Group #16789970 — subgroups

Subgroups — #16789970

Order 3328.

538 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 136 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	C₂×#11718261	C₂	1	2	yes	maximal, complemented
2	#13131065	C₂	1	2	yes	maximal
3	#13129880	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₈×D₁₃	C₄	1	1	yes	characteristic
6	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₄²×D₁₃	C₄	1	1	yes	characteristic
8	C₂×#88106	C₂²	1	4	yes	—
9	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
10	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
11	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
13	C₄×C₈×D₁₃	—	2	4	no	—
14	#11718261	—	2	4	no	—
15	#11718259	—	2	4	no	—
16	C₂²×C₄×D₁₃	—	2	1	no	—
17	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×Dic₁₃	—	2	1	no	—
22	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
24	C₂²×#1055	C₂³	1	1	yes	characteristic
25	C₂×C₈×D₁₃	—	2	2	no	—
26	C₂×C₈×D₁₃	—	2	2	no	—
27	C₂×C₈×D₁₃	—	2	2	no	—
28	C₂×C₈×D₁₃	—	2	2	no	—
29	C₂×C₈×D₁₃	C₈	1	4	yes	—
30	C₂×C₈×D₁₃	D₄	1	2	yes	—
31	C₂×C₈×D₁₃	Q₈	1	2	yes	—
32	C₄²×D₁₃	—	2	2	no	—
33	C₄²×D₁₃	—	2	2	no	—
34	#88106	—	2	4	no	—
35	#88106	—	2	4	no	—
36	C₂×#6092	—	2	4	no	—
37	C₄×C₈×C₁₃	—	2	2	no	—
38	C₈×Dic₁₃	—	2	2	no	—
39	C₈×Dic₁₃	D₄	1	4	yes	—
40	C₄×#1055	—	2	2	no	—
41	#12788	—	13	1	no	maximal, Sylow
42	C₂³×D₁₃	M₁₆	1	1	yes	characteristic
43	C₂²×C₄×C₁₃	—	2	1	no	—
44	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
45	C₂²×Dic₁₃	—	2	1	no	—
46	C₂²×Dic₁₃	M₁₆	1	1	yes	characteristic
47	C₂×C₄×D₁₃	—	2	4	no	—
48	C₂×C₄×D₁₃	—	2	8	no	—
49	C₂×C₄×D₁₃	—	2	1	no	—
50	C₂×C₄×D₁₃	—	2	1	no	—
51	C₂×C₄×D₁₃	—	2	1	no	—
52	C₂×C₄×D₁₃	—	2	1	no	—
53	C₂×C₄×D₁₃	C₄⋊C₄	1	2	yes	—
54	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
55	C₂×C₈×C₁₃	—	2	1	no	—
56	C₂×C₈×C₁₃	—	2	1	no	—
57	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
58	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
59	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
60	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
61	C₄²×C₁₃	—	2	1	no	—
62	C₄²×C₁₃	M₁₆	1	2	yes	—
63	C₄×Dic₁₃	—	2	4	no	—
64	C₄×Dic₁₃	—	2	1	no	—
65	C₄×Dic₁₃	C₂²⋊C₄	1	2	yes	—
66	C₂×#1055	—	2	1	no	—
67	C₂×#1055	—	2	1	no	—
68	C₂×#1055	C₂×C₈	1	2	yes	—
69	C₂×#1055	C₂×D₄	1	1	yes	characteristic
70	C₂×#1055	C₂×D₄	1	2	yes	—
71	C₂×#1055	C₂×Q₈	1	1	yes	characteristic
72	C₂×#1055	#41	1	2	yes	—
73	C₈×D₁₃	—	2	8	no	—
74	C₈×D₁₃	—	2	4	no	—
75	C₈×D₁₃	—	2	4	no	—
76	#6092	—	4	4	no	—
77	C₂²×C₄×C₈	—	13	1	no	—
78	C₂×#364	—	13	2	no	—
79	#2112	—	13	2	no	—
80	#1376	—	13	2	no	—
81	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
82	C₂²×D₁₃	—	2	1	no	—
83	C₂²×D₁₃	—	2	1	no	—
84	C₂²×D₁₃	—	2	4	no	—
85	C₂²×D₁₃	C₄⋊C₈	1	2	yes	—
86	C₂×C₄×C₁₃	—	2	4	no	—
87	C₂×C₄×C₁₃	—	2	2	no	—
88	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
90	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
91	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
92	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
93	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
94	C₂×Dic₁₃	—	2	4	no	—
95	C₂×Dic₁₃	—	2	1	no	—
96	C₂×Dic₁₃	—	2	2	no	—
97	C₂×Dic₁₃	—	2	1	no	—
98	C₂×Dic₁₃	C₄⋊C₈	1	2	yes	—
99	C₄×D₁₃	—	2	16	no	—
100	C₄×D₁₃	—	2	2	no	—
101	C₄×D₁₃	—	2	2	no	—
102	C₄×D₁₃	—	2	2	no	—
103	C₄×D₁₃	—	2	2	no	—
104	C₈×C₁₃	—	2	2	no	—
105	C₈×C₁₃	C₂²⋊C₈	1	4	yes	—
106	#1055	—	2	2	no	—
107	#1055	#121	1	2	yes	—
108	#1055	C₂²⋊Q₈	1	2	yes	—
109	C₂³×C₈	—	13	1	no	—
110	C₂³×C₈	—	13	1	no	—
111	C₂²×C₄²	—	13	1	no	—
112	C₂×M₃₂	—	13	4	no	—
113	C₂×C₄×C₈	—	13	1	no	—
114	C₂×C₄×C₈	—	13	1	no	—
115	C₂×C₄×C₈	—	13	1	no	—
116	C₂×C₄×C₈	—	26	4	no	—
117	C₂×C₄×C₈	#261	1	1	yes	characteristic
118	#364	—	26	4	no	—
119	C₂²⋊C₁₆	—	26	4	no	—
120	C₂²×C₁₃	—	2	2	no	—
121	C₂²×C₁₃	#407	1	1	yes	characteristic
122	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
123	C₂²×C₁₃	#432	1	1	yes	characteristic
124	C₂×D₁₃	—	2	4	no	—
125	C₂×D₁₃	—	2	4	no	—
126	C₂×D₁₃	—	2	2	no	—
127	C₂×D₁₃	—	2	2	no	—
128	C₂×D₁₃	#364	1	4	yes	complemented
129	C₄×C₁₃	—	2	4	no	—
130	C₄×C₁₃	#380	1	1	yes	characteristic
131	C₄×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
132	C₄×C₁₃	#423	1	1	yes	characteristic
133	C₄×C₁₃	#431	1	1	yes	characteristic
134	Dic₁₃	—	2	4	no	—
135	Dic₁₃	—	2	2	no	—
136	C₂³×C₄	—	13	1	no	—
137	C₂³×C₄	—	26	1	no	—
138	C₂²×C₈	—	13	1	no	—
139	C₂²×C₈	—	13	1	no	—
140	C₂²×C₈	—	13	4	no	—
141	C₂²×C₈	—	13	2	no	—
142	C₂²×C₈	—	13	2	no	—
143	C₂²×C₈	—	26	2	no	—
144	C₂²×C₈	—	26	2	no	—
145	C₂²×C₈	—	26	2	no	—
146	C₂²×C₈	—	26	2	no	—
147	C₂²×C₈	C₂×#261	1	1	yes	characteristic
148	C₂²×C₈	C₂×#261	1	1	yes	characteristic
149	C₂×C₄²	—	13	1	no	—
150	C₂×C₄²	—	26	2	no	—
151	C₂×C₄²	—	26	1	no	—
152	C₂×C₄²	—	26	2	no	—
153	C₂×C₄²	C₂×#261	1	1	yes	characteristic
154	M₃₂	—	26	4	no	—
155	M₃₂	—	26	4	no	—
156	C₂×C₁₆	—	26	4	no	—
157	C₄×C₈	—	2	2	no	—
158	C₄×C₈	—	13	4	no	—
159	C₄×C₈	—	26	2	no	—
160	C₄×C₈	—	26	2	no	—
161	C₂×C₁₃	—	2	1	no	—
162	C₂×C₁₃	—	2	1	no	—
163	C₂×C₁₃	#1797	1	1	yes	characteristic
164	C₂×C₁₃	C₂×#364	1	2	yes	—
165	D₁₃	—	2	4	no	—
166	C₂⁴	—	13	1	no	—
167	C₂²×C₄	—	2	1	no	—
168	C₂²×C₄	—	13	1	no	—
169	C₂²×C₄	—	13	2	no	—
170	C₂²×C₄	—	13	2	no	—
171	C₂²×C₄	—	26	4	no	—
172	C₂²×C₄	—	26	8	no	—
173	C₂²×C₄	—	26	1	no	—
174	C₂²×C₄	—	26	1	no	—
175	C₂²×C₄	—	26	1	no	—
176	C₂²×C₄	—	26	1	no	—
177	C₂²×C₄	—	26	1	no	—
178	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
179	C₂×C₈	—	2	1	no	—
180	C₂×C₈	—	2	1	no	—
181	C₂×C₈	—	13	1	no	—
182	C₂×C₈	—	13	1	no	—
183	C₂×C₈	—	13	2	no	—
184	C₂×C₈	—	13	2	no	—
185	C₂×C₈	—	13	2	no	—
186	C₂×C₈	—	26	4	no	—
187	C₂×C₈	—	26	4	no	—
188	C₂×C₈	—	26	1	no	—
189	C₂×C₈	—	26	1	no	—
190	C₂×C₈	—	26	8	no	—
191	C₂×C₈	D₁₃⋊C₈	1	2	yes	—
192	C₂×C₈	#6118	1	2	yes	—
193	C₂×C₈	C₄⋊#261	1	2	yes	—
194	C₂×C₈	C₂²⋊#261	1	2	yes	—
195	C₄²	—	2	1	no	—
196	C₄²	—	13	2	no	—
197	C₄²	—	26	4	no	—
198	C₄²	—	26	1	no	—
199	C₄²	#6118	1	2	yes	—
200	C₁₆	—	52	4	no	—
201	C₁₃	#12788	1	1	yes	characteristic, complemented, Sylow
202	C₂³	—	13	2	no	—
203	C₂³	—	26	4	no	—
204	C₂³	—	26	1	no	—
205	C₂³	—	26	1	no	—
206	C₂³	D₁₃⋊M₁₆	1	1	yes	characteristic
207	C₂×C₄	—	2	4	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	13	2	no	—
210	C₂×C₄	—	26	16	no	—
211	C₂×C₄	—	26	4	no	—
212	C₂×C₄	—	26	1	no	—
213	C₂×C₄	—	26	2	no	—
214	C₂×C₄	—	26	1	no	—
215	C₂×C₄	—	26	2	no	—
216	C₂×C₄	—	26	2	no	—
217	C₂×C₄	—	26	2	no	—
218	C₂×C₄	—	26	2	no	—
219	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
220	C₂×C₄	C₂×#6118	1	1	yes	characteristic
221	C₂×C₄	C₂×#6118	1	1	yes	characteristic
222	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
223	C₂×C₄	#88237	1	1	yes	characteristic
224	C₂×C₄	C₂×C₂²⋊#261	1	1	yes	characteristic
225	C₈	—	2	2	no	—
226	C₈	—	13	2	no	—
227	C₈	—	13	2	no	—
228	C₈	—	26	2	no	—
229	C₈	#88111	1	4	yes	—
230	C₂²	—	2	2	no	—
231	C₂²	—	13	4	no	—
232	C₂²	—	26	4	no	—
233	C₂²	—	26	4	no	—
234	C₂²	—	26	2	no	—
235	C₂²	—	26	2	no	—
236	C₂²	D₁₃⋊(C₄⋊C₈)	1	1	yes	characteristic
237	C₂²	#11719054	1	1	yes	characteristic
238	C₂²	#11719127	1	1	yes	characteristic
239	C₄	—	2	4	no	—
240	C₄	—	26	4	no	—
241	C₄	—	26	2	no	—
242	C₄	#11719051	1	1	yes	characteristic
243	C₄	#11719052	1	1	yes	characteristic
244	C₄	C₂×#88111	1	1	yes	characteristic
245	C₄	#11719136	1	1	yes	characteristic
246	C₂	—	2	1	no	—
247	C₂	—	2	1	no	—
248	C₂	—	26	4	no	—
249	C₂	#13130691	1	1	yes	characteristic
250	C₂	D₁₃⋊#364	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11718261

C₂

yes

maximal, complemented

#13131065

C₂

yes

maximal

#13129880

C₂

yes

maximal, complemented

C₂×C₄×C₈×D₁₃

C₂

yes

maximal, characteristic

C₂²×C₈×D₁₃

C₄

yes

characteristic

C₂²×C₈×D₁₃

C₂²

yes

characteristic

C₂×C₄²×D₁₃

C₄

yes

characteristic

C₂×#88106

C₂²

yes

—

C₂×C₄×C₈×C₁₃

C₄

yes

characteristic

C₂×C₈×Dic₁₃

C₄

yes

characteristic

C₂×C₈×Dic₁₃

C₂²

yes

characteristic

C₂×C₄×#1055

C₂²

yes

characteristic

C₄×C₈×D₁₃

—

#11718261

—

#11718259

—

C₂²×C₄×D₁₃

—

C₂²×C₄×D₁₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₃

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₃

—

C₂×C₄×Dic₁₃

C₂×C₄

yes

characteristic

C₂²×#1055

C₂×C₄

yes

characteristic

C₂²×#1055

C₂³

yes

characteristic

C₂×C₈×D₁₃

—

C₂×C₈×D₁₃

—

C₂×C₈×D₁₃

—

C₂×C₈×D₁₃

—

C₂×C₈×D₁₃

C₈

yes

—

C₂×C₈×D₁₃

D₄

yes

—

C₂×C₈×D₁₃

Q₈

yes

—

C₄²×D₁₃

—

C₄²×D₁₃

—

#88106

—

#88106

—

C₂×#6092

—

C₄×C₈×C₁₃

—

C₈×Dic₁₃

—

C₈×Dic₁₃

D₄

yes

—

C₄×#1055

—

#12788

—

maximal, Sylow

C₂³×D₁₃

M₁₆

yes

characteristic

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂²×Dic₁₃

—

C₂²×Dic₁₃

M₁₆

yes

characteristic

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

C₄⋊C₄

yes

—

C₂×C₄×D₁₃

C₂×C₈

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂²⋊C₄

yes

—

C₂×C₈×C₁₃

C₄⋊C₄

yes

—

C₂×C₈×C₁₃

C₂×C₈

yes

—

C₂×C₈×C₁₃

M₁₆

yes

—

C₄²×C₁₃

—

C₄²×C₁₃

M₁₆

yes

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

C₄×Dic₁₃

C₂²⋊C₄

yes

—

C₂×#1055

—

C₂×#1055

—

C₂×#1055

C₂×C₈

yes

—

C₂×#1055

C₂×D₄

yes

characteristic

C₂×#1055

C₂×D₄

yes

—

C₂×#1055

C₂×Q₈

yes

characteristic

C₂×#1055

#41

yes

—

C₈×D₁₃

—

C₈×D₁₃

—

C₈×D₁₃

—

#6092

—

C₂²×C₄×C₈

—

C₂×#364

—

#2112

—

#1376

—

C₂³×C₁₃

C₂×M₁₆

yes

characteristic

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

C₄⋊C₈

yes

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₃

#117

yes

characteristic

C₂×C₄×C₁₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₃

C₂×M₁₆

yes

characteristic

C₂×C₄×C₁₃

C₂×M₁₆

yes

characteristic

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

C₄⋊C₈

yes

—

C₄×D₁₃

—

100

C₄×D₁₃

—

101

C₄×D₁₃

—

102

C₄×D₁₃

—

103

C₄×D₁₃

—

104

C₈×C₁₃

—

105

C₈×C₁₃

C₂²⋊C₈

yes

—

106

#1055

—

107

#1055

#121

yes

—

108

#1055

C₂²⋊Q₈

yes

—

109

C₂³×C₈

—

110

C₂³×C₈

—

111

C₂²×C₄²

—

112

C₂×M₃₂

—

113

C₂×C₄×C₈

—

114

C₂×C₄×C₈

—

115

C₂×C₄×C₈

—

116

C₂×C₄×C₈

—

117

C₂×C₄×C₈

#261

yes

characteristic

118

#364

—

119

C₂²⋊C₁₆

—

120

C₂²×C₁₃

—

121

C₂²×C₁₃

#407

yes

characteristic

122

C₂²×C₁₃

C₂×C₄⋊C₈

yes

characteristic

123

C₂²×C₁₃

#432

yes

characteristic

124

C₂×D₁₃

—

125

C₂×D₁₃

—

126

C₂×D₁₃

—

127

C₂×D₁₃

—

128

C₂×D₁₃

#364

yes

complemented

129

C₄×C₁₃

—

130

C₄×C₁₃

#380

yes

characteristic

131

C₄×C₁₃

C₂×C₂²⋊C₈

yes

characteristic

132

C₄×C₁₃

#423

yes

characteristic

133

C₄×C₁₃

#431

yes

characteristic

134

Dic₁₃

—

135

Dic₁₃

—

136

C₂³×C₄

—

137

C₂³×C₄

—

138

C₂²×C₈

—

139

C₂²×C₈

—

140

C₂²×C₈

—

141

C₂²×C₈

—

142

C₂²×C₈

—

143

C₂²×C₈

—

144

C₂²×C₈

—

145

C₂²×C₈

—

146

C₂²×C₈

—

147

C₂²×C₈

C₂×#261

yes

characteristic

148

C₂²×C₈

C₂×#261

yes

characteristic

149

C₂×C₄²

—

150

C₂×C₄²

—

151

C₂×C₄²

—

152

C₂×C₄²

—

153

C₂×C₄²

C₂×#261

yes

characteristic

154

M₃₂

—

155

M₃₂

—

156

C₂×C₁₆

—

157

C₄×C₈

—

158

C₄×C₈

—

159

C₄×C₈

—

160

C₄×C₈

—

161

C₂×C₁₃

—

162

C₂×C₁₃

—

163

C₂×C₁₃

#1797

yes

characteristic

164

C₂×C₁₃

C₂×#364

yes

—

165

D₁₃

—

166

C₂⁴

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

—

178

C₂²×C₄

C₂²×#261

yes

characteristic

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₂×C₈

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

D₁₃⋊C₈

yes

—

192

C₂×C₈

#6118

yes

—

193

C₂×C₈

C₄⋊#261

yes

—

194

C₂×C₈

C₂²⋊#261

yes

—

195

C₄²

—

196

C₄²

—

197

C₄²

—

198

C₄²

—

199

C₄²

#6118

yes

—

200

C₁₆

—

201

C₁₃

#12788

yes

characteristic, complemented, Sylow

202

C₂³

—

203

C₂³

—

204

C₂³

—

205

C₂³

—

206

C₂³

D₁₃⋊M₁₆

yes

characteristic

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

—

218

C₂×C₄

—

219

C₂×C₄

C₂×D₁₃⋊C₈

yes

characteristic

220

C₂×C₄

C₂×#6118

yes

characteristic

221

C₂×C₄

C₂×#6118

yes

characteristic

222

C₂×C₄

C₂×C₄⋊#261

yes

characteristic

223

C₂×C₄

#88237

yes

characteristic

224

C₂×C₄

C₂×C₂²⋊#261

yes

characteristic

225

C₈

—

226

C₈

—

227

C₈

—

228

C₈

—

229

C₈

#88111

yes

—

230

C₂²

—

231

C₂²

—

232

C₂²

—

233

C₂²

—

234

C₂²

—

235

C₂²

—

236

C₂²

D₁₃⋊(C₄⋊C₈)

yes

characteristic

237

C₂²

#11719054

yes

characteristic

238

C₂²

#11719127

yes

characteristic

239

C₄

—

240

C₄

—

241

C₄

—

242

C₄

#11719051

yes

characteristic

243

C₄

#11719052

yes

characteristic

244

C₄

C₂×#88111

yes

characteristic

245

C₄

#11719136

yes

characteristic

246

C₂

—

247

C₂

—

248

C₂

—

249

C₂

#13130691

yes

characteristic

250

C₂

D₁₃⋊#364

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₄⋊#261
commutator	C₂×C₄×C₁₃	C₂²×C₈
Frattini	C₂²×C₄	C₂²×#261
Fitting	C₂×C₄×C₈×C₁₃	C₄
socle	C₂²×C₁₃	C₂×C₄⋊C₈
prime radical	C₂³×D₁₃	M₁₆
cosocle	C₂²×#1055	C₂³
hypercenter	C₂×C₄×C₈	#261
hypocenter	C₁₃	#12788
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂×C₄

C₂×C₄⋊#261

commutator

C₂×C₄×C₁₃

C₂²×C₈

Frattini

C₂²×C₄

C₂²×#261

Fitting

C₂×C₄×C₈×C₁₃

C₄

socle

C₂²×C₁₃

C₂×C₄⋊C₈

prime radical

C₂³×D₁₃

M₁₆

cosocle

C₂²×#1055

C₂³

C₂×C₄×C₈

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

N	H ≅ G/N	type
1. C₂×#11718261	C₂	semidirect
3. #13129880	C₂	semidirect
128. C₂×D₁₃	#364	semidirect
201. C₁₃	#12788	semidirect

H ≅ G/N

type

1. C₂×#11718261

C₂

semidirect

3. #13129880

C₂

semidirect

128. C₂×D₁₃

#364

semidirect

201. C₁₃

#12788

semidirect

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

subgroup	index
C₂×#11718261	2
#13131065	2
#13129880	2
C₂×C₄×C₈×D₁₃	2
#12788	13

subgroup

index

C₂×C₄×C₈×D₁₃

Subgroups — #16789970

Conjugacy classes of subgroups

Complements

Maximal subgroups