Group #14439833 — subgroups

Subgroups — #14439833

Order 1920.

712 conjugacy classes of subgroups; only the 211 normal subgroups are shown.

normal subgroups only

This group has 712 conjugacy classes of subgroups — too many to draw. Only its 211 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	#11756487	C₂	1	2	yes	maximal
2	C₃×C₅×#498	C₂	1	1	yes	maximal, characteristic, complemented
3	#11751179	C₂	1	2	yes	maximal, complemented
4	#11750961	C₂	1	4	yes	maximal
5	#11750959	C₂	1	4	yes	maximal, complemented
6	C₄×C₈×D₁₅	C₂	1	1	yes	maximal, characteristic
7	#11750781	C₂	1	1	yes	maximal, characteristic, complemented
8	#10613622	—	3	1	no	maximal, Hall
9	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
10	#91835	—	2	2	no	—
11	Q₈×Dic₁₅	—	2	2	no	—
12	C₂×C₈×D₁₅	C₂²	1	2	yes	—
13	#91786	—	2	2	no	—
14	#91781	C₂²	1	4	yes	—
15	#91779	C₂²	1	4	yes	—
16	#91776	—	2	2	no	—
17	C₄²×D₁₅	C₂²	1	1	yes	characteristic
18	#91758	C₂²	1	2	yes	—
19	C₃×C₅×#106	C₂²	1	4	yes	—
20	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
21	#91101	C₂²	1	4	yes	—
22	C₈×Dic₁₅	C₂²	1	2	yes	—
23	#91091	C₂²	1	8	yes	—
24	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
25	#81891	—	5	1	no	maximal, Hall
26	#66062	—	3	2	no	—
27	C₅×#498	D₃	1	1	yes	characteristic, complemented
28	#65367	—	3	2	no	—
29	#65149	—	3	4	no	—
30	#65147	—	3	4	no	—
31	C₄×C₈×D₅	—	3	1	no	—
32	#64969	—	3	1	no	—
33	C₂×C₃×C₅×Q₈	—	2	2	no	—
34	C₂×C₄×D₁₅	D₄	1	2	yes	—
35	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
36	C₂×Dic₃₀	—	2	2	no	—
37	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
38	C₃×C₅×C₄⋊C₄	—	2	2	no	—
39	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
40	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
41	#6714	—	2	4	no	—
42	C₄⋊Dic₁₅	—	2	2	no	—
43	C₄⋊Dic₁₅	—	2	4	no	—
44	C₄⋊Dic₁₅	C₂³	1	4	yes	—
45	#6712	—	2	4	no	—
46	C₄×Dic₁₅	—	2	4	no	—
47	C₄×Dic₁₅	D₄	1	2	yes	—
48	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
49	C₂×C₃⋊#168	C₂³	1	2	yes	—
50	C₈×D₁₅	Q₈	1	8	yes	complemented
51	#5728	—	5	2	no	—
52	C₃×#498	D₅	1	1	yes	characteristic, complemented
53	#5078	—	5	2	no	—
54	#4860	—	5	4	no	—
55	#4858	—	5	4	no	—
56	C₄×D₃×C₈	—	5	1	no	—
57	#4680	—	5	1	no	—
58	C₅×C₄⋊Q₈	C₂×D₃	1	2	yes	—
59	#4092	—	6	2	no	—
60	Q₈×Dic₅	—	6	2	no	—
61	C₂×C₈×D₅	—	3	2	no	—
62	#4043	—	6	2	no	—
63	#4038	—	3	4	no	—
64	#4036	—	3	4	no	—
65	#4033	—	6	2	no	—
66	C₄²×D₅	—	3	1	no	—
67	#4015	—	3	2	no	—
68	C₅×#106	C₂×D₃	1	4	yes	—
69	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
70	#3949	—	3	4	no	—
71	C₈×Dic₅	—	3	2	no	—
72	#3939	—	3	8	no	—
73	C₄×#168	—	3	1	no	—
74	#3160	—	15	1	no	Sylow
75	C₂²×D₁₅	C₂×D₄	1	1	yes	characteristic
76	C₃×C₅×Q₈	—	4	4	no	—
77	C₂×C₃×C₄×C₅	—	2	4	no	—
78	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
79	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
80	C₂×Dic₁₅	—	2	4	no	—
81	C₂×Dic₁₅	C₂×D₄	1	2	yes	—
82	C₂×Dic₁₅	C₂×D₄	1	1	yes	characteristic
83	C₄×D₁₅	—	2	4	no	—
84	C₄×D₁₅	C₂×Q₈	1	4	yes	—
85	Dic₃₀	—	4	4	no	—
86	C₃×C₅×C₈	C₂×Q₈	1	4	yes	—
87	C₃⋊#168	C₂×Q₈	1	4	yes	—
88	C₃×C₄⋊Q₈	C₂×D₅	1	2	yes	—
89	#946	—	10	2	no	—
90	Q₈×Dic₃	—	10	2	no	—
91	C₂×D₃×C₈	—	5	2	no	—
92	#897	—	10	2	no	—
93	#892	—	5	4	no	—
94	#890	—	5	4	no	—
95	#887	—	10	2	no	—
96	C₄²×D₃	—	5	1	no	—
97	#869	—	5	2	no	—
98	C₃×#106	C₂×D₅	1	4	yes	—
99	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
100	#817	—	5	4	no	—
101	C₈×Dic₃	—	5	2	no	—
102	#807	—	5	8	no	—
103	C₄×C₃⋊C₈	—	5	1	no	—
104	C₂×C₅×Q₈	—	2	2	no	—
105	C₂×C₄×D₅	—	3	1	no	—
106	C₂×C₄×D₅	—	3	2	no	—
107	C₂×Dic₁₀	—	6	2	no	—
108	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
109	C₅×C₄⋊C₄	—	2	2	no	—
110	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
111	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
112	#685	—	6	4	no	—
113	C₄⋊Dic₅	—	3	4	no	—
114	C₄⋊Dic₅	—	6	4	no	—
115	C₄⋊Dic₅	—	6	2	no	—
116	#683	—	6	4	no	—
117	C₄×Dic₅	—	3	2	no	—
118	C₄×Dic₅	—	3	1	no	—
119	C₄×Dic₅	—	6	4	no	—
120	C₂×#168	—	3	2	no	—
121	C₈×D₅	—	3	8	no	—
122	#533	—	15	2	no	—
123	#500	—	15	2	no	—
124	#499	—	15	4	no	—
125	#498	—	15	1	no	—
126	#498	D₁₅	1	1	yes	characteristic, complemented
127	#427	—	15	4	no	—
128	C₂×C₄×C₈	—	15	1	no	—
129	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
130	C₂×D₁₅	—	2	2	no	—
131	C₂×D₁₅	C₄⋊Q₈	1	2	yes	—
132	C₃×C₄×C₅	—	4	4	no	—
133	C₃×C₄×C₅	#135	1	4	yes	—
134	C₃×C₄×C₅	C₂²×Q₈	1	2	yes	—
135	Dic₁₅	—	2	2	no	—
136	Dic₁₅	—	4	4	no	—
137	Dic₁₅	C₄⋊Q₈	1	2	yes	—
138	C₂×C₃×Q₈	—	2	2	no	—
139	C₂×C₄×D₃	—	5	1	no	—
140	C₂×C₄×D₃	—	5	2	no	—
141	C₂×Dic₆	—	10	2	no	—
142	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
143	C₃×C₄⋊C₄	—	2	2	no	—
144	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
145	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
146	(C₂×D₃)⋊C₄	—	10	4	no	—
147	C₄⋊Dic₃	—	5	4	no	—
148	C₄⋊Dic₃	—	10	4	no	—
149	C₄⋊Dic₃	—	10	2	no	—
150	Dic₃⋊C₄	—	10	4	no	—
151	C₄×Dic₃	—	5	2	no	—
152	C₄×Dic₃	—	5	1	no	—
153	C₄×Dic₃	—	10	4	no	—
154	C₂×C₃⋊C₈	—	5	2	no	—
155	D₃×C₈	—	5	8	no	—
156	C₂²×D₅	—	3	1	no	—
157	C₅×Q₈	—	4	4	no	—
158	C₂×C₄×C₅	—	2	4	no	—
159	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
160	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
161	C₂×Dic₅	—	3	1	no	—
162	C₂×Dic₅	—	3	2	no	—
163	C₂×Dic₅	—	6	4	no	—
164	C₄×D₅	—	3	4	no	—
165	C₄×D₅	—	6	4	no	—
166	Dic₁₀	—	12	4	no	—
167	C₅×C₈	D₃×Q₈	1	4	yes	—
168	#168	—	3	4	no	—
169	C₂²×C₈	—	15	2	no	—
170	C₄⋊Q₈	—	15	2	no	—
171	C₄⋊Q₈	C₂×D₁₅	1	2	yes	—
172	#125	—	15	4	no	—
173	C₂²⋊Q₈	—	30	2	no	—
174	C₂²⋊Q₈	—	30	2	no	—
175	C₄×Q₈	—	30	2	no	—
176	C₄×Q₈	—	30	2	no	—
177	#117	—	15	4	no	—
178	C₂×C₄²	—	15	1	no	—
179	#107	—	15	8	no	—
180	#106	—	15	4	no	—
181	#106	C₂×D₁₅	1	4	yes	—
182	C₄×C₈	—	15	2	no	—
183	C₄×C₈	—	15	1	no	—
184	C₄×C₈	C₂×D₁₅	1	1	yes	characteristic
185	C₂×C₃×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
186	C₂×C₃×C₅	C₂×#135	1	2	yes	—
187	D₁₅	—	2	2	no	—
188	C₂²×D₃	—	5	1	no	—
189	C₃×Q₈	—	4	4	no	—
190	C₂×C₃×C₄	—	2	4	no	—
191	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
192	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
193	C₂×Dic₃	—	5	1	no	—
194	C₂×Dic₃	—	5	2	no	—
195	C₂×Dic₃	—	10	4	no	—
196	C₄×D₃	—	5	4	no	—
197	C₄×D₃	—	10	4	no	—
198	Dic₆	—	20	4	no	—
199	C₃×C₈	Q₈×D₅	1	4	yes	—
200	C₃⋊C₈	—	5	4	no	—
201	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
202	C₂×D₅	—	3	2	no	—
203	C₂×D₅	—	6	2	no	—
204	C₄×C₅	—	4	4	no	—
205	C₄×C₅	#916	1	4	yes	—
206	C₄×C₅	C₂×D₃×Q₈	1	2	yes	—
207	Dic₅	—	3	2	no	—
208	Dic₅	—	6	2	no	—
209	Dic₅	—	12	4	no	—
210	C₂×Q₈	—	2	2	no	—
211	C₂×Q₈	—	30	2	no	—
212	C₂²×C₄	—	15	1	no	—
213	C₂²×C₄	—	15	2	no	—
214	C₂×C₈	—	15	2	no	—
215	C₂×C₈	—	15	8	no	—
216	C₂×C₈	C₂²×D₁₅	1	2	yes	—
217	C₄⋊C₄	—	2	2	no	—
218	C₄⋊C₄	—	15	4	no	—
219	C₄⋊C₄	—	30	4	no	—
220	C₄⋊C₄	—	30	4	no	—
221	C₄⋊C₄	—	30	2	no	—
222	C₄⋊C₄	C₂²×D₁₅	1	4	yes	—
223	C₂²⋊C₄	—	30	4	no	—
224	C₄²	—	15	2	no	—
225	C₄²	—	15	1	no	—
226	C₄²	—	30	4	no	—
227	C₄²	C₂²×D₁₅	1	1	yes	characteristic
228	C₃×C₅	#3160	1	1	yes	characteristic, complemented, Hall
229	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
230	C₂×D₃	—	5	2	no	—
231	C₂×D₃	—	10	2	no	—
232	C₃×C₄	—	4	4	no	—
233	C₃×C₄	#4062	1	4	yes	—
234	C₃×C₄	C₂×Q₈×D₅	1	2	yes	—
235	Dic₃	—	5	2	no	—
236	Dic₃	—	10	2	no	—
237	Dic₃	—	20	4	no	—
238	C₂×C₅	D₃×C₄⋊Q₈	1	1	yes	characteristic
239	C₂×C₅	C₂×#916	1	2	yes	—
240	D₅	—	6	2	no	—
241	C₂³	—	15	1	no	—
242	Q₈	—	4	4	no	—
243	Q₈	—	60	4	no	—
244	C₂×C₄	—	2	4	no	—
245	C₂×C₄	—	15	1	no	—
246	C₂×C₄	—	15	4	no	—
247	C₂×C₄	—	15	2	no	—
248	C₂×C₄	—	30	4	no	—
249	C₂×C₄	—	30	4	no	—
250	C₂×C₄	D₄×D₁₅	1	2	yes	—
251	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
252	C₈	—	15	4	no	—
253	C₈	Q₈×D₁₅	1	4	yes	—
254	C₂×C₃	D₅×C₄⋊Q₈	1	1	yes	characteristic
255	C₂×C₃	C₂×#4062	1	2	yes	—
256	D₃	—	10	2	no	—
257	C₅	#81891	1	1	yes	characteristic, complemented, Sylow
258	C₂²	—	15	2	no	—
259	C₂²	—	30	2	no	—
260	C₂²	C₂×D₄×D₁₅	1	1	yes	characteristic
261	C₄	—	4	4	no	—
262	C₄	—	15	2	no	—
263	C₄	—	30	2	no	—
264	C₄	—	60	4	no	—
265	C₄	#91805	1	4	yes	—
266	C₄	C₂×Q₈×D₁₅	1	2	yes	—
267	C₃	#10613622	1	1	yes	characteristic, complemented, Sylow
268	C₂	—	30	2	no	—
269	C₂	D₁₅×C₄⋊Q₈	1	1	yes	characteristic
270	C₂	C₂×#91805	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11756487

C₂

yes

maximal

C₃×C₅×#498

C₂

yes

maximal, characteristic, complemented

#11751179

C₂

yes

maximal, complemented

#11750961

C₂

yes

maximal

#11750959

C₂

yes

maximal, complemented

C₄×C₈×D₁₅

C₂

yes

maximal, characteristic

#11750781

C₂

yes

maximal, characteristic, complemented

#10613622

—

maximal, Hall

C₃×C₅×C₄⋊Q₈

C₂²

yes

—

#91835

—

Q₈×Dic₁₅

—

C₂×C₈×D₁₅

C₂²

yes

—

#91786

—

#91781

C₂²

yes

—

#91779

C₂²

yes

—

#91776

—

C₄²×D₁₅

C₂²

yes

characteristic

#91758

C₂²

yes

—

C₃×C₅×#106

C₂²

yes

—

C₃×C₄×C₅×C₈

C₂²

yes

characteristic

#91101

C₂²

yes

—

C₈×Dic₁₅

C₂²

yes

—

#91091

C₂²

yes

—

C₄×C₃⋊#168

C₂²

yes

—

—

D₃

yes

characteristic, complemented

#65367

—

#65149

—

#65147

—

C₄×C₈×D₅

—

#64969

—

C₂×C₃×C₅×Q₈

—

C₂×C₄×D₁₅

D₄

yes

—

C₂×C₄×D₁₅

C₂³

yes

characteristic

C₂×Dic₃₀

—

C₂×C₃×C₅×C₈

C₂³

yes

—

C₃×C₅×C₄⋊C₄

—

C₃×C₅×C₄⋊C₄

C₂³

yes

—

C₃×C₄²×C₅

C₂³

yes

characteristic

#6714

—

C₄⋊Dic₁₅

—

C₄⋊Dic₁₅

—

C₄⋊Dic₁₅

C₂³

yes

—

#6712

—

C₄×Dic₁₅

—

C₄×Dic₁₅

D₄

yes

—

C₄×Dic₁₅

C₂³

yes

characteristic

C₂×C₃⋊#168

C₂³

yes

—

C₈×D₁₅

Q₈

yes

complemented

#5728

—

C₃×#498

D₅

yes

characteristic, complemented

#5078

—

#4860

—

#4858

—

C₄×D₃×C₈

—

#4680

—

C₅×C₄⋊Q₈

C₂×D₃

yes

—

#4092

—

Q₈×Dic₅

—

C₂×C₈×D₅

—

—

—

—

—

C₄²×D₅

—

#4015

—

C₅×#106

C₂×D₃

yes

—

C₄×C₅×C₈

C₂×D₃

yes

characteristic

#3949

—

C₈×Dic₅

—

—

—

—

C₂²×D₁₅

C₂×D₄

yes

characteristic

C₃×C₅×Q₈

—

C₂×C₃×C₄×C₅

—

C₂×C₃×C₄×C₅

C₂×D₄

yes

—

C₂×C₃×C₄×C₅

C₂⁴

yes

characteristic

C₂×Dic₁₅

—

C₂×Dic₁₅

C₂×D₄

yes

—

C₂×Dic₁₅

C₂×D₄

yes

characteristic

C₄×D₁₅

—

C₄×D₁₅

C₂×Q₈

yes

—

Dic₃₀

—

C₃×C₅×C₈

C₂×Q₈

yes

—

C₃⋊#168

C₂×Q₈

yes

—

C₃×C₄⋊Q₈

C₂×D₅

yes

—

#946

—

Q₈×Dic₃

—

C₂×D₃×C₈

—

—

—

—

—

C₄²×D₃

—

#869

—

C₃×#106

C₂×D₅

yes

—

C₃×C₄×C₈

C₂×D₅

yes

characteristic

100

#817

—

101

C₈×Dic₃

—

102

#807

—

103

C₄×C₃⋊C₈

—

104

C₂×C₅×Q₈

—

105

C₂×C₄×D₅

—

106

C₂×C₄×D₅

—

107

C₂×Dic₁₀

—

108

C₂×C₅×C₈

C₂²×D₃

yes

—

109

C₅×C₄⋊C₄

—

110

C₅×C₄⋊C₄

C₂²×D₃

yes

—

111

C₄²×C₅

C₂²×D₃

yes

characteristic

112

#685

—

113

C₄⋊Dic₅

—

114

C₄⋊Dic₅

—

115

C₄⋊Dic₅

—

116

#683

—

117

C₄×Dic₅

—

118

C₄×Dic₅

—

119

C₄×Dic₅

—

120

C₂×#168

—

121

C₈×D₅

—

122

#533

—

123

#500

—

124

#499

—

125

#498

—

126

#498

D₁₅

yes

characteristic, complemented

127

#427

—

128

C₂×C₄×C₈

—

129

C₂²×C₃×C₅

C₂²×D₄

yes

characteristic

130

C₂×D₁₅

—

131

C₂×D₁₅

C₄⋊Q₈

yes

—

132

C₃×C₄×C₅

—

133

C₃×C₄×C₅

#135

yes

—

134

C₃×C₄×C₅

C₂²×Q₈

yes

—

135

Dic₁₅

—

136

Dic₁₅

—

137

Dic₁₅

C₄⋊Q₈

yes

—

138

C₂×C₃×Q₈

—

139

C₂×C₄×D₃

—

140

C₂×C₄×D₃

—

141

C₂×Dic₆

—

142

C₂×C₃×C₈

C₂²×D₅

yes

—

143

C₃×C₄⋊C₄

—

144

C₃×C₄⋊C₄

C₂²×D₅

yes

—

145

C₃×C₄²

C₂²×D₅

yes

characteristic

146

(C₂×D₃)⋊C₄

—

147

C₄⋊Dic₃

—

148

C₄⋊Dic₃

—

149

C₄⋊Dic₃

—

150

Dic₃⋊C₄

—

151

C₄×Dic₃

—

152

C₄×Dic₃

—

153

C₄×Dic₃

—

154

C₂×C₃⋊C₈

—

155

D₃×C₈

—

156

C₂²×D₅

—

157

C₅×Q₈

—

158

C₂×C₄×C₅

—

159

C₂×C₄×C₅

D₃×D₄

yes

—

160

C₂×C₄×C₅

C₂³×D₃

yes

characteristic

161

C₂×Dic₅

—

162

C₂×Dic₅

—

163

C₂×Dic₅

—

164

C₄×D₅

—

165

C₄×D₅

—

166

Dic₁₀

—

167

C₅×C₈

D₃×Q₈

yes

—

168

#168

—

169

C₂²×C₈

—

170

C₄⋊Q₈

—

171

C₄⋊Q₈

C₂×D₁₅

yes

—

172

#125

—

173

C₂²⋊Q₈

—

174

C₂²⋊Q₈

—

175

C₄×Q₈

—

176

C₄×Q₈

—

177

#117

—

178

C₂×C₄²

—

179

#107

—

180

#106

—

181

#106

C₂×D₁₅

yes

—

182

C₄×C₈

—

183

C₄×C₈

—

184

C₄×C₈

C₂×D₁₅

yes

characteristic

185

C₂×C₃×C₅

C₂×C₄⋊Q₈

yes

characteristic

186

C₂×C₃×C₅

C₂×#135

yes

—

187

D₁₅

—

188

C₂²×D₃

—

189

C₃×Q₈

—

190

C₂×C₃×C₄

—

191

C₂×C₃×C₄

D₄×D₅

yes

—

192

C₂×C₃×C₄

C₂³×D₅

yes

characteristic

193

C₂×Dic₃

—

194

C₂×Dic₃

—

195

C₂×Dic₃

—

196

C₄×D₃

—

197

C₄×D₃

—

198

Dic₆

—

199

C₃×C₈

Q₈×D₅

yes

—

200

C₃⋊C₈

—

201

C₂²×C₅

C₂×D₃×D₄

yes

characteristic

202

C₂×D₅

—

203

C₂×D₅

—

204

C₄×C₅

—

205

C₄×C₅

#916

yes

—

206

C₄×C₅

C₂×D₃×Q₈

yes

—

207

Dic₅

—

208

Dic₅

—

209

Dic₅

—

210

C₂×Q₈

—

211

C₂×Q₈

—

212

C₂²×C₄

—

213

C₂²×C₄

—

214

C₂×C₈

—

215

C₂×C₈

—

216

C₂×C₈

C₂²×D₁₅

yes

—

217

C₄⋊C₄

—

218

C₄⋊C₄

—

219

C₄⋊C₄

—

220

C₄⋊C₄

—

221

C₄⋊C₄

—

222

C₄⋊C₄

C₂²×D₁₅

yes

—

223

C₂²⋊C₄

—

224

C₄²

—

225

C₄²

—

226

C₄²

—

227

C₄²

C₂²×D₁₅

yes

characteristic

228

C₃×C₅

#3160

yes

characteristic, complemented, Hall

229

C₂²×C₃

C₂×D₄×D₅

yes

characteristic

230

C₂×D₃

—

231

C₂×D₃

—

232

C₃×C₄

—

233

C₃×C₄

#4062

yes

—

234

C₃×C₄

C₂×Q₈×D₅

yes

—

235

Dic₃

—

236

Dic₃

—

237

Dic₃

—

238

C₂×C₅

D₃×C₄⋊Q₈

yes

characteristic

239

C₂×C₅

C₂×#916

yes

—

240

D₅

—

241

C₂³

—

242

Q₈

—

243

Q₈

—

244

C₂×C₄

—

245

C₂×C₄

—

246

C₂×C₄

—

247

C₂×C₄

—

248

C₂×C₄

—

249

C₂×C₄

—

250

C₂×C₄

D₄×D₁₅

yes

—

251

C₂×C₄

C₂³×D₁₅

yes

characteristic

252

C₈

—

253

C₈

Q₈×D₁₅

yes

—

254

C₂×C₃

D₅×C₄⋊Q₈

yes

characteristic

255

C₂×C₃

C₂×#4062

yes

—

256

D₃

—

257

C₅

#81891

yes

characteristic, complemented, Sylow

258

C₂²

—

259

C₂²

—

260

C₂²

C₂×D₄×D₁₅

yes

characteristic

261

C₄

—

262

C₄

—

263

C₄

—

264

C₄

—

265

C₄

#91805

yes

—

266

C₄

C₂×Q₈×D₁₅

yes

—

267

C₃

#10613622

yes

characteristic, complemented, Sylow

268

C₂

—

269

C₂

D₁₅×C₄⋊Q₈

yes

characteristic

270

C₂

C₂×#91805

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₅
commutator, cosocle	C₂×C₃×C₄×C₅	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₅
Fitting	C₃×C₅×#498	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×D₁₅	C₂×D₄
hypercenter	#498	D₁₅
hypocenter	C₃×C₅	#3160
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #498

subgroup

G/H

center

C₂²

C₂×D₄×D₁₅

commutator, cosocle

C₂×C₃×C₄×C₅

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₅

Fitting

C₃×C₅×#498

C₂

socle

C₂²×C₃×C₅

C₂²×D₄

prime radical

C₂²×D₁₅

C₂×D₄

D₁₅

C₃×C₅

G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #498

N	H ≅ G/N	type
2. C₃×C₅×#498	C₂	semidirect
3. #11751179	C₂	semidirect
5. #11750959	C₂	semidirect
7. #11750781	C₂	semidirect
27. C₅×#498	D₃	semidirect
50. C₈×D₁₅	Q₈	semidirect
52. C₃×#498	D₅	semidirect
126. #498	D₁₅	semidirect
228. C₃×C₅	#3160	semidirect
257. C₅	#81891	semidirect
267. C₃	#10613622	semidirect

H ≅ G/N

type

2. C₃×C₅×#498

C₂

semidirect

3. #11751179

C₂

semidirect

5. #11750959

C₂

semidirect

7. #11750781

C₂

semidirect

27. C₅×#498

D₃

semidirect

50. C₈×D₁₅

Q₈

semidirect

52. C₃×#498

D₅

semidirect

126. #498

D₁₅

semidirect

228. C₃×C₅

#3160

semidirect

257. C₅

#81891

semidirect

267. C₃

#10613622

semidirect

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

subgroup	index
#11756487	2
C₃×C₅×#498	2
#11751179	2
#11750961	2
#11750959	2
C₄×C₈×D₁₅	2
#11750781	2
#10613622	3
#81891	5

subgroup

index

C₃×C₅×#498

C₄×C₈×D₁₅

Subgroups — #14439833

Conjugacy classes of subgroups

Complements

Maximal subgroups