Group #14285440 — subgroups

Subgroups — #14285440

Order 1920.

508 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 120 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	C₅×#5725	C₂	1	1	yes	maximal, characteristic
2	#11747011	C₂	1	2	yes	maximal, complemented
3	#11746367	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64766	C₂	1	1	yes	maximal, characteristic, complemented
5	#11745853	C₂	1	2	yes	maximal, complemented
6	#10602603	—	3	1	no	maximal, Hall
7	C₂×C₅×#239	C₄	1	2	yes	—
8	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₅×#947	C₄	1	2	yes	—
10	C₅×#895	—	2	2	no	—
11	C₅×#893	—	2	2	no	—
12	C₅×#874	C₂²	1	1	yes	characteristic
13	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
14	C₂×#6650	—	2	2	no	—
15	C₄⋊(C₃⋊#168)	C₂²	1	2	yes	—
16	C₃×C₄⋊#168	C₂²	1	2	yes	—
17	Dic₃⋊#168	—	2	2	no	—
18	#68489	—	5	1	no	maximal, Hall
19	C₅×#532	—	3	1	no	—
20	#65213	—	3	2	no	—
21	#64766	—	3	1	no	—
22	#64766	D₃	1	1	yes	characteristic, complemented
23	#64764	—	3	2	no	—
24	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	—
25	C₅×#239	—	4	4	no	—
26	C₂×C₅×D₁₂	—	2	2	no	—
27	C₂×C₅×D₁₂	—	2	2	no	—
28	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
29	C₂×C₄×C₅×D₃	—	2	2	no	—
30	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
32	C₃×C₅×C₄⋊C₄	—	2	2	no	—
33	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
34	C₂×C₃⋊#168	—	2	2	no	—
35	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
36	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
37	C₄×C₅×Dic₃	D₄	1	2	yes	—
38	C₂×C₃×#168	—	2	2	no	—
39	#6650	—	4	4	no	—
40	#5725	D₅	1	1	yes	characteristic
41	#4837	—	5	2	no	—
42	C₃×#333	—	5	1	no	—
43	#4546	—	5	1	no	—
44	#4485	—	5	2	no	—
45	C₂×C₅×#41	—	3	2	no	—
46	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
47	C₅×#127	—	3	1	no	—
48	C₅×#124	—	3	2	no	—
49	C₅×#121	—	6	2	no	—
50	C₄×C₅×D₄	—	6	2	no	—
51	C₂×C₄²×C₅	—	3	1	no	—
52	C₂×#681	—	6	2	no	—
53	C₄⋊#168	—	3	2	no	—
54	C₄⋊#168	—	6	2	no	—
55	C₄⋊#168	C₂×D₃	1	2	yes	—
56	#1560	—	15	1	no	Sylow
57	C₂²×C₅×D₃	—	2	2	no	—
58	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
59	C₃×C₅×Q₈	—	4	2	no	—
60	C₂×C₃×C₄×C₅	—	2	2	no	—
61	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
62	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
63	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
64	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
65	C₅×D₁₂	—	4	2	no	—
66	C₅×D₁₂	—	4	4	no	—
67	C₅×D₁₂	—	4	2	no	—
68	C₅×D₁₂	—	4	2	no	—
69	C₄×C₅×D₃	—	2	2	no	—
70	C₄×C₅×D₃	—	2	2	no	—
71	C₄×C₅×D₃	—	2	2	no	—
72	C₄×C₅×D₃	—	4	4	no	—
73	C₃⋊#168	—	4	2	no	—
74	C₃×#168	—	4	2	no	—
75	C₂×#239	Dic₅	1	2	yes	—
76	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
77	#947	Dic₅	1	2	yes	—
78	C₂×ΓL(1,𝔽₂₅)	—	10	2	no	—
79	#895	—	2	2	no	—
80	#893	—	2	2	no	—
81	#874	C₂×D₅	1	1	yes	characteristic
82	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
83	C₃×C₄⋊C₈	—	5	2	no	—
84	Dic₃⋊C₈	—	10	2	no	—
85	C₄⋊(C₃⋊C₈)	—	5	2	no	—
86	C₅×#41	—	12	4	no	—
87	C₂×C₅×Q₈	C₄×D₃	1	2	yes	—
88	C₂×C₅×D₄	—	3	2	no	—
89	C₂×C₅×D₄	—	6	2	no	—
90	C₂×C₅×D₄	—	6	2	no	—
91	C₂²×C₄×C₅	—	3	1	no	—
92	C₂²×C₄×C₅	—	3	2	no	—
93	C₂²×C₄×C₅	—	6	2	no	—
94	C₅×C₄⋊C₄	—	2	2	no	—
95	C₅×C₂²⋊C₄	—	6	4	no	—
96	C₄²×C₅	—	3	1	no	—
97	C₄²×C₅	—	3	2	no	—
98	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
99	#681	—	12	4	no	—
100	C₂×#168	—	2	2	no	—
101	C₂×#168	—	6	2	no	—
102	#532	—	3	1	no	—
103	#423	—	15	2	no	—
104	#333	—	5	1	no	—
105	#333	—	15	1	no	—
106	#331	—	15	2	no	—
107	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
108	C₂×C₅×D₃	—	2	1	no	—
109	C₂×C₅×D₃	—	2	2	no	—
110	C₂×C₅×D₃	—	4	2	no	—
111	C₂×C₅×D₃	—	4	4	no	—
112	C₃×C₄×C₅	—	2	1	no	—
113	C₃×C₄×C₅	—	4	2	no	—
114	C₃×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
115	C₃×C₄×C₅	#137	1	2	yes	—
116	C₅×Dic₃	—	2	2	no	—
117	C₅×Dic₃	#100	1	2	yes	—
118	C₂×C₃×Q₈	C₂×Dic₅	1	2	yes	—
119	#239	—	4	4	no	—
120	C₂×D₁₂	—	2	2	no	—
121	C₂×D₁₂	—	2	2	no	—
122	C₂×D₁₂	C₂×Dic₅	1	2	yes	—
123	C₂×C₄×D₃	—	2	2	no	—
124	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
125	C₂×C₄×D₃	C₂²⋊D₅	1	2	yes	—
126	C₂×C₃×C₈	—	10	2	no	—
127	C₃×C₄⋊C₄	—	2	2	no	—
128	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
129	(C₂×D₃)⋊C₄	—	2	4	no	—
130	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
131	C₄×Dic₃	C₂²⋊D₅	1	2	yes	—
132	C₂×C₃⋊C₈	—	10	2	no	—
133	ΓL(1,𝔽₂₅)	—	20	4	no	—
134	C₂³×C₅	—	3	1	no	—
135	C₂³×C₅	—	6	2	no	—
136	C₅×Q₈	—	4	2	no	—
137	C₅×D₄	—	12	2	no	—
138	C₅×D₄	—	12	4	no	—
139	C₅×D₄	—	12	2	no	—
140	C₅×D₄	—	12	2	no	—
141	C₂×C₄×C₅	—	2	2	no	—
142	C₂×C₄×C₅	—	3	1	no	—
143	C₂×C₄×C₅	—	3	2	no	—
144	C₂×C₄×C₅	—	6	2	no	—
145	C₂×C₄×C₅	—	6	2	no	—
146	C₂×C₄×C₅	—	6	2	no	—
147	C₂×C₄×C₅	—	12	4	no	—
148	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
149	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
150	#168	—	4	2	no	—
151	#168	—	12	2	no	—
152	C₂×#41	—	3	2	no	—
153	C₂×M₁₆	—	30	2	no	—
154	C₄⋊Q₈	D₃×D₅	1	1	yes	characteristic
155	#127	—	3	1	no	—
156	#124	—	3	2	no	—
157	#121	—	6	2	no	—
158	C₄×D₄	—	6	2	no	—
159	C₂×C₄²	—	3	1	no	—
160	C₄⋊C₈	—	5	2	no	—
161	C₄⋊C₈	—	15	2	no	—
162	C₄⋊C₈	—	30	2	no	—
163	C₂×C₃×C₅	C₂×#100	1	1	yes	characteristic
164	C₂×C₃×C₅	#417	1	2	yes	—
165	C₅×D₃	—	4	1	no	—
166	C₅×D₃	—	8	2	no	—
167	C₂²×D₃	—	2	2	no	—
168	C₂²×D₃	C₂²⋊Dic₅	1	1	yes	characteristic
169	C₃×Q₈	—	4	2	no	—
170	C₂×C₃×C₄	—	2	2	no	—
171	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
172	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
173	C₂×Dic₃	C₂²⋊Dic₅	1	2	yes	—
174	C₂×Dic₃	C₂²⋊Dic₅	1	1	yes	characteristic
175	D₁₂	—	4	2	no	—
176	D₁₂	—	4	4	no	—
177	D₁₂	—	4	2	no	—
178	D₁₂	—	4	2	no	—
179	C₄×D₃	—	2	2	no	—
180	C₄×D₃	—	2	2	no	—
181	C₄×D₃	—	2	2	no	—
182	C₄×D₃	—	4	4	no	—
183	C₃×C₈	—	20	2	no	—
184	C₃⋊C₈	—	20	2	no	—
185	C₂²×C₅	—	6	1	no	—
186	C₂²×C₅	—	6	2	no	—
187	C₂²×C₅	—	12	2	no	—
188	C₂²×C₅	—	12	4	no	—
189	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
190	C₄×C₅	—	2	1	no	—
191	C₄×C₅	—	3	2	no	—
192	C₄×C₅	—	4	2	no	—
193	C₄×C₅	—	6	2	no	—
194	C₄×C₅	#914	1	2	yes	—
195	C₄×C₅	#918	1	2	yes	—
196	#41	—	12	4	no	—
197	C₂×Q₈	D₃×Dic₅	1	2	yes	—
198	C₂×D₄	—	3	2	no	—
199	C₂×D₄	—	6	2	no	—
200	C₂×D₄	—	6	2	no	—
201	C₂²×C₄	—	3	1	no	—
202	C₂²×C₄	—	3	2	no	—
203	C₂²×C₄	—	6	2	no	—
204	M₁₆	—	60	4	no	—
205	C₂×C₈	—	10	2	no	—
206	C₂×C₈	—	30	2	no	—
207	C₄⋊C₄	—	2	2	no	—
208	C₂²⋊C₄	—	6	4	no	—
209	C₄²	—	3	1	no	—
210	C₄²	—	3	2	no	—
211	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
212	C₃×C₅	#1560	1	1	yes	characteristic, complemented, Hall
213	C₂²×C₃	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
214	C₂×D₃	—	2	1	no	—
215	C₂×D₃	—	2	2	no	—
216	C₂×D₃	—	4	2	no	—
217	C₂×D₃	—	4	4	no	—
218	C₃×C₄	—	2	1	no	—
219	C₃×C₄	—	4	2	no	—
220	C₃×C₄	#4095	1	2	yes	—
221	C₃×C₄	#4097	1	2	yes	—
222	Dic₃	—	2	2	no	—
223	Dic₃	#3965	1	2	yes	—
224	C₂×C₅	—	12	1	no	—
225	C₂×C₅	—	24	2	no	—
226	C₂×C₅	D₃×#100	1	1	yes	characteristic
227	C₂×C₅	#4803	1	2	yes	—
228	C₂³	—	3	1	no	—
229	C₂³	—	6	2	no	—
230	Q₈	—	4	2	no	—
231	D₄	—	12	2	no	—
232	D₄	—	12	4	no	—
233	D₄	—	12	2	no	—
234	D₄	—	12	2	no	—
235	C₂×C₄	—	2	2	no	—
236	C₂×C₄	—	3	1	no	—
237	C₂×C₄	—	3	2	no	—
238	C₂×C₄	—	6	2	no	—
239	C₂×C₄	—	6	2	no	—
240	C₂×C₄	—	6	2	no	—
241	C₂×C₄	—	12	4	no	—
242	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
243	C₂×C₄	D₃×C₂²⋊D₅	1	2	yes	—
244	C₈	—	20	2	no	—
245	C₈	—	60	2	no	—
246	C₂×C₃	C₂×#3965	1	1	yes	characteristic
247	C₂×C₃	#65521	1	2	yes	—
248	D₃	—	4	1	no	—
249	D₃	—	8	2	no	—
250	C₅	#68489	1	1	yes	characteristic, complemented, Sylow
251	C₂²	—	6	1	no	—
252	C₂²	—	6	2	no	—
253	C₂²	—	12	2	no	—
254	C₂²	—	12	4	no	—
255	C₂²	D₃×C₂²⋊Dic₅	1	1	yes	characteristic
256	C₄	—	2	1	no	—
257	C₄	—	3	2	no	—
258	C₄	—	4	2	no	—
259	C₄	—	6	2	no	—
260	C₄	#91504	1	2	yes	—
261	C₄	#91510	1	2	yes	—
262	C₃	#10602603	1	1	yes	characteristic, complemented, Sylow
263	C₂	—	12	1	no	—
264	C₂	—	24	2	no	—
265	C₂	D₃×#3965	1	1	yes	characteristic
266	C₂	#11749201	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#5725

C₂

yes

maximal, characteristic

#11747011

C₂

yes

maximal, complemented

#11746367

C₂

yes

maximal, characteristic, complemented

C₃×#64766

C₂

yes

maximal, characteristic, complemented

#11745853

C₂

yes

maximal, complemented

#10602603

—

maximal, Hall

C₂×C₅×#239

C₄

yes

—

C₃×C₅×C₄⋊Q₈

C₂²

yes

characteristic

C₅×#947

C₄

yes

—

C₅×#895

—

C₅×#893

—

C₅×#874

C₂²

yes

characteristic

C₄²×C₅×D₃

C₂²

yes

characteristic

C₂×#6650

—

C₄⋊(C₃⋊#168)

C₂²

yes

—

C₃×C₄⋊#168

C₂²

yes

—

—

—

—

—

—

D₃

yes

characteristic, complemented

#64764

—

C₂×C₃×C₅×Q₈

C₂×C₄

yes

—

C₅×#239

—

C₂×C₅×D₁₂

—

C₂×C₅×D₁₂

—

C₂×C₅×D₁₂

C₂×C₄

yes

—

C₂×C₄×C₅×D₃

—

C₂×C₄×C₅×D₃

C₂×C₄

yes

characteristic

C₂×C₄×C₅×D₃

D₄

yes

—

C₃×C₅×C₄⋊C₄

—

C₃×C₄²×C₅

C₂³

yes

characteristic

C₂×C₃⋊#168

—

C₅×(C₂×D₃)⋊C₄

—

C₄×C₅×Dic₃

C₂×C₄

yes

characteristic

C₄×C₅×Dic₃

D₄

yes

—

C₂×C₃×#168

—

#6650

—

#5725

D₅

yes

—

—

—

—

C₂×C₅×#41

—

C₅×C₄⋊Q₈

C₂×D₃

yes

—

—

—

C₄×C₅×D₄

—

C₂×C₄²×C₅

—

—

—

—

C₂×D₃

yes

—

#1560

—

Sylow

C₂²×C₅×D₃

—

C₂²×C₅×D₃

C₂²⋊C₄

yes

characteristic

C₃×C₅×Q₈

—

C₂×C₃×C₄×C₅

—

C₂×C₃×C₄×C₅

C₂²×C₄

yes

characteristic

C₂×C₃×C₄×C₅

C₂×D₄

yes

—

C₂×C₅×Dic₃

C₂²⋊C₄

yes

—

C₂×C₅×Dic₃

C₂²⋊C₄

yes

characteristic

C₅×D₁₂

—

C₅×D₁₂

—

C₅×D₁₂

—

C₅×D₁₂

—

C₄×C₅×D₃

—

C₄×C₅×D₃

—

C₄×C₅×D₃

—

C₄×C₅×D₃

—

C₃⋊#168

—

C₃×#168

—

C₂×#239

Dic₅

yes

—

C₃×C₄⋊Q₈

C₂×D₅

yes

characteristic

#947

Dic₅

yes

—

C₂×ΓL(1,𝔽₂₅)

—

#895

—

#893

—

#874

C₂×D₅

yes

characteristic

C₄²×D₃

C₂×D₅

yes

characteristic

C₃×C₄⋊C₈

—

Dic₃⋊C₈

—

C₄⋊(C₃⋊C₈)

—

C₅×#41

—

C₂×C₅×Q₈

C₄×D₃

yes

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₅×C₄⋊C₄

—

C₅×C₂²⋊C₄

—

C₄²×C₅

—

C₄²×C₅

—

C₄²×C₅

C₂²×D₃

yes

characteristic

#681

—

100

C₂×#168

—

101

C₂×#168

—

102

#532

—

103

#423

—

104

#333

—

105

#333

—

106

#331

—

107

C₂²×C₃×C₅

C₂×C₂²⋊C₄

yes

characteristic

108

C₂×C₅×D₃

—

109

C₂×C₅×D₃

—

110

C₂×C₅×D₃

—

111

C₂×C₅×D₃

—

112

C₃×C₄×C₅

—

113

C₃×C₄×C₅

—

114

C₃×C₄×C₅

AGL(1,ℤ/8)

yes

—

115

C₃×C₄×C₅

#137

yes

—

116

C₅×Dic₃

—

117

C₅×Dic₃

#100

yes

—

118

C₂×C₃×Q₈

C₂×Dic₅

yes

—

119

#239

—

120

C₂×D₁₂

—

121

C₂×D₁₂

—

122

C₂×D₁₂

C₂×Dic₅

yes

—

123

C₂×C₄×D₃

—

124

C₂×C₄×D₃

C₂×Dic₅

yes

characteristic

125

C₂×C₄×D₃

C₂²⋊D₅

yes

—

126

C₂×C₃×C₈

—

127

C₃×C₄⋊C₄

—

128

C₃×C₄²

C₂²×D₅

yes

characteristic

129

(C₂×D₃)⋊C₄

—

130

C₄×Dic₃

C₂×Dic₅

yes

characteristic

131

C₄×Dic₃

C₂²⋊D₅

yes

—

132

C₂×C₃⋊C₈

—

133

ΓL(1,𝔽₂₅)

—

134

C₂³×C₅

—

135

C₂³×C₅

—

136

C₅×Q₈

—

137

C₅×D₄

—

138

C₅×D₄

—

139

C₅×D₄

—

140

C₅×D₄

—

141

C₂×C₄×C₅

—

142

C₂×C₄×C₅

—

143

C₂×C₄×C₅

—

144

C₂×C₄×C₅

—

145

C₂×C₄×C₅

—

146

C₂×C₄×C₅

—

147

C₂×C₄×C₅

—

148

C₂×C₄×C₅

C₂×C₄×D₃

yes

characteristic

149

C₂×C₄×C₅

D₃×D₄

yes

—

150

#168

—

151

#168

—

152

C₂×#41

—

153

C₂×M₁₆

—

154

C₄⋊Q₈

D₃×D₅

yes

characteristic

155

#127

—

156

#124

—

157

#121

—

158

C₄×D₄

—

159

C₂×C₄²

—

160

C₄⋊C₈

—

161

C₄⋊C₈

—

162

C₄⋊C₈

—

163

C₂×C₃×C₅

C₂×#100

yes

characteristic

164

C₂×C₃×C₅

#417

yes

—

165

C₅×D₃

—

166

C₅×D₃

—

167

C₂²×D₃

—

168

C₂²×D₃

C₂²⋊Dic₅

yes

characteristic

169

C₃×Q₈

—

170

C₂×C₃×C₄

—

171

C₂×C₃×C₄

C₂²×Dic₅

yes

characteristic

172

C₂×C₃×C₄

C₂×C₂²⋊D₅

yes

—

173

C₂×Dic₃

C₂²⋊Dic₅

yes

—

174

C₂×Dic₃

C₂²⋊Dic₅

yes

characteristic

175

D₁₂

—

176

D₁₂

—

177

D₁₂

—

178

D₁₂

—

179

C₄×D₃

—

180

C₄×D₃

—

181

C₄×D₃

—

182

C₄×D₃

—

183

C₃×C₈

—

184

C₃⋊C₈

—

185

C₂²×C₅

—

186

C₂²×C₅

—

187

C₂²×C₅

—

188

C₂²×C₅

—

189

C₂²×C₅

D₃×C₂²⋊C₄

yes

characteristic

190

C₄×C₅

—

191

C₄×C₅

—

192

C₄×C₅

—

193

C₄×C₅

—

194

C₄×C₅

#914

yes

—

195

C₄×C₅

#918

yes

—

196

#41

—

197

C₂×Q₈

D₃×Dic₅

yes

—

198

C₂×D₄

—

199

C₂×D₄

—

200

C₂×D₄

—

201

C₂²×C₄

—

202

C₂²×C₄

—

203

C₂²×C₄

—

204

M₁₆

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₄⋊C₄

—

208

C₂²⋊C₄

—

209

C₄²

—

210

C₄²

—

211

C₄²

C₂×D₃×D₅

yes

characteristic

212

C₃×C₅

#1560

yes

characteristic, complemented, Hall

213

C₂²×C₃

C₂×C₂²⋊Dic₅

yes

characteristic

214

C₂×D₃

—

215

C₂×D₃

—

216

C₂×D₃

—

217

C₂×D₃

—

218

C₃×C₄

—

219

C₃×C₄

—

220

C₃×C₄

#4095

yes

—

221

C₃×C₄

#4097

yes

—

222

Dic₃

—

223

Dic₃

#3965

yes

—

224

C₂×C₅

—

225

C₂×C₅

—

226

C₂×C₅

D₃×#100

yes

characteristic

227

C₂×C₅

#4803

yes

—

228

C₂³

—

229

C₂³

—

230

Q₈

—

231

D₄

—

232

D₄

—

233

D₄

—

234

D₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

C₂×D₃×Dic₅

yes

characteristic

243

C₂×C₄

D₃×C₂²⋊D₅

yes

—

244

C₈

—

245

C₈

—

246

C₂×C₃

C₂×#3965

yes

characteristic

247

C₂×C₃

#65521

yes

—

248

D₃

—

249

D₃

—

250

C₅

#68489

yes

characteristic, complemented, Sylow

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

—

255

C₂²

D₃×C₂²⋊Dic₅

yes

characteristic

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

260

C₄

#91504

yes

—

261

C₄

#91510

yes

—

262

C₃

#10602603

yes

characteristic, complemented, Sylow

263

C₂

—

264

C₂

—

265

C₂

D₃×#3965

yes

characteristic

266

C₂

#11749201

yes

—

	subgroup	G/H
center	C₂²	D₃×C₂²⋊Dic₅
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₄²	C₂×D₃×D₅
Fitting	C₃×C₅×C₄⋊Q₈	C₂²
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₅×#5725	C₂
cosocle	C₃×C₄²×C₅	C₂³
hypercenter	C₄⋊Q₈	D₃×D₅
hypocenter	C₃×C₅	#1560
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

subgroup

G/H

center

C₂²

D₃×C₂²⋊Dic₅

commutator

C₂×C₃×C₄×C₅

C₂²×C₄

Frattini

C₄²

C₂×D₃×D₅

Fitting

C₃×C₅×C₄⋊Q₈

C₂²

socle

C₂²×C₃×C₅

C₂×C₂²⋊C₄

prime radical

C₅×#5725

C₂

cosocle

C₃×C₄²×C₅

C₂³

hypercenter

C₄⋊Q₈

D₃×D₅

hypocenter

C₃×C₅

#1560

LCS

G ▷ C₂×C₃×C₄×C₅ ▷ C₂²×C₃×C₅ ▷ C₃×C₅

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

N	H ≅ G/N	type
2. #11747011	C₂	semidirect
3. #11746367	C₂	semidirect
4. C₃×#64766	C₂	semidirect
5. #11745853	C₂	semidirect
22. #64766	D₃	semidirect
212. C₃×C₅	#1560	semidirect
250. C₅	#68489	semidirect
262. C₃	#10602603	semidirect

H ≅ G/N

type

2. #11747011

C₂

semidirect

3. #11746367

C₂

semidirect

4. C₃×#64766

C₂

semidirect

5. #11745853

C₂

semidirect

22. #64766

D₃

semidirect

212. C₃×C₅

#1560

semidirect

250. C₅

#68489

semidirect

262. C₃

#10602603

semidirect

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

subgroup	index
C₅×#5725	2
#11747011	2
#11746367	2
C₃×#64766	2
#11745853	2
#10602603	3
#68489	5

subgroup

index

Subgroups — #14285440

Conjugacy classes of subgroups

Complements

Maximal subgroups