Group #15696688 — subgroups

Subgroups — C₁₃×#10349 #15696688

Order 3328.

504 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 154 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×#2551	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1987	C₂	1	2	yes	maximal
3	C₁₃×#1956	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1296	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1279	C₂	1	2	yes	maximal
6	C₂×C₁₃×C₄⋊Q₈	—	2	2	no	—
7	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
8	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
9	C₂×C₁₃×#103	—	2	2	no	—
10	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₁₃×#395	—	2	2	no	—
12	C₁₃×#389	—	2	2	no	—
13	C₁₃×#384	C₂²	1	1	yes	characteristic
14	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
15	C₁₃×#340	—	2	2	no	—
16	C₁₃×#340	—	2	2	no	—
17	C₂²×Q₈×C₁₃	—	2	2	no	—
18	C₂²×Q₈×C₁₃	—	2	1	no	—
19	C₂²×C₈×C₁₃	—	2	1	no	—
20	C₂²×C₈×C₁₃	—	2	2	no	—
21	C₁₃×C₄⋊Q₈	—	2	2	no	—
22	C₁₃×C₄⋊Q₈	—	2	1	no	—
23	C₁₃×C₄⋊Q₈	—	4	4	no	—
24	C₁₃×C₄⋊Q₈	—	4	4	no	—
25	C₁₃×C₄⋊Q₈	Q₈	1	2	yes	complemented
26	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
27	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
28	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
29	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
30	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
31	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
32	C₂×C₄²×C₁₃	—	2	2	no	—
33	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
34	C₁₃×C₄⋊C₈	—	2	2	no	—
35	C₁₃×C₄⋊C₈	—	2	2	no	—
36	C₁₃×#103	—	4	4	no	—
37	C₄×C₈×C₁₃	—	2	2	no	—
38	C₁₃×#95	—	2	2	no	—
39	C₁₃×#95	—	2	2	no	—
40	#10349	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂×Q₈×C₁₃	—	2	2	no	—
42	C₂×Q₈×C₁₃	—	4	8	no	—
43	C₂×Q₈×C₁₃	—	4	2	no	—
44	C₂×Q₈×C₁₃	—	4	2	no	—
45	C₂×Q₈×C₁₃	—	4	1	no	—
46	C₂×Q₈×C₁₃	—	8	2	no	—
47	C₂²×C₄×C₁₃	—	2	2	no	—
48	C₂²×C₄×C₁₃	—	2	2	no	—
49	C₂²×C₄×C₁₃	—	2	2	no	—
50	C₂²×C₄×C₁₃	—	4	1	no	—
51	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
53	C₂×C₈×C₁₃	—	2	2	no	—
54	C₂×C₈×C₁₃	—	4	1	no	—
55	C₂×C₈×C₁₃	—	4	1	no	—
56	C₂×C₈×C₁₃	—	4	2	no	—
57	C₂×C₈×C₁₃	—	4	2	no	—
58	C₂×C₈×C₁₃	—	4	2	no	—
59	C₁₃×C₄⋊C₄	—	2	2	no	—
60	C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₁₃×C₄⋊C₄	—	2	4	no	—
62	C₁₃×C₄⋊C₄	—	4	2	no	—
63	C₁₃×C₄⋊C₄	—	4	8	no	—
64	C₁₃×C₄⋊C₄	—	4	2	no	—
65	C₁₃×C₄⋊C₄	—	4	2	no	—
66	C₁₃×C₄⋊C₄	—	4	2	no	—
67	C₁₃×C₄⋊C₄	SD₁₆	1	4	yes	—
68	C₁₃×C₄⋊C₄	Q₁₆	1	4	yes	—
69	C₄²×C₁₃	—	4	2	no	—
70	C₄²×C₁₃	—	4	2	no	—
71	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
72	C₄²×C₁₃	#41	1	2	yes	—
73	C₄²×C₁₃	#41	1	1	yes	characteristic
74	#2551	C₂×C₁₃	1	1	yes	characteristic
75	#1987	C₂×C₁₃	1	2	yes	—
76	#1956	C₂×C₁₃	1	1	yes	characteristic
77	#1296	C₂×C₁₃	1	1	yes	characteristic
78	#1279	C₂×C₁₃	1	2	yes	—
79	C₂³×C₁₃	#120	1	1	yes	characteristic
80	Q₈×C₁₃	—	4	4	no	—
81	Q₈×C₁₃	—	8	2	no	—
82	Q₈×C₁₃	—	8	8	no	—
83	C₂×C₄×C₁₃	—	2	1	no	—
84	C₂×C₄×C₁₃	—	2	1	no	—
85	C₂×C₄×C₁₃	—	2	4	no	—
86	C₂×C₄×C₁₃	—	2	4	no	—
87	C₂×C₄×C₁₃	—	4	2	no	—
88	C₂×C₄×C₁₃	—	4	2	no	—
89	C₂×C₄×C₁₃	—	4	2	no	—
90	C₂×C₄×C₁₃	—	4	2	no	—
91	C₂×C₄×C₁₃	—	4	2	no	—
92	C₂×C₄×C₁₃	—	4	4	no	—
93	C₂×C₄×C₁₃	—	4	2	no	—
94	C₂×C₄×C₁₃	—	8	1	no	—
95	C₂×C₄×C₁₃	—	8	1	no	—
96	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
97	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
98	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
99	C₂×C₄×C₁₃	#124	1	2	yes	—
100	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
101	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
102	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
103	C₂×C₄×C₁₃	#137	1	2	yes	—
104	C₈×C₁₃	—	4	2	no	—
105	C₈×C₁₃	—	8	2	no	—
106	C₂×C₄⋊Q₈	—	2	2	no	—
107	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
108	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
109	C₂×#103	—	2	2	no	—
110	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
111	#395	—	2	2	no	—
112	#389	—	2	2	no	—
113	#384	C₂²×C₁₃	1	1	yes	characteristic
114	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
115	#340	—	2	2	no	—
116	#340	—	2	2	no	—
117	C₂²×C₁₃	#393	1	1	yes	characteristic
118	C₂²×C₁₃	#450	1	2	yes	—
119	C₂²×C₁₃	#451	1	2	yes	—
120	C₂²×C₁₃	#453	1	1	yes	characteristic
121	C₂²×C₁₃	#454	1	1	yes	characteristic
122	C₄×C₁₃	—	2	1	no	—
123	C₄×C₁₃	—	2	1	no	—
124	C₄×C₁₃	—	4	4	no	—
125	C₄×C₁₃	—	4	4	no	—
126	C₄×C₁₃	—	8	2	no	—
127	C₄×C₁₃	—	8	2	no	—
128	C₄×C₁₃	#475	1	2	yes	—
129	C₄×C₁₃	#477	1	2	yes	—
130	C₄×C₁₃	#487	1	2	yes	—
131	C₄×C₁₃	#489	1	2	yes	—
132	C₂²×Q₈	—	2	2	no	—
133	C₂²×Q₈	—	2	1	no	—
134	C₂²×C₈	—	2	1	no	—
135	C₂²×C₈	—	2	2	no	—
136	C₄⋊Q₈	—	2	2	no	—
137	C₄⋊Q₈	—	2	1	no	—
138	C₄⋊Q₈	—	4	4	no	—
139	C₄⋊Q₈	—	4	4	no	—
140	C₄⋊Q₈	Q₈×C₁₃	1	2	yes	complemented
141	C₂×C₄⋊C₄	—	2	2	no	—
142	C₂×C₄⋊C₄	—	2	4	no	—
143	C₂×C₄⋊C₄	—	2	2	no	—
144	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
145	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
146	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
147	C₂×C₄²	—	2	2	no	—
148	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
149	C₄⋊C₈	—	2	2	no	—
150	C₄⋊C₈	—	2	2	no	—
151	#103	—	4	4	no	—
152	C₄×C₈	—	2	2	no	—
153	#95	—	2	2	no	—
154	#95	—	2	2	no	—
155	C₂×C₁₃	#1629	1	1	yes	characteristic
156	C₂×C₁₃	#1633	1	1	yes	characteristic
157	C₂×C₁₃	#1637	1	2	yes	—
158	C₂×C₁₃	#2024	1	2	yes	—
159	C₂×C₁₃	#2027	1	1	yes	characteristic
160	C₂×Q₈	—	2	2	no	—
161	C₂×Q₈	—	4	8	no	—
162	C₂×Q₈	—	4	2	no	—
163	C₂×Q₈	—	4	2	no	—
164	C₂×Q₈	—	4	1	no	—
165	C₂×Q₈	—	8	2	no	—
166	C₂²×C₄	—	2	2	no	—
167	C₂²×C₄	—	2	2	no	—
168	C₂²×C₄	—	2	2	no	—
169	C₂²×C₄	—	4	1	no	—
170	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
171	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
172	C₂×C₈	—	2	2	no	—
173	C₂×C₈	—	4	1	no	—
174	C₂×C₈	—	4	1	no	—
175	C₂×C₈	—	4	2	no	—
176	C₂×C₈	—	4	2	no	—
177	C₂×C₈	—	4	2	no	—
178	C₄⋊C₄	—	2	2	no	—
179	C₄⋊C₄	—	2	2	no	—
180	C₄⋊C₄	—	2	4	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₄⋊C₄	—	4	8	no	—
183	C₄⋊C₄	—	4	2	no	—
184	C₄⋊C₄	—	4	2	no	—
185	C₄⋊C₄	—	4	2	no	—
186	C₄⋊C₄	C₁₃×SD₁₆	1	4	yes	—
187	C₄⋊C₄	C₁₃×Q₁₆	1	4	yes	—
188	C₄²	—	4	2	no	—
189	C₄²	—	4	2	no	—
190	C₄²	C₂×Q₈×C₁₃	1	1	yes	characteristic
191	C₄²	C₁₃×#41	1	2	yes	—
192	C₄²	C₁₃×#41	1	1	yes	characteristic
193	C₁₃	#10349	1	1	yes	characteristic, direct product factor, Sylow
194	C₂³	C₁₃×#120	1	1	yes	characteristic
195	Q₈	—	4	4	no	—
196	Q₈	—	8	2	no	—
197	Q₈	—	8	8	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	2	4	no	—
201	C₂×C₄	—	2	4	no	—
202	C₂×C₄	—	4	2	no	—
203	C₂×C₄	—	4	2	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	4	2	no	—
206	C₂×C₄	—	4	2	no	—
207	C₂×C₄	—	4	4	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	8	1	no	—
210	C₂×C₄	—	8	1	no	—
211	C₂×C₄	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
212	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
213	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
214	C₂×C₄	C₁₃×#124	1	2	yes	—
215	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
216	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
217	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
218	C₂×C₄	C₁₃×#137	1	2	yes	—
219	C₈	—	4	2	no	—
220	C₈	—	8	2	no	—
221	C₂²	C₁₃×#393	1	1	yes	characteristic
222	C₂²	C₁₃×#450	1	2	yes	—
223	C₂²	C₁₃×#451	1	2	yes	—
224	C₂²	C₁₃×#453	1	1	yes	characteristic
225	C₂²	C₁₃×#454	1	1	yes	characteristic
226	C₄	—	2	1	no	—
227	C₄	—	2	1	no	—
228	C₄	—	4	4	no	—
229	C₄	—	4	4	no	—
230	C₄	—	8	2	no	—
231	C₄	—	8	2	no	—
232	C₄	C₁₃×#475	1	2	yes	—
233	C₄	C₁₃×#477	1	2	yes	—
234	C₄	C₁₃×#487	1	2	yes	—
235	C₄	C₁₃×#489	1	2	yes	—
236	C₂	C₁₃×#1629	1	1	yes	characteristic
237	C₂	C₁₃×#1633	1	1	yes	characteristic
238	C₂	C₁₃×#1637	1	2	yes	—
239	C₂	C₁₃×#2024	1	2	yes	—
240	C₂	C₁₃×#2027	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#2551

C₂

yes

maximal, characteristic

C₁₃×#1987

C₂

yes

maximal

C₁₃×#1956

C₂

yes

maximal, characteristic

C₁₃×#1296

C₂

yes

maximal, characteristic

C₁₃×#1279

C₂

yes

maximal

C₂×C₁₃×C₄⋊Q₈

—

C₂×C₁₃×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₁₃×C₄⋊C₈

C₂²

yes

—

C₂×C₁₃×#103

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₁₃×#395

—

C₁₃×#389

—

C₁₃×#384

C₂²

yes

characteristic

C₄×C₁₃×C₄⋊C₄

C₂²

yes

—

C₁₃×#340

—

C₁₃×#340

—

C₂²×Q₈×C₁₃

—

C₂²×Q₈×C₁₃

—

C₂²×C₈×C₁₃

—

C₂²×C₈×C₁₃

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

Q₈

yes

complemented

C₂×C₁₃×C₄⋊C₄

—

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×#103

—

C₄×C₈×C₁₃

—

C₁₃×#95

—

C₁₃×#95

—

#10349

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

—

C₂²×C₄×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

—

C₁₃×C₄⋊C₄

SD₁₆

yes

—

C₁₃×C₄⋊C₄

Q₁₆

yes

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

C₂×Q₈

yes

characteristic

C₄²×C₁₃

#41

yes

—

C₄²×C₁₃

#41

yes

characteristic

#2551

C₂×C₁₃

yes

characteristic

#1987

C₂×C₁₃

yes

—

#1956

C₂×C₁₃

yes

characteristic

#1296

C₂×C₁₃

yes

characteristic

#1279

C₂×C₁₃

yes

—

C₂³×C₁₃

#120

yes

characteristic

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

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₃

#124

yes

characteristic

C₂×C₄×C₁₃

#124

yes

—

100

C₂×C₄×C₁₃

C₂×SD₁₆

yes

—

101

C₂×C₄×C₁₃

C₂×Q₁₆

yes

—

102

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

—

103

C₂×C₄×C₁₃

#137

yes

—

104

C₈×C₁₃

—

105

C₈×C₁₃

—

106

C₂×C₄⋊Q₈

—

107

C₂×C₄⋊Q₈

C₂²×C₁₃

yes

characteristic

108

C₂×C₄⋊C₈

C₂²×C₁₃

yes

—

109

C₂×#103

—

110

C₂×C₄×C₈

C₂²×C₁₃

yes

characteristic

111

#395

—

112

#389

—

113

#384

C₂²×C₁₃

yes

characteristic

114

C₄×C₄⋊C₄

C₂²×C₁₃

yes

—

115

#340

—

116

#340

—

117

C₂²×C₁₃

#393

yes

characteristic

118

C₂²×C₁₃

#450

yes

—

119

C₂²×C₁₃

#451

yes

—

120

C₂²×C₁₃

#453

yes

characteristic

121

C₂²×C₁₃

#454

yes

characteristic

122

C₄×C₁₃

—

123

C₄×C₁₃

—

124

C₄×C₁₃

—

125

C₄×C₁₃

—

126

C₄×C₁₃

—

127

C₄×C₁₃

—

128

C₄×C₁₃

#475

yes

—

129

C₄×C₁₃

#477

yes

—

130

C₄×C₁₃

#487

yes

—

131

C₄×C₁₃

#489

yes

—

132

C₂²×Q₈

—

133

C₂²×Q₈

—

134

C₂²×C₈

—

135

C₂²×C₈

—

136

C₄⋊Q₈

—

137

C₄⋊Q₈

—

138

C₄⋊Q₈

—

139

C₄⋊Q₈

—

140

C₄⋊Q₈

Q₈×C₁₃

yes

complemented

141

C₂×C₄⋊C₄

—

142

C₂×C₄⋊C₄

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

D₄×C₁₃

yes

—

145

C₂×C₄⋊C₄

D₄×C₁₃

yes

—

146

C₂×C₄⋊C₄

D₄×C₁₃

yes

—

147

C₂×C₄²

—

148

C₂×C₄²

C₂³×C₁₃

yes

characteristic

149

C₄⋊C₈

—

150

C₄⋊C₈

—

151

#103

—

152

C₄×C₈

—

153

#95

—

154

#95

—

155

C₂×C₁₃

#1629

yes

characteristic

156

C₂×C₁₃

#1633

yes

characteristic

157

C₂×C₁₃

#1637

yes

—

158

C₂×C₁₃

#2024

yes

—

159

C₂×C₁₃

#2027

yes

characteristic

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂²×C₄

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

C₂×D₄×C₁₃

yes

characteristic

171

C₂²×C₄

C₂×D₄×C₁₃

yes

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

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

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

C₁₃×SD₁₆

yes

—

187

C₄⋊C₄

C₁₃×Q₁₆

yes

—

188

C₄²

—

189

C₄²

—

190

C₄²

C₂×Q₈×C₁₃

yes

characteristic

191

C₄²

C₁₃×#41

yes

—

192

C₄²

C₁₃×#41

yes

characteristic

193

C₁₃

#10349

yes

characteristic, direct product factor, Sylow

194

C₂³

C₁₃×#120

yes

characteristic

195

Q₈

—

196

Q₈

—

197

Q₈

—

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

—

211

C₂×C₄

C₁₃×C₂²⋊Q₈

yes

characteristic

212

C₂×C₄

C₁₃×C₂²⋊Q₈

yes

—

213

C₂×C₄

C₁₃×#124

yes

characteristic

214

C₂×C₄

C₁₃×#124

yes

—

215

C₂×C₄

C₂×C₁₃×SD₁₆

yes

—

216

C₂×C₄

C₂×C₁₃×Q₁₆

yes

—

217

C₂×C₄

C₁₃×AGL(1,ℤ/8)

yes

—

218

C₂×C₄

C₁₃×#137

yes

—

219

C₈

—

220

C₈

—

221

C₂²

C₁₃×#393

yes

characteristic

222

C₂²

C₁₃×#450

yes

—

223

C₂²

C₁₃×#451

yes

—

224

C₂²

C₁₃×#453

yes

characteristic

225

C₂²

C₁₃×#454

yes

characteristic

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

C₁₃×#475

yes

—

233

C₄

C₁₃×#477

yes

—

234

C₄

C₁₃×#487

yes

—

235

C₄

C₁₃×#489

yes

—

236

C₂

C₁₃×#1629

yes

characteristic

237

C₂

C₁₃×#1633

yes

characteristic

238

C₂

C₁₃×#1637

yes

—

239

C₂

C₁₃×#2024

yes

—

240

C₂

C₁₃×#2027

yes

characteristic

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

subgroup

G/H

center, socle, prime radical

C₂³×C₁₃

#120

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₁₃

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

N	H ≅ G/N	type
25. C₁₃×C₄⋊Q₈	Q₈	semidirect
40. #10349	C₁₃	direct (N × H)
140. C₄⋊Q₈	Q₈×C₁₃	semidirect
193. C₁₃	#10349	direct (N × H)

H ≅ G/N

type

25. C₁₃×C₄⋊Q₈

Q₈

semidirect

40. #10349

C₁₃

direct (N × H)

140. C₄⋊Q₈

Q₈×C₁₃

semidirect

193. C₁₃

#10349

direct (N × H)

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

subgroup	index
C₁₃×#2551	2
C₁₃×#1987	2
C₁₃×#1956	2
C₁₃×#1296	2
C₁₃×#1279	2
#10349	13

subgroup

index

C₁₃×#2551

C₁₃×#1987

C₁₃×#1956

C₁₃×#1296

C₁₃×#1279

#10349

Subgroups — C₁₃×#10349 #15696688

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#10349 #15696688

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10349 #15696688