Group #15695741 — subgroups

Subgroups — C₁₃×#9402 #15695741

Order 3328.

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

normal subgroups only

This group has 486 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×#2983	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2546	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1801	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1546	C₂	1	2	yes	maximal
5	C₁₃×#1303	C₂	1	2	yes	maximal
6	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
7	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
8	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₁₃×#446	—	2	4	no	—
10	C₁₃×#432	—	2	2	no	—
11	C₁₃×#431	C₂²	1	2	yes	—
12	C₁₃×#423	C₂²	1	2	yes	—
13	C₂×C₁₃×#101	—	2	1	no	—
14	C₁₃×#398	C₄	1	4	yes	—
15	C₁₃×#391	—	2	1	no	—
16	C₁₃×#389	—	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×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	C₁₃×C₄⋊Q₈	—	4	4	no	—
26	C₄×Q₈×C₁₃	—	2	2	no	—
27	C₄×Q₈×C₁₃	—	2	2	no	—
28	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
29	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
30	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
31	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
32	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
33	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₃	—	2	1	no	—
35	C₂×C₄²×C₁₃	D₄	1	2	yes	—
36	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
37	C₁₃×C₄⋊C₈	—	2	4	no	—
38	C₁₃×C₄⋊C₈	—	2	2	no	—
39	C₁₃×C₄⋊C₈	—	2	2	no	—
40	C₁₃×C₄⋊C₈	D₄	1	4	yes	—
41	C₁₃×#101	—	4	2	no	—
42	C₁₃×C₂²⋊C₈	—	2	2	no	—
43	C₁₃×#97	—	2	4	no	—
44	C₄×C₈×C₁₃	—	2	2	no	—
45	C₁₃×#95	—	2	4	no	—
46	C₁₃×#95	C₂×C₄	1	2	yes	—
47	#9402	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×Q₈×C₁₃	—	2	2	no	—
49	C₂×Q₈×C₁₃	—	2	1	no	—
50	C₂×Q₈×C₁₃	—	2	2	no	—
51	C₂×Q₈×C₁₃	—	2	1	no	—
52	C₂×Q₈×C₁₃	—	4	2	no	—
53	C₂×Q₈×C₁₃	—	4	2	no	—
54	C₂×Q₈×C₁₃	—	4	1	no	—
55	C₂×Q₈×C₁₃	—	4	1	no	—
56	C₂²×C₄×C₁₃	—	2	2	no	—
57	C₂²×C₄×C₁₃	—	2	2	no	—
58	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
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	C₁₃×C₄⋊C₄	—	2	4	no	—
68	C₁₃×C₄⋊C₄	—	2	4	no	—
69	C₁₃×C₄⋊C₄	—	2	2	no	—
70	C₁₃×C₄⋊C₄	—	2	4	no	—
71	C₁₃×C₄⋊C₄	—	4	8	no	—
72	C₁₃×C₄⋊C₄	—	4	1	no	—
73	C₁₃×C₄⋊C₄	—	4	1	no	—
74	C₄²×C₁₃	—	2	2	no	—
75	C₄²×C₁₃	—	2	2	no	—
76	C₄²×C₁₃	—	4	2	no	—
77	C₄²×C₁₃	C₂×D₄	1	2	yes	—
78	C₄²×C₁₃	#41	1	2	yes	—
79	#2983	C₂×C₁₃	1	1	yes	characteristic
80	#2546	C₂×C₁₃	1	1	yes	characteristic
81	#1801	C₂×C₁₃	1	1	yes	characteristic
82	#1546	C₂×C₁₃	1	2	yes	—
83	#1303	C₂×C₁₃	1	2	yes	—
84	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	Q₈×C₁₃	—	4	2	no	—
86	Q₈×C₁₃	—	4	2	no	—
87	Q₈×C₁₃	—	8	2	no	—
88	Q₈×C₁₃	—	8	2	no	—
89	C₂×C₄×C₁₃	—	2	2	no	—
90	C₂×C₄×C₁₃	—	2	4	no	—
91	C₂×C₄×C₁₃	—	2	2	no	—
92	C₂×C₄×C₁₃	—	2	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	2	no	—
97	C₂×C₄×C₁₃	—	4	2	no	—
98	C₂×C₄×C₁₃	—	4	2	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	C₄×D₄	1	2	yes	—
103	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
104	C₂×C₄×C₁₃	#121	1	2	yes	—
105	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
106	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
107	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
108	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
109	C₈×C₁₃	—	4	4	no	—
110	C₈×C₁₃	—	8	2	no	—
111	C₂×C₄⋊Q₈	—	2	1	no	—
112	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
113	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
114	#446	—	2	4	no	—
115	#432	—	2	2	no	—
116	#431	C₂²×C₁₃	1	2	yes	—
117	#423	C₂²×C₁₃	1	2	yes	—
118	C₂×#101	—	2	1	no	—
119	#398	C₄×C₁₃	1	4	yes	—
120	#391	—	2	1	no	—
121	#389	—	2	2	no	—
122	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
123	#343	—	2	1	no	—
124	#332	—	2	4	no	—
125	C₂²×C₁₃	—	2	1	no	—
126	C₂²×C₁₃	—	2	1	no	—
127	C₂²×C₁₃	#386	1	1	yes	characteristic
128	C₂²×C₁₃	#417	1	1	yes	characteristic
129	C₂²×C₁₃	#418	1	1	yes	characteristic
130	C₄×C₁₃	—	2	1	no	—
131	C₄×C₁₃	—	2	2	no	—
132	C₄×C₁₃	—	4	4	no	—
133	C₄×C₁₃	—	4	2	no	—
134	C₄×C₁₃	—	4	2	no	—
135	C₄×C₁₃	—	8	2	no	—
136	C₄×C₁₃	#456	1	2	yes	—
137	C₄×C₁₃	#468	1	2	yes	—
138	C₄×C₁₃	#469	1	2	yes	—
139	C₂²×Q₈	—	2	1	no	—
140	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
141	C₂×M₁₆	—	2	2	no	—
142	C₄⋊Q₈	—	2	2	no	—
143	C₄⋊Q₈	—	2	2	no	—
144	C₄⋊Q₈	—	4	4	no	—
145	C₄×Q₈	—	2	2	no	—
146	C₄×Q₈	—	2	2	no	—
147	C₂×C₄⋊C₄	—	2	1	no	—
148	C₂×C₄⋊C₄	—	2	4	no	—
149	C₂×C₄⋊C₄	—	2	1	no	—
150	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
151	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
152	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
153	C₂×C₄²	—	2	1	no	—
154	C₂×C₄²	D₄×C₁₃	1	2	yes	—
155	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
156	C₄⋊C₈	—	2	4	no	—
157	C₄⋊C₈	—	2	2	no	—
158	C₄⋊C₈	—	2	2	no	—
159	C₄⋊C₈	D₄×C₁₃	1	4	yes	—
160	#101	—	4	2	no	—
161	C₂²⋊C₈	—	2	2	no	—
162	#97	—	2	4	no	—
163	C₄×C₈	—	2	2	no	—
164	#95	—	2	4	no	—
165	#95	C₂×C₄×C₁₃	1	2	yes	—
166	C₂×C₁₃	—	2	1	no	—
167	C₂×C₁₃	—	2	1	no	—
168	C₂×C₁₃	#1886	1	1	yes	characteristic
169	C₂×C₁₃	#1895	1	1	yes	characteristic
170	C₂×C₁₃	#1915	1	1	yes	characteristic
171	C₂×Q₈	—	2	2	no	—
172	C₂×Q₈	—	2	1	no	—
173	C₂×Q₈	—	2	2	no	—
174	C₂×Q₈	—	2	1	no	—
175	C₂×Q₈	—	4	2	no	—
176	C₂×Q₈	—	4	2	no	—
177	C₂×Q₈	—	4	1	no	—
178	C₂×Q₈	—	4	1	no	—
179	C₂²×C₄	—	2	2	no	—
180	C₂²×C₄	—	2	2	no	—
181	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
182	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
183	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
184	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
185	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
186	M₁₆	—	4	2	no	—
187	M₁₆	—	4	2	no	—
188	C₂×C₈	—	2	4	no	—
189	C₂×C₈	—	4	2	no	—
190	C₄⋊C₄	—	2	4	no	—
191	C₄⋊C₄	—	2	4	no	—
192	C₄⋊C₄	—	2	2	no	—
193	C₄⋊C₄	—	2	4	no	—
194	C₄⋊C₄	—	4	8	no	—
195	C₄⋊C₄	—	4	1	no	—
196	C₄⋊C₄	—	4	1	no	—
197	C₄²	—	2	2	no	—
198	C₄²	—	2	2	no	—
199	C₄²	—	4	2	no	—
200	C₄²	C₂×D₄×C₁₃	1	2	yes	—
201	C₄²	C₁₃×#41	1	2	yes	—
202	C₁₃	#9402	1	1	yes	characteristic, direct product factor, Sylow
203	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
204	Q₈	—	4	2	no	—
205	Q₈	—	4	2	no	—
206	Q₈	—	8	2	no	—
207	Q₈	—	8	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	4	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	2	2	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	4	1	no	—
215	C₂×C₄	—	4	2	no	—
216	C₂×C₄	—	4	2	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	4	2	no	—
219	C₂×C₄	—	4	2	no	—
220	C₂×C₄	—	4	2	no	—
221	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
222	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
223	C₂×C₄	C₁₃×#121	1	2	yes	—
224	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
225	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
226	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
227	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
228	C₈	—	4	4	no	—
229	C₈	—	8	2	no	—
230	C₂²	—	2	1	no	—
231	C₂²	—	2	1	no	—
232	C₂²	C₁₃×#386	1	1	yes	characteristic
233	C₂²	C₁₃×#417	1	1	yes	characteristic
234	C₂²	C₁₃×#418	1	1	yes	characteristic
235	C₄	—	2	1	no	—
236	C₄	—	2	2	no	—
237	C₄	—	4	4	no	—
238	C₄	—	4	2	no	—
239	C₄	—	4	2	no	—
240	C₄	—	8	2	no	—
241	C₄	C₁₃×#456	1	2	yes	—
242	C₄	C₁₃×#468	1	2	yes	—
243	C₄	C₁₃×#469	1	2	yes	—
244	C₂	—	2	1	no	—
245	C₂	—	2	1	no	—
246	C₂	C₁₃×#1886	1	1	yes	characteristic
247	C₂	C₁₃×#1895	1	1	yes	characteristic
248	C₂	C₁₃×#1915	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#2983

C₂

yes

maximal, characteristic

C₁₃×#2546

C₂

yes

maximal, characteristic

C₁₃×#1801

C₂

yes

maximal, characteristic

C₁₃×#1546

C₂

yes

maximal

C₁₃×#1303

C₂

yes

maximal

C₂×C₁₃×C₄⋊Q₈

—

C₂×C₁₃×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₄×Q₈×C₁₃

C₂²

yes

characteristic

C₁₃×#446

—

C₁₃×#432

—

C₁₃×#431

C₂²

yes

—

C₁₃×#423

C₂²

yes

—

C₂×C₁₃×#101

—

C₁₃×#398

C₄

yes

—

C₁₃×#391

—

C₁₃×#389

—

C₄×C₁₃×C₄⋊C₄

C₂²

yes

characteristic

C₁₃×#343

—

C₁₃×#332

—

C₂²×Q₈×C₁₃

—

C₂²×Q₈×C₁₃

D₄

yes

characteristic

C₂×C₁₃×M₁₆

—

C₁₃×C₄⋊Q₈

—

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×C₄

yes

—

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

—

C₁₃×#97

—

C₄×C₈×C₁₃

—

C₁₃×#95

—

C₁₃×#95

C₂×C₄

yes

—

#9402

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

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

—

#2983

C₂×C₁₃

yes

characteristic

#2546

C₂×C₁₃

yes

characteristic

#1801

C₂×C₁₃

yes

characteristic

#1546

C₂×C₁₃

yes

—

#1303

C₂×C₁₃

yes

—

C₂³×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₁₃

—

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

—

100

C₂×C₄×C₁₃

—

101

C₂×C₄×C₁₃

—

102

C₂×C₄×C₁₃

C₄×D₄

yes

—

103

C₂×C₄×C₁₃

#120

yes

characteristic

104

C₂×C₄×C₁₃

#121

yes

—

105

C₂×C₄×C₁₃

#123

yes

characteristic

106

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

—

107

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

characteristic

108

C₂×C₄×C₁₃

#137

yes

characteristic

109

C₈×C₁₃

—

110

C₈×C₁₃

—

111

C₂×C₄⋊Q₈

—

112

C₂×C₄⋊Q₈

C₂²×C₁₃

yes

characteristic

113

C₂×C₄×Q₈

C₂²×C₁₃

yes

characteristic

114

#446

—

115

#432

—

116

#431

C₂²×C₁₃

yes

—

117

#423

C₂²×C₁₃

yes

—

118

C₂×#101

—

119

#398

C₄×C₁₃

yes

—

120

#391

—

121

#389

—

122

C₄×C₄⋊C₄

C₂²×C₁₃

yes

characteristic

123

#343

—

124

#332

—

125

C₂²×C₁₃

—

126

C₂²×C₁₃

—

127

C₂²×C₁₃

#386

yes

characteristic

128

C₂²×C₁₃

#417

yes

characteristic

129

C₂²×C₁₃

#418

yes

characteristic

130

C₄×C₁₃

—

131

C₄×C₁₃

—

132

C₄×C₁₃

—

133

C₄×C₁₃

—

134

C₄×C₁₃

—

135

C₄×C₁₃

—

136

C₄×C₁₃

#456

yes

—

137

C₄×C₁₃

#468

yes

—

138

C₄×C₁₃

#469

yes

—

139

C₂²×Q₈

—

140

C₂²×Q₈

D₄×C₁₃

yes

characteristic

141

C₂×M₁₆

—

142

C₄⋊Q₈

—

143

C₄⋊Q₈

—

144

C₄⋊Q₈

—

145

C₄×Q₈

—

146

C₄×Q₈

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

C₂×C₄×C₁₃

yes

—

151

C₂×C₄⋊C₄

C₂×C₄×C₁₃

yes

—

152

C₂×C₄⋊C₄

D₄×C₁₃

yes

characteristic

153

C₂×C₄²

—

154

C₂×C₄²

D₄×C₁₃

yes

—

155

C₂×C₄²

C₂³×C₁₃

yes

characteristic

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

D₄×C₁₃

yes

—

160

#101

—

161

C₂²⋊C₈

—

162

#97

—

163

C₄×C₈

—

164

#95

—

165

#95

C₂×C₄×C₁₃

yes

—

166

C₂×C₁₃

—

167

C₂×C₁₃

—

168

C₂×C₁₃

#1886

yes

characteristic

169

C₂×C₁₃

#1895

yes

characteristic

170

C₂×C₁₃

#1915

yes

characteristic

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂×Q₈

—

177

C₂×Q₈

—

178

C₂×Q₈

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

C₁₃×C₂²⋊C₄

yes

—

182

C₂²×C₄

C₁₃×C₂²⋊C₄

yes

—

183

C₂²×C₄

C₂²×C₄×C₁₃

yes

characteristic

184

C₂²×C₄

C₂×D₄×C₁₃

yes

characteristic

185

C₂²×C₄

C₂×D₄×C₁₃

yes

characteristic

186

M₁₆

—

187

M₁₆

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄²

—

198

C₄²

—

199

C₄²

—

200

C₄²

C₂×D₄×C₁₃

yes

—

201

C₄²

C₁₃×#41

yes

—

202

C₁₃

#9402

yes

characteristic, direct product factor, Sylow

203

C₂³

C₂×C₁₃×C₂²⋊C₄

yes

characteristic

204

Q₈

—

205

Q₈

—

206

Q₈

—

207

Q₈

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

C₄×D₄×C₁₃

yes

—

222

C₂×C₄

C₁₃×#120

yes

characteristic

223

C₂×C₄

C₁₃×#121

yes

—

224

C₂×C₄

C₁₃×#123

yes

characteristic

225

C₂×C₄

C₁₃×AGL(1,ℤ/8)

yes

—

226

C₂×C₄

C₁₃×AGL(1,ℤ/8)

yes

characteristic

227

C₂×C₄

C₁₃×#137

yes

characteristic

228

C₈

—

229

C₈

—

230

C₂²

—

231

C₂²

—

232

C₂²

C₁₃×#386

yes

characteristic

233

C₂²

C₁₃×#417

yes

characteristic

234

C₂²

C₁₃×#418

yes

characteristic

235

C₄

—

236

C₄

—

237

C₄

—

238

C₄

—

239

C₄

—

240

C₄

—

241

C₄

C₁₃×#456

yes

—

242

C₄

C₁₃×#468

yes

—

243

C₄

C₁₃×#469

yes

—

244

C₂

—

245

C₂

—

246

C₂

C₁₃×#1886

yes

characteristic

247

C₂

C₁₃×#1895

yes

characteristic

248

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	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
47. #9402	C₁₃	direct (N × H)
202. C₁₃	#9402	direct (N × H)

H ≅ G/N

type

47. #9402

C₁₃

direct (N × H)

202. C₁₃

#9402

direct (N × H)

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

subgroup	index
C₁₃×#2983	2
C₁₃×#2546	2
C₁₃×#1801	2
C₁₃×#1546	2
C₁₃×#1303	2
#9402	13

subgroup

index

C₁₃×#2983

C₁₃×#2546

C₁₃×#1801

C₁₃×#1546

C₁₃×#1303

#9402

Subgroups — C₁₃×#9402 #15695741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#9402 #15695741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#9402 #15695741