Group #18083517 — subgroups

Subgroups — #18083517

Order 4864.

584 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 103 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	#14574081	C₂	1	1	yes	maximal, characteristic
2	#14573666	C₂	1	2	yes	maximal, complemented
3	#14562033	C₂	1	2	yes	maximal, complemented
4	#14561466	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1985	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597350	—	2	2	no	—
7	#11927094	C₂²	1	2	yes	—
8	#11926938	—	2	2	no	—
9	#11926933	—	2	2	no	—
10	#11926862	—	2	2	no	—
11	#11926829	—	2	2	no	—
12	#11926744	—	2	2	no	—
13	#11926683	—	2	2	no	—
14	C₄×#64527	—	2	4	no	—
15	#11926597	C₂²	1	2	yes	—
16	#11926271	—	2	4	no	—
17	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
20	C₁₉×#336	—	2	2	no	—
21	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
22	C₂×#64541	—	2	2	no	—
23	C₂²×C₈×C₁₉	—	2	1	no	—
24	C₂²×C₈×C₁₉	D₄	1	2	yes	—
25	C₄×Q₈×C₁₉	—	2	2	no	—
26	C₄×Q₈×C₁₉	—	2	2	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₂×C₄²×C₁₉	—	2	1	no	—
30	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
31	C₂×#64527	—	2	4	no	—
32	#10597376	—	2	2	no	—
33	#10597376	—	2	2	no	—
34	C₂×Dic₇₆	—	2	2	no	—
35	#10597350	—	4	4	no	—
36	#10597350	—	4	4	no	—
37	C₂×D₁₅₂	—	2	2	no	—
38	C₂×#64516	—	2	4	no	—
39	#10597321	—	2	2	no	—
40	#10597320	D₄	1	2	yes	—
41	C₄×D₇₆	—	2	2	no	—
42	C₄×D₇₆	—	2	2	no	—
43	#10597315	D₄	1	2	yes	—
44	C₁₉×C₄⋊C₈	—	2	2	no	—
45	C₁₉×#97	—	2	2	no	—
46	#10597292	—	2	4	no	—
47	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
48	#10597266	—	2	4	no	—
49	#10597265	—	2	4	no	—
50	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
51	C₄×C₁₉⋊C₈	D₄	1	4	yes	—
52	C₂×Q₈×C₁₉	—	2	2	no	—
53	C₂×Q₈×C₁₉	—	4	2	no	—
54	C₂²×C₄×C₁₉	—	2	1	no	—
55	C₂²×C₄×C₁₉	—	2	1	no	—
56	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
59	C₂×C₂²⋊D₁₉	—	4	2	no	—
60	#64541	—	4	4	no	—
61	#64541	—	4	4	no	—
62	C₂×D₇₆	—	2	2	no	—
63	C₂×D₇₆	—	2	2	no	—
64	C₂×D₇₆	—	2	2	no	—
65	C₂×C₄×D₁₉	—	4	2	no	—
66	C₂×Dic₃₈	—	2	2	no	—
67	C₂×C₈×C₁₉	—	2	2	no	—
68	C₂×C₈×C₁₉	—	2	2	no	—
69	C₂×C₈×C₁₉	—	4	1	no	—
70	C₂×C₈×C₁₉	—	4	2	no	—
71	C₂×C₈×C₁₉	SD₁₆	1	4	yes	complemented
72	C₄⋊C₄×C₁₉	—	2	2	no	—
73	C₄⋊C₄×C₁₉	—	4	2	no	—
74	C₄²×C₁₉	—	4	1	no	—
75	C₄²×C₁₉	—	4	1	no	—
76	C₄²×C₁₉	C₂×D₄	1	2	yes	—
77	C₄²×C₁₉	C₂×D₄	1	2	yes	—
78	#64527	—	4	8	no	—
79	(C₂×D₁₉)⋊C₄	—	4	2	no	—
80	(C₂×D₁₉)⋊C₄	—	4	2	no	—
81	C₄⋊Dic₁₉	—	2	2	no	—
82	C₄⋊Dic₁₉	—	2	2	no	—
83	C₂×C₁₉⋊C₈	—	2	4	no	—
84	Dic₇₆	—	4	4	no	—
85	D₁₅₂	—	4	4	no	—
86	#64516	—	4	8	no	—
87	#10034	—	19	1	no	maximal, Sylow
88	C₂³×C₁₉	#121	1	1	yes	characteristic
89	C₂²×D₁₉	—	4	2	no	—
90	Q₈×C₁₉	—	2	4	no	—
91	Q₈×C₁₉	—	4	2	no	—
92	C₂×C₄×C₁₉	—	2	2	no	—
93	C₂×C₄×C₁₉	—	4	1	no	—
94	C₂×C₄×C₁₉	—	4	1	no	—
95	C₂×C₄×C₁₉	—	4	1	no	—
96	C₂×C₄×C₁₉	—	4	1	no	—
97	C₂×C₄×C₁₉	—	4	2	no	—
98	C₂×C₄×C₁₉	—	4	1	no	—
99	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
100	C₂×C₄×C₁₉	#120	1	2	yes	—
101	C₂×C₄×C₁₉	#121	1	2	yes	—
102	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
103	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
104	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
105	C₂²⋊D₁₉	—	8	4	no	—
106	C₂×Dic₁₉	—	4	2	no	—
107	D₇₆	—	4	4	no	—
108	D₇₆	—	4	4	no	—
109	D₇₆	—	4	4	no	—
110	C₄×D₁₉	—	8	2	no	—
111	C₄×D₁₉	—	8	2	no	—
112	Dic₃₈	—	4	4	no	—
113	C₈×C₁₉	—	2	4	no	—
114	C₈×C₁₉	—	8	1	no	—
115	C₁₉⋊C₈	—	4	4	no	—
116	#3150	—	19	1	no	—
117	#3103	—	19	2	no	—
118	#1985	D₁₉	1	1	yes	characteristic, complemented
119	#1480	—	19	2	no	—
120	#1275	—	19	1	no	—
121	C₂²×C₁₉	—	2	1	no	—
122	C₂²×C₁₉	—	2	1	no	—
123	C₂²×C₁₉	#392	1	1	yes	characteristic
124	C₂²×C₁₉	#460	1	2	yes	—
125	C₂×D₁₉	—	8	2	no	—
126	C₂×D₁₉	—	8	2	no	—
127	C₂×D₁₉	—	8	2	no	—
128	C₄×C₁₉	—	2	2	no	—
129	C₄×C₁₉	—	2	2	no	—
130	C₄×C₁₉	—	4	2	no	—
131	C₄×C₁₉	—	8	1	no	—
132	C₄×C₁₉	#450	1	2	yes	—
133	C₄×C₁₉	#492	1	1	yes	characteristic
134	C₄×C₁₉	#496	1	1	yes	characteristic
135	Dic₁₉	—	8	2	no	—
136	C₂×#135	—	38	2	no	—
137	#532	—	19	2	no	—
138	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
139	#497	—	38	2	no	—
140	#496	—	38	2	no	—
141	#481	—	38	2	no	—
142	#475	—	38	2	no	—
143	#460	—	38	2	no	—
144	#448	—	38	2	no	—
145	C₄×SD₁₆	—	38	4	no	—
146	#431	—	19	2	no	—
147	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
148	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
149	#336	—	2	2	no	—
150	D₄⋊C₈	—	38	4	no	—
151	C₂×C₁₉	—	2	2	no	—
152	C₂×C₁₉	#2010	1	1	yes	characteristic
153	C₂×C₁₉	#2014	1	1	yes	characteristic
154	C₂×C₁₉	#2017	1	1	yes	characteristic
155	D₁₉	—	16	2	no	—
156	C₂×#41	—	38	2	no	—
157	C₂²×Q₈	D₇₆	1	1	yes	characteristic
158	#135	—	76	4	no	—
159	#135	—	76	4	no	—
160	C₂×Q₁₆	—	38	2	no	—
161	C₂×SD₁₆	—	38	4	no	—
162	C₂×SD₁₆	—	38	4	no	—
163	C₂×D₈	—	38	2	no	—
164	C₂²×C₈	—	2	1	no	—
165	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
166	C₄⋊Q₈	—	19	2	no	—
167	#127	—	19	2	no	—
168	#124	—	38	2	no	—
169	#121	—	38	2	no	—
170	#121	—	38	2	no	—
171	C₄×Q₈	—	2	2	no	—
172	C₄×Q₈	—	2	2	no	—
173	C₄×D₄	—	38	2	no	—
174	C₄×D₄	—	38	2	no	—
175	C₂×C₄⋊C₄	—	2	1	no	—
176	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
177	C₂×C₄²	—	2	1	no	—
178	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
179	#106	—	38	4	no	—
180	C₄⋊C₈	—	2	2	no	—
181	C₄⋊C₈	—	38	2	no	—
182	#103	—	38	4	no	—
183	#102	—	38	4	no	—
184	C₂²⋊C₈	—	38	2	no	—
185	#97	—	2	2	no	—
186	C₄×C₈	—	19	4	no	—
187	C₁₉	#10034	1	1	yes	characteristic, complemented, Sylow
188	#41	—	76	4	no	—
189	#41	—	76	4	no	—
190	C₂×Q₈	—	2	2	no	—
191	C₂×Q₈	—	4	2	no	—
192	C₂×Q₈	—	38	2	no	—
193	C₂×D₄	—	38	2	no	—
194	C₂×D₄	—	38	2	no	—
195	C₂×D₄	—	38	2	no	—
196	C₂×D₄	—	76	2	no	—
197	C₂²×C₄	—	2	1	no	—
198	C₂²×C₄	—	2	1	no	—
199	C₂²×C₄	—	76	2	no	—
200	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
201	C₂²×C₄	#64541	1	1	yes	characteristic
202	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
203	Q₁₆	—	76	4	no	—
204	SD₁₆	—	76	8	no	—
205	SD₁₆	—	76	8	no	—
206	D₈	—	76	4	no	—
207	C₂×C₈	—	2	2	no	—
208	C₂×C₈	—	2	2	no	—
209	C₂×C₈	—	4	1	no	—
210	C₂×C₈	—	4	2	no	—
211	C₂×C₈	—	38	4	no	—
212	C₂×C₈	#64527	1	4	yes	complemented
213	C₄⋊C₄	—	2	2	no	—
214	C₄⋊C₄	—	4	2	no	—
215	C₄⋊C₄	—	38	2	no	—
216	C₄⋊C₄	—	38	2	no	—
217	C₂²⋊C₄	—	76	2	no	—
218	C₂²⋊C₄	—	76	2	no	—
219	C₄²	—	4	1	no	—
220	C₄²	—	4	1	no	—
221	C₄²	D₄×D₁₉	1	2	yes	—
222	C₄²	D₄×D₁₉	1	2	yes	—
223	C₂³	—	76	2	no	—
224	C₂³	#10597376	1	1	yes	characteristic
225	Q₈	—	2	4	no	—
226	Q₈	—	4	2	no	—
227	Q₈	—	76	4	no	—
228	D₄	—	76	4	no	—
229	D₄	—	76	4	no	—
230	D₄	—	76	4	no	—
231	D₄	—	152	4	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	4	1	no	—
234	C₂×C₄	—	4	1	no	—
235	C₂×C₄	—	4	1	no	—
236	C₂×C₄	—	4	1	no	—
237	C₂×C₄	—	4	2	no	—
238	C₂×C₄	—	4	1	no	—
239	C₂×C₄	—	76	2	no	—
240	C₂×C₄	—	152	2	no	—
241	C₂×C₄	—	152	2	no	—
242	C₂×C₄	#10597328	1	2	yes	—
243	C₂×C₄	#10597330	1	2	yes	—
244	C₂×C₄	#10597383	1	1	yes	characteristic
245	C₂×C₄	#10597386	1	1	yes	characteristic
246	C₂×C₄	C₂×#64527	1	2	yes	—
247	C₂×C₄	#10597395	1	2	yes	—
248	C₈	—	2	4	no	—
249	C₈	—	8	1	no	—
250	C₈	—	76	4	no	—
251	C₂²	—	2	1	no	—
252	C₂²	—	2	1	no	—
253	C₂²	—	152	2	no	—
254	C₂²	—	152	2	no	—
255	C₂²	—	152	2	no	—
256	C₂²	#11926453	1	1	yes	characteristic
257	C₂²	#11926744	1	2	yes	—
258	C₄	—	2	2	no	—
259	C₄	—	2	2	no	—
260	C₄	—	4	2	no	—
261	C₄	—	8	1	no	—
262	C₄	—	152	2	no	—
263	C₄	#11926694	1	2	yes	—
264	C₄	#11926918	1	1	yes	characteristic
265	C₄	#11926934	1	1	yes	characteristic
266	C₂	—	2	2	no	—
267	C₂	—	304	2	no	—
268	C₂	#14564702	1	1	yes	characteristic
269	C₂	#14564722	1	1	yes	characteristic
270	C₂	#14564739	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14574081

C₂

yes

maximal, characteristic

#14573666

C₂

yes

maximal, complemented

#14562033

C₂

yes

maximal, complemented

#14561466

C₂

yes

maximal, characteristic, complemented

C₁₉×#1985

C₂

yes

maximal, characteristic, complemented

C₂×#10597350

—

#11927094

C₂²

yes

—

—

—

—

—

—

—

—

C₂²

yes

—

#11926271

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂×C₁₉×#97

C₂²

yes

characteristic

C₁₉×#336

—

C₂²×Q₈×C₁₉

D₄

yes

characteristic

C₂×#64541

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

C₂×Dic₇₆

—

#10597350

—

#10597350

—

C₂×D₁₅₂

—

C₂×#64516

—

#10597321

—

#10597320

D₄

yes

—

C₄×D₇₆

—

C₄×D₇₆

—

#10597315

D₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×#97

—

#10597292

—

C₂²⋊(C₁₉⋊C₈)

—

#10597266

—

#10597265

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂×C₂²⋊D₁₉

—

#64541

—

#64541

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

SD₁₆

yes

complemented

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

#64527

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

Dic₇₆

—

D₁₅₂

—

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#120

yes

characteristic

100

C₂×C₄×C₁₉

#120

yes

—

101

C₂×C₄×C₁₉

#121

yes

—

102

C₂×C₄×C₁₉

#127

yes

characteristic

103

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

104

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

105

C₂²⋊D₁₉

—

106

C₂×Dic₁₉

—

107

D₇₆

—

108

D₇₆

—

109

D₇₆

—

110

C₄×D₁₉

—

111

C₄×D₁₉

—

112

Dic₃₈

—

113

C₈×C₁₉

—

114

C₈×C₁₉

—

115

C₁₉⋊C₈

—

116

#3150

—

117

#3103

—

118

#1985

D₁₉

yes

characteristic, complemented

119

#1480

—

120

#1275

—

121

C₂²×C₁₉

—

122

C₂²×C₁₉

—

123

C₂²×C₁₉

#392

yes

characteristic

124

C₂²×C₁₉

#460

yes

—

125

C₂×D₁₉

—

126

C₂×D₁₉

—

127

C₂×D₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

#450

yes

—

133

C₄×C₁₉

#492

yes

characteristic

134

C₄×C₁₉

#496

yes

characteristic

135

Dic₁₉

—

136

C₂×#135

—

137

#532

—

138

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

139

#497

—

140

#496

—

141

#481

—

142

#475

—

143

#460

—

144

#448

—

145

C₄×SD₁₆

—

146

#431

—

147

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

148

C₂×#97

C₂×D₁₉

yes

characteristic

149

#336

—

150

D₄⋊C₈

—

151

C₂×C₁₉

—

152

C₂×C₁₉

#2010

yes

characteristic

153

C₂×C₁₉

#2014

yes

characteristic

154

C₂×C₁₉

#2017

yes

characteristic

155

D₁₉

—

156

C₂×#41

—

157

C₂²×Q₈

D₇₆

yes

characteristic

158

#135

—

159

#135

—

160

C₂×Q₁₆

—

161

C₂×SD₁₆

—

162

C₂×SD₁₆

—

163

C₂×D₈

—

164

C₂²×C₈

—

165

C₂²×C₈

C₂²⋊D₁₉

yes

—

166

C₄⋊Q₈

—

167

#127

—

168

#124

—

169

#121

—

170

#121

—

171

C₄×Q₈

—

172

C₄×Q₈

—

173

C₄×D₄

—

174

C₄×D₄

—

175

C₂×C₄⋊C₄

—

176

C₂×C₄⋊C₄

D₇₆

yes

characteristic

177

C₂×C₄²

—

178

C₂×C₄²

C₂²×D₁₉

yes

characteristic

179

#106

—

180

C₄⋊C₈

—

181

C₄⋊C₈

—

182

#103

—

183

#102

—

184

C₂²⋊C₈

—

185

#97

—

186

C₄×C₈

—

187

C₁₉

#10034

yes

characteristic, complemented, Sylow

188

#41

—

189

#41

—

190

C₂×Q₈

—

191

C₂×Q₈

—

192

C₂×Q₈

—

193

C₂×D₄

—

194

C₂×D₄

—

195

C₂×D₄

—

196

C₂×D₄

—

197

C₂²×C₄

—

198

C₂²×C₄

—

199

C₂²×C₄

—

200

C₂²×C₄

C₂×D₇₆

yes

characteristic

201

C₂²×C₄

#64541

yes

characteristic

202

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

203

Q₁₆

—

204

SD₁₆

—

205

SD₁₆

—

206

D₈

—

207

C₂×C₈

—

208

C₂×C₈

—

209

C₂×C₈

—

210

C₂×C₈

—

211

C₂×C₈

—

212

C₂×C₈

#64527

yes

complemented

213

C₄⋊C₄

—

214

C₄⋊C₄

—

215

C₄⋊C₄

—

216

C₄⋊C₄

—

217

C₂²⋊C₄

—

218

C₂²⋊C₄

—

219

C₄²

—

220

C₄²

—

221

C₄²

D₄×D₁₉

yes

—

222

C₄²

D₄×D₁₉

yes

—

223

C₂³

—

224

C₂³

#10597376

yes

characteristic

225

Q₈

—

226

Q₈

—

227

Q₈

—

228

D₄

—

229

D₄

—

230

D₄

—

231

D₄

—

152

—

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

—

152

—

241

C₂×C₄

—

152

—

242

C₂×C₄

#10597328

yes

—

243

C₂×C₄

#10597330

yes

—

244

C₂×C₄

#10597383

yes

characteristic

245

C₂×C₄

#10597386

yes

characteristic

246

C₂×C₄

C₂×#64527

yes

—

247

C₂×C₄

#10597395

yes

—

248

C₈

—

249

C₈

—

250

C₈

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

152

—

254

C₂²

—

152

—

255

C₂²

—

152

—

256

C₂²

#11926453

yes

characteristic

257

C₂²

#11926744

yes

—

258

C₄

—

259

C₄

—

260

C₄

—

261

C₄

—

262

C₄

—

152

—

263

C₄

#11926694

yes

—

264

C₄

#11926918

yes

characteristic

265

C₄

#11926934

yes

characteristic

266

C₂

—

267

C₂

—

304

—

268

C₂

#14564702

yes

characteristic

269

C₂

#14564722

yes

characteristic

270

C₂

#14564739

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597386
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1985	C₂
socle	C₂²×C₁₉	#392
prime radical	#14574081	C₂
hypercenter	#1985	D₁₉
hypocenter	C₁₉	#10034
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1985

subgroup

G/H

center

C₂×C₄

#10597386

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1985

C₂

C₂²×C₁₉

C₂

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1985

N	H ≅ G/N	type
2. #14573666	C₂	semidirect
3. #14562033	C₂	semidirect
4. #14561466	C₂	semidirect
5. C₁₉×#1985	C₂	semidirect
71. C₂×C₈×C₁₉	SD₁₆	semidirect
118. #1985	D₁₉	semidirect
187. C₁₉	#10034	semidirect
212. C₂×C₈	#64527	semidirect

H ≅ G/N

type

2. #14573666

C₂

semidirect

3. #14562033

C₂

semidirect

4. #14561466

C₂

semidirect

5. C₁₉×#1985

C₂

semidirect

71. C₂×C₈×C₁₉

SD₁₆

semidirect

118. #1985

D₁₉

semidirect

187. C₁₉

#10034

semidirect

212. C₂×C₈

#64527

semidirect

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

subgroup	index
#14574081	2
#14573666	2
#14562033	2
#14561466	2
C₁₉×#1985	2
#10034	19

subgroup

index

C₁₉×#1985

Subgroups — #18083517

Conjugacy classes of subgroups

Complements

Maximal subgroups