Group #15696776 — subgroups

Subgroups — C₁₃×#10437 #15696776

Order 3328.

478 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 146 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×#2582	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1844	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1803	C₂	1	2	yes	maximal
4	C₂×C₁₃×Q₈⋊C₈	C₂	1	2	yes	maximal
5	C₁₃×#1296	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
7	C₂×C₁₃×#106	—	2	2	no	—
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×#398	—	2	2	no	—
12	C₁₃×#391	—	2	2	no	—
13	C₁₃×#389	—	2	2	no	—
14	C₁₃×#384	C₂²	1	1	yes	characteristic
15	C₁₃×#384	C₂²	1	1	yes	characteristic
16	C₁₃×#340	—	2	2	no	—
17	C₁₃×Q₈⋊C₈	—	2	4	no	—
18	C₂²×Q₈×C₁₃	D₄	1	2	yes	—
19	C₂²×C₈×C₁₃	—	2	1	no	—
20	C₂²×C₈×C₁₃	—	2	2	no	—
21	C₄×Q₈×C₁₃	—	2	2	no	—
22	C₄×Q₈×C₁₃	—	2	2	no	—
23	C₄×Q₈×C₁₃	—	2	2	no	—
24	C₄×Q₈×C₁₃	—	2	2	no	—
25	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
26	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
27	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
28	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
29	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
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×#106	—	4	4	no	—
35	C₁₃×C₄⋊C₈	—	2	2	no	—
36	C₁₃×C₄⋊C₈	—	2	2	no	—
37	C₁₃×#103	—	4	4	no	—
38	C₄×C₈×C₁₃	—	2	1	no	—
39	C₄×C₈×C₁₃	D₄	1	2	yes	—
40	C₁₃×#95	—	2	4	no	—
41	C₁₃×#95	—	2	2	no	—
42	#10437	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂×Q₈×C₁₃	—	2	2	no	—
44	C₂×Q₈×C₁₃	—	2	2	no	—
45	C₂×Q₈×C₁₃	—	2	2	no	—
46	C₂×Q₈×C₁₃	—	2	2	no	—
47	C₂×Q₈×C₁₃	—	2	2	no	—
48	C₂×Q₈×C₁₃	SD₁₆	1	4	yes	—
49	C₂²×C₄×C₁₃	—	2	2	no	—
50	C₂²×C₄×C₁₃	—	2	2	no	—
51	C₂²×C₄×C₁₃	—	2	2	no	—
52	C₂²×C₄×C₁₃	—	4	1	no	—
53	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
55	C₂×C₈×C₁₃	—	2	2	no	—
56	C₂×C₈×C₁₃	—	2	2	no	—
57	C₂×C₈×C₁₃	—	2	2	no	—
58	C₂×C₈×C₁₃	—	4	2	no	—
59	C₂×C₈×C₁₃	—	4	2	no	—
60	C₂×C₈×C₁₃	—	4	2	no	—
61	C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₁₃×C₄⋊C₄	—	2	2	no	—
63	C₁₃×C₄⋊C₄	—	4	2	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	—	4	2	no	—
68	C₁₃×C₄⋊C₄	—	4	2	no	—
69	C₁₃×C₄⋊C₄	—	4	2	no	—
70	C₁₃×C₄⋊C₄	—	4	2	no	—
71	C₁₃×C₄⋊C₄	—	8	2	no	—
72	C₄²×C₁₃	—	4	2	no	—
73	C₄²×C₁₃	—	4	2	no	—
74	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₁₃	#41	1	1	yes	characteristic
76	C₄²×C₁₃	#41	1	2	yes	—
77	#2582	C₂×C₁₃	1	1	yes	characteristic
78	#1844	C₂×C₁₃	1	1	yes	characteristic
79	#1803	C₂×C₁₃	1	2	yes	—
80	C₂×Q₈⋊C₈	C₂×C₁₃	1	2	yes	—
81	#1296	C₂×C₁₃	1	1	yes	characteristic
82	C₂³×C₁₃	#120	1	1	yes	characteristic
83	Q₈×C₁₃	—	2	4	no	—
84	Q₈×C₁₃	—	2	4	no	—
85	Q₈×C₁₃	—	4	2	no	—
86	Q₈×C₁₃	—	4	2	no	—
87	C₂×C₄×C₁₃	—	2	1	no	—
88	C₂×C₄×C₁₃	—	2	1	no	—
89	C₂×C₄×C₁₃	—	2	4	no	—
90	C₂×C₄×C₁₃	—	4	2	no	—
91	C₂×C₄×C₁₃	—	4	2	no	—
92	C₂×C₄×C₁₃	—	4	2	no	—
93	C₂×C₄×C₁₃	—	4	4	no	—
94	C₂×C₄×C₁₃	—	4	2	no	—
95	C₂×C₄×C₁₃	—	4	2	no	—
96	C₂×C₄×C₁₃	—	4	2	no	—
97	C₂×C₄×C₁₃	—	8	2	no	—
98	C₂×C₄×C₁₃	—	8	1	no	—
99	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
100	C₂×C₄×C₁₃	#121	1	2	yes	—
101	C₂×C₄×C₁₃	#123	1	2	yes	—
102	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
103	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
104	C₂×C₄×C₁₃	#135	1	2	yes	—
105	C₂×C₄×C₁₃	#137	1	2	yes	—
106	C₂×C₄×C₁₃	#137	1	2	yes	—
107	C₈×C₁₃	—	2	4	no	—
108	C₈×C₁₃	—	8	2	no	—
109	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
110	C₂×#106	—	2	2	no	—
111	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
112	C₂×#103	—	2	2	no	—
113	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
114	#398	—	2	2	no	—
115	#391	—	2	2	no	—
116	#389	—	2	2	no	—
117	#384	C₂²×C₁₃	1	1	yes	characteristic
118	#384	C₂²×C₁₃	1	1	yes	characteristic
119	#340	—	2	2	no	—
120	Q₈⋊C₈	—	2	4	no	—
121	C₂²×C₁₃	#394	1	1	yes	characteristic
122	C₂²×C₁₃	#448	1	2	yes	—
123	C₂²×C₁₃	#452	1	2	yes	—
124	C₂²×C₁₃	#453	1	1	yes	characteristic
125	C₂²×C₁₃	#456	1	1	yes	characteristic
126	C₄×C₁₃	—	2	1	no	—
127	C₄×C₁₃	—	2	1	no	—
128	C₄×C₁₃	—	4	4	no	—
129	C₄×C₁₃	—	8	2	no	—
130	C₄×C₁₃	—	8	2	no	—
131	C₄×C₁₃	—	16	1	no	—
132	C₄×C₁₃	#465	1	2	yes	—
133	C₄×C₁₃	#470	1	2	yes	—
134	C₄×C₁₃	#483	1	2	yes	—
135	C₄×C₁₃	#485	1	2	yes	—
136	C₂²×Q₈	D₄×C₁₃	1	2	yes	—
137	C₂²×C₈	—	2	1	no	—
138	C₂²×C₈	—	2	2	no	—
139	C₄×Q₈	—	2	2	no	—
140	C₄×Q₈	—	2	2	no	—
141	C₄×Q₈	—	2	2	no	—
142	C₄×Q₈	—	2	2	no	—
143	C₂×C₄⋊C₄	—	2	2	no	—
144	C₂×C₄⋊C₄	—	2	2	no	—
145	C₂×C₄⋊C₄	—	2	2	no	—
146	C₂×C₄⋊C₄	—	2	1	no	—
147	C₂×C₄⋊C₄	—	2	2	no	—
148	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
149	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
150	C₂×C₄²	—	2	2	no	—
151	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
152	#106	—	4	4	no	—
153	C₄⋊C₈	—	2	2	no	—
154	C₄⋊C₈	—	2	2	no	—
155	#103	—	4	4	no	—
156	C₄×C₈	—	2	1	no	—
157	C₄×C₈	D₄×C₁₃	1	2	yes	—
158	#95	—	2	4	no	—
159	#95	—	2	2	no	—
160	C₂×C₁₃	#1623	1	1	yes	characteristic
161	C₂×C₁₃	#1630	1	1	yes	characteristic
162	C₂×C₁₃	#1653	1	2	yes	—
163	C₂×C₁₃	#2035	1	2	yes	—
164	C₂×C₁₃	#2039	1	1	yes	characteristic
165	C₂×Q₈	—	2	2	no	—
166	C₂×Q₈	—	2	2	no	—
167	C₂×Q₈	—	2	2	no	—
168	C₂×Q₈	—	2	2	no	—
169	C₂×Q₈	—	2	2	no	—
170	C₂×Q₈	C₁₃×SD₁₆	1	4	yes	—
171	C₂²×C₄	—	2	2	no	—
172	C₂²×C₄	—	2	2	no	—
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	—	4	1	no	—
175	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
176	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
177	C₂×C₈	—	2	2	no	—
178	C₂×C₈	—	2	2	no	—
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	4	2	no	—
181	C₂×C₈	—	4	2	no	—
182	C₂×C₈	—	4	2	no	—
183	C₄⋊C₄	—	2	2	no	—
184	C₄⋊C₄	—	2	2	no	—
185	C₄⋊C₄	—	4	2	no	—
186	C₄⋊C₄	—	4	2	no	—
187	C₄⋊C₄	—	4	2	no	—
188	C₄⋊C₄	—	4	2	no	—
189	C₄⋊C₄	—	4	2	no	—
190	C₄⋊C₄	—	4	2	no	—
191	C₄⋊C₄	—	4	2	no	—
192	C₄⋊C₄	—	4	2	no	—
193	C₄⋊C₄	—	8	2	no	—
194	C₄²	—	4	2	no	—
195	C₄²	—	4	2	no	—
196	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
197	C₄²	C₁₃×#41	1	1	yes	characteristic
198	C₄²	C₁₃×#41	1	2	yes	—
199	C₁₃	#10437	1	1	yes	characteristic, direct product factor, Sylow
200	C₂³	C₁₃×#120	1	1	yes	characteristic
201	Q₈	—	2	4	no	—
202	Q₈	—	2	4	no	—
203	Q₈	—	4	2	no	—
204	Q₈	—	4	2	no	—
205	C₂×C₄	—	2	1	no	—
206	C₂×C₄	—	2	1	no	—
207	C₂×C₄	—	2	4	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	2	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	—	4	4	no	—
212	C₂×C₄	—	4	2	no	—
213	C₂×C₄	—	4	2	no	—
214	C₂×C₄	—	4	2	no	—
215	C₂×C₄	—	8	2	no	—
216	C₂×C₄	—	8	1	no	—
217	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
218	C₂×C₄	C₁₃×#121	1	2	yes	—
219	C₂×C₄	C₁₃×#123	1	2	yes	—
220	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
221	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
222	C₂×C₄	C₁₃×#135	1	2	yes	—
223	C₂×C₄	C₁₃×#137	1	2	yes	—
224	C₂×C₄	C₁₃×#137	1	2	yes	—
225	C₈	—	2	4	no	—
226	C₈	—	8	2	no	—
227	C₂²	C₁₃×#394	1	1	yes	characteristic
228	C₂²	C₁₃×#448	1	2	yes	—
229	C₂²	C₁₃×#452	1	2	yes	—
230	C₂²	C₁₃×#453	1	1	yes	characteristic
231	C₂²	C₁₃×#456	1	1	yes	characteristic
232	C₄	—	2	1	no	—
233	C₄	—	2	1	no	—
234	C₄	—	4	4	no	—
235	C₄	—	8	2	no	—
236	C₄	—	8	2	no	—
237	C₄	—	16	1	no	—
238	C₄	C₁₃×#465	1	2	yes	—
239	C₄	C₁₃×#470	1	2	yes	—
240	C₄	C₁₃×#483	1	2	yes	—
241	C₄	C₁₃×#485	1	2	yes	—
242	C₂	C₁₃×#1623	1	1	yes	characteristic
243	C₂	C₁₃×#1630	1	1	yes	characteristic
244	C₂	C₁₃×#1653	1	2	yes	—
245	C₂	C₁₃×#2035	1	2	yes	—
246	C₂	C₁₃×#2039	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#2582

C₂

yes

maximal, characteristic

C₁₃×#1844

C₂

yes

maximal, characteristic

C₁₃×#1803

C₂

yes

maximal

C₂×C₁₃×Q₈⋊C₈

C₂

yes

maximal

C₁₃×#1296

C₂

yes

maximal, characteristic

C₂×C₄×Q₈×C₁₃

C₂²

yes

—

C₂×C₁₃×#106

—

C₂×C₁₃×C₄⋊C₈

C₂²

yes

—

C₂×C₁₃×#103

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₁₃×#398

—

C₁₃×#391

—

C₁₃×#389

—

C₁₃×#384

C₂²

yes

characteristic

C₁₃×#384

C₂²

yes

characteristic

C₁₃×#340

—

C₁₃×Q₈⋊C₈

—

C₂²×Q₈×C₁₃

D₄

yes

—

C₂²×C₈×C₁₃

—

C₂²×C₈×C₁₃

—

C₄×Q₈×C₁₃

—

C₄×Q₈×C₁₃

—

C₄×Q₈×C₁₃

—

C₄×Q₈×C₁₃

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

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×C₄²×C₁₃

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₁₃×#106

—

C₁₃×C₄⋊C₈

—

C₁₃×C₄⋊C₈

—

C₁₃×#103

—

C₄×C₈×C₁₃

—

C₄×C₈×C₁₃

D₄

yes

—

C₁₃×#95

—

C₁₃×#95

—

#10437

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

SD₁₆

yes

—

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

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

C₂×D₄

yes

C₄²×C₁₃

yes

C₄²×C₁₃

yes

—

#2582

C₂×C₁₃

yes

characteristic

#1844

C₂×C₁₃

yes

characteristic

#1803

C₂×C₁₃

yes

—

C₂×Q₈⋊C₈

C₂×C₁₃

yes

—

#1296

C₂×C₁₃

yes

characteristic

C₂³×C₁₃

#120

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

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#121

yes

characteristic

100

C₂×C₄×C₁₃

#121

yes

—

101

C₂×C₄×C₁₃

#123

yes

—

102

C₂×C₄×C₁₃

#124

yes

characteristic

103

C₂×C₄×C₁₃

C₂×SD₁₆

yes

—

104

C₂×C₄×C₁₃

#135

yes

—

105

C₂×C₄×C₁₃

#137

yes

—

106

C₂×C₄×C₁₃

#137

yes

—

107

C₈×C₁₃

—

108

C₈×C₁₃

—

109

C₂×C₄×Q₈

C₂²×C₁₃

yes

—

110

C₂×#106

—

111

C₂×C₄⋊C₈

C₂²×C₁₃

yes

—

112

C₂×#103

—

113

C₂×C₄×C₈

C₂²×C₁₃

yes

characteristic

114

#398

—

115

#391

—

116

#389

—

117

#384

C₂²×C₁₃

yes

characteristic

118

#384

C₂²×C₁₃

yes

characteristic

119

#340

—

120

Q₈⋊C₈

—

121

C₂²×C₁₃

#394

yes

characteristic

122

C₂²×C₁₃

#448

yes

—

123

C₂²×C₁₃

#452

yes

—

124

C₂²×C₁₃

#453

yes

characteristic

125

C₂²×C₁₃

#456

yes

characteristic

126

C₄×C₁₃

—

127

C₄×C₁₃

—

128

C₄×C₁₃

—

129

C₄×C₁₃

—

130

C₄×C₁₃

—

131

C₄×C₁₃

—

132

C₄×C₁₃

#465

yes

—

133

C₄×C₁₃

#470

yes

—

134

C₄×C₁₃

#483

yes

—

135

C₄×C₁₃

#485

yes

—

136

C₂²×Q₈

D₄×C₁₃

yes

—

137

C₂²×C₈

—

138

C₂²×C₈

—

139

C₄×Q₈

—

140

C₄×Q₈

—

141

C₄×Q₈

—

142

C₄×Q₈

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

—

145

C₂×C₄⋊C₄

—

146

C₂×C₄⋊C₄

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

D₄×C₁₃

yes

—

149

C₂×C₄⋊C₄

D₄×C₁₃

yes

—

150

C₂×C₄²

—

151

C₂×C₄²

C₂³×C₁₃

yes

characteristic

152

#106

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

#103

—

156

C₄×C₈

—

157

C₄×C₈

D₄×C₁₃

yes

—

158

#95

—

159

#95

—

160

C₂×C₁₃

#1623

yes

characteristic

161

C₂×C₁₃

#1630

yes

characteristic

162

C₂×C₁₃

#1653

yes

—

163

C₂×C₁₃

#2035

yes

—

164

C₂×C₁₃

#2039

yes

characteristic

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

C₁₃×SD₁₆

yes

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

C₂×D₄×C₁₃

yes

characteristic

176

C₂²×C₄

C₂×D₄×C₁₃

yes

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄²

—

195

C₄²

—

196

C₄²

C₂×D₄×C₁₃

yes

characteristic

197

C₄²

C₁₃×#41

yes

characteristic

198

C₄²

C₁₃×#41

yes

—

199

C₁₃

#10437

yes

characteristic, direct product factor, Sylow

200

C₂³

C₁₃×#120

yes

characteristic

201

Q₈

—

202

Q₈

—

203

Q₈

—

204

Q₈

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

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

C₁₃×#121

yes

characteristic

218

C₂×C₄

C₁₃×#121

yes

—

219

C₂×C₄

C₁₃×#123

yes

—

220

C₂×C₄

C₁₃×#124

yes

characteristic

221

C₂×C₄

C₂×C₁₃×SD₁₆

yes

—

222

C₂×C₄

C₁₃×#135

yes

—

223

C₂×C₄

C₁₃×#137

yes

—

224

C₂×C₄

C₁₃×#137

yes

—

225

C₈

—

226

C₈

—

227

C₂²

C₁₃×#394

yes

characteristic

228

C₂²

C₁₃×#448

yes

—

229

C₂²

C₁₃×#452

yes

—

230

C₂²

C₁₃×#453

yes

characteristic

231

C₂²

C₁₃×#456

yes

characteristic

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

237

C₄

—

238

C₄

C₁₃×#465

yes

—

239

C₄

C₁₃×#470

yes

—

240

C₄

C₁₃×#483

yes

—

241

C₄

C₁₃×#485

yes

—

242

C₂

C₁₃×#1623

yes

characteristic

243

C₂

C₁₃×#1630

yes

characteristic

244

C₂

C₁₃×#1653

yes

—

245

C₂

C₁₃×#2035

yes

—

246

C₂

C₁₃×#2039

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
42. #10437	C₁₃	direct (N × H)
199. C₁₃	#10437	direct (N × H)

H ≅ G/N

type

42. #10437

C₁₃

direct (N × H)

199. C₁₃

#10437

direct (N × H)

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

subgroup	index
C₁₃×#2582	2
C₁₃×#1844	2
C₁₃×#1803	2
C₂×C₁₃×Q₈⋊C₈	2
C₁₃×#1296	2
#10437	13

subgroup

index

C₁₃×#2582

C₁₃×#1844

C₁₃×#1803

C₂×C₁₃×Q₈⋊C₈

C₁₃×#1296

#10437

Subgroups — C₁₃×#10437 #15696776

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#10437 #15696776

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10437 #15696776