Group #18075466 — subgroups

Subgroups — #18075466

Order 4864.

486 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 121 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	C₂×#11926609	C₂	1	1	yes	maximal, characteristic
2	#14563624	C₂	1	2	yes	maximal
3	#14562393	C₂	1	2	yes	maximal, complemented
4	#14561510	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1292	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×D₁₉	C₄	1	2	yes	—
7	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
8	#11926609	—	2	2	no	—
9	#11926609	—	2	2	no	—
10	#11926568	C₂²	1	2	yes	—
11	C₂×#10597280	—	2	2	no	—
12	C₂×(C₂×D₁₉)⋊C₈	C₄	1	2	yes	—
13	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	#11926312	—	2	2	no	—
15	#11926296	—	2	2	no	—
16	#11926296	—	2	2	no	—
17	C₁₉×#423	C₂²	1	2	yes	—
18	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂²×D₇₆	D₄	1	1	yes	characteristic
20	C₂²×C₄×D₁₉	C₂×C₄	1	2	yes	—
21	C₂×M₁₆×C₁₉	—	2	2	no	—
22	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
23	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
24	C₂×(C₂×D₁₉)⋊C₄	Q₈	1	2	yes	—
25	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
26	C₂×#64520	—	2	2	no	—
27	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
29	C₂×C₈×D₁₉	—	2	2	no	—
30	C₂×C₈×D₁₉	—	2	2	no	—
31	C₂×C₈×D₁₉	—	4	4	no	—
32	C₄×D₇₆	—	2	2	no	—
33	C₄×D₇₆	—	2	2	no	—
34	C₁₉×C₄⋊C₈	—	2	2	no	—
35	C₁₉×C₄⋊C₈	—	2	2	no	—
36	C₁₉×C₄⋊C₈	—	2	2	no	—
37	#10597280	—	4	4	no	—
38	(C₂×D₁₉)⋊C₈	—	2	4	no	—
39	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
40	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
41	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
42	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
43	C₂³×D₁₉	C₄⋊C₄	1	2	yes	—
44	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
47	C₂²×Dic₁₉	C₄⋊C₄	1	2	yes	—
48	C₂×D₇₆	—	2	2	no	—
49	C₂×D₇₆	—	2	2	no	—
50	C₂×D₇₆	D₈	1	2	yes	—
51	C₂×D₇₆	Q₁₆	1	2	yes	—
52	C₂×C₄×D₁₉	—	2	2	no	—
53	C₂×C₄×D₁₉	—	2	2	no	—
54	C₂×C₄×D₁₉	—	4	2	no	—
55	C₂×C₄×D₁₉	—	4	2	no	—
56	M₁₆×C₁₉	—	4	2	no	—
57	M₁₆×C₁₉	—	4	2	no	—
58	C₂×C₈×C₁₉	—	2	2	no	—
59	C₂×C₈×C₁₉	—	4	2	no	—
60	C₂×C₈×C₁₉	—	4	2	no	—
61	C₄²×C₁₉	C₂×D₄	1	2	yes	—
62	C₄²×C₁₉	#41	1	2	yes	—
63	(C₂×D₁₉)⋊C₄	—	2	4	no	—
64	C₄⋊Dic₁₉	—	2	2	no	—
65	#64520	—	4	2	no	—
66	#64520	—	4	2	no	—
67	C₂×C₁₉⋊C₈	—	2	2	no	—
68	C₂×C₁₉⋊C₈	—	4	1	no	—
69	C₂×C₁₉⋊C₈	—	4	2	no	—
70	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
71	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
73	C₈×D₁₉	—	4	4	no	—
74	C₈×D₁₉	—	4	4	no	—
75	#8616	—	19	1	no	maximal, Sylow
76	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
77	C₂²×D₁₉	—	2	2	no	—
78	C₂²×D₁₉	—	2	2	no	—
79	C₂²×D₁₉	—	4	2	no	—
80	C₂²×D₁₉	—	4	2	no	—
81	C₂²×D₁₉	#107	1	4	yes	—
82	C₂×C₄×C₁₉	—	2	1	no	—
83	C₂×C₄×C₁₉	—	2	1	no	—
84	C₂×C₄×C₁₉	—	4	1	no	—
85	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
87	C₂×C₄×C₁₉	#121	1	2	yes	—
88	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
89	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
90	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
91	C₂×C₄×C₁₉	#135	1	2	yes	—
92	C₂×Dic₁₉	—	2	2	no	—
93	C₂×Dic₁₉	—	4	2	no	—
94	D₇₆	—	2	4	no	—
95	D₇₆	—	2	4	no	—
96	C₄×D₁₉	—	4	4	no	—
97	C₄×D₁₉	—	4	2	no	—
98	C₄×D₁₉	—	4	2	no	—
99	C₈×C₁₉	—	4	2	no	—
100	C₈×C₁₉	—	8	2	no	—
101	C₁₉⋊C₈	—	2	1	no	—
102	C₁₉⋊C₈	—	2	2	no	—
103	C₁₉⋊C₈	—	8	2	no	—
104	C₁₉⋊C₈	#100	1	2	yes	complemented
105	C₂×C₈×D₄	—	19	1	no	—
106	#1800	—	19	2	no	—
107	#1567	—	19	2	no	—
108	#1292	—	19	1	no	—
109	#1292	D₁₉	1	1	yes	characteristic, complemented
110	C₂²×C₁₉	—	2	1	no	—
111	C₂²×C₁₉	—	2	1	no	—
112	C₂²×C₁₉	#380	1	1	yes	characteristic
113	C₂²×C₁₉	C₂×#107	1	1	yes	characteristic
114	C₂²×C₁₉	#427	1	1	yes	characteristic
115	C₂×D₁₉	—	2	4	no	—
116	C₂×D₁₉	—	4	4	no	—
117	C₂×D₁₉	—	4	2	no	—
118	C₂×D₁₉	—	4	2	no	—
119	C₂×D₁₉	—	4	4	no	—
120	C₄×C₁₉	—	2	1	no	—
121	C₄×C₁₉	—	2	2	no	—
122	C₄×C₁₉	C₂×#100	1	1	yes	characteristic
123	C₄×C₁₉	#413	1	1	yes	characteristic
124	C₄×C₁₉	#466	1	2	yes	—
125	C₄×C₁₉	#467	1	2	yes	—
126	Dic₁₉	—	4	2	no	—
127	C₂³×C₈	—	19	2	no	—
128	C₂×C₄×D₄	—	19	1	no	—
129	C₈×D₄	—	38	2	no	—
130	C₈×D₄	—	38	2	no	—
131	#423	—	19	2	no	—
132	#423	C₂×D₁₉	1	2	yes	—
133	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
134	C₂×#100	—	38	2	no	—
135	C₂×C₂²⋊C₈	—	19	2	no	—
136	C₂×C₄×C₈	—	19	1	no	—
137	#343	—	38	2	no	—
138	#335	—	38	2	no	—
139	#335	—	38	2	no	—
140	C₂×C₁₉	—	2	1	no	—
141	C₂×C₁₉	—	2	1	no	—
142	C₂×C₁₉	#1800	1	1	yes	characteristic
143	C₂×C₁₉	#1808	1	1	yes	characteristic
144	C₂×C₁₉	#1813	1	1	yes	characteristic
145	D₁₉	—	4	4	no	—
146	C₂²×D₄	—	19	1	no	—
147	C₂³×C₄	—	19	2	no	—
148	C₂×M₁₆	—	2	2	no	—
149	C₂×M₁₆	—	38	2	no	—
150	C₂²×C₈	—	19	1	no	—
151	C₂²×C₈	—	19	1	no	—
152	C₂²×C₈	—	38	2	no	—
153	C₂²×C₈	—	38	2	no	—
154	C₂²×C₈	—	76	4	no	—
155	C₂²×C₈	C₄×D₁₉	1	2	yes	—
156	C₄×D₄	—	38	2	no	—
157	C₄×D₄	—	38	2	no	—
158	C₂×C₄⋊C₄	—	19	1	no	—
159	C₂×C₂²⋊C₄	—	19	2	no	—
160	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
161	C₄⋊C₈	—	2	2	no	—
162	C₄⋊C₈	—	2	2	no	—
163	C₄⋊C₈	—	2	2	no	—
164	C₄⋊C₈	—	38	2	no	—
165	C₄⋊C₈	—	38	2	no	—
166	#100	—	76	4	no	—
167	C₂²⋊C₈	—	38	4	no	—
168	C₄×C₈	—	19	2	no	—
169	C₄×C₈	—	19	2	no	—
170	C₁₉	#8616	1	1	yes	characteristic, complemented, Sylow
171	C₂⁴	—	19	2	no	—
172	C₂×D₄	—	19	2	no	—
173	C₂×D₄	—	19	2	no	—
174	C₂×D₄	—	38	2	no	—
175	C₂×D₄	—	38	2	no	—
176	C₂²×C₄	—	19	2	no	—
177	C₂²×C₄	—	38	2	no	—
178	C₂²×C₄	—	38	2	no	—
179	C₂²×C₄	—	76	2	no	—
180	C₂²×C₄	—	76	2	no	—
181	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
182	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
183	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
184	M₁₆	—	4	2	no	—
185	M₁₆	—	4	2	no	—
186	M₁₆	—	76	2	no	—
187	M₁₆	—	76	2	no	—
188	C₂×C₈	—	2	2	no	—
189	C₂×C₈	—	4	2	no	—
190	C₂×C₈	—	4	2	no	—
191	C₂×C₈	—	19	1	no	—
192	C₂×C₈	—	19	2	no	—
193	C₂×C₈	—	19	1	no	—
194	C₂×C₈	—	38	2	no	—
195	C₂×C₈	—	76	4	no	—
196	C₂×C₈	—	76	4	no	—
197	C₂×C₈	—	76	1	no	—
198	C₂×C₈	—	76	2	no	—
199	C₄⋊C₄	—	38	2	no	—
200	C₂²⋊C₄	—	38	4	no	—
201	C₄²	#64541	1	2	yes	—
202	C₄²	D₄×D₁₉	1	2	yes	—
203	C₂³	—	19	4	no	—
204	C₂³	—	38	2	no	—
205	C₂³	—	38	2	no	—
206	C₂³	—	76	2	no	—
207	C₂³	—	76	2	no	—
208	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
209	D₄	—	38	4	no	—
210	D₄	—	38	4	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	4	1	no	—
214	C₂×C₄	—	38	2	no	—
215	C₂×C₄	—	76	4	no	—
216	C₂×C₄	—	76	2	no	—
217	C₂×C₄	—	76	2	no	—
218	C₂×C₄	—	76	2	no	—
219	C₂×C₄	#10597318	1	1	yes	characteristic
220	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
221	C₂×C₄	#10597330	1	2	yes	—
222	C₂×C₄	#10597342	1	2	yes	—
223	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
224	C₂×C₄	#10597362	1	2	yes	—
225	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
226	C₈	—	4	2	no	—
227	C₈	—	8	2	no	—
228	C₈	—	19	2	no	—
229	C₈	—	38	1	no	—
230	C₈	—	38	2	no	—
231	C₈	—	152	2	no	—
232	C₂²	—	2	1	no	—
233	C₂²	—	2	1	no	—
234	C₂²	—	38	4	no	—
235	C₂²	—	76	4	no	—
236	C₂²	—	76	4	no	—
237	C₂²	—	76	2	no	—
238	C₂²	—	76	2	no	—
239	C₂²	#11926403	1	1	yes	characteristic
240	C₂²	#107×D₁₉	1	1	yes	characteristic
241	C₂²	#11926579	1	1	yes	characteristic
242	C₄	—	2	1	no	—
243	C₄	—	2	2	no	—
244	C₄	—	76	2	no	—
245	C₄	#100×D₁₉	1	1	yes	characteristic
246	C₄	#11926527	1	1	yes	characteristic
247	C₄	#11926779	1	2	yes	—
248	C₄	#11926784	1	2	yes	—
249	C₂	—	2	1	no	—
250	C₂	—	2	1	no	—
251	C₂	—	76	4	no	—
252	C₂	#14563626	1	1	yes	characteristic
253	C₂	#14563663	1	1	yes	characteristic
254	C₂	#14563684	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926609

C₂

yes

maximal, characteristic

#14563624

C₂

yes

maximal

#14562393

C₂

yes

maximal, complemented

#14561510

C₂

yes

maximal, characteristic, complemented

C₁₉×#1292

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×D₁₉

C₄

yes

—

C₂×C₄×D₇₆

C₂²

yes

—

—

C₂²

yes

—

C₂×#10597280

—

C₂×(C₂×D₁₉)⋊C₈

C₄

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

—

—

C₁₉×#423

C₂²

yes

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂²×D₇₆

D₄

yes

characteristic

C₂²×C₄×D₁₉

C₂×C₄

yes

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

Q₈

yes

—

C₂×C₄⋊Dic₁₉

D₄

yes

characteristic

C₂×#64520

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂×C₈×D₁₉

—

C₂×C₈×D₁₉

—

C₂×C₈×D₁₉

—

C₄×D₇₆

—

C₄×D₇₆

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

#10597280

—

(C₂×D₁₉)⋊C₈

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂³×D₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂²×Dic₁₉

C₄⋊C₄

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

D₈

yes

—

C₂×D₇₆

Q₁₆

yes

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

characteristic

C₈×D₁₉

—

C₈×D₁₉

—

#8616

—

maximal, Sylow

C₂³×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

#107

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₁₉

#135

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

—

C₈×C₁₉

—

100

C₈×C₁₉

—

101

C₁₉⋊C₈

—

102

C₁₉⋊C₈

—

103

C₁₉⋊C₈

—

104

C₁₉⋊C₈

#100

yes

complemented

105

C₂×C₈×D₄

—

106

#1800

—

107

#1567

—

108

#1292

—

109

#1292

D₁₉

yes

characteristic, complemented

110

C₂²×C₁₉

—

111

C₂²×C₁₉

—

112

C₂²×C₁₉

#380

yes

characteristic

113

C₂²×C₁₉

C₂×#107

yes

characteristic

114

C₂²×C₁₉

#427

yes

characteristic

115

C₂×D₁₉

—

116

C₂×D₁₉

—

117

C₂×D₁₉

—

118

C₂×D₁₉

—

119

C₂×D₁₉

—

120

C₄×C₁₉

—

121

C₄×C₁₉

—

122

C₄×C₁₉

C₂×#100

yes

characteristic

123

C₄×C₁₉

#413

yes

characteristic

124

C₄×C₁₉

#466

yes

—

125

C₄×C₁₉

#467

yes

—

126

Dic₁₉

—

127

C₂³×C₈

—

128

C₂×C₄×D₄

—

129

C₈×D₄

—

130

C₈×D₄

—

131

#423

—

132

#423

C₂×D₁₉

yes

—

133

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

134

C₂×#100

—

135

C₂×C₂²⋊C₈

—

136

C₂×C₄×C₈

—

137

#343

—

138

#335

—

139

#335

—

140

C₂×C₁₉

—

141

C₂×C₁₉

—

142

C₂×C₁₉

#1800

yes

characteristic

143

C₂×C₁₉

#1808

yes

characteristic

144

C₂×C₁₉

#1813

yes

characteristic

145

D₁₉

—

146

C₂²×D₄

—

147

C₂³×C₄

—

148

C₂×M₁₆

—

149

C₂×M₁₆

—

150

C₂²×C₈

—

151

C₂²×C₈

—

152

C₂²×C₈

—

153

C₂²×C₈

—

154

C₂²×C₈

—

155

C₂²×C₈

C₄×D₁₉

yes

—

156

C₄×D₄

—

157

C₄×D₄

—

158

C₂×C₄⋊C₄

—

159

C₂×C₂²⋊C₄

—

160

C₂×C₄²

C₂²×D₁₉

yes

characteristic

161

C₄⋊C₈

—

162

C₄⋊C₈

—

163

C₄⋊C₈

—

164

C₄⋊C₈

—

165

C₄⋊C₈

—

166

#100

—

167

C₂²⋊C₈

—

168

C₄×C₈

—

169

C₄×C₈

—

170

C₁₉

#8616

yes

characteristic, complemented, Sylow

171

C₂⁴

—

172

C₂×D₄

—

173

C₂×D₄

—

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂²×C₄

—

177

C₂²×C₄

—

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

182

C₂²×C₄

D₄×D₁₉

yes

characteristic

183

C₂²×C₄

Q₈×D₁₉

yes

characteristic

184

M₁₆

—

185

M₁₆

—

186

M₁₆

—

187

M₁₆

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₄⋊C₄

—

200

C₂²⋊C₄

—

201

C₄²

#64541

yes

—

202

C₄²

D₄×D₁₉

yes

—

203

C₂³

—

204

C₂³

—

205

C₂³

—

206

C₂³

—

207

C₂³

—

208

C₂³

C₄⋊C₄×D₁₉

yes

characteristic

209

D₄

—

210

D₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

#10597318

yes

characteristic

220

C₂×C₄

C₂²⋊C₄×D₁₉

yes

characteristic

221

C₂×C₄

#10597330

yes

—

222

C₂×C₄

#10597342

yes

—

223

C₂×C₄

D₈×D₁₉

yes

characteristic

224

C₂×C₄

#10597362

yes

—

225

C₂×C₄

Q₁₆×D₁₉

yes

characteristic

226

C₈

—

227

C₈

—

228

C₈

—

229

C₈

—

230

C₈

—

231

C₈

—

152

—

232

C₂²

—

233

C₂²

—

234

C₂²

—

235

C₂²

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

#11926403

yes

characteristic

240

C₂²

#107×D₁₉

yes

characteristic

241

C₂²

#11926579

yes

characteristic

242

C₄

—

243

C₄

—

244

C₄

—

245

C₄

#100×D₁₉

yes

characteristic

246

C₄

#11926527

yes

characteristic

247

C₄

#11926779

yes

—

248

C₄

#11926784

yes

—

249

C₂

—

250

C₂

—

251

C₂

—

252

C₂

#14563626

yes

characteristic

253

C₂

#14563663

yes

characteristic

254

C₂

#14563684

yes

characteristic

	subgroup	G/H
center	C₂²	#11926403
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1292	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂²×D₇₆	D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1292	D₁₉
hypocenter	C₁₉	#8616
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1292

subgroup

G/H

center

C₂²

#11926403

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1292

C₂

socle

C₂²×C₁₉

#380

prime radical

C₂²×D₇₆

D₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1292

N	H ≅ G/N	type
3. #14562393	C₂	semidirect
4. #14561510	C₂	semidirect
5. C₁₉×#1292	C₂	semidirect
104. C₁₉⋊C₈	#100	semidirect
109. #1292	D₁₉	semidirect
170. C₁₉	#8616	semidirect

H ≅ G/N

type

3. #14562393

C₂

semidirect

4. #14561510

C₂

semidirect

5. C₁₉×#1292

C₂

semidirect

104. C₁₉⋊C₈

#100

semidirect

109. #1292

D₁₉

semidirect

170. C₁₉

#8616

semidirect

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

subgroup	index
C₂×#11926609	2
#14563624	2
#14562393	2
#14561510	2
C₁₉×#1292	2
#8616	19

subgroup

index

C₁₉×#1292

Subgroups — #18075466

Conjugacy classes of subgroups

Complements

Maximal subgroups