Group #14298911 — subgroups

Subgroups — #14298911

Order 1920.

376 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 126 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	#11752340	C₂	1	1	yes	maximal, characteristic
2	C₃×#65681	C₂	1	1	yes	maximal, characteristic
3	C₄×D₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#11746532	C₂	1	4	yes	maximal
5	#10603856	—	3	1	no	maximal, Hall
6	C₂×#6758	C₂²	1	2	yes	—
7	C₂×C₃×#700	C₂²	1	2	yes	—
8	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
9	C₂×D₅×C₃⋊C₈	C₂²	1	2	yes	—
10	C₄⋊(C₃⋊#170)	—	2	1	no	—
11	C₄⋊(C₃⋊#170)	—	2	1	no	—
12	C₃×C₄⋊#170	—	2	1	no	—
13	C₃×C₄⋊#170	—	2	1	no	—
14	C₄×C₃⋊#168	C₄	1	1	yes	characteristic
15	C₄×C₅×C₃⋊C₈	C₄	1	1	yes	characteristic
16	Dic₅×C₃⋊C₈	C₄	1	2	yes	—
17	#70516	—	5	1	no	maximal, Hall
18	#65681	—	3	1	no	—
19	#65681	D₃	1	1	yes	characteristic
20	C₄×C₈×D₅	—	3	1	no	—
21	#64896	—	3	4	no	—
22	C₂×C₃×C₄×D₅	Q₈	1	1	yes	characteristic
23	C₂×C₃×C₄×D₅	Q₈	1	1	yes	characteristic
24	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
25	C₂×C₃⋊#170	—	2	2	no	—
26	#6758	—	2	4	no	—
27	C₂×C₃×#170	—	2	2	no	—
28	C₃×#700	—	2	4	no	—
29	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
30	C₂×C₃⋊#168	C₂×C₄	1	2	yes	—
31	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
32	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
33	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
34	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
35	D₅×C₃⋊C₈	—	2	2	no	—
36	D₅×C₃⋊C₈	—	2	2	no	—
37	C₃×#423	—	5	1	no	—
38	#4924	—	5	1	no	—
39	C₂×C₄×C₃⋊C₈	—	5	1	no	—
40	#4558	—	5	4	no	—
41	C₂×#700	—	3	2	no	—
42	C₂×#700	C₂×D₃	1	2	yes	—
43	C₂×C₈×D₅	—	3	2	no	—
44	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
45	C₄⋊#170	—	2	1	no	—
46	C₄⋊#170	—	2	1	no	—
47	C₄⋊#170	—	6	1	no	—
48	C₄⋊#170	—	6	1	no	—
49	C₄×C₅×C₈	—	3	1	no	—
50	C₈×Dic₅	—	3	2	no	—
51	C₄×#168	—	3	1	no	—
52	#1837	—	15	1	no	Sylow
53	C₂²×C₃×D₅	C₂×Q₈	1	1	yes	characteristic
54	C₂×C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
55	C₂×C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
56	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
57	C₂×C₃×Dic₅	C₄⋊C₄	1	1	yes	characteristic
58	C₂×C₃×Dic₅	C₄⋊C₄	1	1	yes	characteristic
59	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
60	C₃×C₄×D₅	—	2	2	no	—
61	C₃×C₄×D₅	—	2	2	no	—
62	C₃×C₄×D₅	#41	1	2	yes	—
63	C₃×C₄×D₅	#41	1	2	yes	—
64	C₃⋊#170	—	4	2	no	—
65	C₃×#170	—	4	2	no	—
66	C₃⋊#168	—	2	2	no	—
67	C₅×C₃⋊C₈	—	2	2	no	—
68	C₂×C₃×M₁₆	—	5	2	no	—
69	C₂×C₃×C₄²	—	5	1	no	—
70	C₂×#208	—	5	2	no	—
71	C₂²×C₃⋊C₈	—	5	2	no	—
72	C₃×C₄⋊C₈	—	10	1	no	—
73	C₃×C₄⋊C₈	—	10	1	no	—
74	C₄⋊(C₃⋊C₈)	—	10	1	no	—
75	C₄⋊(C₃⋊C₈)	—	10	1	no	—
76	C₄×C₃⋊C₈	—	5	1	no	—
77	C₄×C₃⋊C₈	—	5	2	no	—
78	C₄×C₃⋊C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
79	C₂×C₄×D₅	Dic₆	1	1	yes	characteristic
80	C₂×C₄×D₅	Dic₆	1	1	yes	characteristic
81	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
82	C₂×#170	—	2	2	no	—
83	C₂×#170	—	6	2	no	—
84	#700	—	2	4	no	—
85	#700	—	6	4	no	—
86	C₂×C₅×C₈	—	3	2	no	—
87	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
88	C₄×Dic₅	C₄×D₃	1	1	yes	characteristic
89	C₄×Dic₅	#67	1	1	yes	characteristic
90	C₄×Dic₅	#67	1	1	yes	characteristic
91	C₂×#168	—	3	2	no	—
92	C₈×D₅	—	6	2	no	—
93	C₈×D₅	—	6	2	no	—
94	#423	—	5	1	no	—
95	#423	—	15	1	no	—
96	C₂×C₄×C₈	—	15	1	no	—
97	#341	—	15	4	no	—
98	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₃×D₅	—	2	1	no	—
100	C₂×C₃×D₅	—	2	1	no	—
101	C₂×C₃×D₅	#125	1	2	yes	—
102	C₃×C₄×C₅	#108	1	2	yes	—
103	C₃×C₄×C₅	#108	1	2	yes	—
104	C₃×C₄×C₅	#117	1	2	yes	—
105	C₃×Dic₅	—	2	1	no	—
106	C₃×Dic₅	—	2	1	no	—
107	C₃×Dic₅	#124	1	1	yes	characteristic
108	C₃×Dic₅	#124	1	1	yes	characteristic
109	C₂²×C₃×C₄	—	5	1	no	—
110	C₂²×C₃×C₄	—	5	1	no	—
111	C₂²×C₃×C₄	—	5	1	no	—
112	C₃×M₁₆	—	10	4	no	—
113	C₂×C₃×C₈	—	10	2	no	—
114	C₃×C₄²	—	5	1	no	—
115	C₃×C₄²	—	5	1	no	—
116	C₃×C₄²	—	5	1	no	—
117	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
118	#208	—	10	4	no	—
119	C₂×C₃⋊C₈	—	5	2	no	—
120	C₂×C₃⋊C₈	—	10	2	no	—
121	C₂×C₃⋊C₈	—	10	2	no	—
122	C₂×C₃⋊C₈	—	10	2	no	—
123	C₂×C₃⋊C₈	C₂×AGL(1,𝔽₅)	1	2	yes	—
124	C₂²×D₅	C₂×Dic₆	1	1	yes	characteristic
125	C₂×C₄×C₅	Dic₃⋊C₄	1	1	yes	characteristic
126	C₂×C₄×C₅	Dic₃⋊C₄	1	1	yes	characteristic
127	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
128	C₂×Dic₅	Dic₃⋊C₄	1	1	yes	characteristic
129	C₂×Dic₅	Dic₃⋊C₄	1	1	yes	characteristic
130	C₂×Dic₅	C₂×#67	1	1	yes	characteristic
131	C₄×D₅	—	2	2	no	—
132	C₄×D₅	—	2	2	no	—
133	C₄×D₅	#237	1	2	yes	—
134	C₄×D₅	#239	1	2	yes	—
135	#170	—	4	2	no	—
136	#170	—	12	2	no	—
137	C₅×C₈	—	6	2	no	—
138	#168	—	6	2	no	—
139	C₂×M₁₆	—	5	2	no	—
140	C₂×M₁₆	—	15	2	no	—
141	C₂²×C₈	—	15	2	no	—
142	C₂×C₄²	—	5	1	no	—
143	C₄⋊C₈	—	10	1	no	—
144	C₄⋊C₈	—	10	1	no	—
145	C₄⋊C₈	—	30	1	no	—
146	C₄⋊C₈	—	30	1	no	—
147	C₄×C₈	—	3	1	no	—
148	C₄×C₈	—	15	2	no	—
149	C₄×C₈	—	15	1	no	—
150	C₂×C₃×C₅	#382	1	1	yes	characteristic
151	C₂×C₃×C₅	C₂×#108	1	1	yes	characteristic
152	C₂×C₃×C₅	C₂×#108	1	1	yes	characteristic
153	C₃×D₅	—	2	2	no	—
154	C₂³×C₃	—	5	1	no	—
155	C₂×C₃×C₄	—	5	1	no	—
156	C₂×C₃×C₄	—	5	2	no	—
157	C₂×C₃×C₄	—	5	2	no	—
158	C₂×C₃×C₄	—	5	1	no	—
159	C₂×C₃×C₄	—	5	1	no	—
160	C₂×C₃×C₄	—	10	2	no	—
161	C₂×C₃×C₄	—	10	2	no	—
162	C₂×C₃×C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
163	C₂×C₃×C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
164	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
165	C₃×C₈	—	20	2	no	—
166	C₃⋊C₈	—	2	2	no	—
167	C₃⋊C₈	—	10	2	no	—
168	C₃⋊C₈	—	20	2	no	—
169	C₂²×C₅	C₂×Dic₃⋊C₄	1	1	yes	characteristic
170	C₂×D₅	—	2	1	no	—
171	C₂×D₅	—	2	1	no	—
172	C₂×D₅	#890	1	2	yes	—
173	C₄×C₅	#822	1	2	yes	—
174	C₄×C₅	#822	1	2	yes	—
175	C₄×C₅	#892	1	2	yes	—
176	Dic₅	—	2	1	no	—
177	Dic₅	—	2	1	no	—
178	Dic₅	#936	1	1	yes	characteristic
179	Dic₅	#947	1	1	yes	characteristic
180	C₂²×C₄	—	5	1	no	—
181	C₂²×C₄	—	5	1	no	—
182	C₂²×C₄	—	5	1	no	—
183	M₁₆	—	10	4	no	—
184	M₁₆	—	30	4	no	—
185	C₂×C₈	—	3	2	no	—
186	C₂×C₈	—	10	2	no	—
187	C₂×C₈	—	15	2	no	—
188	C₂×C₈	—	30	2	no	—
189	C₂×C₈	—	30	2	no	—
190	C₂×C₈	—	30	2	no	—
191	C₄²	—	5	1	no	—
192	C₄²	—	5	1	no	—
193	C₄²	—	5	1	no	—
194	C₄²	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
195	C₃×C₅	#1837	1	1	yes	characteristic, complemented, Hall
196	C₂²×C₃	—	5	2	no	—
197	C₂²×C₃	—	10	1	no	—
198	C₂²×C₃	—	10	1	no	—
199	C₂²×C₃	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
200	C₃×C₄	—	5	1	no	—
201	C₃×C₄	—	5	1	no	—
202	C₃×C₄	—	10	1	no	—
203	C₃×C₄	—	10	1	no	—
204	C₃×C₄	#3995	1	2	yes	—
205	C₃×C₄	#3996	1	2	yes	—
206	C₃×C₄	#4130	1	2	yes	—
207	C₂×C₅	#4977	1	1	yes	characteristic
208	C₂×C₅	C₂×#822	1	1	yes	characteristic
209	C₂×C₅	C₂×#822	1	1	yes	characteristic
210	D₅	—	2	2	no	—
211	C₂³	—	5	1	no	—
212	C₂×C₄	—	5	1	no	—
213	C₂×C₄	—	5	2	no	—
214	C₂×C₄	—	5	2	no	—
215	C₂×C₄	—	5	1	no	—
216	C₂×C₄	—	5	1	no	—
217	C₂×C₄	—	10	2	no	—
218	C₂×C₄	—	10	2	no	—
219	C₂×C₄	Dic₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic
220	C₂×C₄	Dic₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic
221	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
222	C₈	—	6	2	no	—
223	C₈	—	20	2	no	—
224	C₈	—	30	2	no	—
225	C₈	—	60	2	no	—
226	C₂×C₃	—	10	2	no	—
227	C₂×C₃	#65689	1	1	yes	characteristic
228	C₂×C₃	C₂×#3995	1	1	yes	characteristic
229	C₂×C₃	C₂×#3996	1	1	yes	characteristic
230	C₅	#70516	1	1	yes	characteristic, complemented, Sylow
231	C₂²	—	5	2	no	—
232	C₂²	—	10	1	no	—
233	C₂²	—	10	1	no	—
234	C₂²	C₂×Dic₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic
235	C₄	—	5	1	no	—
236	C₄	—	5	1	no	—
237	C₄	—	10	1	no	—
238	C₄	—	10	1	no	—
239	C₄	#91161	1	2	yes	—
240	C₄	#91162	1	2	yes	—
241	C₄	#91907	1	2	yes	—
242	C₃	#10603856	1	1	yes	characteristic, complemented, Sylow
243	C₂	—	10	2	no	—
244	C₂	C₂×#91161	1	1	yes	characteristic
245	C₂	C₂×#91162	1	1	yes	characteristic
246	C₂	#11751751	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11752340

C₂

yes

maximal, characteristic

C₃×#65681

C₂

yes

maximal, characteristic

C₄×D₅×C₃⋊C₈

C₂

yes

maximal, characteristic

#11746532

C₂

yes

—

C₂²

yes

—

C₂×C₃×#700

C₂²

yes

—

C₃×C₄²×D₅

C₂²

yes

characteristic

C₂×D₅×C₃⋊C₈

C₂²

yes

—

C₄⋊(C₃⋊#170)

—

C₄⋊(C₃⋊#170)

—

C₃×C₄⋊#170

—

C₃×C₄⋊#170

—

C₄×C₃⋊#168

C₄

yes

characteristic

C₄×C₅×C₃⋊C₈

C₄

yes

characteristic

Dic₅×C₃⋊C₈

C₄

yes

—

—

—

D₃

yes

characteristic

C₄×C₈×D₅

—

#64896

—

C₂×C₃×C₄×D₅

Q₈

yes

characteristic

C₂×C₃×C₄×D₅

Q₈

yes

characteristic

C₂×C₃×C₄×D₅

C₂³

yes

characteristic

C₂×C₃⋊#170

—

#6758

—

C₂×C₃×#170

—

C₃×#700

—

C₃×C₄²×C₅

C₂×C₄

yes

characteristic

C₂×C₃⋊#168

C₂×C₄

yes

—

C₂×C₅×C₃⋊C₈

C₂×C₄

yes

—

C₃×C₄×Dic₅

C₂×C₄

yes

characteristic

C₃×C₄×Dic₅

D₄

yes

characteristic

C₃×C₄×Dic₅

D₄

yes

characteristic

D₅×C₃⋊C₈

—

D₅×C₃⋊C₈

—

C₃×#423

—

#4924

—

C₂×C₄×C₃⋊C₈

—

#4558

—

C₂×#700

—

C₂×#700

C₂×D₃

yes

—

C₂×C₈×D₅

—

C₄²×D₅

C₂×D₃

yes

—

—

—

—

C₄×C₅×C₈

—

C₈×Dic₅

—

C₄×#168

—

#1837

—

Sylow

C₂²×C₃×D₅

C₂×Q₈

yes

characteristic

C₂×C₃×C₄×C₅

C₄⋊C₄

yes

characteristic

C₂×C₃×C₄×C₅

C₄⋊C₄

yes

characteristic

C₂×C₃×C₄×C₅

C₂²×C₄

yes

characteristic

C₂×C₃×Dic₅

C₄⋊C₄

yes

characteristic

C₂×C₃×Dic₅

C₄⋊C₄

yes

characteristic

C₂×C₃×Dic₅

C₂×D₄

yes

characteristic

C₃×C₄×D₅

—

C₃×C₄×D₅

—

C₃×C₄×D₅

#41

yes

—

C₃×C₄×D₅

#41

yes

—

C₃⋊#170

—

C₃×#170

—

C₃⋊#168

—

C₅×C₃⋊C₈

—

C₂×C₃×M₁₆

—

C₂×C₃×C₄²

—

C₂×#208

—

C₂²×C₃⋊C₈

—

C₃×C₄⋊C₈

—

C₃×C₄⋊C₈

—

C₄⋊(C₃⋊C₈)

—

C₄⋊(C₃⋊C₈)

—

C₄×C₃⋊C₈

—

C₄×C₃⋊C₈

—

C₄×C₃⋊C₈

AGL(1,𝔽₅)

yes

characteristic

C₂×C₄×D₅

Dic₆

yes

characteristic

C₂×C₄×D₅

Dic₆

yes

characteristic

C₂×C₄×D₅

C₂²×D₃

yes

—

—

—

—

C₂×C₅×C₈

—

C₄²×C₅

C₄×D₃

yes

characteristic

C₄×Dic₅

C₄×D₃

yes

C₄×Dic₅

yes

C₄×Dic₅

yes

—

C₈×D₅

—

C₈×D₅

—

#423

—

#423

—

C₂×C₄×C₈

—

#341

—

C₂²×C₃×C₅

C₂×C₄⋊C₄

yes

characteristic

C₂×C₃×D₅

—

100

C₂×C₃×D₅

—

101

C₂×C₃×D₅

#125

yes

—

102

C₃×C₄×C₅

#108

yes

—

103

C₃×C₄×C₅

#108

yes

—

104

C₃×C₄×C₅

#117

yes

—

105

C₃×Dic₅

—

106

C₃×Dic₅

—

107

C₃×Dic₅

#124

yes

characteristic

108

C₃×Dic₅

#124

yes

characteristic

109

C₂²×C₃×C₄

—

110

C₂²×C₃×C₄

—

111

C₂²×C₃×C₄

—

112

C₃×M₁₆

—

113

C₂×C₃×C₈

—

114

C₃×C₄²

—

115

C₃×C₄²

—

116

C₃×C₄²

—

117

C₃×C₄²

C₂×AGL(1,𝔽₅)

yes

characteristic

118

#208

—

119

C₂×C₃⋊C₈

—

120

C₂×C₃⋊C₈

—

121

C₂×C₃⋊C₈

—

122

C₂×C₃⋊C₈

—

123

C₂×C₃⋊C₈

C₂×AGL(1,𝔽₅)

yes

—

124

C₂²×D₅

C₂×Dic₆

yes

characteristic

125

C₂×C₄×C₅

Dic₃⋊C₄

yes

characteristic

126

C₂×C₄×C₅

Dic₃⋊C₄

yes

characteristic

127

C₂×C₄×C₅

C₂×C₄×D₃

yes

characteristic

128

C₂×Dic₅

Dic₃⋊C₄

yes

characteristic

129

C₂×Dic₅

Dic₃⋊C₄

yes

characteristic

130

C₂×Dic₅

C₂×#67

yes

characteristic

131

C₄×D₅

—

132

C₄×D₅

—

133

C₄×D₅

#237

yes

—

134

C₄×D₅

#239

yes

—

135

#170

—

136

#170

—

137

C₅×C₈

—

138

#168

—

139

C₂×M₁₆

—

140

C₂×M₁₆

—

141

C₂²×C₈

—

142

C₂×C₄²

—

143

C₄⋊C₈

—

144

C₄⋊C₈

—

145

C₄⋊C₈

—

146

C₄⋊C₈

—

147

C₄×C₈

—

148

C₄×C₈

—

149

C₄×C₈

—

150

C₂×C₃×C₅

#382

yes

characteristic

151

C₂×C₃×C₅

C₂×#108

yes

characteristic

152

C₂×C₃×C₅

C₂×#108

yes

characteristic

153

C₃×D₅

—

154

C₂³×C₃

—

155

C₂×C₃×C₄

—

156

C₂×C₃×C₄

—

157

C₂×C₃×C₄

—

158

C₂×C₃×C₄

—

159

C₂×C₃×C₄

—

160

C₂×C₃×C₄

—

161

C₂×C₃×C₄

—

162

C₂×C₃×C₄

C₄⋊AGL(1,𝔽₅)

yes

characteristic

163

C₂×C₃×C₄

C₄⋊AGL(1,𝔽₅)

yes

characteristic

164

C₂×C₃×C₄

C₂²×AGL(1,𝔽₅)

yes

characteristic

165

C₃×C₈

—

166

C₃⋊C₈

—

167

C₃⋊C₈

—

168

C₃⋊C₈

—

169

C₂²×C₅

C₂×Dic₃⋊C₄

yes

characteristic

170

C₂×D₅

—

171

C₂×D₅

—

172

C₂×D₅

#890

yes

—

173

C₄×C₅

#822

yes

—

174

C₄×C₅

#822

yes

—

175

C₄×C₅

#892

yes

—

176

Dic₅

—

177

Dic₅

—

178

Dic₅

#936

yes

characteristic

179

Dic₅

#947

yes

characteristic

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

—

183

M₁₆

—

184

M₁₆

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₂×C₈

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₄²

—

192

C₄²

—

193

C₄²

—

194

C₄²

D₃×AGL(1,𝔽₅)

yes

characteristic

195

C₃×C₅

#1837

yes

characteristic, complemented, Hall

196

C₂²×C₃

—

197

C₂²×C₃

—

198

C₂²×C₃

—

199

C₂²×C₃

C₂×C₄⋊AGL(1,𝔽₅)

yes

characteristic

200

C₃×C₄

—

201

C₃×C₄

—

202

C₃×C₄

—

203

C₃×C₄

—

204

C₃×C₄

#3995

yes

—

205

C₃×C₄

#3996

yes

—

206

C₃×C₄

#4130

yes

—

207

C₂×C₅

#4977

yes

characteristic

208

C₂×C₅

C₂×#822

yes

characteristic

209

C₂×C₅

C₂×#822

yes

characteristic

210

D₅

—

211

C₂³

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

Dic₃⋊AGL(1,𝔽₅)

yes

characteristic

220

C₂×C₄

Dic₃⋊AGL(1,𝔽₅)

yes

characteristic

221

C₂×C₄

C₂×D₃×AGL(1,𝔽₅)

yes

characteristic

222

C₈

—

223

C₈

—

224

C₈

—

225

C₈

—

226

C₂×C₃

—

227

C₂×C₃

#65689

yes

characteristic

228

C₂×C₃

C₂×#3995

yes

characteristic

229

C₂×C₃

C₂×#3996

yes

characteristic

230

C₅

#70516

yes

characteristic, complemented, Sylow

231

C₂²

—

232

C₂²

—

233

C₂²

—

234

C₂²

C₂×Dic₃⋊AGL(1,𝔽₅)

yes

characteristic

235

C₄

—

236

C₄

—

237

C₄

—

238

C₄

—

239

C₄

#91161

yes

—

240

C₄

#91162

yes

—

241

C₄

#91907

yes

—

242

C₃

#10603856

yes

characteristic, complemented, Sylow

243

C₂

—

244

C₂

C₂×#91161

yes

characteristic

245

C₂

C₂×#91162

yes

characteristic

246

C₂

#11751751

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×Dic₃⋊AGL(1,𝔽₅)
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)
Fitting	C₃×C₄²×C₅	C₂×C₄
socle	C₂²×C₃×C₅	C₂×C₄⋊C₄
prime radical	C₂²×C₃×D₅	C₂×Q₈
cosocle	C₂×C₃×C₄×D₅	C₂³
hypercenter	C₄²	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	#1837
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₄²

subgroup

G/H

center

C₂²

C₂×Dic₃⋊AGL(1,𝔽₅)

commutator

C₂×C₃×C₄×C₅

C₂²×C₄

Frattini

C₂×C₄

C₂×D₃×AGL(1,𝔽₅)

Fitting

C₃×C₄²×C₅

C₂×C₄

socle

C₂²×C₃×C₅

C₂×C₄⋊C₄

prime radical

C₂²×C₃×D₅

C₂×Q₈

cosocle

C₂×C₃×C₄×D₅

C₂³

C₄²

C₃×C₅

G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅

UCS

C₁ ◁ C₂² ◁ C₄²

N	H ≅ G/N	type
195. C₃×C₅	#1837	semidirect
230. C₅	#70516	semidirect
242. C₃	#10603856	semidirect

H ≅ G/N

type

195. C₃×C₅

#1837

semidirect

230. C₅

#70516

semidirect

242. C₃

#10603856

semidirect

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

subgroup	index
#11752340	2
C₃×#65681	2
C₄×D₅×C₃⋊C₈	2
#11746532	2
#10603856	3
#70516	5

subgroup

index

C₄×D₅×C₃⋊C₈

Subgroups — #14298911

Conjugacy classes of subgroups

Complements

Maximal subgroups