Group #15719129 — subgroups

Subgroups — C₁₃×#32790 #15719129

Order 3328.

716 conjugacy classes of subgroups; only the 234 normal subgroups are shown.

normal subgroups only

This group has 716 conjugacy classes of subgroups — too many to draw. Only its 234 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×#2857	C₂	1	2	yes	maximal
2	C₁₃×#2100	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2076	C₂	1	4	yes	maximal
4	C₁₃×#2057	C₂	1	4	yes	maximal, complemented
5	C₁₃×#1817	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
7	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
8	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×#107	C₂²	1	4	yes	—
10	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
11	C₁₃×#391	—	2	2	no	—
12	C₁₃×#389	—	2	2	no	—
13	C₁₃×#389	C₂²	1	4	yes	—
14	C₁₃×#384	C₂²	1	2	yes	—
15	C₁₃×#380	—	2	2	no	—
16	C₁₃×#380	C₂²	1	4	yes	—
17	C₁₃×#340	C₂²	1	8	yes	—
18	C₁₃×#340	C₂²	1	4	yes	—
19	C₁₃×#336	C₂²	1	4	yes	—
20	C₂²×Q₈×C₁₃	—	2	2	no	—
21	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
24	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
25	C₁₃×C₄⋊Q₈	—	4	4	no	—
26	C₁₃×C₂²⋊Q₈	—	4	8	no	—
27	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
28	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
29	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
30	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
31	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
32	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
33	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
34	C₂×C₄²×C₁₃	—	4	2	no	—
35	C₂×C₄²×C₁₃	D₄	1	2	yes	—
36	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
37	C₁₃×#107	—	4	4	no	—
38	C₁₃×C₂²⋊C₈	—	4	2	no	—
39	C₁₃×#95	—	2	4	no	—
40	C₁₃×#95	—	2	4	no	—
41	#32790	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
43	C₂×Q₈×C₁₃	—	4	4	no	—
44	C₂×Q₈×C₁₃	—	4	4	no	—
45	C₂×Q₈×C₁₃	—	4	4	no	—
46	C₂²×C₄×C₁₃	—	2	4	no	—
47	C₂²×C₄×C₁₃	—	2	2	no	—
48	C₂²×C₄×C₁₃	—	2	4	no	—
49	C₂²×C₄×C₁₃	—	2	4	no	—
50	C₂²×C₄×C₁₃	—	2	4	no	—
51	C₂²×C₄×C₁₃	—	4	1	no	—
52	C₂²×C₄×C₁₃	—	4	1	no	—
53	C₂²×C₄×C₁₃	—	4	1	no	—
54	C₂²×C₄×C₁₃	Q₁₆	1	4	yes	—
55	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
57	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
58	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
59	C₂×C₈×C₁₃	—	2	4	no	—
60	C₂×C₈×C₁₃	—	2	8	no	—
61	C₁₃×C₄⋊C₄	—	2	8	no	—
62	C₁₃×C₄⋊C₄	—	2	8	no	—
63	C₁₃×C₄⋊C₄	—	4	4	no	—
64	C₁₃×C₄⋊C₄	—	4	4	no	—
65	C₁₃×C₄⋊C₄	—	4	4	no	—
66	C₁₃×C₄⋊C₄	—	4	8	no	—
67	C₁₃×C₂²⋊C₄	—	4	8	no	—
68	C₄²×C₁₃	—	2	4	no	—
69	C₄²×C₁₃	—	4	2	no	—
70	#2857	C₂×C₁₃	1	2	yes	—
71	#2100	C₂×C₁₃	1	4	yes	complemented
72	#2076	C₂×C₁₃	1	4	yes	—
73	#2057	C₂×C₁₃	1	4	yes	complemented
74	#1817	C₂×C₁₃	1	1	yes	characteristic
75	C₂³×C₁₃	—	2	1	no	—
76	C₂³×C₁₃	—	2	2	no	—
77	C₂³×C₁₃	—	2	2	no	—
78	C₂³×C₁₃	—	2	1	no	—
79	C₂³×C₁₃	C₂×Q₁₆	1	2	yes	—
80	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
81	Q₈×C₁₃	—	8	8	no	—
82	C₂×C₄×C₁₃	—	2	2	no	—
83	C₂×C₄×C₁₃	—	2	2	no	—
84	C₂×C₄×C₁₃	—	2	2	no	—
85	C₂×C₄×C₁₃	—	2	2	no	—
86	C₂×C₄×C₁₃	—	2	1	no	—
87	C₂×C₄×C₁₃	—	2	2	no	—
88	C₂×C₄×C₁₃	—	4	4	no	—
89	C₂×C₄×C₁₃	—	4	4	no	—
90	C₂×C₄×C₁₃	—	4	4	no	—
91	C₂×C₄×C₁₃	—	4	4	no	—
92	C₂×C₄×C₁₃	—	4	4	no	—
93	C₂×C₄×C₁₃	—	4	4	no	—
94	C₂×C₄×C₁₃	—	4	4	no	—
95	C₂×C₄×C₁₃	—	4	4	no	—
96	C₂×C₄×C₁₃	—	4	4	no	—
97	C₂×C₄×C₁₃	C₂×Q₁₆	1	4	yes	—
98	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
99	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
100	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
101	C₈×C₁₃	—	4	4	no	—
102	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
103	C₂×C₂²⋊Q₈	—	2	2	no	—
104	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
105	C₂×#107	C₂²×C₁₃	1	4	yes	—
106	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
107	#391	—	2	2	no	—
108	#389	—	2	2	no	—
109	#389	C₂²×C₁₃	1	4	yes	—
110	#384	C₂²×C₁₃	1	2	yes	—
111	#380	—	2	2	no	—
112	#380	C₂²×C₁₃	1	4	yes	—
113	#340	C₂²×C₁₃	1	8	yes	—
114	#340	C₂²×C₁₃	1	4	yes	—
115	#336	C₂²×C₁₃	1	4	yes	—
116	C₂²×C₁₃	—	2	2	no	—
117	C₂²×C₁₃	—	2	4	no	—
118	C₂²×C₁₃	—	4	1	no	—
119	C₂²×C₁₃	—	4	1	no	—
120	C₂²×C₁₃	—	4	2	no	—
121	C₂²×C₁₃	#534	1	1	yes	characteristic
122	C₂²×C₁₃	#536	1	2	yes	—
123	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
124	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
125	C₂²×C₁₃	#575	1	1	yes	characteristic
126	C₄×C₁₃	—	2	4	no	—
127	C₄×C₁₃	—	2	4	no	—
128	C₄×C₁₃	—	4	1	no	—
129	C₄×C₁₃	—	8	4	no	—
130	C₄×C₁₃	—	8	4	no	—
131	C₄×C₁₃	#563	1	4	yes	—
132	C₂²×Q₈	—	2	2	no	—
133	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
134	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
135	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
136	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
137	C₄⋊Q₈	—	4	4	no	—
138	C₂²⋊Q₈	—	4	8	no	—
139	C₂×C₄⋊C₄	—	2	2	no	—
140	C₂×C₄⋊C₄	—	2	4	no	—
141	C₂×C₄⋊C₄	—	2	2	no	—
142	C₂×C₄⋊C₄	—	2	2	no	—
143	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
144	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
145	C₂×C₂²⋊C₄	—	2	4	no	—
146	C₂×C₄²	—	4	2	no	—
147	C₂×C₄²	D₄×C₁₃	1	2	yes	—
148	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
149	#107	—	4	4	no	—
150	C₂²⋊C₈	—	4	2	no	—
151	#95	—	2	4	no	—
152	#95	—	2	4	no	—
153	C₂×C₁₃	—	4	2	no	—
154	C₂×C₁₃	#2817	1	1	yes	characteristic
155	C₂×C₁₃	#3189	1	1	yes	characteristic
156	C₂×C₁₃	#3192	1	1	yes	characteristic
157	C₂×C₁₃	#3230	1	2	yes	—
158	C₂×C₁₃	#3235	1	2	yes	—
159	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
160	C₂×Q₈	—	4	4	no	—
161	C₂×Q₈	—	4	4	no	—
162	C₂×Q₈	—	4	4	no	—
163	C₂²×C₄	—	2	4	no	—
164	C₂²×C₄	—	2	2	no	—
165	C₂²×C₄	—	2	4	no	—
166	C₂²×C₄	—	2	4	no	—
167	C₂²×C₄	—	2	4	no	—
168	C₂²×C₄	—	4	1	no	—
169	C₂²×C₄	—	4	1	no	—
170	C₂²×C₄	—	4	1	no	—
171	C₂²×C₄	C₁₃×Q₁₆	1	4	yes	—
172	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
173	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
174	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
175	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
176	C₂×C₈	—	2	4	no	—
177	C₂×C₈	—	2	8	no	—
178	C₄⋊C₄	—	2	8	no	—
179	C₄⋊C₄	—	2	8	no	—
180	C₄⋊C₄	—	4	4	no	—
181	C₄⋊C₄	—	4	4	no	—
182	C₄⋊C₄	—	4	4	no	—
183	C₄⋊C₄	—	4	8	no	—
184	C₂²⋊C₄	—	4	8	no	—
185	C₄²	—	2	4	no	—
186	C₄²	—	4	2	no	—
187	C₁₃	#32790	1	1	yes	characteristic, direct product factor, Sylow
188	C₂³	—	2	1	no	—
189	C₂³	—	2	2	no	—
190	C₂³	—	2	2	no	—
191	C₂³	—	2	1	no	—
192	C₂³	C₂×C₁₃×Q₁₆	1	2	yes	—
193	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
194	Q₈	—	8	8	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	4	4	no	—
202	C₂×C₄	—	4	4	no	—
203	C₂×C₄	—	4	4	no	—
204	C₂×C₄	—	4	4	no	—
205	C₂×C₄	—	4	4	no	—
206	C₂×C₄	—	4	4	no	—
207	C₂×C₄	—	4	4	no	—
208	C₂×C₄	—	4	4	no	—
209	C₂×C₄	—	4	4	no	—
210	C₂×C₄	C₂×C₁₃×Q₁₆	1	4	yes	—
211	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
212	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
213	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
214	C₈	—	4	4	no	—
215	C₂²	—	2	2	no	—
216	C₂²	—	2	4	no	—
217	C₂²	—	4	1	no	—
218	C₂²	—	4	1	no	—
219	C₂²	—	4	2	no	—
220	C₂²	C₁₃×#534	1	1	yes	characteristic
221	C₂²	C₁₃×#536	1	2	yes	—
222	C₂²	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
223	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
224	C₂²	C₁₃×#575	1	1	yes	characteristic
225	C₄	—	2	4	no	—
226	C₄	—	2	4	no	—
227	C₄	—	4	1	no	—
228	C₄	—	8	4	no	—
229	C₄	—	8	4	no	—
230	C₄	C₁₃×#563	1	4	yes	—
231	C₂	—	4	2	no	—
232	C₂	C₁₃×#2817	1	1	yes	characteristic
233	C₂	C₁₃×#3189	1	1	yes	characteristic
234	C₂	C₁₃×#3192	1	1	yes	characteristic
235	C₂	C₁₃×#3230	1	2	yes	—
236	C₂	C₁₃×#3235	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#2857

C₂

yes

maximal

C₁₃×#2100

C₂

yes

maximal, complemented

C₁₃×#2076

C₂

yes

maximal

C₁₃×#2057

C₂

yes

maximal, complemented

C₁₃×#1817

C₂

yes

maximal, characteristic

C₂×C₁₃×C₄⋊Q₈

C₂²

yes

—

C₂×C₁₃×C₂²⋊Q₈

—

C₂²×C₄²×C₁₃

C₂²

yes

characteristic

C₂×C₁₃×#107

C₂²

yes

—

C₂×C₁₃×C₂²⋊C₈

C₂²

yes

—

C₁₃×#391

—

C₁₃×#389

—

C₁₃×#389

C₂²

yes

—

C₁₃×#384

C₂²

yes

—

C₁₃×#380

—

C₁₃×#380

C₂²

yes

—

C₁₃×#340

C₂²

yes

—

C₁₃×#340

C₂²

yes

—

C₁₃×#336

C₂²

yes

—

C₂²×Q₈×C₁₃

—

C₂³×C₄×C₁₃

D₄

yes

characteristic

C₂³×C₄×C₁₃

D₄

yes

characteristic

C₂³×C₄×C₁₃

C₂³

yes

characteristic

C₂²×C₈×C₁₃

C₂³

yes

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₂²⋊Q₈

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

C₂³

yes

—

C₂×C₁₃×C₄⋊C₄

C₂³

yes

—

C₂×C₁₃×C₂²⋊C₄

—

C₂×C₄²×C₁₃

—

C₂×C₄²×C₁₃

D₄

yes

—

C₂×C₄²×C₁₃

C₂³

yes

—

C₁₃×#107

—

C₁₃×C₂²⋊C₈

—

C₁₃×#95

—

C₁₃×#95

—

#32790

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂⁴×C₁₃

C₂×D₄

yes

characteristic

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

Q₁₆

yes

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂²×C₄×C₁₃

C₂⁴

yes

characteristic

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×C₂²⋊C₄

—

C₄²×C₁₃

—

C₄²×C₁₃

—

#2857

C₂×C₁₃

yes

—

#2100

C₂×C₁₃

yes

complemented

#2076

C₂×C₁₃

yes

—

#2057

C₂×C₁₃

yes

complemented

#1817

C₂×C₁₃

yes

characteristic

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

C₂×Q₁₆

yes

—

C₂³×C₁₃

C₂²×D₄

yes

characteristic

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

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×Q₁₆

yes

—

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₃

H(5,𝔽₂)

yes

—

100

C₂×C₄×C₁₃

2₋¹⁺⁴

yes

—

101

C₈×C₁₃

—

102

C₂×C₄⋊Q₈

C₂²×C₁₃

yes

—

103

C₂×C₂²⋊Q₈

—

104

C₂²×C₄²

C₂²×C₁₃

yes

characteristic

105

C₂×#107

C₂²×C₁₃

yes

—

106

C₂×C₂²⋊C₈

C₂²×C₁₃

yes

—

107

#391

—

108

#389

—

109

#389

C₂²×C₁₃

yes

—

110

#384

C₂²×C₁₃

yes

—

111

#380

—

112

#380

C₂²×C₁₃

yes

—

113

#340

C₂²×C₁₃

yes

—

114

#340

C₂²×C₁₃

yes

—

115

#336

C₂²×C₁₃

yes

—

116

C₂²×C₁₃

—

117

C₂²×C₁₃

—

118

C₂²×C₁₃

—

119

C₂²×C₁₃

—

120

C₂²×C₁₃

—

121

C₂²×C₁₃

#534

yes

characteristic

122

C₂²×C₁₃

#536

yes

—

123

C₂²×C₁₃

C₂²×Q₁₆

yes

characteristic

124

C₂²×C₁₃

C₂×AGL(1,ℤ/8)

yes

—

125

C₂²×C₁₃

#575

yes

characteristic

126

C₄×C₁₃

—

127

C₄×C₁₃

—

128

C₄×C₁₃

—

129

C₄×C₁₃

—

130

C₄×C₁₃

—

131

C₄×C₁₃

#563

yes

—

132

C₂²×Q₈

—

133

C₂³×C₄

D₄×C₁₃

yes

characteristic

134

C₂³×C₄

D₄×C₁₃

yes

characteristic

135

C₂³×C₄

C₂³×C₁₃

yes

characteristic

136

C₂²×C₈

C₂³×C₁₃

yes

—

137

C₄⋊Q₈

—

138

C₂²⋊Q₈

—

139

C₂×C₄⋊C₄

—

140

C₂×C₄⋊C₄

—

141

C₂×C₄⋊C₄

—

142

C₂×C₄⋊C₄

—

143

C₂×C₄⋊C₄

C₂³×C₁₃

yes

—

144

C₂×C₄⋊C₄

C₂³×C₁₃

yes

—

145

C₂×C₂²⋊C₄

—

146

C₂×C₄²

—

147

C₂×C₄²

D₄×C₁₃

yes

—

148

C₂×C₄²

C₂³×C₁₃

yes

—

149

#107

—

150

C₂²⋊C₈

—

151

#95

—

152

#95

—

153

C₂×C₁₃

—

154

C₂×C₁₃

#2817

yes

characteristic

155

C₂×C₁₃

#3189

yes

characteristic

156

C₂×C₁₃

#3192

yes

characteristic

157

C₂×C₁₃

#3230

yes

—

158

C₂×C₁₃

#3235

yes

—

159

C₂⁴

C₂×D₄×C₁₃

yes

characteristic

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂²×C₄

—

164

C₂²×C₄

—

165

C₂²×C₄

—

166

C₂²×C₄

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

C₁₃×Q₁₆

yes

—

172

C₂²×C₄

C₂×D₄×C₁₃

yes

characteristic

173

C₂²×C₄

C₂×D₄×C₁₃

yes

—

174

C₂²×C₄

C₂×D₄×C₁₃

yes

—

175

C₂²×C₄

C₂⁴×C₁₃

yes

characteristic

176

C₂×C₈

—

177

C₂×C₈

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₂²⋊C₄

—

185

C₄²

—

186

C₄²

—

187

C₁₃

#32790

yes

characteristic, direct product factor, Sylow

188

C₂³

—

189

C₂³

—

190

C₂³

—

191

C₂³

—

192

C₂³

C₂×C₁₃×Q₁₆

yes

—

193

C₂³

C₂²×D₄×C₁₃

yes

characteristic

194

Q₈

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

C₂×C₁₃×Q₁₆

yes

—

211

C₂×C₄

C₁₃×AGL(1,ℤ/8)

yes

—

212

C₂×C₄

C₁₃×H(5,𝔽₂)

yes

—

213

C₂×C₄

C₁₃×2₋¹⁺⁴

yes

—

214

C₈

—

215

C₂²

—

216

C₂²

—

217

C₂²

—

218

C₂²

—

219

C₂²

—

220

C₂²

C₁₃×#534

yes

characteristic

221

C₂²

C₁₃×#536

yes

—

222

C₂²

C₂²×C₁₃×Q₁₆

yes

characteristic

223

C₂²

C₂×C₁₃×AGL(1,ℤ/8)

yes

—

224

C₂²

C₁₃×#575

yes

characteristic

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

C₁₃×#563

yes

—

231

C₂

—

232

C₂

C₁₃×#2817

yes

characteristic

233

C₂

C₁₃×#3189

yes

characteristic

234

C₂

C₁₃×#3192

yes

characteristic

235

C₂

C₁₃×#3230

yes

—

236

C₂

C₁₃×#3235

yes

—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

subgroup

G/H

center, socle

C₂³×C₁₃

C₂²×D₄

commutator, Frattini, cosocle

C₂²×C₄

C₂⁴×C₁₃

prime radical

C₂⁴×C₁₃

C₂×D₄

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

N	H ≅ G/N	type
2. C₁₃×#2100	C₂	semidirect
4. C₁₃×#2057	C₂	semidirect
41. #32790	C₁₃	direct (N × H)
71. #2100	C₂×C₁₃	semidirect
73. #2057	C₂×C₁₃	semidirect
187. C₁₃	#32790	direct (N × H)

H ≅ G/N

type

2. C₁₃×#2100

C₂

semidirect

4. C₁₃×#2057

C₂

semidirect

41. #32790

C₁₃

direct (N × H)

71. #2100

C₂×C₁₃

semidirect

73. #2057

C₂×C₁₃

semidirect

187. C₁₃

#32790

direct (N × H)

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

subgroup	index
C₁₃×#2857	2
C₁₃×#2100	2
C₁₃×#2076	2
C₁₃×#2057	2
C₁₃×#1817	2
#32790	13

subgroup

index

C₁₃×#2857

C₁₃×#2100

C₁₃×#2076

C₁₃×#2057

C₁₃×#1817

#32790

Subgroups — C₁₃×#32790 #15719129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#32790 #15719129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32790 #15719129