Group #15695740 — subgroups

Subgroups — C₁₃×#9401 #15695740

Order 3328.

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

normal subgroups only

This group has 534 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×#2547	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1800	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1546	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×C₁₃×#124	—	2	1	no	—
8	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
9	C₁₃×#436	—	2	4	no	—
10	C₁₃×#431	C₂²	1	2	yes	—
11	C₁₃×#423	C₂²	1	2	yes	—
12	C₂×C₁₃×#100	—	2	1	no	—
13	C₁₃×#407	—	2	2	no	—
14	C₁₃×#397	C₄	1	4	yes	—
15	C₁₃×#391	—	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×#332	—	2	4	no	—
20	C₂²×Q₈×C₁₃	—	2	1	no	—
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	C₁₃×#124	—	4	4	no	—
28	C₄×D₄×C₁₃	—	2	2	no	—
29	C₄×D₄×C₁₃	—	2	2	no	—
30	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
31	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
32	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
33	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
34	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
35	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
36	C₂×C₄²×C₁₃	—	2	1	no	—
37	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
38	C₁₃×C₄⋊C₈	—	2	2	no	—
39	C₁₃×C₄⋊C₈	—	2	2	no	—
40	C₁₃×C₄⋊C₈	D₄	1	4	yes	—
41	C₁₃×#100	—	4	2	no	—
42	C₁₃×C₂²⋊C₈	—	2	4	no	—
43	C₁₃×C₂²⋊C₈	—	2	2	no	—
44	C₄×C₈×C₁₃	—	2	2	no	—
45	C₁₃×#95	—	2	4	no	—
46	C₁₃×#95	C₂×C₄	1	2	yes	—
47	#9401	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂⁴×C₁₃	C₂²⋊C₄	1	2	yes	—
49	C₂×Q₈×C₁₃	—	4	2	no	—
50	C₂×Q₈×C₁₃	—	4	2	no	—
51	C₂×Q₈×C₁₃	—	4	1	no	—
52	C₂×Q₈×C₁₃	—	4	1	no	—
53	C₂×D₄×C₁₃	—	2	2	no	—
54	C₂×D₄×C₁₃	—	2	1	no	—
55	C₂×D₄×C₁₃	—	2	2	no	—
56	C₂×D₄×C₁₃	—	2	1	no	—
57	C₂²×C₄×C₁₃	—	2	2	no	—
58	C₂²×C₄×C₁₃	—	2	2	no	—
59	C₂²×C₄×C₁₃	—	2	2	no	—
60	C₂²×C₄×C₁₃	—	2	2	no	—
61	C₂²×C₄×C₁₃	—	4	4	no	—
62	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
63	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
66	C₁₃×M₁₆	—	4	2	no	—
67	C₁₃×M₁₆	—	4	2	no	—
68	C₁₃×M₁₆	—	8	4	no	—
69	C₂×C₈×C₁₃	—	2	4	no	—
70	C₂×C₈×C₁₃	—	4	2	no	—
71	C₁₃×C₄⋊C₄	—	2	2	no	—
72	C₁₃×C₄⋊C₄	—	2	4	no	—
73	C₁₃×C₄⋊C₄	—	4	2	no	—
74	C₁₃×C₄⋊C₄	—	4	1	no	—
75	C₁₃×C₄⋊C₄	—	4	1	no	—
76	C₁₃×C₂²⋊C₄	—	2	4	no	—
77	C₁₃×C₂²⋊C₄	—	4	8	no	—
78	C₄²×C₁₃	—	4	2	no	—
79	C₄²×C₁₃	C₂×D₄	1	2	yes	—
80	C₄²×C₁₃	#41	1	2	yes	—
81	#2975	C₂×C₁₃	1	1	yes	characteristic
82	#2547	C₂×C₁₃	1	1	yes	characteristic
83	#1800	C₂×C₁₃	1	1	yes	characteristic
84	#1546	C₂×C₁₃	1	2	yes	complemented
85	#1303	C₂×C₁₃	1	2	yes	complemented
86	C₂³×C₁₃	—	2	2	no	—
87	C₂³×C₁₃	—	2	2	no	—
88	C₂³×C₁₃	—	2	2	no	—
89	C₂³×C₁₃	—	4	2	no	—
90	C₂³×C₁₃	—	4	2	no	—
91	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
92	Q₈×C₁₃	—	8	2	no	—
93	Q₈×C₁₃	—	8	2	no	—
94	D₄×C₁₃	—	4	2	no	—
95	D₄×C₁₃	—	4	2	no	—
96	C₂×C₄×C₁₃	—	2	2	no	—
97	C₂×C₄×C₁₃	—	2	2	no	—
98	C₂×C₄×C₁₃	—	4	1	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	—	4	2	no	—
104	C₂×C₄×C₁₃	—	4	2	no	—
105	C₂×C₄×C₁₃	—	4	2	no	—
106	C₂×C₄×C₁₃	—	4	2	no	—
107	C₂×C₄×C₁₃	—	8	2	no	—
108	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
109	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
110	C₂×C₄×C₁₃	#121	1	2	yes	—
111	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
112	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
113	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
114	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
115	C₈×C₁₃	—	4	4	no	—
116	C₈×C₁₃	—	8	2	no	—
117	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
118	C₂×#124	—	2	1	no	—
119	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
120	#436	—	2	4	no	—
121	#431	C₂²×C₁₃	1	2	yes	—
122	#423	C₂²×C₁₃	1	2	yes	—
123	C₂×#100	—	2	1	no	—
124	#407	—	2	2	no	—
125	#397	C₄×C₁₃	1	4	yes	—
126	#391	—	2	1	no	—
127	#380	—	2	2	no	—
128	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
129	#343	—	2	1	no	—
130	#332	—	2	4	no	—
131	C₂²×C₁₃	—	2	1	no	—
132	C₂²×C₁₃	—	2	1	no	—
133	C₂²×C₁₃	—	4	4	no	—
134	C₂²×C₁₃	—	4	2	no	—
135	C₂²×C₁₃	—	4	2	no	—
136	C₂²×C₁₃	—	4	2	no	—
137	C₂²×C₁₃	—	8	2	no	—
138	C₂²×C₁₃	#386	1	1	yes	characteristic
139	C₂²×C₁₃	#417	1	1	yes	characteristic
140	C₂²×C₁₃	#418	1	1	yes	characteristic
141	C₄×C₁₃	—	2	1	no	—
142	C₄×C₁₃	—	2	2	no	—
143	C₄×C₁₃	—	4	2	no	—
144	C₄×C₁₃	—	8	2	no	—
145	C₄×C₁₃	—	8	2	no	—
146	C₄×C₁₃	#455	1	2	yes	—
147	C₄×C₁₃	#468	1	2	yes	—
148	C₄×C₁₃	#469	1	2	yes	—
149	C₂²×Q₈	—	2	1	no	—
150	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
151	C₂³×C₄	D₄×C₁₃	1	2	yes	—
152	C₂×M₁₆	—	2	4	no	—
153	C₂×M₁₆	—	2	2	no	—
154	C₄⋊Q₈	—	2	2	no	—
155	C₄⋊Q₈	—	2	2	no	—
156	#124	—	4	4	no	—
157	C₄×D₄	—	2	2	no	—
158	C₄×D₄	—	2	2	no	—
159	C₂×C₄⋊C₄	—	2	1	no	—
160	C₂×C₄⋊C₄	—	2	1	no	—
161	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
162	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
163	C₂×C₂²⋊C₄	—	2	4	no	—
164	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
165	C₂×C₄²	—	2	1	no	—
166	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
167	C₄⋊C₈	—	2	2	no	—
168	C₄⋊C₈	—	2	2	no	—
169	C₄⋊C₈	D₄×C₁₃	1	4	yes	—
170	#100	—	4	2	no	—
171	C₂²⋊C₈	—	2	4	no	—
172	C₂²⋊C₈	—	2	2	no	—
173	C₄×C₈	—	2	2	no	—
174	#95	—	2	4	no	—
175	#95	C₂×C₄×C₁₃	1	2	yes	—
176	C₂×C₁₃	—	2	1	no	—
177	C₂×C₁₃	—	2	1	no	—
178	C₂×C₁₃	—	8	2	no	—
179	C₂×C₁₃	#1885	1	1	yes	characteristic
180	C₂×C₁₃	#1895	1	1	yes	characteristic
181	C₂×C₁₃	#1915	1	1	yes	characteristic
182	C₂⁴	C₁₃×C₂²⋊C₄	1	2	yes	—
183	C₂×Q₈	—	4	2	no	—
184	C₂×Q₈	—	4	2	no	—
185	C₂×Q₈	—	4	1	no	—
186	C₂×Q₈	—	4	1	no	—
187	C₂×D₄	—	2	2	no	—
188	C₂×D₄	—	2	1	no	—
189	C₂×D₄	—	2	2	no	—
190	C₂×D₄	—	2	1	no	—
191	C₂²×C₄	—	2	2	no	—
192	C₂²×C₄	—	2	2	no	—
193	C₂²×C₄	—	2	2	no	—
194	C₂²×C₄	—	2	2	no	—
195	C₂²×C₄	—	4	4	no	—
196	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
197	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
198	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
199	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
200	M₁₆	—	4	2	no	—
201	M₁₆	—	4	2	no	—
202	M₁₆	—	8	4	no	—
203	C₂×C₈	—	2	4	no	—
204	C₂×C₈	—	4	2	no	—
205	C₄⋊C₄	—	2	2	no	—
206	C₄⋊C₄	—	2	4	no	—
207	C₄⋊C₄	—	4	2	no	—
208	C₄⋊C₄	—	4	1	no	—
209	C₄⋊C₄	—	4	1	no	—
210	C₂²⋊C₄	—	2	4	no	—
211	C₂²⋊C₄	—	4	8	no	—
212	C₄²	—	4	2	no	—
213	C₄²	C₂×D₄×C₁₃	1	2	yes	—
214	C₄²	C₁₃×#41	1	2	yes	—
215	C₁₃	#9401	1	1	yes	characteristic, direct product factor, Sylow
216	C₂³	—	2	2	no	—
217	C₂³	—	2	2	no	—
218	C₂³	—	2	2	no	—
219	C₂³	—	4	2	no	—
220	C₂³	—	4	2	no	—
221	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
222	Q₈	—	8	2	no	—
223	Q₈	—	8	2	no	—
224	D₄	—	4	2	no	—
225	D₄	—	4	2	no	—
226	C₂×C₄	—	2	2	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	4	1	no	—
229	C₂×C₄	—	4	4	no	—
230	C₂×C₄	—	4	2	no	—
231	C₂×C₄	—	4	2	no	—
232	C₂×C₄	—	4	2	no	—
233	C₂×C₄	—	4	2	no	—
234	C₂×C₄	—	4	2	no	—
235	C₂×C₄	—	4	2	no	—
236	C₂×C₄	—	4	2	no	—
237	C₂×C₄	—	8	2	no	—
238	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
239	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
240	C₂×C₄	C₁₃×#121	1	2	yes	—
241	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
242	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
243	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
244	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
245	C₈	—	4	4	no	—
246	C₈	—	8	2	no	—
247	C₂²	—	2	1	no	—
248	C₂²	—	2	1	no	—
249	C₂²	—	4	4	no	—
250	C₂²	—	4	2	no	—
251	C₂²	—	4	2	no	—
252	C₂²	—	4	2	no	—
253	C₂²	—	8	2	no	—
254	C₂²	C₁₃×#386	1	1	yes	characteristic
255	C₂²	C₁₃×#417	1	1	yes	characteristic
256	C₂²	C₁₃×#418	1	1	yes	characteristic
257	C₄	—	2	1	no	—
258	C₄	—	2	2	no	—
259	C₄	—	4	2	no	—
260	C₄	—	8	2	no	—
261	C₄	—	8	2	no	—
262	C₄	C₁₃×#455	1	2	yes	—
263	C₄	C₁₃×#468	1	2	yes	—
264	C₄	C₁₃×#469	1	2	yes	—
265	C₂	—	2	1	no	—
266	C₂	—	2	1	no	—
267	C₂	—	8	2	no	—
268	C₂	C₁₃×#1885	1	1	yes	characteristic
269	C₂	C₁₃×#1895	1	1	yes	characteristic
270	C₂	C₁₃×#1915	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#2975

C₂

yes

maximal, characteristic

C₁₃×#2547

C₂

yes

maximal, characteristic

C₁₃×#1800

C₂

yes

maximal, characteristic

C₁₃×#1546

C₂

yes

maximal, complemented

C₁₃×#1303

C₂

yes

maximal, complemented

C₂×C₁₃×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₁₃×#124

—

C₂×C₄×D₄×C₁₃

C₂²

yes

characteristic

C₁₃×#436

—

C₁₃×#431

C₂²

yes

—

C₁₃×#423

C₂²

yes

—

C₂×C₁₃×#100

—

C₁₃×#407

—

C₁₃×#397

C₄

yes

—

C₁₃×#391

—

C₁₃×#380

—

C₄×C₁₃×C₄⋊C₄

C₂²

yes

characteristic

C₁₃×#343

—

C₁₃×#332

—

C₂²×Q₈×C₁₃

—

C₂²×D₄×C₁₃

D₄

yes

characteristic

C₂³×C₄×C₁₃

D₄

yes

—

C₂×C₁₃×M₁₆

—

C₂×C₁₃×M₁₆

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

—

C₁₃×#124

—

C₄×D₄×C₁₃

—

C₄×D₄×C₁₃

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

C₂×C₄

yes

—

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

—

#9401

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂⁴×C₁₃

C₂²⋊C₄

yes

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

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

C₂×D₄

yes

—

C₄²×C₁₃

#41

yes

—

#2975

C₂×C₁₃

yes

characteristic

#2547

C₂×C₁₃

yes

characteristic

#1800

C₂×C₁₃

yes

characteristic

#1546

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

—

Q₈×C₁₃

—

D₄×C₁₃

—

D₄×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

—

105

C₂×C₄×C₁₃

—

106

C₂×C₄×C₁₃

—

107

C₂×C₄×C₁₃

—

108

C₂×C₄×C₁₃

C₄×D₄

yes

—

109

C₂×C₄×C₁₃

#120

yes

characteristic

110

C₂×C₄×C₁₃

#121

yes

—

111

C₂×C₄×C₁₃

#123

yes

characteristic

112

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

—

113

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

characteristic

114

C₂×C₄×C₁₃

#137

yes

characteristic

115

C₈×C₁₃

—

116

C₈×C₁₃

—

117

C₂×C₄⋊Q₈

C₂²×C₁₃

yes

characteristic

118

C₂×#124

—

119

C₂×C₄×D₄

C₂²×C₁₃

yes

characteristic

120

#436

—

121

#431

C₂²×C₁₃

yes

—

122

#423

C₂²×C₁₃

yes

—

123

C₂×#100

—

124

#407

—

125

#397

C₄×C₁₃

yes

—

126

#391

—

127

#380

—

128

C₄×C₄⋊C₄

C₂²×C₁₃

yes

characteristic

129

#343

—

130

#332

—

131

C₂²×C₁₃

—

132

C₂²×C₁₃

—

133

C₂²×C₁₃

—

134

C₂²×C₁₃

—

135

C₂²×C₁₃

—

136

C₂²×C₁₃

—

137

C₂²×C₁₃

—

138

C₂²×C₁₃

#386

yes

characteristic

139

C₂²×C₁₃

#417

yes

characteristic

140

C₂²×C₁₃

#418

yes

characteristic

141

C₄×C₁₃

—

142

C₄×C₁₃

—

143

C₄×C₁₃

—

144

C₄×C₁₃

—

145

C₄×C₁₃

—

146

C₄×C₁₃

#455

yes

—

147

C₄×C₁₃

#468

yes

—

148

C₄×C₁₃

#469

yes

—

149

C₂²×Q₈

—

150

C₂²×D₄

D₄×C₁₃

yes

characteristic

151

C₂³×C₄

D₄×C₁₃

yes

—

152

C₂×M₁₆

—

153

C₂×M₁₆

—

154

C₄⋊Q₈

—

155

C₄⋊Q₈

—

156

#124

—

157

C₄×D₄

—

158

C₄×D₄

—

159

C₂×C₄⋊C₄

—

160

C₂×C₄⋊C₄

—

161

C₂×C₄⋊C₄

C₂×C₄×C₁₃

yes

—

162

C₂×C₄⋊C₄

D₄×C₁₃

yes

characteristic

163

C₂×C₂²⋊C₄

—

164

C₂×C₂²⋊C₄

C₂×C₄×C₁₃

yes

—

165

C₂×C₄²

—

166

C₂×C₄²

C₂³×C₁₃

yes

characteristic

167

C₄⋊C₈

—

168

C₄⋊C₈

—

169

C₄⋊C₈

D₄×C₁₃

yes

—

170

#100

—

171

C₂²⋊C₈

—

172

C₂²⋊C₈

—

173

C₄×C₈

—

174

#95

—

175

#95

C₂×C₄×C₁₃

yes

—

176

C₂×C₁₃

—

177

C₂×C₁₃

—

178

C₂×C₁₃

—

179

C₂×C₁₃

#1885

yes

characteristic

180

C₂×C₁₃

#1895

yes

characteristic

181

C₂×C₁₃

#1915

yes

characteristic

182

C₂⁴

C₁₃×C₂²⋊C₄

yes

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×D₄

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂×D₄

—

191

C₂²×C₄

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

—

196

C₂²×C₄

C₁₃×C₂²⋊C₄

yes

—

197

C₂²×C₄

C₂²×C₄×C₁₃

yes

characteristic

198

C₂²×C₄

C₂×D₄×C₁₃

yes

characteristic

199

C₂²×C₄

C₂×D₄×C₁₃

yes

characteristic

200

M₁₆

—

201

M₁₆

—

202

M₁₆

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

210

C₂²⋊C₄

—

211

C₂²⋊C₄

—

212

C₄²

—

213

C₄²

C₂×D₄×C₁₃

yes

—

214

C₄²

C₁₃×#41

yes

—

215

C₁₃

#9401

yes

characteristic, direct product factor, Sylow

216

C₂³

—

217

C₂³

—

218

C₂³

—

219

C₂³

—

220

C₂³

—

221

C₂³

C₂×C₁₃×C₂²⋊C₄

yes

characteristic

222

Q₈

—

223

Q₈

—

224

D₄

—

225

D₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

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

C₄×D₄×C₁₃

yes

—

239

C₂×C₄

C₁₃×#120

yes

characteristic

240

C₂×C₄

C₁₃×#121

yes

—

241

C₂×C₄

C₁₃×#123

yes

characteristic

242

C₂×C₄

C₁₃×AGL(1,ℤ/8)

yes

—

243

C₂×C₄

C₁₃×AGL(1,ℤ/8)

yes

characteristic

244

C₂×C₄

C₁₃×#137

yes

characteristic

245

C₈

—

246

C₈

—

247

C₂²

—

248

C₂²

—

249

C₂²

—

250

C₂²

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

C₁₃×#386

yes

characteristic

255

C₂²

C₁₃×#417

yes

characteristic

256

C₂²

C₁₃×#418

yes

characteristic

257

C₄

—

258

C₄

—

259

C₄

—

260

C₄

—

261

C₄

—

262

C₄

C₁₃×#455

yes

—

263

C₄

C₁₃×#468

yes

—

264

C₄

C₁₃×#469

yes

—

265

C₂

—

266

C₂

—

267

C₂

—

268

C₂

C₁₃×#1885

yes

characteristic

269

C₂

C₁₃×#1895

yes

characteristic

270

C₂

C₁₃×#1915

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×#1546	C₂	semidirect
5. C₁₃×#1303	C₂	semidirect
47. #9401	C₁₃	direct (N × H)
84. #1546	C₂×C₁₃	semidirect
85. #1303	C₂×C₁₃	semidirect
215. C₁₃	#9401	direct (N × H)

H ≅ G/N

type

4. C₁₃×#1546

C₂

semidirect

5. C₁₃×#1303

C₂

semidirect

47. #9401

C₁₃

direct (N × H)

84. #1546

C₂×C₁₃

semidirect

85. #1303

C₂×C₁₃

semidirect

215. C₁₃

#9401

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×#2547	2
C₁₃×#1800	2
C₁₃×#1546	2
C₁₃×#1303	2
#9401	13

subgroup

index

C₁₃×#2975

C₁₃×#2547

C₁₃×#1800

C₁₃×#1546

C₁₃×#1303

#9401

Subgroups — C₁₃×#9401 #15695740

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#9401 #15695740

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#9401 #15695740