Group #18083518 — subgroups

Subgroups — #18083518

Order 4864.

584 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 105 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	#14573667	C₂	1	2	yes	maximal, complemented
3	#14564575	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562035	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1275	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597350	—	2	2	no	—
7	#11927094	C₂²	1	2	yes	—
8	C₂×C₄×Dic₃₈	C₂²	1	1	yes	characteristic
9	#11926938	—	2	2	no	—
10	#11926933	—	2	2	no	—
11	#11926863	—	2	2	no	—
12	#11926830	—	2	2	no	—
13	#11926745	—	2	2	no	—
14	#11926685	—	2	2	no	—
15	C₄×#64516	—	2	4	no	—
16	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
17	#11926298	—	2	2	no	—
18	#11926273	—	2	4	no	—
19	C₁₉×#431	C₂²	1	2	yes	—
20	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
21	C₂×#64541	—	2	2	no	—
22	C₂²×Dic₃₈	D₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₉	D₄	1	2	yes	—
24	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
25	#10597376	—	2	2	no	—
26	#10597376	—	2	2	no	—
27	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
28	C₂×Dic₁₉⋊C₄	—	2	1	no	—
29	C₂×C₄×Dic₁₉	—	2	1	no	—
30	C₂²×C₁₉⋊C₈	—	2	1	no	—
31	C₂×Dic₇₆	—	2	2	no	—
32	#10597350	—	4	4	no	—
33	#10597350	—	4	4	no	—
34	C₂×D₁₅₂	—	2	2	no	—
35	C₂×#64516	—	2	4	no	—
36	C₂×#64516	—	2	4	no	—
37	#10597321	—	2	2	no	—
38	#10597320	D₄	1	2	yes	—
39	C₄×D₇₆	—	2	2	no	—
40	C₄×D₇₆	—	2	2	no	—
41	#10597315	D₄	1	2	yes	—
42	C₄×Dic₃₈	—	2	2	no	—
43	C₄×Dic₃₈	—	2	2	no	—
44	C₁₉×C₄⋊C₈	—	2	2	no	—
45	C₁₉×C₂²⋊C₈	—	2	2	no	—
46	C₁₉×#97	—	2	2	no	—
47	C₄×C₈×C₁₉	D₄	1	4	yes	—
48	#10597278	—	2	4	no	—
49	#10597274	—	2	4	no	—
50	#10597273	—	2	4	no	—
51	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
52	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
55	C₂×C₂²⋊D₁₉	—	4	2	no	—
56	C₂²×Dic₁₉	—	2	1	no	—
57	C₂²×Dic₁₉	—	2	1	no	—
58	#64541	—	4	4	no	—
59	#64541	—	4	4	no	—
60	C₂×D₇₆	—	2	2	no	—
61	C₂×D₇₆	—	2	2	no	—
62	C₂×D₇₆	—	2	2	no	—
63	C₂×C₄×D₁₉	—	4	2	no	—
64	C₂×Dic₃₈	—	2	2	no	—
65	C₂×Dic₃₈	—	2	2	no	—
66	C₂×Dic₃₈	—	4	2	no	—
67	C₂×C₈×C₁₉	—	2	2	no	—
68	C₂×C₈×C₁₉	—	2	2	no	—
69	C₂×C₈×C₁₉	—	2	4	no	—
70	C₂×C₈×C₁₉	SD₁₆	1	4	yes	complemented
71	C₄²×C₁₉	C₂×D₄	1	2	yes	—
72	C₄²×C₁₉	C₂×D₄	1	2	yes	—
73	(C₂×D₁₉)⋊C₄	—	4	2	no	—
74	(C₂×D₁₉)⋊C₄	—	4	2	no	—
75	C₄⋊Dic₁₉	—	2	2	no	—
76	C₄⋊Dic₁₉	—	2	2	no	—
77	C₄⋊Dic₁₉	—	2	2	no	—
78	Dic₁₉⋊C₄	—	4	2	no	—
79	C₄×Dic₁₉	—	4	1	no	—
80	C₄×Dic₁₉	—	4	1	no	—
81	C₂×C₁₉⋊C₈	—	4	1	no	—
82	C₂×C₁₉⋊C₈	—	4	2	no	—
83	Dic₇₆	—	4	4	no	—
84	D₁₅₂	—	4	4	no	—
85	#64516	—	4	8	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	C₂×C₄×C₁₉	—	4	1	no	—
91	C₂×C₄×C₁₉	—	4	1	no	—
92	C₂×C₄×C₁₉	#120	1	2	yes	—
93	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
94	C₂×C₄×C₁₉	#121	1	2	yes	—
95	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
96	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
97	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
98	C₂²⋊D₁₉	—	8	4	no	—
99	C₂×Dic₁₉	—	2	2	no	—
100	C₂×Dic₁₉	—	4	1	no	—
101	C₂×Dic₁₉	—	4	1	no	—
102	C₂×Dic₁₉	—	4	2	no	—
103	C₂×Dic₁₉	—	4	1	no	—
104	C₂×Dic₁₉	—	4	2	no	—
105	D₇₆	—	4	4	no	—
106	D₇₆	—	4	4	no	—
107	D₇₆	—	4	4	no	—
108	C₄×D₁₉	—	8	2	no	—
109	C₄×D₁₉	—	8	2	no	—
110	Dic₃₈	—	2	4	no	—
111	Dic₃₈	—	4	2	no	—
112	Dic₃₈	—	4	4	no	—
113	C₈×C₁₉	—	2	4	no	—
114	C₈×C₁₉	—	4	4	no	—
115	C₁₉⋊C₈	—	8	1	no	—
116	#3150	—	19	1	no	—
117	#3103	—	19	2	no	—
118	#1985	—	19	1	no	—
119	#1480	—	19	2	no	—
120	#1275	D₁₉	1	1	yes	characteristic, complemented
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	#450	1	2	yes	—
131	C₄×C₁₉	#492	1	1	yes	characteristic
132	C₄×C₁₉	#496	1	1	yes	characteristic
133	Dic₁₉	—	4	2	no	—
134	Dic₁₉	—	8	2	no	—
135	Dic₁₉	—	8	1	no	—
136	C₂×#135	—	38	2	no	—
137	#532	—	19	2	no	—
138	C₂×C₄×Q₈	—	19	1	no	—
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	C₂×D₁₉	1	2	yes	—
147	C₂×C₄⋊C₈	—	19	1	no	—
148	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
149	#336	—	38	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	—	19	1	no	—
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	—	38	1	no	—
165	C₂²×C₈	D₇₆	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	—	38	2	no	—
172	C₄×Q₈	—	38	2	no	—
173	C₄×D₄	—	38	2	no	—
174	C₄×D₄	—	38	2	no	—
175	C₂×C₄⋊C₄	—	19	1	no	—
176	C₂×C₄⋊C₄	—	38	1	no	—
177	C₂×C₄²	—	38	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	—	2	2	no	—
185	#97	—	2	2	no	—
186	C₄×C₈	D₇₆	1	4	yes	—
187	C₁₉	#10034	1	1	yes	characteristic, complemented, Sylow
188	#41	—	76	4	no	—
189	#41	—	76	4	no	—
190	C₂×Q₈	—	38	2	no	—
191	C₂×Q₈	—	38	2	no	—
192	C₂×Q₈	—	76	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	—	38	1	no	—
198	C₂²×C₄	—	38	1	no	—
199	C₂²×C₄	—	76	2	no	—
200	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
201	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
202	C₂²×C₄	#64545	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	—	2	4	no	—
210	C₂×C₈	—	76	1	no	—
211	C₂×C₈	—	76	2	no	—
212	C₂×C₈	#64516	1	4	yes	complemented
213	C₄⋊C₄	—	38	2	no	—
214	C₄⋊C₄	—	38	2	no	—
215	C₄⋊C₄	—	38	2	no	—
216	C₄⋊C₄	—	76	2	no	—
217	C₂²⋊C₄	—	76	2	no	—
218	C₂²⋊C₄	—	76	2	no	—
219	C₄²	—	76	1	no	—
220	C₄²	—	76	1	no	—
221	C₄²	C₂×D₇₆	1	2	yes	—
222	C₄²	D₄×D₁₉	1	2	yes	—
223	C₂³	—	76	2	no	—
224	C₂³	#10597341	1	1	yes	characteristic
225	Q₈	—	38	4	no	—
226	Q₈	—	76	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	—	4	1	no	—
233	C₂×C₄	—	4	1	no	—
234	C₂×C₄	—	38	2	no	—
235	C₂×C₄	—	76	1	no	—
236	C₂×C₄	—	76	1	no	—
237	C₂×C₄	—	76	2	no	—
238	C₂×C₄	—	76	1	no	—
239	C₂×C₄	—	76	2	no	—
240	C₂×C₄	—	152	2	no	—
241	C₂×C₄	—	152	2	no	—
242	C₂×C₄	#10597320	1	1	yes	characteristic
243	C₂×C₄	#10597328	1	2	yes	—
244	C₂×C₄	#10597328	1	1	yes	characteristic
245	C₂×C₄	#10597341	1	2	yes	—
246	C₂×C₄	C₂×#64516	1	2	yes	—
247	C₂×C₄	#10597354	1	2	yes	—
248	C₈	—	2	4	no	—
249	C₈	—	4	4	no	—
250	C₈	—	152	1	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	#11926454	1	1	yes	characteristic
257	C₂²	#11926745	1	2	yes	—
258	C₄	—	2	2	no	—
259	C₄	—	2	2	no	—
260	C₄	—	76	2	no	—
261	C₄	—	152	2	no	—
262	C₄	—	152	1	no	—
263	C₄	#11926697	1	2	yes	—
264	C₄	#11926917	1	1	yes	characteristic
265	C₄	#11926933	1	1	yes	characteristic
266	C₂	—	2	2	no	—
267	C₂	—	304	2	no	—
268	C₂	#14564703	1	1	yes	characteristic
269	C₂	#14564725	1	1	yes	characteristic
270	C₂	#14564740	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14574081

C₂

yes

maximal, characteristic

#14573667

C₂

yes

maximal, complemented

#14564575

C₂

yes

maximal, characteristic, complemented

#14562035

C₂

yes

maximal, complemented

C₁₉×#1275

C₂

yes

maximal, characteristic, complemented

C₂×#10597350

—

#11927094

C₂²

yes

—

C₂×C₄×Dic₃₈

C₂²

yes

—

—

—

—

—

—

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

#11926298

—

#11926273

—

C₁₉×#431

C₂²

yes

—

C₂×C₁₉×#97

C₂²

yes

characteristic

C₂×#64541

—

C₂²×Dic₃₈

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597376

—

#10597376

—

C₂×C₄⋊Dic₁₉

D₄

yes

characteristic

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₂×Dic₇₆

—

#10597350

—

#10597350

—

C₂×D₁₅₂

—

—

—

—

D₄

yes

—

C₄×D₇₆

—

C₄×D₇₆

—

#10597315

D₄

yes

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₄×C₈×C₁₉

D₄

yes

—

#10597278

—

#10597274

—

#10597273

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂×C₂²⋊D₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

#64541

—

#64541

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

SD₁₆

yes

complemented

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

Dic₇₆

—

D₁₅₂

—

—

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#120

yes

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#127

yes

characteristic

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

100

C₂×Dic₁₉

—

101

C₂×Dic₁₉

—

102

C₂×Dic₁₉

—

103

C₂×Dic₁₉

—

104

C₂×Dic₁₉

—

105

D₇₆

—

106

D₇₆

—

107

D₇₆

—

108

C₄×D₁₉

—

109

C₄×D₁₉

—

110

Dic₃₈

—

111

Dic₃₈

—

112

Dic₃₈

—

113

C₈×C₁₉

—

114

C₈×C₁₉

—

115

C₁₉⋊C₈

—

116

#3150

—

117

#3103

—

118

#1985

—

119

#1480

—

120

#1275

D₁₉

yes

characteristic, complemented

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

#450

yes

—

131

C₄×C₁₉

#492

yes

characteristic

132

C₄×C₁₉

#496

yes

characteristic

133

Dic₁₉

—

134

Dic₁₉

—

135

Dic₁₉

—

136

C₂×#135

—

137

#532

—

138

C₂×C₄×Q₈

—

139

#497

—

140

#496

—

141

#481

—

142

#475

—

143

#460

—

144

#448

—

145

C₄×SD₁₆

—

146

#431

C₂×D₁₉

yes

—

147

C₂×C₄⋊C₈

—

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

—

158

#135

—

159

#135

—

160

C₂×Q₁₆

—

161

C₂×SD₁₆

—

162

C₂×SD₁₆

—

163

C₂×D₈

—

164

C₂²×C₈

—

165

C₂²×C₈

D₇₆

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

—

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

D₇₆

yes

—

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

D₄×D₁₉

yes

characteristic

202

C₂²×C₄

#64545

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

#64516

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

C₂×D₇₆

yes

—

222

C₄²

D₄×D₁₉

yes

—

223

C₂³

—

224

C₂³

#10597341

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

#10597320

yes

characteristic

243

C₂×C₄

#10597328

yes

—

244

C₂×C₄

#10597328

yes

characteristic

245

C₂×C₄

#10597341

yes

—

246

C₂×C₄

C₂×#64516

yes

—

247

C₂×C₄

#10597354

yes

—

248

C₈

—

249

C₈

—

250

C₈

—

152

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

152

—

254

C₂²

—

152

—

255

C₂²

—

152

—

256

C₂²

#11926454

yes

characteristic

257

C₂²

#11926745

yes

—

258

C₄

—

259

C₄

—

260

C₄

—

261

C₄

—

152

—

262

C₄

—

152

—

263

C₄

#11926697

yes

—

264

C₄

#11926917

yes

characteristic

265

C₄

#11926933

yes

characteristic

266

C₂

—

267

C₂

—

304

—

268

C₂

#14564703

yes

characteristic

269

C₂

#14564725

yes

characteristic

270

C₂

#14564740

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597320
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1275	C₂
socle	C₂²×C₁₉	#392
prime radical	#14574081	C₂
hypercenter	#1275	D₁₉
hypocenter	C₁₉	#10034
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1275

subgroup

G/H

center

C₂×C₄

#10597320

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1275

C₂

C₂²×C₁₉

C₂

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1275

N	H ≅ G/N	type
2. #14573667	C₂	semidirect
3. #14564575	C₂	semidirect
4. #14562035	C₂	semidirect
5. C₁₉×#1275	C₂	semidirect
70. C₂×C₈×C₁₉	SD₁₆	semidirect
120. #1275	D₁₉	semidirect
187. C₁₉	#10034	semidirect
212. C₂×C₈	#64516	semidirect

H ≅ G/N

type

2. #14573667

C₂

semidirect

3. #14564575

C₂

semidirect

4. #14562035

C₂

semidirect

5. C₁₉×#1275

C₂

semidirect

70. C₂×C₈×C₁₉

SD₁₆

semidirect

120. #1275

D₁₉

semidirect

187. C₁₉

#10034

semidirect

212. C₂×C₈

#64516

semidirect

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

subgroup	index
#14574081	2
#14573667	2
#14564575	2
#14562035	2
C₁₉×#1275	2
#10034	19

subgroup

index

C₁₉×#1275

Subgroups — #18083518

Conjugacy classes of subgroups

Complements

Maximal subgroups