Group #18081745 — subgroups

Subgroups — #18081745

Order 4864.

392 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 115 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	C₄×#10597276	C₂	1	1	yes	maximal, characteristic
2	#14562230	C₂	1	2	yes	maximal
3	#14562056	C₂	1	2	yes	maximal
4	#14561924	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#3170	C₂	1	1	yes	maximal, characteristic
6	#11926597	C₂²	1	1	yes	characteristic
7	C₂×#10597276	—	2	1	no	—
8	C₄×#64520	C₂²	1	2	yes	—
9	C₄×#64520	C₂²	1	1	yes	characteristic
10	#11926309	—	2	1	no	—
11	#11926286	—	2	4	no	—
12	Q₈⋊(C₁₉⋊C₈)	—	2	4	no	—
13	#11926266	—	2	1	no	—
14	#11926265	—	2	1	no	—
15	C₁₉×#533	C₂²	1	2	yes	—
16	C₁₉×#500	C₄	1	1	yes	characteristic
17	C₁₉×#494	C₄	1	1	yes	characteristic
18	C₁₉×#487	C₄	1	2	yes	—
19	C₁₉×#467	—	2	1	no	—
20	C₁₉×#467	—	2	1	no	—
21	C₄×Q₁₆×C₁₉	—	2	1	no	—
22	C₄×Q₁₆×C₁₉	—	2	1	no	—
23	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×Q₁₆×C₁₉	—	2	1	no	—
25	C₂×Q₁₆×C₁₉	—	2	1	no	—
26	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
28	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
29	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
30	C₁₉×#125	—	2	2	no	—
31	C₁₉×C₂²⋊Q₈	—	2	2	no	—
32	C₁₉×C₂²⋊Q₈	—	2	2	no	—
33	C₄×Q₈×C₁₉	—	2	2	no	—
34	C₄×Q₈×C₁₉	—	2	2	no	—
35	C₁₉×#117	—	2	2	no	—
36	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
37	C₂×#64520	—	2	1	no	—
38	C₂×#64520	—	2	2	no	—
39	C₁₉×#107	—	2	1	no	—
40	C₁₉×#107	—	2	1	no	—
41	C₁₉×#103	—	2	2	no	—
42	C₁₉×#103	—	2	2	no	—
43	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
45	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
46	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
47	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
48	#10597276	—	2	4	no	—
49	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
50	#10597260	—	2	2	no	—
51	#10597260	D₄	1	2	yes	—
52	C₄×C₁₉⋊C₈	—	2	1	no	—
53	C₄×C₁₉⋊C₈	—	2	1	no	—
54	C₄×C₁₉⋊C₈	—	2	2	no	—
55	C₂×Q₈×C₁₉	—	2	2	no	—
56	C₂×Q₈×C₁₉	—	2	2	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	Q₁₆×C₁₉	—	4	2	no	—
61	Q₁₆×C₁₉	—	4	2	no	—
62	C₂×C₈×C₁₉	—	2	2	no	—
63	C₂×C₈×C₁₉	—	4	1	no	—
64	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
65	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
68	C₄⋊C₄×C₁₉	—	2	2	no	—
69	C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₄⋊C₄×C₁₉	—	2	2	no	—
71	C₄⋊C₄×C₁₉	—	2	2	no	—
72	C₄⋊C₄×C₁₉	—	4	2	no	—
73	C₄⋊C₄×C₁₉	—	4	2	no	—
74	C₂²⋊C₄×C₁₉	—	4	2	no	—
75	C₄²×C₁₉	—	4	2	no	—
76	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
77	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
80	#64520	—	2	4	no	—
81	#64520	—	4	2	no	—
82	#64520	—	4	2	no	—
83	C₂×C₁₉⋊C₈	—	2	2	no	—
84	C₂×C₁₉⋊C₈	—	2	2	no	—
85	C₂×C₁₉⋊C₈	—	4	2	no	—
86	#9727	—	19	1	no	maximal, Sylow
87	C₂³×C₁₉	#124	1	1	yes	characteristic
88	Q₈×C₁₉	—	4	2	no	—
89	Q₈×C₁₉	—	4	2	no	—
90	Q₈×C₁₉	—	4	4	no	—
91	C₂×C₄×C₁₉	—	2	1	no	—
92	C₂×C₄×C₁₉	—	2	1	no	—
93	C₂×C₄×C₁₉	—	2	2	no	—
94	C₂×C₄×C₁₉	—	2	2	no	—
95	C₂×C₄×C₁₉	—	4	2	no	—
96	C₂×C₄×C₁₉	—	4	2	no	—
97	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
99	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
100	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
101	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
102	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
103	C₈×C₁₉	—	2	1	no	—
104	C₈×C₁₉	—	2	1	no	—
105	C₈×C₁₉	—	2	1	no	—
106	C₈×C₁₉	#104	1	2	yes	—
107	C₁₉⋊C₈	—	4	2	no	—
108	C₁₉⋊C₈	—	4	4	no	—
109	C₁₉⋊C₈	—	4	2	no	—
110	#3170	D₁₉	1	1	yes	characteristic
111	C₄×#108	—	19	1	no	—
112	#1526	—	19	2	no	—
113	#1485	—	19	2	no	—
114	#1451	—	19	1	no	—
115	C₂²×C₁₉	—	2	1	no	—
116	C₂²×C₁₉	—	2	1	no	—
117	C₂²×C₁₉	—	2	1	no	—
118	C₂²×C₁₉	#390	1	1	yes	characteristic
119	C₄×C₁₉	—	2	1	no	—
120	C₄×C₁₉	—	2	1	no	—
121	C₄×C₁₉	—	2	1	no	—
122	C₄×C₁₉	—	8	2	no	—
123	C₄×C₁₉	—	8	2	no	—
124	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
125	C₄×C₁₉	#421	1	1	yes	characteristic
126	C₄×C₁₉	#444	1	2	yes	—
127	C₄×C₁₉	#473	1	2	yes	—
128	#533	C₂×D₁₉	1	2	yes	—
129	#500	Dic₁₉	1	1	yes	characteristic
130	#494	Dic₁₉	1	1	yes	characteristic
131	#487	Dic₁₉	1	2	yes	—
132	#467	—	2	1	no	—
133	#467	—	2	1	no	—
134	C₄×Q₁₆	—	2	1	no	—
135	C₄×Q₁₆	—	2	1	no	—
136	#431	—	19	1	no	—
137	C₂×#108	—	38	1	no	—
138	C₄×M₁₆	—	19	1	no	—
139	C₄×M₁₆	—	19	2	no	—
140	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
141	#341	—	38	1	no	—
142	#330	—	38	4	no	—
143	Q₈⋊C₈	—	38	4	no	—
144	#322	—	38	1	no	—
145	#322	—	38	1	no	—
146	C₂×C₁₉	—	4	1	no	—
147	C₂×C₁₉	#1975	1	1	yes	characteristic
148	C₂×C₁₉	#1979	1	1	yes	characteristic
149	C₂×C₁₉	#1980	1	1	yes	characteristic
150	C₂×Q₁₆	—	2	1	no	—
151	C₂×Q₁₆	—	2	1	no	—
152	C₂×M₁₆	—	38	1	no	—
153	C₂×M₁₆	—	38	2	no	—
154	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
155	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
156	C₄⋊Q₈	C₂×Dic₁₉	1	2	yes	—
157	C₄⋊Q₈	C₂×Dic₁₉	1	2	yes	—
158	#125	—	2	2	no	—
159	C₂²⋊Q₈	—	2	2	no	—
160	C₂²⋊Q₈	—	2	2	no	—
161	C₄×Q₈	—	2	2	no	—
162	C₄×Q₈	—	2	2	no	—
163	#117	—	2	2	no	—
164	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
165	#108	—	38	4	no	—
166	#107	—	2	1	no	—
167	#107	—	2	1	no	—
168	C₄⋊C₈	—	19	2	no	—
169	#103	—	2	2	no	—
170	#103	—	2	2	no	—
171	C₂²⋊C₈	—	38	1	no	—
172	#97	—	19	2	no	—
173	#97	—	38	2	no	—
174	C₄×C₈	—	38	2	no	—
175	C₄×C₈	—	38	1	no	—
176	C₄×C₈	—	38	1	no	—
177	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
178	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
179	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
180	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
181	C₁₉	#9727	1	1	yes	characteristic, complemented, Sylow
182	C₂×Q₈	—	2	2	no	—
183	C₂×Q₈	—	2	2	no	—
184	C₂²×C₄	#64543	1	1	yes	characteristic
185	C₂²×C₄	#64543	1	1	yes	characteristic
186	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
187	Q₁₆	—	4	2	no	—
188	Q₁₆	—	4	2	no	—
189	M₁₆	—	38	4	no	—
190	M₁₆	—	76	2	no	—
191	M₁₆	—	76	2	no	—
192	C₂×C₈	—	2	2	no	—
193	C₂×C₈	—	4	1	no	—
194	C₂×C₈	—	38	2	no	—
195	C₂×C₈	—	38	2	no	—
196	C₂×C₈	—	76	2	no	—
197	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
198	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
199	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
200	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
201	C₄⋊C₄	—	2	2	no	—
202	C₄⋊C₄	—	2	2	no	—
203	C₄⋊C₄	—	2	2	no	—
204	C₄⋊C₄	—	2	2	no	—
205	C₄⋊C₄	—	4	2	no	—
206	C₄⋊C₄	—	4	2	no	—
207	C₂²⋊C₄	—	4	2	no	—
208	C₄²	—	4	2	no	—
209	C₄²	D₄×D₁₉	1	1	yes	characteristic
210	C₄²	D₄×D₁₉	1	1	yes	characteristic
211	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
212	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
213	C₂³	#10597382	1	1	yes	characteristic
214	Q₈	—	4	2	no	—
215	Q₈	—	4	2	no	—
216	Q₈	—	4	4	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	2	2	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	4	2	no	—
222	C₂×C₄	—	4	2	no	—
223	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
224	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
225	C₂×C₄	#10597384	1	1	yes	characteristic
226	C₂×C₄	#10597384	1	1	yes	characteristic
227	C₂×C₄	#10597386	1	1	yes	characteristic
228	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
229	C₈	—	2	1	no	—
230	C₈	—	2	1	no	—
231	C₈	—	2	1	no	—
232	C₈	—	76	2	no	—
233	C₈	—	76	4	no	—
234	C₈	—	76	2	no	—
235	C₈	#10597294	1	2	yes	—
236	C₂²	—	2	1	no	—
237	C₂²	—	2	1	no	—
238	C₂²	—	2	1	no	—
239	C₂²	#11926447	1	1	yes	characteristic
240	C₄	—	2	1	no	—
241	C₄	—	2	1	no	—
242	C₄	—	2	1	no	—
243	C₄	—	8	2	no	—
244	C₄	—	8	2	no	—
245	C₄	C₂×#10597294	1	1	yes	characteristic
246	C₄	#11926561	1	1	yes	characteristic
247	C₄	#11926666	1	2	yes	—
248	C₄	#11926816	1	2	yes	—
249	C₂	—	4	1	no	—
250	C₂	#14564529	1	1	yes	characteristic
251	C₂	#14564551	1	1	yes	characteristic
252	C₂	#14564555	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#10597276

C₂

yes

maximal, characteristic

#14562230

C₂

yes

maximal

#14562056

C₂

yes

maximal

#14561924

C₂

yes

maximal, characteristic

C₁₉×#3170

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

characteristic

C₂×#10597276

—

C₄×#64520

C₂²

yes

—

C₄×#64520

C₂²

yes

characteristic

#11926309

—

#11926286

—

Q₈⋊(C₁₉⋊C₈)

—

#11926266

—

#11926265

—

C₁₉×#533

C₂²

yes

—

C₁₉×#500

C₄

yes

characteristic

C₁₉×#494

C₄

yes

characteristic

C₁₉×#487

C₄

yes

—

C₁₉×#467

—

C₁₉×#467

—

C₄×Q₁₆×C₁₉

—

C₄×Q₁₆×C₁₉

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₁₉×C₄⋊Q₈

C₂×C₄

yes

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

—

C₁₉×#125

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₁₉×#117

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₂×#64520

—

C₁₉×#107

—

C₁₉×#107

—

C₁₉×#103

—

C₁₉×#103

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₂²⋊(C₁₉⋊C₈)

—

#10597276

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

#10597260

—

#10597260

D₄

yes

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

C₂²×C₄×C₁₉

yes

C₂²×C₄×C₁₉

yes

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

—

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

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×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

100

C₂×C₄×C₁₉

#121

yes

characteristic

101

C₂×C₄×C₁₉

#121

yes

characteristic

102

C₂×C₄×C₁₉

#127

yes

characteristic

103

C₈×C₁₉

—

104

C₈×C₁₉

—

105

C₈×C₁₉

—

106

C₈×C₁₉

#104

yes

—

107

C₁₉⋊C₈

—

108

C₁₉⋊C₈

—

109

C₁₉⋊C₈

—

110

#3170

D₁₉

yes

characteristic

111

C₄×#108

—

112

#1526

—

113

#1485

—

114

#1451

—

115

C₂²×C₁₉

—

116

C₂²×C₁₉

—

117

C₂²×C₁₉

—

118

C₂²×C₁₉

#390

yes

characteristic

119

C₄×C₁₉

—

120

C₄×C₁₉

—

121

C₄×C₁₉

—

122

C₄×C₁₉

—

123

C₄×C₁₉

—

124

C₄×C₁₉

C₂×#104

yes

characteristic

125

C₄×C₁₉

#421

yes

characteristic

126

C₄×C₁₉

#444

yes

—

127

C₄×C₁₉

#473

yes

—

128

#533

C₂×D₁₉

yes

—

129

#500

Dic₁₉

yes

characteristic

130

#494

Dic₁₉

yes

characteristic

131

#487

Dic₁₉

yes

—

132

#467

—

133

#467

—

134

C₄×Q₁₆

—

135

C₄×Q₁₆

—

136

#431

—

137

C₂×#108

—

138

C₄×M₁₆

—

139

C₄×M₁₆

—

140

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

141

#341

—

142

#330

—

143

Q₈⋊C₈

—

144

#322

—

145

#322

—

146

C₂×C₁₉

—

147

C₂×C₁₉

#1975

yes

characteristic

148

C₂×C₁₉

#1979

yes

characteristic

149

C₂×C₁₉

#1980

yes

characteristic

150

C₂×Q₁₆

—

151

C₂×Q₁₆

—

152

C₂×M₁₆

—

153

C₂×M₁₆

—

154

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

155

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

156

C₄⋊Q₈

C₂×Dic₁₉

yes

—

157

C₄⋊Q₈

C₂×Dic₁₉

yes

—

158

#125

—

159

C₂²⋊Q₈

—

160

C₂²⋊Q₈

—

161

C₄×Q₈

—

162

C₄×Q₈

—

163

#117

—

164

C₂×C₄²

C₂²×D₁₉

yes

characteristic

165

#108

—

166

#107

—

167

#107

—

168

C₄⋊C₈

—

169

#103

—

170

#103

—

171

C₂²⋊C₈

—

172

#97

—

173

#97

—

174

C₄×C₈

—

175

C₄×C₈

—

176

C₄×C₈

—

177

C₄×C₈

C₂×Dic₁₉

yes

characteristic

178

C₄×C₈

C₂×Dic₁₉

yes

characteristic

179

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

180

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

181

C₁₉

#9727

yes

characteristic, complemented, Sylow

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂²×C₄

#64543

yes

characteristic

185

C₂²×C₄

#64543

yes

characteristic

186

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

187

Q₁₆

—

188

Q₁₆

—

189

M₁₆

—

190

M₁₆

—

191

M₁₆

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

198

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

199

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

200

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₂²⋊C₄

—

208

C₄²

—

209

C₄²

D₄×D₁₉

yes

characteristic

210

C₄²

D₄×D₁₉

yes

characteristic

211

C₄²

C₂²×Dic₁₉

yes

characteristic

212

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

213

C₂³

#10597382

yes

characteristic

214

Q₈

—

215

Q₈

—

216

Q₈

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

D₄×Dic₁₉

yes

characteristic

224

C₂×C₄

D₄×Dic₁₉

yes

characteristic

225

C₂×C₄

#10597384

yes

characteristic

226

C₂×C₄

#10597384

yes

characteristic

227

C₂×C₄

#10597386

yes

characteristic

228

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

229

C₈

—

230

C₈

—

231

C₈

—

232

C₈

—

233

C₈

—

234

C₈

—

235

C₈

#10597294

yes

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

#11926447

yes

characteristic

240

C₄

—

241

C₄

—

242

C₄

—

243

C₄

—

244

C₄

—

245

C₄

C₂×#10597294

yes

characteristic

246

C₄

#11926561

yes

characteristic

247

C₄

#11926666

yes

—

248

C₄

#11926816

yes

—

249

C₂

—

250

C₂

#14564529

yes

characteristic

251

C₂

#14564551

yes

characteristic

252

C₂

#14564555

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597384
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#3170	C₂
socle	C₂²×C₁₉	#390
prime radical	C₂³×C₁₉	#124
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3170	D₁₉
hypocenter	C₁₉	#9727
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

subgroup

G/H

center

C₂×C₄

#10597384

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#3170

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

N	H ≅ G/N	type
181. C₁₉	#9727	semidirect

H ≅ G/N

type

181. C₁₉

#9727

semidirect

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

subgroup	index
C₄×#10597276	2
#14562230	2
#14562056	2
#14561924	2
C₁₉×#3170	2
#9727	19

subgroup

index

C₁₉×#3170

Subgroups — #18081745

Conjugacy classes of subgroups

Complements

Maximal subgroups