₃	—	2	2	no	—
139	C₄×C₁₃	—	4	2	no	—
140	C₄×C₁₃	—	8	2	no	—
141	C₄×C₁₃	—	8	2	no	—
142	C₄×C₁₃	#455	1	2	yes	—
143	C₄×C₁₃	#468	1	2	yes	—
144	C₄×C₁₃	#470	1	2	yes	—
145	C₂²×Q₈	C₂×C₄×C₁₃	1	2	yes	—
146	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
147	C₂³×C₄	D₄×C₁₃	1	2	yes	—
148	C₂×M₁₆	—	2	4	no	—
149	C₂×M₁₆	—	2	2	no	—
150	C₄⋊Q₈	—	2	2	no	—
151	C₄⋊Q₈	—	2	2	no	—
152	C₄×D₄	—	2	2	no	—
153	C₄×D₄	—	2	2	no	—
154	C₂×C₄⋊C₄	—	2	1	no	—
155	C₂×C₄⋊C₄	—	2	1	no	—
156	C₂×C₄⋊C₄	—	2	1	no	—
157	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
158	C₂×C₂²⋊C₄	—	2	4	no	—
159	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
160	C₂×C₄²	—	2	1	no	—
161	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
162	C₄⋊C₈	—	2	2	no	—
163	C₄⋊C₈	—	2	2	no	—
164	C₄⋊C₈	D₄×C₁₃	1	4	yes	—
165	#100	—	4	2	no	—
166	C₂²⋊C₈	—	2	4	no	—
167	C₂²⋊C₈	—	2	2	no	—
168	C₄×C₈	—	2	2	no	—
169	#95	—	2	4	no	—
170	#95	C₂×C₄×C₁₃	1	2	yes	—
171	C₂×C₁₃	—	2	1	no	—
172	C₂×C₁₃	—	2	1	no	—
173	C₂×C₁₃	—	8	2	no	—
174	C₂×C₁₃	#1885	1	1	yes	characteristic
175	C₂×C₁₃	#1894	1	1	yes	characteristic
176	C₂×C₁₃	#1914	1	1	yes	characteristic
177	C₂⁴	C₁₃×C₂²⋊C₄	1	2	yes	—
178	C₂×Q₈	—	2	4	no	—
179	C₂×Q₈	—	8	2	no	—
180	C₂×D₄	—	2	2	no	—
181	C₂×D₄	—	2	1	no	—
182	C₂×D₄	—	2	2	no	—
183	C₂×D₄	—	2	1	no	—
184	C₂²×C₄	—	2	2	no	—
185	C₂²×C₄	—	2	2	no	—
186	C₂²×C₄	—	2	2	no	—
187	C₂²×C₄	—	2	2	no	—
188	C₂²×C₄	—	4	4	no	—
189	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
190	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
191	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
192	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
193	M₁₆	—	4	2	no	—
194	M₁₆	—	4	2	no	—
195	M₁₆	—	8	4	no	—
196	C₂×C₈	—	2	4	no	—
197	C₂×C₈	—	4	2	no	—
198	C₄⋊C₄	—	2	2	no	—
199	C₄⋊C₄	—	4	2	no	—
200	C₄⋊C₄	—	4	1	no	—
201	C₄⋊C₄	—	4	2	no	—
202	C₄⋊C₄	—	4	1	no	—
203	C₂²⋊C₄	—	2	4	no	—
204	C₂²⋊C₄	—	8	4	no	—
205	C₄²	—	4	1	no	—
206	C₄²	—	4	1	no	—
207	C₄²	C₂×D₄×C₁₃	1	2	yes	—
208	C₄²	C₁₃×#41	1	2	yes	—
209	C₁₃	#9399	1	1	yes	characteristic, direct product factor, Sylow
210	C₂³	—	2	2	no	—
211	C₂³	—	2	2	no	—
212	C₂³	—	2	2	no	—
213	C₂³	—	4	2	no	—
214	C₂³	—	4	2	no	—
215	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
216	Q₈	—	8	4	no	—
217	D₄	—	4	2	no	—
218	D₄	—	4	2	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	4	1	no	—
222	C₂×C₄	—	4	4	no	—
223	C₂×C₄	—	4	2	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	—	4	4	no	—
226	C₂×C₄	—	4	2	no	—
227	C₂×C₄	—	4	2	no	—
228	C₂×C₄	—	4	2	no	—
229	C₂×C₄	—	8	2	no	—
230	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
231	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
232	C₂×C₄	C₁₃×#121	1	2	yes	—
233	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
234	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
235	C₂×C₄	C₁₃×#137	1	2	yes	—
236	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
237	C₈	—	4	4	no	—
238	C₈	—	8	2	no	—
239	C₂²	—	2	1	no	—
240	C₂²	—	2	1	no	—
241	C₂²	—	4	4	no	—
242	C₂²	—	4	2	no	—
243	C₂²	—	4	2	no	—
244	C₂²	—	4	2	no	—
245	C₂²	—	8	2	no	—
246	C₂²	C₁₃×#386	1	1	yes	characteristic
247	C₂²	C₁₃×#417	1	1	yes	characteristic
248	C₂²	C₁₃×#419	1	1	yes	characteristic
249	C₄	—	2	1	no	—
250	C₄	—	2	2	no	—
251	C₄	—	4	2	no	—
252	C₄	—	8	2	no	—
253	C₄	—	8	2	no	—
254	C₄	C₁₃×#455	1	2	yes	—
255	C₄	C₁₃×#468	1	2	yes	—
256	C₄	C₁₃×#470	1	2	yes	—
257	C₂	—	2	1	no	—
258	C₂	—	2	1	no	—
259	C₂	—	8	2	no	—
260	C₂	C₁₃×#1885	1	1	yes	characteristic
261	C₂	C₁₃×#1894	1	1	yes	characteristic
262	C₂	C₁₃×#1914	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#2975

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

C₁₃×#436

—

C₁₃×#431

C₂²

yes

—

C₁₃×#423

C₂²

yes

—

C₂×C₁₃×#100

—

C₁₃×#407

—

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

—

C₂×C₁₃×M₁₆

—

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

—

#9399

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

—

C₂×D₄×C₁₃

—

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

—

C₁₃×M₁₆

—

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

—

C₄²×C₁₃

C₂×D₄

yes

—

C₄²×C₁₃

#41

yes

—

#2975

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

—

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

—

100

C₂×C₄×C₁₃

—

101

C₂×C₄×C₁₃

—

102

C₂×C₄×C₁₃

—

103

C₂×C₄×C₁₃

—

104

C₂×C₄×C₁₃

C₄×D₄

yes

—

105

C₂×C₄×C₁₃

#120

yes

characteristic

106

C₂×C₄×C₁₃

#121

yes

—

107

C₂×C₄×C₁₃

#123

yes

characteristic

108

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

characteristic

109

C₂×C₄×C₁₃

#137

yes

—

110

C₂×C₄×C₁₃

#137

yes

characteristic

111

C₈×C₁₃

—

112

C₈×C₁₃

—

113

C₂×C₄⋊Q₈

C₂²×C₁₃

yes

characteristic

114

C₂×C₄×D₄

C₂²×C₁₃

yes

characteristic

115

#436

—

116

#431

C₂²×C₁₃

yes

—

117

#423

C₂²×C₁₃

yes

—

118

C₂×#100

—

119

#407

—

120

#393

C₄×C₁₃

yes

—

121

#390

—

122

#382

—

123

#380

—

124

C₄×C₄⋊C₄

C₂²×C₁₃

yes

characteristic

125

#343

—

126

#333

—

127

C₂²×C₁₃

—

128

C₂²×C₁₃

—

129

C₂²×C₁₃

—

130

C₂²×C₁₃

—

131

C₂²×C₁₃

—

132

C₂²×C₁₃

—

133

C₂²×C₁₃

—

134

C₂²×C₁₃

#386

yes

characteristic

135

C₂²×C₁₃

#417

yes

characteristic

136

C₂²×C₁₃

#419

yes

characteristic

137

C₄×C₁₃

—

138

C₄×C₁₃

—

139

C₄×C₁₃

—

140

C₄×C₁₃

—

141

C₄×C₁₃

—

142

C₄×C₁₃

#455

yes

—

143

C₄×C₁₃

#468

yes

—

144

C₄×C₁₃

#470

yes

—

145

C₂²×Q₈

C₂×C₄×C₁₃

yes

—

146

C₂²×D₄

D₄×C₁₃

yes

characteristic

147

C₂³×C₄

D₄×C₁₃

yes

—

148

C₂×M₁₆

—

149

C₂×M₁₆

—

150

C₄⋊Q₈

—

151

C₄⋊Q₈

—

152

C₄×D₄

—

153

C₄×D₄

—

154

C₂×C₄⋊C₄

—

155

C₂×C₄⋊C₄

—

156

C₂×C₄⋊C₄

—

157

C₂×C₄⋊C₄

D₄×C₁₃

yes

characteristic

158

C₂×C₂²⋊C₄

—

159

C₂×C₂²⋊C₄

C₂×C₄×C₁₃

yes

—

160

C₂×C₄²

—

161

C₂×C₄²

C₂³×C₁₃

yes

characteristic

162

C₄⋊C₈

—

163

C₄⋊C₈

—

164

C₄⋊C₈

D₄×C₁₃

yes

—

165

#100

—

166

C₂²⋊C₈

—

167

C₂²⋊C₈

—

168

C₄×C₈

—

169

#95

—

170

#95

C₂×C₄×C₁₃

yes

—

171

C₂×C₁₃

—

172

C₂×C₁₃

—

173

C₂×C₁₃

—

174

C₂×C₁₃

#1885

yes

characteristic

175

C₂×C₁₃

#1894

yes

characteristic

176

C₂×C₁₃

#1914

yes

characteristic

177

C₂⁴

C₁₃×C₂²⋊C₄

yes

—

178

C₂×Q₈

—

179

C₂×Q₈

—

180

C₂×D₄

—

181

C₂×D₄

—

182

C₂×D₄

—

183

C₂×D₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

—

188

C₂²×C₄

—

189

C₂²×C₄

C₁₃×C₂²⋊C₄

yes

—

190

C₂²×C₄

C₂²×C₄×C₁₃

yes

characteristic

191

C₂²×C₄

C₂×D₄×C₁₃

yes

characteristic

192

C₂²×C₄

C₂×D₄×C₁₃

yes

characteristic

193

M₁₆

—

194

M₁₆

—

195

M₁₆

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄⋊C₄

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₂²⋊C₄

—

204

C₂²⋊C₄

—

205

C₄²

—

206

C₄²

—

207

C₄²

C₂×D₄×C₁₃

yes

—

208

C₄²

C₁₃×#41

yes

—

209

C₁₃

#9399

yes

characteristic, direct product factor, Sylow

210

C₂³

—

211

C₂³

—

212

C₂³

—

213

C₂³

—

214

C₂³

—

215

C₂³

C₂×C₁₃×C₂²⋊C₄

yes

characteristic

216

Q₈

—

217

D₄

—

218

D₄

—

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

—

229

C₂×C₄

—

230

C₂×C₄

C₄×D₄×C₁₃

yes

—

231

C₂×C₄

C₁₃×#120

yes

characteristic

232

C₂×C₄

C₁₃×#121

yes

—

233

C₂×C₄

C₁₃×#123

yes

characteristic

234

C₂×C₄

C₁₃×AGL(1,ℤ/8)

yes

characteristic

235

C₂×C₄

C₁₃×#137

yes

—

236

C₂×C₄

C₁₃×#137

yes

characteristic

237

C₈

—

238

C₈

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

—

245

C₂²

—

246

C₂²

C₁₃×#386

yes

characteristic

247

C₂²

C₁₃×#417

yes

characteristic

248

C₂²

C₁₃×#419

yes

characteristic

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

254

C₄

C₁₃×#455

yes

—

255

C₄

C₁₃×#468

yes

—

256

C₄

C₁₃×#470

yes

—

257

C₂

—

258

C₂

—

259

C₂

—

260

C₂

C₁₃×#1885

yes

characteristic

261

C₂

C₁₃×#1894

yes

characteristic

262

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. #9399	C₁₃	direct (N × H)
82. #1548	C₂×C₁₃	semidirect
83. #1303	C₂×C₁₃	semidirect
209. C₁₃	#9399	direct (N × H)

H ≅ G/N

type

4. C₁₃×#1548

C₂

semidirect

5. C₁₃×#1303

C₂

semidirect

46. #9399

C₁₃

direct (N × H)

82. #1548

C₂×C₁₃

semidirect

83. #1303

C₂×C₁₃

semidirect

209. C₁₃

#9399

direct (N × H)

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

subgroup	index
C₁₃×#2975	2
C₁₃×#2563	2
C₁₃×#1800	2
C₁₃×#1548	2
C₁₃×#1303	2
#9399	13

subgroup

index

C₁₃×#2975

C₁₃×#2563

C₁₃×#1800

C₁₃×#1548

C₁₃×#1303

#9399

Subgroups — C₁₃×#9399 #15695738

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#9399 #15695738

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#9399 #15695738