Group #15696690 — subgroups

Subgroups — C₁₃×#10351 #15696690

Order 3328.

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

normal subgroups only

This group has 500 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×#2571	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#1982	C₂	1	2	yes	maximal
3	C₁₃×#1957	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1296	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1279	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
8	C₂×C₁₃×#102	—	2	2	no	—
9	C₂×C₁₃×#102	—	2	2	no	—
10	C₂×C₁₃×#102	—	2	2	no	—
11	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×#400	—	2	2	no	—
13	C₁₃×#389	—	2	2	no	—
14	C₁₃×#384	C₂²	1	1	yes	characteristic
15	C₁₃×#382	—	2	2	no	—
16	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂²×D₄×C₁₃	—	2	1	no	—
18	C₂²×D₄×C₁₃	—	2	2	no	—
19	C₂²×C₈×C₁₃	—	2	1	no	—
20	C₂²×C₈×C₁₃	—	2	2	no	—
21	C₁₃×#127	—	2	2	no	—
22	C₁₃×#127	—	2	1	no	—
23	C₁₃×#127	Q₈	1	2	yes	—
24	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
25	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
26	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
27	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
28	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
29	C₂×C₄²×C₁₃	—	2	2	no	—
30	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
31	C₁₃×C₄⋊C₈	—	2	2	no	—
32	C₁₃×C₄⋊C₈	—	2	2	no	—
33	C₁₃×#102	—	4	4	no	—
34	C₁₃×#102	—	4	4	no	—
35	C₁₃×#102	—	4	4	no	—
36	C₄×C₈×C₁₃	—	2	2	no	—
37	C₁₃×#95	—	2	2	no	—
38	C₁₃×#95	—	2	4	no	—
39	C₁₃×#95	—	2	2	no	—
40	#10351	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂⁴×C₁₃	—	4	1	no	—
42	C₂×D₄×C₁₃	—	2	2	no	—
43	C₂×D₄×C₁₃	—	2	4	no	—
44	C₂×D₄×C₁₃	—	4	2	no	—
45	C₂×D₄×C₁₃	—	4	2	no	—
46	C₂×D₄×C₁₃	—	4	1	no	—
47	C₂×D₄×C₁₃	—	4	2	no	—
48	C₂×D₄×C₁₃	—	4	2	no	—
49	C₂×D₄×C₁₃	—	4	2	no	—
50	C₂×D₄×C₁₃	—	4	2	no	—
51	C₂×D₄×C₁₃	—	4	2	no	—
52	C₂²×C₄×C₁₃	—	2	2	no	—
53	C₂²×C₄×C₁₃	—	2	2	no	—
54	C₂²×C₄×C₁₃	—	2	2	no	—
55	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
57	C₂×C₈×C₁₃	—	2	2	no	—
58	C₂×C₈×C₁₃	—	4	1	no	—
59	C₂×C₈×C₁₃	—	4	1	no	—
60	C₂×C₈×C₁₃	—	4	2	no	—
61	C₂×C₈×C₁₃	—	4	2	no	—
62	C₂×C₈×C₁₃	—	4	2	no	—
63	C₁₃×C₄⋊C₄	—	2	2	no	—
64	C₁₃×C₄⋊C₄	—	2	2	no	—
65	C₁₃×C₄⋊C₄	—	2	2	no	—
66	C₁₃×C₄⋊C₄	—	2	2	no	—
67	C₁₃×C₄⋊C₄	—	4	2	no	—
68	C₁₃×C₄⋊C₄	—	4	2	no	—
69	C₁₃×C₄⋊C₄	—	4	2	no	—
70	C₁₃×C₄⋊C₄	—	8	2	no	—
71	C₄²×C₁₃	—	4	2	no	—
72	C₄²×C₁₃	—	4	2	no	—
73	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
74	C₄²×C₁₃	#41	1	2	yes	—
75	C₄²×C₁₃	#41	1	1	yes	characteristic
76	#2571	C₂×C₁₃	1	1	yes	characteristic, complemented
77	#1982	C₂×C₁₃	1	2	yes	—
78	#1957	C₂×C₁₃	1	1	yes	characteristic
79	#1296	C₂×C₁₃	1	1	yes	characteristic, complemented
80	#1279	C₂×C₁₃	1	2	yes	complemented
81	C₂³×C₁₃	—	4	2	no	—
82	C₂³×C₁₃	—	8	2	no	—
83	C₂³×C₁₃	—	8	2	no	—
84	C₂³×C₁₃	—	8	1	no	—
85	C₂³×C₁₃	—	8	1	no	—
86	C₂³×C₁₃	#120	1	1	yes	characteristic
87	D₄×C₁₃	—	4	4	no	—
88	D₄×C₁₃	—	4	4	no	—
89	D₄×C₁₃	—	4	4	no	—
90	D₄×C₁₃	—	8	2	no	—
91	D₄×C₁₃	—	8	2	no	—
92	D₄×C₁₃	—	8	2	no	—
93	C₂×C₄×C₁₃	—	2	1	no	—
94	C₂×C₄×C₁₃	—	2	1	no	—
95	C₂×C₄×C₁₃	—	4	2	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	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	C₂²⋊Q₈	1	1	yes	characteristic
104	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
105	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
106	C₂×C₄×C₁₃	#124	1	2	yes	—
107	C₂×C₄×C₁₃	#135	1	2	yes	—
108	C₂×C₄×C₁₃	#135	1	2	yes	—
109	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
110	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
111	C₈×C₁₃	—	4	2	no	—
112	C₈×C₁₃	—	8	2	no	—
113	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
114	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
115	C₂×#102	—	2	2	no	—
116	C₂×#102	—	2	2	no	—
117	C₂×#102	—	2	2	no	—
118	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
119	#400	—	2	2	no	—
120	#389	—	2	2	no	—
121	#384	C₂²×C₁₃	1	1	yes	characteristic
122	#382	—	2	2	no	—
123	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
124	C₂²×C₁₃	—	8	4	no	—
125	C₂²×C₁₃	—	8	2	no	—
126	C₂²×C₁₃	—	16	1	no	—
127	C₂²×C₁₃	—	16	1	no	—
128	C₂²×C₁₃	—	16	2	no	—
129	C₂²×C₁₃	#393	1	1	yes	characteristic
130	C₂²×C₁₃	#449	1	2	yes	—
131	C₂²×C₁₃	#449	1	2	yes	—
132	C₂²×C₁₃	#453	1	1	yes	characteristic
133	C₂²×C₁₃	#454	1	1	yes	characteristic
134	C₄×C₁₃	—	2	1	no	—
135	C₄×C₁₃	—	2	1	no	—
136	C₄×C₁₃	—	8	2	no	—
137	C₄×C₁₃	—	8	2	no	—
138	C₄×C₁₃	—	8	2	no	—
139	C₄×C₁₃	#478	1	2	yes	—
140	C₄×C₁₃	#478	1	2	yes	—
141	C₄×C₁₃	#488	1	2	yes	—
142	C₄×C₁₃	#490	1	2	yes	—
143	C₂²×D₄	—	2	1	no	—
144	C₂²×D₄	—	2	2	no	—
145	C₂²×C₈	—	2	1	no	—
146	C₂²×C₈	—	2	2	no	—
147	#127	—	2	2	no	—
148	#127	—	2	1	no	—
149	#127	Q₈×C₁₃	1	2	yes	—
150	C₂×C₄⋊C₄	—	2	2	no	—
151	C₂×C₄⋊C₄	—	2	2	no	—
152	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
153	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
154	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
155	C₂×C₄²	—	2	2	no	—
156	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
157	C₄⋊C₈	—	2	2	no	—
158	C₄⋊C₈	—	2	2	no	—
159	#102	—	4	4	no	—
160	#102	—	4	4	no	—
161	#102	—	4	4	no	—
162	C₄×C₈	—	2	2	no	—
163	#95	—	2	2	no	—
164	#95	—	2	4	no	—
165	#95	—	2	2	no	—
166	C₂×C₁₃	—	16	2	no	—
167	C₂×C₁₃	#1620	1	1	yes	characteristic
168	C₂×C₁₃	#1624	1	1	yes	characteristic
169	C₂×C₁₃	#1628	1	2	yes	—
170	C₂×C₁₃	#2025	1	2	yes	—
171	C₂×C₁₃	#2027	1	1	yes	characteristic
172	C₂⁴	—	4	1	no	—
173	C₂×D₄	—	2	2	no	—
174	C₂×D₄	—	2	4	no	—
175	C₂×D₄	—	4	2	no	—
176	C₂×D₄	—	4	2	no	—
177	C₂×D₄	—	4	1	no	—
178	C₂×D₄	—	4	2	no	—
179	C₂×D₄	—	4	2	no	—
180	C₂×D₄	—	4	2	no	—
181	C₂×D₄	—	4	2	no	—
182	C₂×D₄	—	4	2	no	—
183	C₂²×C₄	—	2	2	no	—
184	C₂²×C₄	—	2	2	no	—
185	C₂²×C₄	—	2	2	no	—
186	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
187	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
188	C₂×C₈	—	2	2	no	—
189	C₂×C₈	—	4	1	no	—
190	C₂×C₈	—	4	1	no	—
191	C₂×C₈	—	4	2	no	—
192	C₂×C₈	—	4	2	no	—
193	C₂×C₈	—	4	2	no	—
194	C₄⋊C₄	—	2	2	no	—
195	C₄⋊C₄	—	2	2	no	—
196	C₄⋊C₄	—	2	2	no	—
197	C₄⋊C₄	—	2	2	no	—
198	C₄⋊C₄	—	4	2	no	—
199	C₄⋊C₄	—	4	2	no	—
200	C₄⋊C₄	—	4	2	no	—
201	C₄⋊C₄	—	8	2	no	—
202	C₄²	—	4	2	no	—
203	C₄²	—	4	2	no	—
204	C₄²	C₂×Q₈×C₁₃	1	1	yes	characteristic
205	C₄²	C₁₃×#41	1	2	yes	—
206	C₄²	C₁₃×#41	1	1	yes	characteristic
207	C₁₃	#10351	1	1	yes	characteristic, direct product factor, Sylow
208	C₂³	—	4	2	no	—
209	C₂³	—	8	2	no	—
210	C₂³	—	8	2	no	—
211	C₂³	—	8	1	no	—
212	C₂³	—	8	1	no	—
213	C₂³	C₁₃×#120	1	1	yes	characteristic
214	D₄	—	4	4	no	—
215	D₄	—	4	4	no	—
216	D₄	—	4	4	no	—
217	D₄	—	8	2	no	—
218	D₄	—	8	2	no	—
219	D₄	—	8	2	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	4	2	no	—
223	C₂×C₄	—	4	2	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	—	4	2	no	—
226	C₂×C₄	—	4	4	no	—
227	C₂×C₄	—	4	2	no	—
228	C₂×C₄	—	4	2	no	—
229	C₂×C₄	—	4	2	no	—
230	C₂×C₄	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
231	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
232	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
233	C₂×C₄	C₁₃×#124	1	2	yes	—
234	C₂×C₄	C₁₃×#135	1	2	yes	—
235	C₂×C₄	C₁₃×#135	1	2	yes	—
236	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
237	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
238	C₈	—	4	2	no	—
239	C₈	—	8	2	no	—
240	C₂²	—	8	4	no	—
241	C₂²	—	8	2	no	—
242	C₂²	—	16	1	no	—
243	C₂²	—	16	1	no	—
244	C₂²	—	16	2	no	—
245	C₂²	C₁₃×#393	1	1	yes	characteristic
246	C₂²	C₁₃×#449	1	2	yes	—
247	C₂²	C₁₃×#449	1	2	yes	—
248	C₂²	C₁₃×#453	1	1	yes	characteristic
249	C₂²	C₁₃×#454	1	1	yes	characteristic
250	C₄	—	2	1	no	—
251	C₄	—	2	1	no	—
252	C₄	—	8	2	no	—
253	C₄	—	8	2	no	—
254	C₄	—	8	2	no	—
255	C₄	C₁₃×#478	1	2	yes	—
256	C₄	C₁₃×#478	1	2	yes	—
257	C₄	C₁₃×#488	1	2	yes	—
258	C₄	C₁₃×#490	1	2	yes	—
259	C₂	—	16	2	no	—
260	C₂	C₁₃×#1620	1	1	yes	characteristic
261	C₂	C₁₃×#1624	1	1	yes	characteristic
262	C₂	C₁₃×#1628	1	2	yes	—
263	C₂	C₁₃×#2025	1	2	yes	—
264	C₂	C₁₃×#2027	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#2571

C₂

yes

maximal, characteristic, complemented

C₁₃×#1982

C₂

yes

maximal

C₁₃×#1957

C₂

yes

maximal, characteristic

C₁₃×#1296

C₂

yes

maximal, characteristic, complemented

C₁₃×#1279

C₂

yes

maximal, complemented

C₂×C₁₃×#127

C₂²

yes

characteristic

C₂×C₁₃×C₄⋊C₈

C₂²

yes

—

C₂×C₁₃×#102

—

C₂×C₁₃×#102

—

C₂×C₁₃×#102

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₁₃×#400

—

C₁₃×#389

—

C₁₃×#384

C₂²

yes

characteristic

C₁₃×#382

—

C₄×C₁₃×C₄⋊C₄

C₂²

yes

—

C₂²×D₄×C₁₃

—

C₂²×D₄×C₁₃

—

C₂²×C₈×C₁₃

—

C₂²×C₈×C₁₃

—

C₁₃×#127

—

C₁₃×#127

—

C₁₃×#127

Q₈

yes

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

D₄

yes

—

C₂×C₁₃×C₄⋊C₄

D₄

yes

—

C₂×C₁₃×C₄⋊C₄

D₄

yes

—

C₂×C₄²×C₁₃

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₁₃×C₄⋊C₈

—

C₁₃×C₄⋊C₈

—

C₁₃×#102

—

C₁₃×#102

—

C₁₃×#102

—

C₄×C₈×C₁₃

—

C₁₃×#95

—

C₁₃×#95

—

C₁₃×#95

—

#10351

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂⁴×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×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

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

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×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

C₂×Q₈

yes

characteristic

C₄²×C₁₃

#41

yes

—

C₄²×C₁₃

#41

yes

characteristic

#2571

C₂×C₁₃

yes

characteristic, complemented

#1982

C₂×C₁₃

yes

—

#1957

C₂×C₁₃

yes

characteristic

#1296

C₂×C₁₃

yes

characteristic, complemented

#1279

C₂×C₁₃

yes

complemented

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

#120

yes

characteristic

D₄×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

D₄×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

C₂²⋊Q₈

yes

characteristic

104

C₂×C₄×C₁₃

C₂²⋊Q₈

yes

—

105

C₂×C₄×C₁₃

#124

yes

characteristic

106

C₂×C₄×C₁₃

#124

yes

—

107

C₂×C₄×C₁₃

#135

yes

—

108

C₂×C₄×C₁₃

#135

yes

—

109

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

—

110

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

—

111

C₈×C₁₃

—

112

C₈×C₁₃

—

113

C₂×#127

C₂²×C₁₃

yes

characteristic

114

C₂×C₄⋊C₈

C₂²×C₁₃

yes

—

115

C₂×#102

—

116

C₂×#102

—

117

C₂×#102

—

118

C₂×C₄×C₈

C₂²×C₁₃

yes

characteristic

119

#400

—

120

#389

—

121

#384

C₂²×C₁₃

yes

characteristic

122

#382

—

123

C₄×C₄⋊C₄

C₂²×C₁₃

yes

—

124

C₂²×C₁₃

—

125

C₂²×C₁₃

—

126

C₂²×C₁₃

—

127

C₂²×C₁₃

—

128

C₂²×C₁₃

—

129

C₂²×C₁₃

#393

yes

characteristic

130

C₂²×C₁₃

#449

yes

—

131

C₂²×C₁₃

#449

yes

—

132

C₂²×C₁₃

#453

yes

characteristic

133

C₂²×C₁₃

#454

yes

characteristic

134

C₄×C₁₃

—

135

C₄×C₁₃

—

136

C₄×C₁₃

—

137

C₄×C₁₃

—

138

C₄×C₁₃

—

139

C₄×C₁₃

#478

yes

—

140

C₄×C₁₃

#478

yes

—

141

C₄×C₁₃

#488

yes

—

142

C₄×C₁₃

#490

yes

—

143

C₂²×D₄

—

144

C₂²×D₄

—

145

C₂²×C₈

—

146

C₂²×C₈

—

147

#127

—

148

#127

—

149

#127

Q₈×C₁₃

yes

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄⋊C₄

D₄×C₁₃

yes

—

153

C₂×C₄⋊C₄

D₄×C₁₃

yes

—

154

C₂×C₄⋊C₄

D₄×C₁₃

yes

—

155

C₂×C₄²

—

156

C₂×C₄²

C₂³×C₁₃

yes

characteristic

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

#102

—

160

#102

—

161

#102

—

162

C₄×C₈

—

163

#95

—

164

#95

—

165

#95

—

166

C₂×C₁₃

—

167

C₂×C₁₃

#1620

yes

characteristic

168

C₂×C₁₃

#1624

yes

characteristic

169

C₂×C₁₃

#1628

yes

—

170

C₂×C₁₃

#2025

yes

—

171

C₂×C₁₃

#2027

yes

characteristic

172

C₂⁴

—

173

C₂×D₄

—

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂×D₄

—

179

C₂×D₄

—

180

C₂×D₄

—

181

C₂×D₄

—

182

C₂×D₄

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

C₂×D₄×C₁₃

yes

characteristic

187

C₂²×C₄

C₂×D₄×C₁₃

yes

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄⋊C₄

—

201

C₄⋊C₄

—

202

C₄²

—

203

C₄²

—

204

C₄²

C₂×Q₈×C₁₃

yes

characteristic

205

C₄²

C₁₃×#41

yes

—

206

C₄²

C₁₃×#41

yes

characteristic

207

C₁₃

#10351

yes

characteristic, direct product factor, Sylow

208

C₂³

—

209

C₂³

—

210

C₂³

—

211

C₂³

—

212

C₂³

—

213

C₂³

C₁₃×#120

yes

characteristic

214

D₄

—

215

D₄

—

216

D₄

—

217

D₄

—

218

D₄

—

219

D₄

—

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

C₁₃×C₂²⋊Q₈

yes

characteristic

231

C₂×C₄

C₁₃×C₂²⋊Q₈

yes

—

232

C₂×C₄

C₁₃×#124

yes

characteristic

233

C₂×C₄

C₁₃×#124

yes

—

234

C₂×C₄

C₁₃×#135

yes

—

235

C₂×C₄

C₁₃×#135

yes

—

236

C₂×C₄

C₁₃×AGL(1,ℤ/8)

yes

—

237

C₂×C₄

C₁₃×AGL(1,ℤ/8)

yes

—

238

C₈

—

239

C₈

—

240

C₂²

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

—

245

C₂²

C₁₃×#393

yes

characteristic

246

C₂²

C₁₃×#449

yes

—

247

C₂²

C₁₃×#449

yes

—

248

C₂²

C₁₃×#453

yes

characteristic

249

C₂²

C₁₃×#454

yes

characteristic

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

254

C₄

—

255

C₄

C₁₃×#478

yes

—

256

C₄

C₁₃×#478

yes

—

257

C₄

C₁₃×#488

yes

—

258

C₄

C₁₃×#490

yes

—

259

C₂

—

260

C₂

C₁₃×#1620

yes

characteristic

261

C₂

C₁₃×#1624

yes

characteristic

262

C₂

C₁₃×#1628

yes

—

263

C₂

C₁₃×#2025

yes

—

264

C₂

C₁₃×#2027

yes

characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

subgroup

G/H

center, socle

C₂³×C₁₃

#120

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₁₃

prime radical

C₂×C₁₃×#127

C₂²

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

N	H ≅ G/N	type
1. C₁₃×#2571	C₂	semidirect
4. C₁₃×#1296	C₂	semidirect
5. C₁₃×#1279	C₂	semidirect
40. #10351	C₁₃	direct (N × H)
76. #2571	C₂×C₁₃	semidirect
79. #1296	C₂×C₁₃	semidirect
80. #1279	C₂×C₁₃	semidirect
207. C₁₃	#10351	direct (N × H)

H ≅ G/N

type

1. C₁₃×#2571

C₂

semidirect

4. C₁₃×#1296

C₂

semidirect

5. C₁₃×#1279

C₂

semidirect

40. #10351

C₁₃

direct (N × H)

76. #2571

C₂×C₁₃

semidirect

79. #1296

C₂×C₁₃

semidirect

80. #1279

C₂×C₁₃

semidirect

207. C₁₃

#10351

direct (N × H)

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

subgroup	index
C₁₃×#2571	2
C₁₃×#1982	2
C₁₃×#1957	2
C₁₃×#1296	2
C₁₃×#1279	2
#10351	13

subgroup

index

C₁₃×#2571

C₁₃×#1982

C₁₃×#1957

C₁₃×#1296

C₁₃×#1279

#10351

Subgroups — C₁₃×#10351 #15696690

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#10351 #15696690

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10351 #15696690