Group #18081963 — subgroups

Subgroups — #18081963

Order 4864.

374 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 107 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	#14563386	C₂	1	1	yes	maximal, characteristic
2	#14562398	C₂	1	1	yes	maximal, characteristic
3	#14562250	C₂	1	2	yes	maximal
4	#14562147	C₂	1	2	yes	maximal
5	C₁₉×#3170	C₂	1	1	yes	maximal, characteristic
6	#11926601	C₂²	1	2	yes	—
7	C₂×#10597260	C₂²	1	1	yes	characteristic
8	#11926390	C₂²	1	1	yes	characteristic
9	#11926298	—	2	1	no	—
10	#11926298	—	2	1	no	—
11	#11926297	—	2	1	no	—
12	#11926295	—	2	1	no	—
13	#11926286	—	2	4	no	—
14	#11926281	—	2	4	no	—
15	C₁₉×#533	C₂²	1	2	yes	—
16	C₁₉×#500	C₄	1	1	yes	characteristic, complemented
17	C₁₉×#494	C₄	1	1	yes	characteristic, complemented
18	C₁₉×#487	C₄	1	2	yes	complemented
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×C₄×Dic₁₉	—	2	1	no	—
38	C₂²×C₁₉⋊C₈	—	2	1	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	C₁₉⋊#95	—	2	1	no	—
48	C₁₉⋊#95	D₄	1	2	yes	—
49	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
50	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
51	#10597260	—	2	1	no	—
52	#10597260	—	2	2	no	—
53	#10597260	D₄	1	2	yes	—
54	C₂×Q₈×C₁₉	—	2	2	no	—
55	C₂×Q₈×C₁₉	—	2	2	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	C₂²×Dic₁₉	—	2	2	no	—
60	Q₁₆×C₁₉	—	4	2	no	—
61	Q₁₆×C₁₉	—	4	2	no	—
62	C₂×C₈×C₁₉	—	4	1	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	#41	1	1	yes	characteristic
80	C₄×Dic₁₉	—	4	1	no	—
81	C₄×Dic₁₉	—	4	1	no	—
82	C₂×C₁₉⋊C₈	—	2	2	no	—
83	C₂×C₁₉⋊C₈	—	4	1	no	—
84	C₂×C₁₉⋊C₈	—	4	1	no	—
85	C₂×C₁₉⋊C₈	—	4	2	no	—
86	#9765	—	19	1	no	maximal, Sylow
87	C₂³×C₁₉	#121	1	1	yes	characteristic
88	Q₈×C₁₉	—	4	2	no	—
89	Q₈×C₁₉	—	4	2	no	—
90	Q₈×C₁₉	—	8	2	no	—
91	C₂×C₄×C₁₉	—	2	2	no	—
92	C₂×C₄×C₁₉	—	2	1	no	—
93	C₂×C₄×C₁₉	—	2	1	no	—
94	C₂×C₄×C₁₉	—	4	1	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	#124	1	1	yes	characteristic
102	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
103	C₂×Dic₁₉	—	4	2	no	—
104	C₂×Dic₁₉	—	4	2	no	—
105	C₂×Dic₁₉	—	4	2	no	—
106	C₈×C₁₉	—	2	1	no	—
107	C₈×C₁₉	—	2	1	no	—
108	C₈×C₁₉	—	2	1	no	—
109	C₈×C₁₉	—	2	1	no	—
110	C₁₉⋊C₈	—	4	2	no	—
111	C₁₉⋊C₈	—	8	2	no	—
112	#3170	D₁₉	1	1	yes	characteristic
113	#1746	—	19	1	no	—
114	#1568	—	19	1	no	—
115	#1531	—	19	2	no	—
116	#1506	—	19	2	no	—
117	C₂²×C₁₉	—	2	1	no	—
118	C₂²×C₁₉	—	2	1	no	—
119	C₂²×C₁₉	#390	1	1	yes	characteristic
120	C₂²×C₁₉	#473	1	2	yes	—
121	C₄×C₁₉	—	2	1	no	—
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	2	no	—
127	C₄×C₁₉	—	8	2	no	—
128	C₄×C₁₉	#421	1	1	yes	characteristic
129	C₄×C₁₉	#421	1	1	yes	characteristic
130	Dic₁₉	—	8	2	no	—
131	#533	C₂×D₁₉	1	2	yes	—
132	#500	Dic₁₉	1	1	yes	characteristic, complemented
133	#494	Dic₁₉	1	1	yes	characteristic, complemented
134	#487	Dic₁₉	1	2	yes	complemented
135	#467	—	2	1	no	—
136	#467	—	2	1	no	—
137	C₄×Q₁₆	—	2	1	no	—
138	C₄×Q₁₆	—	2	1	no	—
139	#432	—	19	2	no	—
140	C₂×#97	—	19	1	no	—
141	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
142	#376	—	19	1	no	—
143	#336	—	38	1	no	—
144	#336	—	38	1	no	—
145	#335	—	38	1	no	—
146	#334	—	38	1	no	—
147	#330	—	38	4	no	—
148	#328	—	38	4	no	—
149	C₂×C₁₉	—	2	2	no	—
150	C₂×C₁₉	#1963	1	1	yes	characteristic
151	C₂×C₁₉	#1976	1	1	yes	characteristic
152	C₂×C₁₉	#1979	1	1	yes	characteristic
153	C₂×Q₁₆	—	2	1	no	—
154	C₂×Q₁₆	—	2	1	no	—
155	C₂²×C₈	—	38	1	no	—
156	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
157	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
158	C₄⋊Q₈	C₂×Dic₁₉	1	2	yes	—
159	C₄⋊Q₈	C₂×Dic₁₉	1	2	yes	—
160	#125	—	2	2	no	—
161	C₂²⋊Q₈	—	2	2	no	—
162	C₂²⋊Q₈	—	2	2	no	—
163	C₄×Q₈	—	2	2	no	—
164	C₄×Q₈	—	2	2	no	—
165	#117	—	2	2	no	—
166	C₂×C₄²	—	38	1	no	—
167	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
168	#107	—	2	1	no	—
169	#107	—	2	1	no	—
170	C₄⋊C₈	—	38	2	no	—
171	#103	—	2	2	no	—
172	#103	—	2	2	no	—
173	C₂²⋊C₈	—	38	2	no	—
174	#97	—	19	2	no	—
175	#97	—	38	2	no	—
176	#97	—	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	#95	—	19	2	no	—
182	#95	—	38	1	no	—
183	C₁₉	#9765	1	1	yes	characteristic, complemented, Sylow
184	C₂×Q₈	—	2	2	no	—
185	C₂×Q₈	—	2	2	no	—
186	C₂²×C₄	—	38	2	no	—
187	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
188	C₂²×C₄	#64543	1	1	yes	characteristic
189	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
190	Q₁₆	—	4	2	no	—
191	Q₁₆	—	4	2	no	—
192	C₂×C₈	—	4	1	no	—
193	C₂×C₈	—	4	1	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	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	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
202	C₄⋊C₄	—	2	2	no	—
203	C₄⋊C₄	—	2	2	no	—
204	C₄⋊C₄	—	2	2	no	—
205	C₄⋊C₄	—	2	2	no	—
206	C₄⋊C₄	—	4	2	no	—
207	C₄⋊C₄	—	4	2	no	—
208	C₂²⋊C₄	—	4	2	no	—
209	C₄²	—	4	2	no	—
210	C₄²	—	76	1	no	—
211	C₄²	—	76	1	no	—
212	C₄²	D₄×D₁₉	1	1	yes	characteristic
213	C₄²	#64543	1	1	yes	characteristic
214	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
215	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
216	C₂³	#10597384	1	1	yes	characteristic
217	Q₈	—	4	2	no	—
218	Q₈	—	4	2	no	—
219	Q₈	—	8	2	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	4	1	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	—	4	2	no	—
226	C₂×C₄	—	76	2	no	—
227	C₂×C₄	—	76	2	no	—
228	C₂×C₄	—	76	2	no	—
229	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
230	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
231	C₂×C₄	#10597382	1	1	yes	characteristic
232	C₂×C₄	#10597384	1	1	yes	characteristic
233	C₂×C₄	#10597386	1	1	yes	characteristic
234	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
235	C₈	—	2	1	no	—
236	C₈	—	2	1	no	—
237	C₈	—	2	1	no	—
238	C₈	—	2	1	no	—
239	C₈	—	76	2	no	—
240	C₈	—	152	2	no	—
241	C₂²	—	2	1	no	—
242	C₂²	—	2	1	no	—
243	C₂²	#11926447	1	1	yes	characteristic
244	C₂²	#11926816	1	2	yes	—
245	C₄	—	2	1	no	—
246	C₄	—	2	1	no	—
247	C₄	—	2	1	no	—
248	C₄	—	2	1	no	—
249	C₄	—	2	1	no	—
250	C₄	—	8	2	no	—
251	C₄	—	8	2	no	—
252	C₄	—	152	2	no	—
253	C₄	#11926561	1	1	yes	characteristic
254	C₄	#11926561	1	1	yes	characteristic
255	C₂	—	2	2	no	—
256	C₂	#14564468	1	1	yes	characteristic
257	C₂	#14564534	1	1	yes	characteristic
258	C₂	#14564551	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563386

C₂

yes

maximal, characteristic

#14562398

C₂

yes

maximal, characteristic

#14562250

C₂

yes

maximal

#14562147

C₂

yes

maximal

C₁₉×#3170

C₂

yes

maximal, characteristic

#11926601

C₂²

yes

—

C₂×#10597260

C₂²

yes

characteristic

#11926390

C₂²

yes

—

—

—

—

—

—

C₁₉×#533

C₂²

yes

—

C₁₉×#500

C₄

yes

characteristic, complemented

C₁₉×#494

C₄

yes

characteristic, complemented

C₁₉×#487

C₄

yes

complemented

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×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

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

C₁₉⋊#95

—

C₁₉⋊#95

D₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

#10597260

—

#10597260

D₄

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

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

#41

yes

characteristic

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

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

#124

yes

characteristic

102

C₂×C₄×C₁₉

#127

yes

characteristic

103

C₂×Dic₁₉

—

104

C₂×Dic₁₉

—

105

C₂×Dic₁₉

—

106

C₈×C₁₉

—

107

C₈×C₁₉

—

108

C₈×C₁₉

—

109

C₈×C₁₉

—

110

C₁₉⋊C₈

—

111

C₁₉⋊C₈

—

112

#3170

D₁₉

yes

characteristic

113

#1746

—

114

#1568

—

115

#1531

—

116

#1506

—

117

C₂²×C₁₉

—

118

C₂²×C₁₉

—

119

C₂²×C₁₉

#390

yes

characteristic

120

C₂²×C₁₉

#473

yes

—

121

C₄×C₁₉

—

122

C₄×C₁₉

—

123

C₄×C₁₉

—

124

C₄×C₁₉

—

125

C₄×C₁₉

—

126

C₄×C₁₉

—

127

C₄×C₁₉

—

128

C₄×C₁₉

#421

yes

characteristic

129

C₄×C₁₉

#421

yes

characteristic

130

Dic₁₉

—

131

#533

C₂×D₁₉

yes

—

132

#500

Dic₁₉

yes

characteristic, complemented

133

#494

Dic₁₉

yes

characteristic, complemented

134

#487

Dic₁₉

yes

complemented

135

#467

—

136

#467

—

137

C₄×Q₁₆

—

138

C₄×Q₁₆

—

139

#432

—

140

C₂×#97

—

141

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

142

#376

—

143

#336

—

144

#336

—

145

#335

—

146

#334

—

147

#330

—

148

#328

—

149

C₂×C₁₉

—

150

C₂×C₁₉

#1963

yes

characteristic

151

C₂×C₁₉

#1976

yes

characteristic

152

C₂×C₁₉

#1979

yes

characteristic

153

C₂×Q₁₆

—

154

C₂×Q₁₆

—

155

C₂²×C₈

—

156

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

157

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

158

C₄⋊Q₈

C₂×Dic₁₉

yes

—

159

C₄⋊Q₈

C₂×Dic₁₉

yes

—

160

#125

—

161

C₂²⋊Q₈

—

162

C₂²⋊Q₈

—

163

C₄×Q₈

—

164

C₄×Q₈

—

165

#117

—

166

C₂×C₄²

—

167

C₂×C₄²

C₂²×D₁₉

yes

characteristic

168

#107

—

169

#107

—

170

C₄⋊C₈

—

171

#103

—

172

#103

—

173

C₂²⋊C₈

—

174

#97

—

175

#97

—

176

#97

—

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

#95

—

182

#95

—

183

C₁₉

#9765

yes

characteristic, complemented, Sylow

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂²×C₄

—

187

C₂²×C₄

D₄×D₁₉

yes

characteristic

188

C₂²×C₄

#64543

yes

characteristic

189

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

190

Q₁₆

—

191

Q₁₆

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

199

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

200

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

201

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

202

C₄⋊C₄

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₂²⋊C₄

—

209

C₄²

—

210

C₄²

—

211

C₄²

—

212

C₄²

D₄×D₁₉

yes

characteristic

213

C₄²

#64543

yes

characteristic

214

C₄²

C₂²×Dic₁₉

yes

characteristic

215

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

216

C₂³

#10597384

yes

characteristic

217

Q₈

—

218

Q₈

—

219

Q₈

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

D₄×Dic₁₉

yes

characteristic

230

C₂×C₄

D₄×Dic₁₉

yes

characteristic

231

C₂×C₄

#10597382

yes

characteristic

232

C₂×C₄

#10597384

yes

characteristic

233

C₂×C₄

#10597386

yes

characteristic

234

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

235

C₈

—

236

C₈

—

237

C₈

—

238

C₈

—

239

C₈

—

240

C₈

—

152

—

241

C₂²

—

242

C₂²

—

243

C₂²

#11926447

yes

characteristic

244

C₂²

#11926816

yes

—

245

C₄

—

246

C₄

—

247

C₄

—

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

—

152

—

253

C₄

#11926561

yes

characteristic

254

C₄

#11926561

yes

characteristic

255

C₂

—

256

C₂

#14564468

yes

characteristic

257

C₂

#14564534

yes

characteristic

258

C₂

#14564551

yes

characteristic

	subgroup	G/H
center	C₂²	#11926447
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#3170	C₂
socle	C₂²×C₁₉	#390
prime radical	C₂³×C₁₉	#121
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3170	D₁₉
hypocenter	C₁₉	#9765
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3170

subgroup

G/H

center

C₂²

#11926447

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 ◁ C₂² ◁ C₂×C₄² ◁ #3170

N	H ≅ G/N	type
16. C₁₉×#500	C₄	semidirect
17. C₁₉×#494	C₄	semidirect
18. C₁₉×#487	C₄	semidirect
132. #500	Dic₁₉	semidirect
133. #494	Dic₁₉	semidirect
134. #487	Dic₁₉	semidirect
183. C₁₉	#9765	semidirect

H ≅ G/N

type

16. C₁₉×#500

C₄

semidirect

17. C₁₉×#494

C₄

semidirect

18. C₁₉×#487

C₄

semidirect

132. #500

Dic₁₉

semidirect

133. #494

Dic₁₉

semidirect

134. #487

Dic₁₉

semidirect

183. C₁₉

#9765

semidirect

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

subgroup	index
#14563386	2
#14562398	2
#14562250	2
#14562147	2
C₁₉×#3170	2
#9765	19

subgroup

index

C₁₉×#3170

Subgroups — #18081963

Conjugacy classes of subgroups

Complements

Maximal subgroups