Group #18087544 — subgroups

Subgroups — #18087544

Order 4864.

334 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 91 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	#14564468	C₂	1	1	yes	maximal, characteristic
2	#14563754	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562409	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562406	C₂	1	1	yes	maximal, characteristic, complemented
5	#14562034	C₂	1	1	yes	maximal, characteristic
6	#14561463	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1480	C₂	1	1	yes	maximal, characteristic
8	#11926597	C₂²	1	1	yes	characteristic
9	#11926568	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×#10597294	—	2	2	no	—
12	#11926390	C₂²	1	1	yes	characteristic
13	#11926298	—	2	2	no	—
14	#11926296	—	2	2	no	—
15	#11926295	—	2	2	no	—
16	D₄⋊(C₁₉⋊C₈)	—	2	2	no	—
17	C₁₉×#532	C₂²	1	1	yes	characteristic
18	C₁₉×#431	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₁₉×D₄⋊C₈	—	2	2	no	—
21	C₂×#41×C₁₉	—	2	1	no	—
22	C₂²×C₈×C₁₉	—	2	1	no	—
23	C₁₉×C₄⋊Q₈	Q₈	1	1	yes	characteristic
24	C₁₉×#127	Q₈	1	1	yes	characteristic
25	C₁₉×#124	—	2	1	no	—
26	C₁₉×#121	—	2	1	no	—
27	C₁₉×#121	—	2	1	no	—
28	C₄×D₄×C₁₉	—	2	1	no	—
29	C₄×D₄×C₁₉	—	2	1	no	—
30	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
31	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
32	C₂×#64520	—	2	1	no	—
33	C₂²×C₁₉⋊C₈	—	2	1	no	—
34	C₁₉×C₄⋊C₈	—	2	1	no	—
35	C₁₉×C₄⋊C₈	—	2	1	no	—
36	C₁₉×C₄⋊C₈	—	2	1	no	—
37	C₁₉×C₂²⋊C₈	—	2	1	no	—
38	C₄×C₈×C₁₉	D₄	1	2	yes	—
39	#10597294	—	4	4	no	—
40	C₁₉⋊#95	—	2	1	no	—
41	C₁₉⋊#95	—	2	1	no	—
42	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
43	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
44	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
45	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
46	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
47	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
48	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
49	#41×C₁₉	—	4	2	no	—
50	#41×C₁₉	—	4	2	no	—
51	C₂×Q₈×C₁₉	—	2	1	no	—
52	C₂×D₄×C₁₉	—	2	1	no	—
53	C₂×D₄×C₁₉	—	2	1	no	—
54	C₂×D₄×C₁₉	—	2	1	no	—
55	C₂×D₄×C₁₉	—	4	1	no	—
56	C₂²×C₄×C₁₉	—	4	1	no	—
57	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
60	C₂²×Dic₁₉	—	2	2	no	—
61	C₂×C₈×C₁₉	—	2	2	no	—
62	C₂×C₈×C₁₉	—	4	1	no	—
63	C₂×C₈×C₁₉	—	4	2	no	—
64	C₄⋊C₄×C₁₉	—	2	1	no	—
65	C₄⋊C₄×C₁₉	—	2	1	no	—
66	C₂²⋊C₄×C₁₉	—	4	1	no	—
67	C₂²⋊C₄×C₁₉	—	4	1	no	—
68	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
69	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
71	C₄²×C₁₉	#41	1	1	yes	characteristic
72	C₄×Dic₁₉	—	2	2	no	—
73	C₄×Dic₁₉	—	2	2	no	—
74	#64520	—	4	2	no	—
75	C₂×C₁₉⋊C₈	—	2	2	no	—
76	C₂×C₁₉⋊C₈	—	4	1	no	—
77	C₂×C₁₉⋊C₈	—	4	1	no	—
78	C₂×C₁₉⋊C₈	—	4	2	no	—
79	#10665	—	19	1	no	maximal, Sylow
80	C₂³×C₁₉	—	4	1	no	—
81	C₂³×C₁₉	#123	1	1	yes	characteristic
82	Q₈×C₁₉	—	4	2	no	—
83	D₄×C₁₉	—	4	2	no	—
84	D₄×C₁₉	—	4	2	no	—
85	D₄×C₁₉	—	4	2	no	—
86	D₄×C₁₉	—	8	2	no	—
87	C₂×C₄×C₁₉	—	4	1	no	—
88	C₂×C₄×C₁₉	—	4	1	no	—
89	C₂×C₄×C₁₉	—	4	1	no	—
90	C₂×C₄×C₁₉	—	8	1	no	—
91	C₂×C₄×C₁₉	—	8	1	no	—
92	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
93	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
94	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
96	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
97	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
98	C₂×C₄×C₁₉	#135	1	2	yes	—
99	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
100	C₂×Dic₁₉	—	4	2	no	—
101	C₂×Dic₁₉	—	4	2	no	—
102	C₂×Dic₁₉	—	4	2	no	—
103	C₈×C₁₉	—	4	2	no	—
104	C₈×C₁₉	—	8	1	no	—
105	C₁₉⋊C₈	—	4	2	no	—
106	C₁₉⋊C₈	—	8	1	no	—
107	C₁₉⋊C₈	—	8	1	no	—
108	#1963	—	19	1	no	—
109	#1832	—	19	1	no	—
110	#1571	—	19	1	no	—
111	#1570	—	19	1	no	—
112	#1480	—	19	1	no	—
113	#1480	D₁₉	1	1	yes	characteristic
114	#1274	—	19	1	no	—
115	C₂²×C₁₉	—	2	1	no	—
116	C₂²×C₁₉	—	2	1	no	—
117	C₂²×C₁₉	—	8	1	no	—
118	C₂²×C₁₉	—	8	1	no	—
119	C₂²×C₁₉	—	8	1	no	—
120	C₂²×C₁₉	#399	1	1	yes	characteristic
121	C₂²×C₁₉	#482	1	2	yes	—
122	C₄×C₁₉	—	2	1	no	—
123	C₄×C₁₉	—	2	1	no	—
124	C₄×C₁₉	—	2	1	no	—
125	C₄×C₁₉	—	2	1	no	—
126	C₄×C₁₉	—	8	1	no	—
127	C₄×C₁₉	#478	1	2	yes	—
128	C₄×C₁₉	#495	1	1	yes	characteristic
129	C₄×C₁₉	#496	1	1	yes	characteristic
130	Dic₁₉	—	8	2	no	—
131	#532	C₂×D₁₉	1	1	yes	characteristic
132	#431	—	19	1	no	—
133	#431	C₂×D₁₉	1	1	yes	characteristic
134	#423	—	19	1	no	—
135	C₂×C₄⋊C₈	—	19	1	no	—
136	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
137	C₂×#104	—	38	2	no	—
138	#376	—	19	1	no	—
139	#336	—	38	2	no	—
140	#335	—	38	2	no	—
141	#334	—	38	2	no	—
142	D₄⋊C₈	—	2	2	no	—
143	D₄⋊C₈	—	38	2	no	—
144	C₂×C₁₉	—	2	2	no	—
145	C₂×C₁₉	—	16	1	no	—
146	C₂×C₁₉	#2092	1	1	yes	characteristic
147	C₂×C₁₉	#2098	1	1	yes	characteristic
148	C₂×C₁₉	#2098	1	1	yes	characteristic
149	C₂×#41	—	2	1	no	—
150	C₂×M₁₆	—	38	1	no	—
151	C₂²×C₈	—	2	1	no	—
152	C₂²×C₈	—	38	1	no	—
153	C₄⋊Q₈	Dic₃₈	1	1	yes	characteristic
154	#127	Dic₃₈	1	1	yes	characteristic
155	#124	—	2	1	no	—
156	#121	—	2	1	no	—
157	#121	—	2	1	no	—
158	C₄×D₄	—	2	1	no	—
159	C₄×D₄	—	2	1	no	—
160	C₂×C₄²	—	19	2	no	—
161	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
162	C₄⋊C₈	—	2	1	no	—
163	C₄⋊C₈	—	2	1	no	—
164	C₄⋊C₈	—	2	1	no	—
165	C₄⋊C₈	—	38	1	no	—
166	C₄⋊C₈	—	38	1	no	—
167	C₄⋊C₈	—	38	1	no	—
168	C₄⋊C₈	—	38	1	no	—
169	C₄⋊C₈	—	38	1	no	—
170	#104	—	76	4	no	—
171	C₂²⋊C₈	—	2	1	no	—
172	C₂²⋊C₈	—	38	1	no	—
173	C₄×C₈	—	19	2	no	—
174	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
175	#95	—	38	1	no	—
176	#95	—	38	1	no	—
177	C₁₉	#10665	1	1	yes	characteristic, complemented, Sylow
178	#41	—	4	2	no	—
179	#41	—	4	2	no	—
180	C₂×Q₈	—	2	1	no	—
181	C₂×D₄	—	2	1	no	—
182	C₂×D₄	—	2	1	no	—
183	C₂×D₄	—	2	1	no	—
184	C₂×D₄	—	4	1	no	—
185	C₂²×C₄	—	4	1	no	—
186	C₂²×C₄	—	38	2	no	—
187	C₂²×C₄	#64541	1	1	yes	characteristic
188	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
189	C₂²×C₄	#64543	1	1	yes	characteristic
190	M₁₆	—	76	2	no	—
191	C₂×C₈	—	2	2	no	—
192	C₂×C₈	—	4	1	no	—
193	C₂×C₈	—	4	2	no	—
194	C₂×C₈	—	38	2	no	—
195	C₂×C₈	—	76	1	no	—
196	C₂×C₈	—	76	1	no	—
197	C₂×C₈	—	76	2	no	—
198	C₄⋊C₄	—	2	1	no	—
199	C₄⋊C₄	—	2	1	no	—
200	C₂²⋊C₄	—	4	1	no	—
201	C₂²⋊C₄	—	4	1	no	—
202	C₄²	—	38	2	no	—
203	C₄²	—	38	2	no	—
204	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
205	C₄²	D₄×D₁₉	1	1	yes	characteristic
206	C₄²	#64543	1	1	yes	characteristic
207	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
208	C₂³	—	4	1	no	—
209	C₂³	#10597329	1	1	yes	characteristic
210	Q₈	—	4	2	no	—
211	D₄	—	4	2	no	—
212	D₄	—	4	2	no	—
213	D₄	—	4	2	no	—
214	D₄	—	8	2	no	—
215	C₂×C₄	—	4	1	no	—
216	C₂×C₄	—	4	1	no	—
217	C₂×C₄	—	4	1	no	—
218	C₂×C₄	—	8	1	no	—
219	C₂×C₄	—	8	1	no	—
220	C₂×C₄	—	76	2	no	—
221	C₂×C₄	—	76	2	no	—
222	C₂×C₄	—	76	2	no	—
223	C₂×C₄	#10597324	1	1	yes	characteristic
224	C₂×C₄	#10597324	1	1	yes	characteristic
225	C₂×C₄	#10597329	1	1	yes	characteristic
226	C₂×C₄	#10597357	1	2	yes	—
227	C₂×C₄	#10597362	1	2	yes	—
228	C₂×C₄	#10597370	1	1	yes	characteristic
229	C₂×C₄	#10597381	1	1	yes	characteristic
230	C₂×C₄	#10597386	1	1	yes	characteristic
231	C₈	—	4	2	no	—
232	C₈	—	8	1	no	—
233	C₈	—	76	2	no	—
234	C₈	—	152	1	no	—
235	C₈	—	152	1	no	—
236	C₂²	—	2	1	no	—
237	C₂²	—	2	1	no	—
238	C₂²	—	8	1	no	—
239	C₂²	—	8	1	no	—
240	C₂²	—	8	1	no	—
241	C₂²	#11926480	1	1	yes	characteristic
242	C₂²	#11926867	1	2	yes	—
243	C₄	—	2	1	no	—
244	C₄	—	2	1	no	—
245	C₄	—	2	1	no	—
246	C₄	—	2	1	no	—
247	C₄	—	8	1	no	—
248	C₄	—	152	2	no	—
249	C₄	#11926846	1	2	yes	—
250	C₄	#11926925	1	1	yes	characteristic
251	C₄	#11926932	1	1	yes	characteristic
252	C₂	—	2	2	no	—
253	C₂	—	16	1	no	—
254	C₂	#14565158	1	1	yes	characteristic
255	C₂	#14565188	1	1	yes	characteristic
256	C₂	#14565190	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564468

C₂

yes

maximal, characteristic

#14563754

C₂

yes

maximal, characteristic, complemented

#14562409

C₂

yes

maximal, characteristic, complemented

#14562406

C₂

yes

maximal, characteristic, complemented

#14562034

C₂

yes

maximal, characteristic

#14561463

C₂

yes

maximal, characteristic, complemented

C₁₉×#1480

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

characteristic

#11926568

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×#10597294

—

#11926390

C₂²

yes

—

—

—

D₄⋊(C₁₉⋊C₈)

—

C₁₉×#532

C₂²

yes

characteristic

C₁₉×#431

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₁₉×D₄⋊C₈

—

C₂×#41×C₁₉

—

C₂²×C₈×C₁₉

—

C₁₉×C₄⋊Q₈

Q₈

yes

characteristic

C₁₉×#127

Q₈

yes

characteristic

C₁₉×#124

—

C₁₉×#121

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄×Dic₁₉

D₄

yes

—

C₂×#64520

—

C₂²×C₁₉⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

D₄

yes

—

#10597294

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

D₄

yes

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

C₂²×C₄×C₁₉

yes

C₂²×C₄×C₁₉

yes

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

characteristic

C₄×Dic₁₉

—

C₄×Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#10665

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#123

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

100

C₂×Dic₁₉

—

101

C₂×Dic₁₉

—

102

C₂×Dic₁₉

—

103

C₈×C₁₉

—

104

C₈×C₁₉

—

105

C₁₉⋊C₈

—

106

C₁₉⋊C₈

—

107

C₁₉⋊C₈

—

108

#1963

—

109

#1832

—

110

#1571

—

111

#1570

—

112

#1480

—

113

#1480

D₁₉

yes

characteristic

114

#1274

—

115

C₂²×C₁₉

—

116

C₂²×C₁₉

—

117

C₂²×C₁₉

—

118

C₂²×C₁₉

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

#399

yes

characteristic

121

C₂²×C₁₉

#482

yes

—

122

C₄×C₁₉

—

123

C₄×C₁₉

—

124

C₄×C₁₉

—

125

C₄×C₁₉

—

126

C₄×C₁₉

—

127

C₄×C₁₉

#478

yes

—

128

C₄×C₁₉

#495

yes

characteristic

129

C₄×C₁₉

#496

yes

characteristic

130

Dic₁₉

—

131

#532

C₂×D₁₉

yes

characteristic

132

#431

—

133

#431

C₂×D₁₉

yes

characteristic

134

#423

—

135

C₂×C₄⋊C₈

—

136

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

137

C₂×#104

—

138

#376

—

139

#336

—

140

#335

—

141

#334

—

142

D₄⋊C₈

—

143

D₄⋊C₈

—

144

C₂×C₁₉

—

145

C₂×C₁₉

—

146

C₂×C₁₉

#2092

yes

characteristic

147

C₂×C₁₉

#2098

yes

characteristic

148

C₂×C₁₉

#2098

yes

characteristic

149

C₂×#41

—

150

C₂×M₁₆

—

151

C₂²×C₈

—

152

C₂²×C₈

—

153

C₄⋊Q₈

Dic₃₈

yes

characteristic

154

#127

Dic₃₈

yes

characteristic

155

#124

—

156

#121

—

157

#121

—

158

C₄×D₄

—

159

C₄×D₄

—

160

C₂×C₄²

—

161

C₂×C₄²

C₂²×D₁₉

yes

characteristic

162

C₄⋊C₈

—

163

C₄⋊C₈

—

164

C₄⋊C₈

—

165

C₄⋊C₈

—

166

C₄⋊C₈

—

167

C₄⋊C₈

—

168

C₄⋊C₈

—

169

C₄⋊C₈

—

170

#104

—

171

C₂²⋊C₈

—

172

C₂²⋊C₈

—

173

C₄×C₈

—

174

C₄×C₈

C₂²⋊D₁₉

yes

—

175

#95

—

176

#95

—

177

C₁₉

#10665

yes

characteristic, complemented, Sylow

178

#41

—

179

#41

—

180

C₂×Q₈

—

181

C₂×D₄

—

182

C₂×D₄

—

183

C₂×D₄

—

184

C₂×D₄

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

#64541

yes

characteristic

188

C₂²×C₄

D₄×D₁₉

yes

characteristic

189

C₂²×C₄

#64543

yes

characteristic

190

M₁₆

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₂²⋊C₄

—

201

C₂²⋊C₄

—

202

C₄²

—

203

C₄²

—

204

C₄²

C₂×Dic₃₈

yes

characteristic

205

C₄²

D₄×D₁₉

yes

characteristic

206

C₄²

#64543

yes

characteristic

207

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

208

C₂³

—

209

C₂³

#10597329

yes

characteristic

210

Q₈

—

211

D₄

—

212

D₄

—

213

D₄

—

214

D₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

#10597324

yes

characteristic

224

C₂×C₄

#10597324

yes

characteristic

225

C₂×C₄

#10597329

yes

characteristic

226

C₂×C₄

#10597357

yes

—

227

C₂×C₄

#10597362

yes

—

228

C₂×C₄

#10597370

yes

characteristic

229

C₂×C₄

#10597381

yes

characteristic

230

C₂×C₄

#10597386

yes

characteristic

231

C₈

—

232

C₈

—

233

C₈

—

234

C₈

—

152

—

235

C₈

—

152

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

241

C₂²

#11926480

yes

characteristic

242

C₂²

#11926867

yes

—

243

C₄

—

244

C₄

—

245

C₄

—

246

C₄

—

247

C₄

—

248

C₄

—

152

—

249

C₄

#11926846

yes

—

250

C₄

#11926925

yes

characteristic

251

C₄

#11926932

yes

characteristic

252

C₂

—

253

C₂

—

254

C₂

#14565158

yes

characteristic

255

C₂

#14565188

yes

characteristic

256

C₂

#14565190

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597386
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1480	C₂
socle	C₂²×C₁₉	#399
prime radical	C₁₉×#532	C₂²
hypercenter	#1480	D₁₉
hypocenter	C₁₉	#10665
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1480

subgroup

G/H

center

C₂×C₄

#10597386

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1480

C₂

socle

C₂²×C₁₉

#399

prime radical

C₁₉×#532

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1480

N	H ≅ G/N	type
2. #14563754	C₂	semidirect
3. #14562409	C₂	semidirect
4. #14562406	C₂	semidirect
6. #14561463	C₂	semidirect
177. C₁₉	#10665	semidirect

H ≅ G/N

type

2. #14563754

C₂

semidirect

3. #14562409

C₂

semidirect

4. #14562406

C₂

semidirect

6. #14561463

C₂

semidirect

177. C₁₉

#10665

semidirect

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

subgroup	index
#14564468	2
#14563754	2
#14562409	2
#14562406	2
#14562034	2
#14561463	2
C₁₉×#1480	2
#10665	19

subgroup

index

C₁₉×#1480

Subgroups — #18087544

Conjugacy classes of subgroups

Complements

Maximal subgroups