Group #14305260 — subgroups

Subgroups — #14305260

Order 1920.

416 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 114 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×C₈×ΓL(1,𝔽₁₆)	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#3995	C₂	1	1	yes	maximal, characteristic
3	#11751825	C₂	1	2	yes	maximal
4	#11747671	C₂	1	1	yes	maximal, characteristic
5	#11746524	C₂	1	2	yes	maximal
6	#10604057	—	3	1	no	maximal, Hall
7	C₂×C₄×ΓL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic
8	C₂×D₅⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
9	C₂×C₃×#700	C₂²	1	2	yes	—
10	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
11	#91358	C₂²	1	2	yes	—
12	C₈×ΓL(1,𝔽₁₆)	—	2	2	no	—
13	C₃×#3995	—	2	2	no	—
14	#91177	—	2	2	no	—
15	Dic₃⋊#170	—	2	2	no	—
16	#91101	C₄	1	1	yes	characteristic, complemented
17	C₅×#817	C₄	1	1	yes	characteristic, complemented
18	#90988	C₄	1	2	yes	complemented
19	#70704	—	5	1	no	maximal, Hall
20	C₂×#3995	D₃	1	1	yes	characteristic
21	C₂×C₈×AGL(1,𝔽₅)	—	3	1	no	—
22	#65708	—	3	2	no	—
23	#65149	—	3	1	no	—
24	#64875	—	3	2	no	—
25	C₂²×ΓL(1,𝔽₁₆)	—	2	1	no	—
26	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
27	C₂×C₃⋊#170	D₄	1	2	yes	—
28	C₄×ΓL(1,𝔽₁₆)	—	2	1	no	—
29	C₄×ΓL(1,𝔽₁₆)	Q₈	1	2	yes	—
30	D₅⋊(C₃⋊C₈)	—	2	1	no	—
31	D₅⋊(C₃⋊C₈)	—	2	1	no	—
32	C₂×C₃×#170	—	2	2	no	—
33	C₃×#700	—	2	2	no	—
34	C₃×#700	—	2	2	no	—
35	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
36	C₄⋊Dic₁₅	C₂×C₄	1	2	yes	—
37	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
38	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic
39	C₃×C₈×D₅	D₄	1	2	yes	—
40	C₃×C₈×D₅	Q₈	1	2	yes	—
41	#6665	—	2	2	no	—
42	Dic₃×Dic₅	—	2	2	no	—
43	C₂×C₃×#108	—	5	1	no	—
44	#5119	—	5	2	no	—
45	#5106	—	5	1	no	—
46	C₂×C₈×Dic₃	—	5	1	no	—
47	#4555	—	5	2	no	—
48	C₂×C₄×AGL(1,𝔽₅)	—	3	1	no	—
49	C₂×#700	C₂×D₃	1	2	yes	—
50	C₂×D₅⋊C₈	—	3	1	no	—
51	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
52	#4038	—	3	2	no	—
53	#4004	—	6	2	no	—
54	C₄⋊#170	—	6	2	no	—
55	#3995	—	2	2	no	—
56	C₈×AGL(1,𝔽₅)	—	6	2	no	—
57	C₅×#106	—	3	1	no	—
58	#3949	—	3	1	no	—
59	#3939	—	3	2	no	—
60	#1945	—	15	1	no	Sylow
61	C₂²×C₃×D₅	#41	1	1	yes	characteristic
62	C₂×ΓL(1,𝔽₁₆)	—	2	4	no	—
63	C₂×ΓL(1,𝔽₁₆)	—	2	2	no	—
64	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
65	C₂×Dic₁₅	—	2	2	no	—
66	C₂×C₅×Dic₃	—	2	2	no	—
67	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
68	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
69	C₃×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
70	C₃×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
71	C₃×C₄×D₅	#41	1	1	yes	characteristic
72	C₃⋊#170	—	2	2	no	—
73	C₃×#170	—	4	2	no	—
74	C₃×C₅×C₈	C₄⋊C₄	1	2	yes	—
75	C₃×#168	C₄⋊C₄	1	2	yes	—
76	C₂×C₃×M₁₆	—	5	2	no	—
77	C₂²×C₃×C₈	—	5	1	no	—
78	#926	—	5	2	no	—
79	C₂×C₄×Dic₃	—	5	1	no	—
80	C₂²×C₃⋊C₈	—	5	1	no	—
81	C₃×#108	—	10	2	no	—
82	#818	—	5	2	no	—
83	#817	—	5	1	no	—
84	#817	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
85	Dic₃⋊C₈	—	10	2	no	—
86	Dic₃⋊C₈	—	10	2	no	—
87	C₈×Dic₃	—	10	2	no	—
88	C₂²×AGL(1,𝔽₅)	—	6	1	no	—
89	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
90	C₂×#170	—	2	2	no	—
91	C₂×#170	—	3	2	no	—
92	C₄×AGL(1,𝔽₅)	—	3	2	no	—
93	C₄×AGL(1,𝔽₅)	—	6	1	no	—
94	#700	—	2	2	no	—
95	#700	—	2	2	no	—
96	D₅⋊C₈	—	6	1	no	—
97	D₅⋊C₈	—	6	1	no	—
98	C₂×C₅×C₈	C₄×D₃	1	1	yes	characteristic
99	C₅×C₄⋊C₄	—	3	2	no	—
100	#685	—	6	2	no	—
101	C₄⋊Dic₅	—	3	2	no	—
102	C₄×Dic₅	—	6	2	no	—
103	C₂×#168	C₄×D₃	1	1	yes	characteristic
104	C₈×D₅	Dic₆	1	2	yes	—
105	C₈×D₅	#67	1	2	yes	—
106	C₂×#108	—	5	1	no	—
107	#427	—	15	1	no	—
108	#424	—	15	2	no	—
109	C₂×C₄×C₈	—	15	1	no	—
110	#339	—	15	2	no	—
111	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
112	C₂×C₃×D₅	—	2	2	no	—
113	C₂×C₃×D₅	C₂²⋊Q₈	1	1	yes	characteristic
114	C₂×C₃×D₅	#125	1	1	yes	characteristic
115	ΓL(1,𝔽₁₆)	—	2	4	no	—
116	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
117	C₃×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
118	Dic₁₅	—	4	2	no	—
119	C₃×Dic₅	#121	1	1	yes	characteristic
120	C₃×Dic₅	C₄⋊Q₈	1	1	yes	characteristic
121	C₅×Dic₃	—	4	2	no	—
122	C₂²×C₃×C₄	—	5	1	no	—
123	C₂²×Dic₃	—	10	1	no	—
124	C₃×M₁₆	—	10	2	no	—
125	C₃×M₁₆	—	10	2	no	—
126	C₂×C₃×C₈	—	5	1	no	—
127	C₂×C₃×C₈	—	5	2	no	—
128	C₂×C₃×C₈	—	5	2	no	—
129	C₂×C₃×C₈	—	10	2	no	—
130	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
131	#217	—	10	2	no	—
132	C₄⋊Dic₃	—	5	2	no	—
133	C₄⋊Dic₃	C₂×AGL(1,𝔽₅)	1	2	yes	—
134	C₄×Dic₃	—	5	2	no	—
135	C₄×Dic₃	—	10	2	no	—
136	C₄×Dic₃	—	10	1	no	—
137	C₂×C₃⋊C₈	—	5	2	no	—
138	C₂×C₃⋊C₈	—	10	1	no	—
139	C₂×C₃⋊C₈	—	10	1	no	—
140	C₂²×D₅	#239	1	1	yes	characteristic
141	C₂×AGL(1,𝔽₅)	—	6	4	no	—
142	C₂×AGL(1,𝔽₅)	—	6	2	no	—
143	C₂×C₄×C₅	—	6	2	no	—
144	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
145	C₂×Dic₅	—	6	2	no	—
146	C₂×Dic₅	D₃×D₄	1	1	yes	characteristic
147	C₄×D₅	C₂×Dic₆	1	1	yes	characteristic
148	C₄×D₅	#237	1	1	yes	characteristic
149	C₄×D₅	D₃×Q₈	1	1	yes	characteristic
150	C₄×D₅	C₂×#67	1	1	yes	characteristic
151	#170	—	4	2	no	—
152	#170	—	6	2	no	—
153	C₅×C₈	Dic₃⋊C₄	1	2	yes	—
154	#168	Dic₃⋊C₄	1	2	yes	—
155	C₂×M₁₆	—	5	2	no	—
156	C₂²×C₈	—	5	1	no	—
157	C₂²×C₈	—	15	1	no	—
158	#117	—	15	2	no	—
159	C₂×C₄²	—	15	1	no	—
160	#108	—	10	2	no	—
161	#107	—	15	2	no	—
162	#106	—	3	1	no	—
163	#106	—	15	1	no	—
164	C₄⋊C₈	—	30	2	no	—
165	C₄⋊C₈	—	30	2	no	—
166	C₄×C₈	—	30	2	no	—
167	C₂×C₃×C₅	#389	1	1	yes	characteristic
168	C₂×C₃×C₅	#443	1	2	yes	—
169	C₃×D₅	—	2	1	no	—
170	C₃×D₅	—	2	1	no	—
171	C₂³×C₃	—	5	1	no	—
172	C₂×C₃×C₄	—	5	1	no	—
173	C₂×C₃×C₄	—	5	1	no	—
174	C₂×C₃×C₄	—	5	1	no	—
175	C₂×C₃×C₄	—	5	1	no	—
176	C₂×C₃×C₄	—	5	1	no	—
177	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
178	C₂×Dic₃	—	2	2	no	—
179	C₂×Dic₃	—	10	2	no	—
180	C₂×Dic₃	—	10	4	no	—
181	C₂×Dic₃	—	10	2	no	—
182	C₃×C₈	—	5	2	no	—
183	C₃×C₈	—	20	2	no	—
184	C₃×C₈	C₄⋊AGL(1,𝔽₅)	1	2	yes	—
185	C₃⋊C₈	—	10	2	no	—
186	C₂²×C₅	#893	1	1	yes	characteristic
187	C₂×D₅	—	2	2	no	—
188	C₂×D₅	#890	1	1	yes	characteristic
189	C₂×D₅	#946	1	1	yes	characteristic
190	AGL(1,𝔽₅)	—	6	4	no	—
191	C₄×C₅	—	12	2	no	—
192	C₄×C₅	#887	1	1	yes	characteristic
193	C₄×C₅	C₂×Dic₃⋊C₄	1	1	yes	characteristic
194	Dic₅	—	12	2	no	—
195	Dic₅	#888	1	1	yes	characteristic
196	Dic₅	#938	1	1	yes	characteristic
197	C₂²×C₄	—	5	1	no	—
198	C₂²×C₄	—	30	1	no	—
199	M₁₆	—	10	2	no	—
200	M₁₆	—	10	2	no	—
201	C₂×C₈	—	5	1	no	—
202	C₂×C₈	—	5	2	no	—
203	C₂×C₈	—	5	2	no	—
204	C₂×C₈	—	10	2	no	—
205	C₂×C₈	—	15	2	no	—
206	C₂×C₈	—	30	1	no	—
207	C₂×C₈	—	30	1	no	—
208	C₂×C₈	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
209	C₄⋊C₄	—	3	2	no	—
210	C₄⋊C₄	—	15	2	no	—
211	C₂²⋊C₄	—	30	2	no	—
212	C₄²	—	15	2	no	—
213	C₄²	—	30	2	no	—
214	C₄²	—	30	1	no	—
215	C₃×C₅	#1945	1	1	yes	characteristic, complemented, Hall
216	C₂²×C₃	—	5	1	no	—
217	C₂²×C₃	—	5	1	no	—
218	C₂²×C₃	—	10	2	no	—
219	C₂²×C₃	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
220	C₃×C₄	—	5	1	no	—
221	C₃×C₄	—	5	1	no	—
222	C₃×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
223	C₃×C₄	Q₈×AGL(1,𝔽₅)	1	1	yes	characteristic
224	Dic₃	—	4	2	no	—
225	Dic₃	—	10	4	no	—
226	Dic₃	—	20	2	no	—
227	C₂×C₅	#4895	1	2	yes	—
228	C₂×C₅	#4972	1	1	yes	characteristic
229	D₅	—	2	1	no	—
230	D₅	—	2	1	no	—
231	C₂³	—	5	1	no	—
232	C₂×C₄	—	5	1	no	—
233	C₂×C₄	—	5	1	no	—
234	C₂×C₄	—	5	1	no	—
235	C₂×C₄	—	5	1	no	—
236	C₂×C₄	—	5	1	no	—
237	C₂×C₄	—	6	2	no	—
238	C₂×C₄	—	30	2	no	—
239	C₂×C₄	—	30	4	no	—
240	C₂×C₄	—	30	2	no	—
241	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
242	C₈	—	5	2	no	—
243	C₈	—	20	2	no	—
244	C₈	—	30	2	no	—
245	C₈	Dic₃⋊AGL(1,𝔽₅)	1	2	yes	—
246	C₂×C₃	—	10	1	no	—
247	C₂×C₃	—	10	1	no	—
248	C₂×C₃	#65712	1	1	yes	characteristic
249	C₂×C₃	#65736	1	2	yes	—
250	C₅	#70704	1	1	yes	characteristic, complemented, Sylow
251	C₂²	—	5	1	no	—
252	C₂²	—	5	1	no	—
253	C₂²	—	10	2	no	—
254	C₂²	#91921	1	1	yes	characteristic
255	C₄	—	5	1	no	—
256	C₄	—	5	1	no	—
257	C₄	—	12	2	no	—
258	C₄	—	30	4	no	—
259	C₄	—	60	2	no	—
260	C₄	ΓL(1,𝔽₁₆)⋊Q₈	1	1	yes	characteristic
261	C₄	C₂×Dic₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic
262	C₃	#10604057	1	1	yes	characteristic, complemented, Sylow
263	C₂	—	10	1	no	—
264	C₂	—	10	1	no	—
265	C₂	#11751685	1	2	yes	—
266	C₂	#11751861	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₈×ΓL(1,𝔽₁₆)

C₂

yes

maximal, characteristic

C₂×C₃×#3995

C₂

yes

maximal, characteristic

#11751825

C₂

yes

maximal

#11747671

C₂

yes

maximal, characteristic

#11746524

C₂

yes

maximal

#10604057

—

maximal, Hall

C₂×C₄×ΓL(1,𝔽₁₆)

C₂²

yes

characteristic

C₂×D₅⋊(C₃⋊C₈)

C₂²

yes

characteristic

C₂×C₃×#700

C₂²

yes

—

C₂×C₃×C₈×D₅

C₂²

yes

characteristic

#91358

C₂²

yes

—

C₈×ΓL(1,𝔽₁₆)

—

—

—

—

C₄

yes

characteristic, complemented

C₅×#817

C₄

yes

characteristic, complemented

#90988

C₄

yes

—

D₃

yes

characteristic

C₂×C₈×AGL(1,𝔽₅)

—

#65708

—

#65149

—

#64875

—

C₂²×ΓL(1,𝔽₁₆)

—

C₂×C₃×C₄×D₅

C₂³

yes

characteristic

C₂×C₃⋊#170

D₄

yes

—

C₄×ΓL(1,𝔽₁₆)

—

C₄×ΓL(1,𝔽₁₆)

Q₈

yes

—

D₅⋊(C₃⋊C₈)

—

D₅⋊(C₃⋊C₈)

—

C₂×C₃×#170

—

C₃×#700

—

C₃×#700

—

C₂×C₃×C₅×C₈

C₂×C₄

yes

characteristic

C₄⋊Dic₁₅

C₂×C₄

yes

—

C₅×C₄⋊Dic₃

C₂×C₄

yes

—

C₂×C₃×#168

C₂×C₄

yes

characteristic

C₃×C₈×D₅

D₄

yes

—

C₃×C₈×D₅

Q₈

yes

—

#6665

—

Dic₃×Dic₅

—

C₂×C₃×#108

—

#5119

—

#5106

—

C₂×C₈×Dic₃

—

#4555

—

C₂×C₄×AGL(1,𝔽₅)

—

C₂×#700

C₂×D₃

yes

—

C₂×D₅⋊C₈

—

C₂×C₈×D₅

C₂×D₃

yes

—

—

—

—

—

—

—

—

—

C₂²×C₃×D₅

yes

C₂×ΓL(1,𝔽₁₆)

—

C₂×ΓL(1,𝔽₁₆)

—

C₂×C₃×C₄×C₅

C₂²×C₄

yes

characteristic

C₂×Dic₁₅

—

C₂×C₅×Dic₃

—

C₂×C₃×Dic₅

C₂×D₄

yes

characteristic

C₃×C₄×D₅

C₂×D₄

yes

characteristic

C₃×C₄×D₅

C₂×Q₈

yes

characteristic

C₃×C₄×D₅

C₂×Q₈

yes

C₃×C₄×D₅

yes

—

—

C₃×C₅×C₈

C₄⋊C₄

yes

—

C₃×#168

C₄⋊C₄

yes

—

C₂×C₃×M₁₆

—

C₂²×C₃×C₈

—

#926

—

C₂×C₄×Dic₃

—

C₂²×C₃⋊C₈

—

—

—

—

yes

characteristic, complemented

Dic₃⋊C₈

—

Dic₃⋊C₈

—

C₈×Dic₃

—

C₂²×AGL(1,𝔽₅)

—

C₂×C₄×D₅

C₂²×D₃

yes

—

—

—

—

—

—

D₅⋊C₈

—

D₅⋊C₈

—

C₂×C₅×C₈

C₄×D₃

yes

characteristic

C₅×C₄⋊C₄

—

100

#685

—

101

C₄⋊Dic₅

—

102

C₄×Dic₅

—

103

C₂×#168

C₄×D₃

yes

characteristic

104

C₈×D₅

Dic₆

yes

—

105

C₈×D₅

#67

yes

—

106

C₂×#108

—

107

#427

—

108

#424

—

109

C₂×C₄×C₈

—

110

#339

—

111

C₂²×C₃×C₅

C₄×D₄

yes

characteristic

112

C₂×C₃×D₅

—

113

C₂×C₃×D₅

C₂²⋊Q₈

yes

characteristic

114

C₂×C₃×D₅

#125

yes

characteristic

115

ΓL(1,𝔽₁₆)

—

116

C₃×C₄×C₅

C₂×C₄⋊C₄

yes

characteristic

117

C₃×C₄×C₅

C₄×Q₈

yes

characteristic

118

Dic₁₅

—

119

C₃×Dic₅

#121

yes

characteristic

120

C₃×Dic₅

C₄⋊Q₈

yes

characteristic

121

C₅×Dic₃

—

122

C₂²×C₃×C₄

—

123

C₂²×Dic₃

—

124

C₃×M₁₆

—

125

C₃×M₁₆

—

126

C₂×C₃×C₈

—

127

C₂×C₃×C₈

—

128

C₂×C₃×C₈

—

129

C₂×C₃×C₈

—

130

C₂×C₃×C₈

C₂×AGL(1,𝔽₅)

yes

characteristic

131

#217

—

132

C₄⋊Dic₃

—

133

C₄⋊Dic₃

C₂×AGL(1,𝔽₅)

yes

—

134

C₄×Dic₃

—

135

C₄×Dic₃

—

136

C₄×Dic₃

—

137

C₂×C₃⋊C₈

—

138

C₂×C₃⋊C₈

—

139

C₂×C₃⋊C₈

—

140

C₂²×D₅

#239

yes

characteristic

141

C₂×AGL(1,𝔽₅)

—

142

C₂×AGL(1,𝔽₅)

—

143

C₂×C₄×C₅

—

144

C₂×C₄×C₅

C₂×C₄×D₃

yes

characteristic

145

C₂×Dic₅

—

146

C₂×Dic₅

D₃×D₄

yes

characteristic

147

C₄×D₅

C₂×Dic₆

yes

characteristic

148

C₄×D₅

#237

yes

characteristic

149

C₄×D₅

D₃×Q₈

yes

characteristic

150

C₄×D₅

C₂×#67

yes

characteristic

151

#170

—

152

#170

—

153

C₅×C₈

Dic₃⋊C₄

yes

—

154

#168

Dic₃⋊C₄

yes

—

155

C₂×M₁₆

—

156

C₂²×C₈

—

157

C₂²×C₈

—

158

#117

—

159

C₂×C₄²

—

160

#108

—

161

#107

—

162

#106

—

163

#106

—

164

C₄⋊C₈

—

165

C₄⋊C₈

—

166

C₄×C₈

—

167

C₂×C₃×C₅

#389

yes

characteristic

168

C₂×C₃×C₅

#443

yes

—

169

C₃×D₅

—

170

C₃×D₅

—

171

C₂³×C₃

—

172

C₂×C₃×C₄

—

173

C₂×C₃×C₄

—

174

C₂×C₃×C₄

—

175

C₂×C₃×C₄

—

176

C₂×C₃×C₄

—

177

C₂×C₃×C₄

C₂²×AGL(1,𝔽₅)

yes

characteristic

178

C₂×Dic₃

—

179

C₂×Dic₃

—

180

C₂×Dic₃

—

181

C₂×Dic₃

—

182

C₃×C₈

—

183

C₃×C₈

—

184

C₃×C₈

C₄⋊AGL(1,𝔽₅)

yes

—

185

C₃⋊C₈

—

186

C₂²×C₅

#893

yes

characteristic

187

C₂×D₅

—

188

C₂×D₅

#890

yes

characteristic

189

C₂×D₅

#946

yes

characteristic

190

AGL(1,𝔽₅)

—

191

C₄×C₅

—

192

C₄×C₅

#887

yes

characteristic

193

C₄×C₅

C₂×Dic₃⋊C₄

yes

characteristic

194

Dic₅

—

195

Dic₅

#888

yes

characteristic

196

Dic₅

#938

yes

characteristic

197

C₂²×C₄

—

198

C₂²×C₄

—

199

M₁₆

—

200

M₁₆

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

—

208

C₂×C₈

D₃×AGL(1,𝔽₅)

yes

characteristic

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₂²⋊C₄

—

212

C₄²

—

213

C₄²

—

214

C₄²

—

215

C₃×C₅

#1945

yes

characteristic, complemented, Hall

216

C₂²×C₃

—

217

C₂²×C₃

—

218

C₂²×C₃

—

219

C₂²×C₃

D₄×AGL(1,𝔽₅)

yes

characteristic

220

C₃×C₄

—

221

C₃×C₄

—

222

C₃×C₄

C₂×C₄⋊AGL(1,𝔽₅)

yes

characteristic

223

C₃×C₄

Q₈×AGL(1,𝔽₅)

yes

characteristic

224

Dic₃

—

225

Dic₃

—

226

Dic₃

—

227

C₂×C₅

#4895

yes

—

228

C₂×C₅

#4972

yes

characteristic

229

D₅

—

230

D₅

—

231

C₂³

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

C₂×D₃×AGL(1,𝔽₅)

yes

characteristic

242

C₈

—

243

C₈

—

244

C₈

—

245

C₈

Dic₃⋊AGL(1,𝔽₅)

yes

—

246

C₂×C₃

—

247

C₂×C₃

—

248

C₂×C₃

#65712

yes

characteristic

249

C₂×C₃

#65736

yes

—

250

C₅

#70704

yes

characteristic, complemented, Sylow

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

#91921

yes

characteristic

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

260

C₄

ΓL(1,𝔽₁₆)⋊Q₈

yes

characteristic

261

C₄

C₂×Dic₃⋊AGL(1,𝔽₅)

yes

characteristic

262

C₃

#10604057

yes

characteristic, complemented, Sylow

263

C₂

—

264

C₂

—

265

C₂

#11751685

yes

—

266

C₂

#11751861

yes

characteristic

	subgroup	G/H
center	C₂²	#91921
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₅×C₈	C₂×C₄
socle	C₂²×C₃×C₅	C₄×D₄
prime radical	C₂²×C₃×D₅	#41
cosocle	C₂×C₃×C₄×D₅	C₂³
hypercenter	C₂×C₈	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	#1945
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

subgroup

G/H

center

C₂²

#91921

commutator

C₂×C₃×C₄×C₅

C₂²×C₄

Frattini

C₂×C₄

C₂×D₃×AGL(1,𝔽₅)

Fitting

C₂×C₃×C₅×C₈

C₂×C₄

socle

C₂²×C₃×C₅

C₄×D₄

prime radical

C₂²×C₃×D₅

#41

cosocle

C₂×C₃×C₄×D₅

C₂³

C₂×C₈

C₃×C₅

G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

N	H ≅ G/N	type
16. #91101	C₄	semidirect
17. C₅×#817	C₄	semidirect
18. #90988	C₄	semidirect
84. #817	AGL(1,𝔽₅)	semidirect
215. C₃×C₅	#1945	semidirect
250. C₅	#70704	semidirect
262. C₃	#10604057	semidirect

H ≅ G/N

type

16. #91101

C₄

semidirect

17. C₅×#817

C₄

semidirect

18. #90988

C₄

semidirect

84. #817

AGL(1,𝔽₅)

semidirect

215. C₃×C₅

#1945

semidirect

250. C₅

#70704

semidirect

262. C₃

#10604057

semidirect

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

subgroup	index
C₂×C₈×ΓL(1,𝔽₁₆)	2
C₂×C₃×#3995	2
#11751825	2
#11747671	2
#11746524	2
#10604057	3
#70704	5

subgroup

index

C₂×C₈×ΓL(1,𝔽₁₆)

C₂×C₃×#3995

Subgroups — #14305260

Conjugacy classes of subgroups

Complements

Maximal subgroups