Group #14285226 — subgroups

Subgroups — C₃×#10602553 #14285226

Order 1920.

664 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 664 conjugacy classes of subgroups — too many to draw. Only its 170 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×C₃×C₅×#127	C₂	1	1	yes	maximal, characteristic
2	C₃×#65215	C₂	1	2	yes	maximal, complemented
3	C₃×#64764	C₂	1	4	yes	maximal, complemented
4	#10602553	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₃×C₅×D₄	—	2	2	no	—
6	C₂²×C₃×C₅×D₄	C₄	1	2	yes	—
7	C₃×C₅×#127	—	2	2	no	—
8	C₃×C₅×#127	C₄	1	2	yes	—
9	C₃×C₅×#127	C₂²	1	2	yes	—
10	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
11	C₃×C₂²⋊#168	—	2	2	no	—
12	C₃×C₄⋊#168	C₂²	1	4	yes	complemented
13	C₃×#3935	—	2	2	no	—
14	C₃×#1555	—	5	1	no	maximal, Hall
15	C₂×C₅×#127	C₂×C₃	1	1	yes	characteristic
16	#65215	C₂×C₃	1	2	yes	complemented
17	#64764	C₂×C₃	1	4	yes	complemented
18	C₂⁴×C₃×C₅	—	2	2	no	—
19	C₂×C₃×C₅×D₄	—	2	4	no	—
20	C₂×C₃×C₅×D₄	—	2	2	no	—
21	C₂×C₃×C₅×D₄	—	2	4	no	—
22	C₂×C₃×C₅×D₄	—	4	8	no	—
23	C₂×C₃×C₅×D₄	—	4	4	no	—
24	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
25	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
27	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
28	C₃×C₄²×C₅	D₄	1	2	yes	—
29	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
30	C₂×C₃×#168	—	2	4	no	—
31	C₂×C₃×#127	D₅	1	1	yes	characteristic
32	C₃×#432	—	5	2	no	—
33	C₃×#331	—	5	4	no	—
34	C₂²×C₅×D₄	—	2	2	no	—
35	C₂²×C₅×D₄	C₃×C₄	1	2	yes	—
36	C₅×#127	—	2	2	no	—
37	C₅×#127	C₃×C₄	1	2	yes	—
38	C₅×#127	C₂²×C₃	1	2	yes	—
39	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
40	C₂²⋊#168	—	2	2	no	—
41	C₄⋊#168	C₂²×C₃	1	4	yes	complemented
42	#3935	—	2	2	no	—
43	#1555	—	5	1	no	Sylow
44	C₂³×C₃×C₅	—	2	4	no	—
45	C₂³×C₃×C₅	—	4	8	no	—
46	C₂³×C₃×C₅	—	4	4	no	—
47	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
48	C₃×C₅×D₄	—	4	4	no	—
49	C₃×C₅×D₄	—	4	8	no	—
50	C₃×C₅×D₄	—	4	4	no	—
51	C₃×C₅×D₄	—	4	8	no	—
52	C₂×C₃×C₄×C₅	—	2	2	no	—
53	C₂×C₃×C₄×C₅	—	2	4	no	—
54	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
55	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
56	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
57	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
58	C₃×#168	—	4	4	no	—
59	C₂²×C₃×D₄	—	2	2	no	—
60	C₂²×C₃×D₄	Dic₅	1	2	yes	—
61	C₃×#127	—	2	2	no	—
62	C₃×#127	Dic₅	1	2	yes	—
63	C₃×#127	C₂×D₅	1	2	yes	—
64	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
65	C₃×C₄⋊C₈	—	5	4	no	—
66	C₃×C₂²⋊C₈	—	10	2	no	—
67	C₃×#97	—	10	2	no	—
68	C₂⁴×C₅	—	2	2	no	—
69	C₂×C₅×D₄	—	2	2	no	—
70	C₂×C₅×D₄	—	2	4	no	—
71	C₂×C₅×D₄	—	2	4	no	—
72	C₂×C₅×D₄	—	4	4	no	—
73	C₂×C₅×D₄	—	4	8	no	—
74	C₂×C₅×D₄	C₂×C₃×C₄	1	4	yes	—
75	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
77	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
78	C₄²×C₅	C₃×D₄	1	2	yes	—
79	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
80	C₂×#168	—	2	4	no	—
81	C₂×#127	C₃×D₅	1	1	yes	characteristic
82	#432	—	5	2	no	—
83	#331	—	5	4	no	—
84	C₂²×C₃×C₅	—	2	2	no	—
85	C₂²×C₃×C₅	—	4	4	no	—
86	C₂²×C₃×C₅	—	4	8	no	—
87	C₂²×C₃×C₅	—	8	8	no	—
88	C₂²×C₃×C₅	#100	1	2	yes	—
89	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
90	C₃×C₄×C₅	—	2	1	no	—
91	C₃×C₄×C₅	—	2	1	no	—
92	C₃×C₄×C₅	—	2	2	no	—
93	C₃×C₄×C₅	AGL(1,ℤ/8)	1	4	yes	—
94	C₂⁴×C₃	—	2	2	no	—
95	C₂×C₃×D₄	—	2	2	no	—
96	C₂×C₃×D₄	—	2	4	no	—
97	C₂×C₃×D₄	—	2	4	no	—
98	C₂×C₃×D₄	—	4	4	no	—
99	C₂×C₃×D₄	—	4	8	no	—
100	C₂×C₃×D₄	C₂×Dic₅	1	4	yes	—
101	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
102	C₂²×C₃×C₄	C₂²⋊D₅	1	2	yes	—
103	C₂×C₃×C₈	—	10	4	no	—
104	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
105	C₃×C₄²	C₂²⋊D₅	1	2	yes	—
106	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
107	C₂³×C₅	—	2	4	no	—
108	C₂³×C₅	—	4	8	no	—
109	C₂³×C₅	—	4	4	no	—
110	C₂³×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
111	C₅×D₄	—	4	4	no	—
112	C₅×D₄	—	4	4	no	—
113	C₅×D₄	—	4	8	no	—
114	C₅×D₄	—	4	8	no	—
115	C₂×C₄×C₅	—	2	2	no	—
116	C₂×C₄×C₅	—	2	4	no	—
117	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
118	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
119	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
120	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
121	#168	—	4	4	no	—
122	C₂²×D₄	—	2	2	no	—
123	C₂²×D₄	C₃×Dic₅	1	2	yes	—
124	#127	—	2	2	no	—
125	#127	C₃×Dic₅	1	2	yes	—
126	#127	C₂×C₃×D₅	1	2	yes	—
127	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
128	C₄⋊C₈	—	5	4	no	—
129	C₂²⋊C₈	—	10	2	no	—
130	#97	—	10	2	no	—
131	C₂×C₃×C₅	—	2	2	no	—
132	C₂×C₃×C₅	—	8	4	no	—
133	C₂×C₃×C₅	C₂×#100	1	1	yes	characteristic
134	C₂×C₃×C₅	#418	1	2	yes	—
135	C₂³×C₃	—	2	4	no	—
136	C₂³×C₃	—	4	8	no	—
137	C₂³×C₃	—	4	4	no	—
138	C₂³×C₃	C₂²⋊Dic₅	1	1	yes	characteristic
139	C₃×D₄	—	4	4	no	—
140	C₃×D₄	—	4	8	no	—
141	C₃×D₄	—	4	4	no	—
142	C₃×D₄	—	4	8	no	—
143	C₂×C₃×C₄	—	2	2	no	—
144	C₂×C₃×C₄	—	2	4	no	—
145	C₂×C₃×C₄	C₂²⋊Dic₅	1	2	yes	—
146	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
147	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
148	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
149	C₃×C₈	—	20	4	no	—
150	C₂²×C₅	—	2	2	no	—
151	C₂²×C₅	—	4	4	no	—
152	C₂²×C₅	—	4	8	no	—
153	C₂²×C₅	—	8	8	no	—
154	C₂²×C₅	C₃×#100	1	2	yes	—
155	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
156	C₄×C₅	—	2	1	no	—
157	C₄×C₅	—	2	1	no	—
158	C₄×C₅	—	2	2	no	—
159	C₄×C₅	C₃×AGL(1,ℤ/8)	1	4	yes	—
160	C₂⁴	—	2	2	no	—
161	C₂×D₄	—	2	2	no	—
162	C₂×D₄	—	2	4	no	—
163	C₂×D₄	—	2	4	no	—
164	C₂×D₄	—	4	4	no	—
165	C₂×D₄	—	4	8	no	—
166	C₂×D₄	C₂×C₃×Dic₅	1	4	yes	—
167	C₂²×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
168	C₂²×C₄	C₃×C₂²⋊D₅	1	2	yes	—
169	C₂×C₈	—	10	4	no	—
170	C₄²	C₂×C₃×Dic₅	1	1	yes	characteristic
171	C₄²	C₃×C₂²⋊D₅	1	2	yes	—
172	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
173	C₃×C₅	#1555	1	1	yes	characteristic, complemented, Hall
174	C₂²×C₃	—	2	2	no	—
175	C₂²×C₃	—	4	8	no	—
176	C₂²×C₃	—	4	4	no	—
177	C₂²×C₃	—	8	8	no	—
178	C₂²×C₃	#3965	1	2	yes	—
179	C₂²×C₃	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
180	C₃×C₄	—	2	2	no	—
181	C₃×C₄	—	2	1	no	—
182	C₃×C₄	—	2	1	no	—
183	C₃×C₄	#4078	1	4	yes	—
184	C₂×C₅	—	2	2	no	—
185	C₂×C₅	—	8	4	no	—
186	C₂×C₅	C₂×C₃×#100	1	1	yes	characteristic
187	C₂×C₅	C₃×#418	1	2	yes	—
188	C₂³	—	2	4	no	—
189	C₂³	—	4	8	no	—
190	C₂³	—	4	4	no	—
191	C₂³	C₃×C₂²⋊Dic₅	1	1	yes	characteristic
192	D₄	—	4	4	no	—
193	D₄	—	4	8	no	—
194	D₄	—	4	4	no	—
195	D₄	—	4	8	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	4	no	—
198	C₂×C₄	C₃×C₂²⋊Dic₅	1	2	yes	—
199	C₂×C₄	C₃×C₂²⋊Dic₅	1	1	yes	characteristic
200	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
201	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
202	C₈	—	20	4	no	—
203	C₂×C₃	—	2	2	no	—
204	C₂×C₃	—	8	4	no	—
205	C₂×C₃	#65504	1	2	yes	—
206	C₂×C₃	C₂×#3965	1	1	yes	characteristic
207	C₅	C₃×#1555	1	1	yes	characteristic, complemented, Sylow
208	C₂²	—	2	2	no	—
209	C₂²	—	4	8	no	—
210	C₂²	—	4	4	no	—
211	C₂²	—	8	8	no	—
212	C₂²	C₃×#3965	1	2	yes	—
213	C₂²	C₂×C₃×C₂²⋊Dic₅	1	1	yes	characteristic
214	C₄	—	2	2	no	—
215	C₄	—	2	1	no	—
216	C₄	—	2	1	no	—
217	C₄	C₃×#4078	1	4	yes	—
218	C₃	#10602553	1	1	yes	characteristic, direct product factor, Sylow
219	C₂	—	2	2	no	—
220	C₂	—	8	4	no	—
221	C₂	C₃×#65504	1	2	yes	—
222	C₂	C₂×C₃×#3965	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₃×C₅×#127

C₂

yes

maximal, characteristic

C₃×#65215

C₂

yes

maximal, complemented

C₃×#64764

C₂

yes

maximal, complemented

#10602553

C₃

yes

maximal, characteristic, direct product factor, Hall

C₂²×C₃×C₅×D₄

—

C₂²×C₃×C₅×D₄

C₄

yes

—

C₃×C₅×#127

—

C₃×C₅×#127

C₄

yes

—

C₃×C₅×#127

C₂²

yes

—

C₂×C₃×C₄²×C₅

C₂²

yes

characteristic

C₃×C₂²⋊#168

—

C₃×C₄⋊#168

C₂²

yes

—

—

C₂×C₅×#127

C₂×C₃

yes

characteristic

#65215

C₂×C₃

yes

complemented

#64764

C₂×C₃

yes

complemented

C₂⁴×C₃×C₅

—

C₂×C₃×C₅×D₄

—

C₂×C₃×C₅×D₄

—

C₂×C₃×C₅×D₄

—

C₂×C₃×C₅×D₄

—

C₂×C₃×C₅×D₄

—

C₂×C₃×C₅×D₄

C₂×C₄

yes

—

C₂²×C₃×C₄×C₅

C₂×C₄

yes

characteristic

C₂²×C₃×C₄×C₅

D₄

yes

—

C₃×C₄²×C₅

C₂×C₄

yes

characteristic

C₃×C₄²×C₅

D₄

yes

—

C₃×C₄²×C₅

C₂³

yes

characteristic

C₂×C₃×#168

—

C₂×C₃×#127

D₅

yes

characteristic

C₃×#432

—

C₃×#331

—

C₂²×C₅×D₄

—

C₂²×C₅×D₄

C₃×C₄

yes

—

C₅×#127

—

C₅×#127

C₃×C₄

yes

—

C₅×#127

C₂²×C₃

yes

—

C₂×C₄²×C₅

C₂²×C₃

yes

characteristic

C₂²⋊#168

—

C₄⋊#168

C₂²×C₃

yes

—

—

C₂³×C₃×C₅

—

C₂³×C₃×C₅

—

C₂³×C₃×C₅

—

C₂³×C₃×C₅

C₂²⋊C₄

yes

characteristic

C₃×C₅×D₄

—

C₃×C₅×D₄

—

C₃×C₅×D₄

—

C₃×C₅×D₄

—

C₂×C₃×C₄×C₅

—

C₂×C₃×C₄×C₅

—

C₂×C₃×C₄×C₅

C₂²⋊C₄

yes

—

C₂×C₃×C₄×C₅

C₂²⋊C₄

yes

characteristic

C₂×C₃×C₄×C₅

C₂²×C₄

yes

characteristic

C₂×C₃×C₄×C₅

C₂×D₄

yes

—

C₃×#168

—

C₂²×C₃×D₄

—

C₂²×C₃×D₄

Dic₅

yes

—

C₃×#127

—

C₃×#127

Dic₅

yes

—

C₃×#127

C₂×D₅

yes

—

C₂×C₃×C₄²

C₂×D₅

yes

characteristic

C₃×C₄⋊C₈

—

C₃×C₂²⋊C₈

—

C₃×#97

—

C₂⁴×C₅

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂×C₅×D₄

C₂×C₃×C₄

yes

—

C₂²×C₄×C₅

C₂×C₃×C₄

yes

characteristic

C₂²×C₄×C₅

C₃×D₄

yes

—

C₄²×C₅

C₂×C₃×C₄

yes

characteristic

C₄²×C₅

C₃×D₄

yes

—

C₄²×C₅

C₂³×C₃

yes

characteristic

C₂×#168

—

C₂×#127

C₃×D₅

yes

characteristic

#432

—

#331

—

C₂²×C₃×C₅

—

C₂²×C₃×C₅

—

C₂²×C₃×C₅

—

C₂²×C₃×C₅

—

C₂²×C₃×C₅

#100

yes

—

C₂²×C₃×C₅

C₂×C₂²⋊C₄

yes

characteristic

C₃×C₄×C₅

—

C₃×C₄×C₅

—

C₃×C₄×C₅

—

C₃×C₄×C₅

AGL(1,ℤ/8)

yes

—

C₂⁴×C₃

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

100

C₂×C₃×D₄

C₂×Dic₅

yes

—

101

C₂²×C₃×C₄

C₂×Dic₅

yes

characteristic

102

C₂²×C₃×C₄

C₂²⋊D₅

yes

—

103

C₂×C₃×C₈

—

104

C₃×C₄²

C₂×Dic₅

yes

characteristic

105

C₃×C₄²

C₂²⋊D₅

yes

—

106

C₃×C₄²

C₂²×D₅

yes

characteristic

107

C₂³×C₅

—

108

C₂³×C₅

—

109

C₂³×C₅

—

110

C₂³×C₅

C₃×C₂²⋊C₄

yes

characteristic

111

C₅×D₄

—

112

C₅×D₄

—

113

C₅×D₄

—

114

C₅×D₄

—

115

C₂×C₄×C₅

—

116

C₂×C₄×C₅

—

117

C₂×C₄×C₅

C₃×C₂²⋊C₄

yes

—

118

C₂×C₄×C₅

C₃×C₂²⋊C₄

yes

characteristic

119

C₂×C₄×C₅

C₂²×C₃×C₄

yes

characteristic

120

C₂×C₄×C₅

C₂×C₃×D₄

yes

—

121

#168

—

122

C₂²×D₄

—

123

C₂²×D₄

C₃×Dic₅

yes

—

124

#127

—

125

#127

C₃×Dic₅

yes

—

126

#127

C₂×C₃×D₅

yes

—

127

C₂×C₄²

C₂×C₃×D₅

yes

characteristic

128

C₄⋊C₈

—

129

C₂²⋊C₈

—

130

#97

—

131

C₂×C₃×C₅

—

132

C₂×C₃×C₅

—

133

C₂×C₃×C₅

C₂×#100

yes

characteristic

134

C₂×C₃×C₅

#418

yes

—

135

C₂³×C₃

—

136

C₂³×C₃

—

137

C₂³×C₃

—

138

C₂³×C₃

C₂²⋊Dic₅

yes

characteristic

139

C₃×D₄

—

140

C₃×D₄

—

141

C₃×D₄

—

142

C₃×D₄

—

143

C₂×C₃×C₄

—

144

C₂×C₃×C₄

—

145

C₂×C₃×C₄

C₂²⋊Dic₅

yes

—

146

C₂×C₃×C₄

C₂²⋊Dic₅

yes

characteristic

147

C₂×C₃×C₄

C₂²×Dic₅

yes

characteristic

148

C₂×C₃×C₄

C₂×C₂²⋊D₅

yes

—

149

C₃×C₈

—

150

C₂²×C₅

—

151

C₂²×C₅

—

152

C₂²×C₅

—

153

C₂²×C₅

—

154

C₂²×C₅

C₃×#100

yes

—

155

C₂²×C₅

C₂×C₃×C₂²⋊C₄

yes

characteristic

156

C₄×C₅

—

157

C₄×C₅

—

158

C₄×C₅

—

159

C₄×C₅

C₃×AGL(1,ℤ/8)

yes

—

160

C₂⁴

—

161

C₂×D₄

—

162

C₂×D₄

—

163

C₂×D₄

—

164

C₂×D₄

—

165

C₂×D₄

—

166

C₂×D₄

C₂×C₃×Dic₅

yes

—

167

C₂²×C₄

C₂×C₃×Dic₅

yes

characteristic

168

C₂²×C₄

C₃×C₂²⋊D₅

yes

—

169

C₂×C₈

—

170

C₄²

C₂×C₃×Dic₅

yes

characteristic

171

C₄²

C₃×C₂²⋊D₅

yes

—

172

C₄²

C₂²×C₃×D₅

yes

characteristic

173

C₃×C₅

#1555

yes

characteristic, complemented, Hall

174

C₂²×C₃

—

175

C₂²×C₃

—

176

C₂²×C₃

—

177

C₂²×C₃

—

178

C₂²×C₃

#3965

yes

—

179

C₂²×C₃

C₂×C₂²⋊Dic₅

yes

characteristic

180

C₃×C₄

—

181

C₃×C₄

—

182

C₃×C₄

—

183

C₃×C₄

#4078

yes

—

184

C₂×C₅

—

185

C₂×C₅

—

186

C₂×C₅

C₂×C₃×#100

yes

characteristic

187

C₂×C₅

C₃×#418

yes

—

188

C₂³

—

189

C₂³

—

190

C₂³

—

191

C₂³

C₃×C₂²⋊Dic₅

yes

characteristic

192

D₄

—

193

D₄

—

194

D₄

—

195

D₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

C₃×C₂²⋊Dic₅

yes

—

199

C₂×C₄

C₃×C₂²⋊Dic₅

yes

characteristic

200

C₂×C₄

C₂²×C₃×Dic₅

yes

characteristic

201

C₂×C₄

C₂×C₃×C₂²⋊D₅

yes

—

202

C₈

—

203

C₂×C₃

—

204

C₂×C₃

—

205

C₂×C₃

#65504

yes

—

206

C₂×C₃

C₂×#3965

yes

characteristic

207

C₅

C₃×#1555

yes

characteristic, complemented, Sylow

208

C₂²

—

209

C₂²

—

210

C₂²

—

211

C₂²

—

212

C₂²

C₃×#3965

yes

—

213

C₂²

C₂×C₃×C₂²⋊Dic₅

yes

characteristic

214

C₄

—

215

C₄

—

216

C₄

—

217

C₄

C₃×#4078

yes

—

218

C₃

#10602553

yes

characteristic, direct product factor, Sylow

219

C₂

—

220

C₂

—

221

C₂

C₃×#65504

yes

—

222

C₂

C₂×C₃×#3965

yes

characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×C₂²⋊Dic₅
commutator	C₂×C₄×C₅	C₂²×C₃×C₄
Frattini	C₄²	C₂²×C₃×D₅
Fitting, prime radical	C₂×C₃×C₅×#127	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
cosocle	C₄²×C₅	C₂³×C₃
hypercenter	C₂×C₃×#127	D₅
hypocenter	C₅	C₃×#1555
LCS	G ▷ C₂×C₄×C₅ ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄² ◁ C₂×C₃×#127

subgroup

G/H

center

C₂²×C₃

C₂×C₂²⋊Dic₅

commutator

C₂×C₄×C₅

C₂²×C₃×C₄

Frattini

C₄²

C₂²×C₃×D₅

Fitting, prime radical

C₂×C₃×C₅×#127

C₂

socle

C₂²×C₃×C₅

C₂×C₂²⋊C₄

cosocle

C₄²×C₅

C₂³×C₃

hypercenter

C₂×C₃×#127

D₅

hypocenter

C₅

C₃×#1555

LCS

G ▷ C₂×C₄×C₅ ▷ C₂²×C₅ ▷ C₅

UCS

C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄² ◁ C₂×C₃×#127

N	H ≅ G/N	type
2. C₃×#65215	C₂	semidirect
3. C₃×#64764	C₂	semidirect
4. #10602553	C₃	direct (N × H)
12. C₃×C₄⋊#168	C₂²	semidirect
16. #65215	C₂×C₃	semidirect
17. #64764	C₂×C₃	semidirect
41. C₄⋊#168	C₂²×C₃	semidirect
173. C₃×C₅	#1555	semidirect
207. C₅	C₃×#1555	semidirect
218. C₃	#10602553	direct (N × H)

H ≅ G/N

type

2. C₃×#65215

C₂

semidirect

3. C₃×#64764

C₂

semidirect

4. #10602553

C₃

direct (N × H)

12. C₃×C₄⋊#168

C₂²

semidirect

16. #65215

C₂×C₃

semidirect

17. #64764

C₂×C₃

semidirect

41. C₄⋊#168

C₂²×C₃

semidirect

173. C₃×C₅

#1555

semidirect

207. C₅

C₃×#1555

semidirect

218. C₃

#10602553

direct (N × H)

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

subgroup	index
C₂×C₃×C₅×#127	2
C₃×#65215	2
C₃×#64764	2
#10602553	3
C₃×#1555	5

subgroup

index

C₂×C₃×C₅×#127

Subgroups — C₃×#10602553 #14285226

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C3×#10602553 #14285226

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10602553 #14285226