Group #14563987 — subgroups

Subgroups — #14563987

Order 2432.

374 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 101 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	C₂²×#64526	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597333	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10597273	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926447	C₂	1	1	yes	maximal, characteristic
5	#11926306	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926298	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#102	C₂	1	1	yes	maximal, characteristic
8	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
13	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
14	C₂×#64526	—	2	2	no	—
15	C₂×#64526	—	2	2	no	—
16	C₂×#64526	C₄	1	4	yes	complemented
17	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
18	C₂×Dic₁₉⋊C₄	—	2	1	no	—
19	C₂×C₄×Dic₁₉	—	2	1	no	—
20	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
21	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
22	#10597333	—	2	2	no	—
23	#10597333	—	2	2	no	—
24	C₁₉×#102	—	2	2	no	—
25	#10597273	—	2	2	no	—
26	C₂⁴×C₁₉	—	2	1	no	—
27	C₂×D₄×C₁₉	—	2	1	no	—
28	C₂×D₄×C₁₉	—	2	1	no	—
29	C₂×D₄×C₁₉	—	2	1	no	—
30	C₂×D₄×C₁₉	—	2	1	no	—
31	C₂×D₄×C₁₉	—	2	1	no	—
32	C₂×D₄×C₁₉	C₂×C₄	1	2	yes	—
33	C₂²×C₄×C₁₉	—	2	1	no	—
34	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
35	C₂²×Dic₁₉	—	2	1	no	—
36	C₂²×Dic₁₉	—	2	1	no	—
37	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
38	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
39	C₂×Dic₃₈	—	2	1	no	—
40	C₂×Dic₃₈	—	2	1	no	—
41	C₂×Dic₃₈	—	2	1	no	—
42	C₂×Dic₃₈	C₂×C₄	1	2	yes	—
43	C₂×Dic₃₈	D₄	1	2	yes	—
44	C₂×Dic₃₈	D₄	1	2	yes	—
45	C₂×C₈×C₁₉	—	2	1	no	—
46	C₂×C₈×C₁₉	—	2	1	no	—
47	C₂×C₈×C₁₉	—	2	1	no	—
48	C₄⋊C₄×C₁₉	—	2	1	no	—
49	C₄⋊C₄×C₁₉	D₄	1	2	yes	—
50	C₂²⋊Dic₁₉	—	4	2	no	—
51	C₂²⋊Dic₁₉	—	4	2	no	—
52	#64526	—	2	8	no	—
53	C₄⋊Dic₁₉	—	2	1	no	—
54	C₄⋊Dic₁₉	—	2	1	no	—
55	Dic₁₉⋊C₄	—	2	4	no	—
56	C₄×Dic₁₉	—	2	4	no	—
57	C₄×Dic₁₉	—	2	1	no	—
58	C₄×Dic₁₉	—	2	1	no	—
59	C₂×C₁₉⋊C₈	—	2	1	no	—
60	C₂×C₁₉⋊C₈	—	2	1	no	—
61	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
62	C₂³×C₁₉	—	2	2	no	—
63	C₂³×C₁₉	—	4	1	no	—
64	C₂³×C₁₉	—	4	1	no	—
65	C₂³×C₁₉	—	4	1	no	—
66	C₂³×C₁₉	—	4	1	no	—
67	C₂³×C₁₉	—	4	1	no	—
68	C₂³×C₁₉	—	4	1	no	—
69	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
70	D₄×C₁₉	—	2	2	no	—
71	D₄×C₁₉	—	2	2	no	—
72	D₄×C₁₉	—	4	1	no	—
73	D₄×C₁₉	—	4	1	no	—
74	C₂×C₄×C₁₉	—	2	2	no	—
75	C₂×C₄×C₁₉	—	4	1	no	—
76	C₂×C₄×C₁₉	—	4	1	no	—
77	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
78	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
82	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
83	C₂×Dic₁₉	—	2	2	no	—
84	C₂×Dic₁₉	—	2	1	no	—
85	C₂×Dic₁₉	—	2	2	no	—
86	C₂×Dic₁₉	—	2	2	no	—
87	C₂×Dic₁₉	—	2	1	no	—
88	C₂×Dic₁₉	—	2	1	no	—
89	C₂×Dic₁₉	—	2	1	no	—
90	C₂×Dic₁₉	—	2	1	no	—
91	C₂×Dic₁₉	—	4	1	no	—
92	C₂×Dic₁₉	—	4	1	no	—
93	C₂×Dic₁₉	—	4	1	no	—
94	C₂×Dic₁₉	SD₁₆	1	2	yes	complemented
95	Dic₃₈	—	2	2	no	—
96	Dic₃₈	—	2	2	no	—
97	Dic₃₈	—	2	2	no	—
98	Dic₃₈	C₂²⋊C₄	1	4	yes	complemented
99	C₈×C₁₉	—	4	1	no	—
100	C₁₉⋊C₈	—	2	2	no	—
101	#1880	—	19	1	no	maximal, Sylow
102	C₂²×C₁₉	—	4	2	no	—
103	C₂²×C₁₉	—	4	2	no	—
104	C₂²×C₁₉	—	4	2	no	—
105	C₂²×C₁₉	—	8	1	no	—
106	C₂²×C₁₉	—	8	1	no	—
107	C₂²×C₁₉	—	8	1	no	—
108	C₂²×C₁₉	—	8	1	no	—
109	C₂²×C₁₉	C₄×D₄	1	1	yes	characteristic
110	C₂²×C₁₉	#120	1	1	yes	characteristic
111	C₂²×C₁₉	#121	1	1	yes	characteristic
112	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
113	C₂²×C₁₉	#135	1	1	yes	characteristic
114	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
115	C₂²×C₁₉	#137	1	1	yes	characteristic
116	C₄×C₁₉	—	4	2	no	—
117	C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
118	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
119	C₄×C₁₉	#121	1	1	yes	characteristic
120	C₄×C₁₉	#123	1	1	yes	characteristic
121	Dic₁₉	—	2	4	no	—
122	Dic₁₉	—	2	2	no	—
123	Dic₁₉	—	4	1	no	—
124	Dic₁₉	—	8	1	no	—
125	C₂²×SD₁₆	—	19	1	no	—
126	C₂×C₄×Q₈	—	19	1	no	—
127	C₂×#103	—	19	1	no	—
128	C₂×#102	D₁₉	1	1	yes	characteristic
129	#390	—	19	1	no	—
130	#340	—	19	1	no	—
131	#336	—	19	1	no	—
132	C₂×C₁₉	—	8	2	no	—
133	C₂×C₁₉	#386	1	1	yes	characteristic
134	C₂×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
135	C₂×C₁₉	#440	1	1	yes	characteristic
136	C₂×C₁₉	#448	1	1	yes	characteristic
137	C₂×C₁₉	#449	1	1	yes	characteristic
138	C₂×C₁₉	#460	1	1	yes	characteristic
139	C₂×C₁₉	#464	1	1	yes	characteristic
140	C₂²×Q₈	—	19	1	no	—
141	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
142	C₂×SD₁₆	—	19	4	no	—
143	C₂×SD₁₆	—	38	2	no	—
144	C₂×SD₁₆	—	38	2	no	—
145	C₂²×C₈	—	19	1	no	—
146	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
147	C₄×Q₈	—	38	2	no	—
148	C₄×Q₈	—	38	2	no	—
149	C₂×C₄⋊C₄	—	19	1	no	—
150	C₂×C₄⋊C₄	—	38	1	no	—
151	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
152	C₂×C₂²⋊C₄	—	38	1	no	—
153	C₂×C₂²⋊C₄	—	38	1	no	—
154	C₂×C₄²	—	19	1	no	—
155	C₂×C₄²	—	38	1	no	—
156	#103	—	38	2	no	—
157	#102	—	2	2	no	—
158	C₁₉	#1880	1	1	yes	characteristic, complemented, Sylow
159	C₂⁴	—	2	1	no	—
160	C₂×Q₈	—	19	2	no	—
161	C₂×Q₈	—	19	2	no	—
162	C₂×Q₈	—	19	2	no	—
163	C₂×Q₈	—	38	1	no	—
164	C₂×Q₈	—	38	1	no	—
165	C₂×Q₈	—	38	1	no	—
166	C₂×D₄	—	2	1	no	—
167	C₂×D₄	—	2	1	no	—
168	C₂×D₄	—	2	1	no	—
169	C₂×D₄	—	2	1	no	—
170	C₂×D₄	—	2	1	no	—
171	C₂×D₄	C₄×D₁₉	1	2	yes	—
172	C₂²×C₄	—	2	1	no	—
173	C₂²×C₄	—	19	1	no	—
174	C₂²×C₄	—	19	1	no	—
175	C₂²×C₄	—	38	1	no	—
176	C₂²×C₄	—	38	1	no	—
177	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
178	SD₁₆	—	38	8	no	—
179	C₂×C₈	—	2	1	no	—
180	C₂×C₈	—	2	1	no	—
181	C₂×C₈	—	2	1	no	—
182	C₂×C₈	—	19	2	no	—
183	C₂×C₈	—	38	1	no	—
184	C₂×C₈	—	38	1	no	—
185	C₄⋊C₄	—	2	1	no	—
186	C₄⋊C₄	—	38	4	no	—
187	C₄⋊C₄	—	38	1	no	—
188	C₄⋊C₄	—	38	1	no	—
189	C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
190	C₂²⋊C₄	—	76	2	no	—
191	C₂²⋊C₄	—	76	2	no	—
192	C₄²	—	38	4	no	—
193	C₄²	—	38	1	no	—
194	C₄²	—	38	1	no	—
195	C₂³	—	2	2	no	—
196	C₂³	—	4	1	no	—
197	C₂³	—	4	1	no	—
198	C₂³	—	4	1	no	—
199	C₂³	—	4	1	no	—
200	C₂³	—	4	1	no	—
201	C₂³	—	4	1	no	—
202	C₂³	D₄×D₁₉	1	1	yes	characteristic
203	Q₈	—	19	4	no	—
204	Q₈	—	38	2	no	—
205	Q₈	—	38	2	no	—
206	Q₈	—	38	2	no	—
207	D₄	—	2	2	no	—
208	D₄	—	2	2	no	—
209	D₄	—	4	1	no	—
210	D₄	—	4	1	no	—
211	C₂×C₄	—	2	2	no	—
212	C₂×C₄	—	4	1	no	—
213	C₂×C₄	—	4	1	no	—
214	C₂×C₄	—	19	2	no	—
215	C₂×C₄	—	38	1	no	—
216	C₂×C₄	—	38	2	no	—
217	C₂×C₄	—	38	2	no	—
218	C₂×C₄	—	38	2	no	—
219	C₂×C₄	—	38	1	no	—
220	C₂×C₄	—	38	1	no	—
221	C₂×C₄	—	38	1	no	—
222	C₂×C₄	—	38	1	no	—
223	C₂×C₄	—	76	1	no	—
224	C₂×C₄	—	76	1	no	—
225	C₂×C₄	—	76	1	no	—
226	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
227	C₂×C₄	#64541	1	1	yes	characteristic
228	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
229	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
230	C₂×C₄	#64543	1	1	yes	characteristic
231	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
232	C₈	—	4	1	no	—
233	C₈	—	38	2	no	—
234	C₂²	—	4	2	no	—
235	C₂²	—	4	2	no	—
236	C₂²	—	4	2	no	—
237	C₂²	—	8	1	no	—
238	C₂²	—	8	1	no	—
239	C₂²	—	8	1	no	—
240	C₂²	—	8	1	no	—
241	C₂²	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
242	C₂²	#10597330	1	1	yes	characteristic
243	C₂²	#10597357	1	1	yes	characteristic
244	C₂²	#10597358	1	1	yes	characteristic
245	C₂²	SD₁₆×D₁₉	1	1	yes	characteristic
246	C₂²	#10597361	1	1	yes	characteristic
247	C₂²	#10597383	1	1	yes	characteristic
248	C₄	—	4	2	no	—
249	C₄	—	38	4	no	—
250	C₄	—	38	2	no	—
251	C₄	—	76	1	no	—
252	C₄	—	152	1	no	—
253	C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
254	C₄	#10597329	1	1	yes	characteristic
255	C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
256	C₄	#10597384	1	1	yes	characteristic
257	C₂	—	8	2	no	—
258	C₂	#11926420	1	1	yes	characteristic
259	C₂	#11926635	1	1	yes	characteristic
260	C₂	#11926641	1	1	yes	characteristic
261	C₂	#11926681	1	1	yes	characteristic
262	C₂	#11926686	1	1	yes	characteristic
263	C₂	#11926743	1	1	yes	characteristic
264	C₂	#11926765	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#64526

C₂

yes

maximal, characteristic

C₂×#10597333

C₂

yes

maximal, characteristic, complemented

C₂×#10597273

C₂

yes

maximal, characteristic, complemented

#11926447

C₂

yes

maximal, characteristic

#11926306

C₂

yes

maximal, characteristic, complemented

#11926298

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#102

C₂

yes

maximal, characteristic

C₂²×D₄×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊Dic₁₉

—

C₂×C₂²⋊Dic₁₉

—

C₂×#64526

—

C₂×#64526

—

C₂×#64526

C₄

yes

complemented

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

#10597333

—

#10597333

—

C₁₉×#102

—

#10597273

—

C₂⁴×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

D₄

yes

characteristic

C₂²×Dic₁₉

D₄

yes

characteristic

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂×C₄

yes

—

C₂×Dic₃₈

D₄

yes

—

C₂×Dic₃₈

D₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

#64526

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

SD₁₆

yes

complemented

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

C₂²⋊C₄

yes

complemented

C₈×C₁₉

—

100

C₁₉⋊C₈

—

101

#1880

—

maximal, Sylow

102

C₂²×C₁₉

—

103

C₂²×C₁₉

—

104

C₂²×C₁₉

—

105

C₂²×C₁₉

—

106

C₂²×C₁₉

—

107

C₂²×C₁₉

—

108

C₂²×C₁₉

—

109

C₂²×C₁₉

C₄×D₄

yes

characteristic

110

C₂²×C₁₉

#120

yes

characteristic

111

C₂²×C₁₉

#121

yes

characteristic

112

C₂²×C₁₉

C₂×SD₁₆

yes

characteristic

113

C₂²×C₁₉

#135

yes

characteristic

114

C₂²×C₁₉

AGL(1,ℤ/8)

yes

characteristic

115

C₂²×C₁₉

#137

yes

characteristic

116

C₄×C₁₉

—

117

C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

118

C₄×C₁₉

C₄×D₄

yes

characteristic

119

C₄×C₁₉

#121

yes

characteristic

120

C₄×C₁₉

#123

yes

characteristic

121

Dic₁₉

—

122

Dic₁₉

—

123

Dic₁₉

—

124

Dic₁₉

—

125

C₂²×SD₁₆

—

126

C₂×C₄×Q₈

—

127

C₂×#103

—

128

C₂×#102

D₁₉

yes

characteristic

129

#390

—

130

#340

—

131

#336

—

132

C₂×C₁₉

—

133

C₂×C₁₉

#386

yes

characteristic

134

C₂×C₁₉

C₄×SD₁₆

yes

characteristic

135

C₂×C₁₉

#440

yes

characteristic

136

C₂×C₁₉

#448

yes

characteristic

137

C₂×C₁₉

#449

yes

characteristic

138

C₂×C₁₉

#460

yes

characteristic

139

C₂×C₁₉

#464

yes

characteristic

140

C₂²×Q₈

—

141

C₂²×D₄

C₂×D₁₉

yes

characteristic

142

C₂×SD₁₆

—

143

C₂×SD₁₆

—

144

C₂×SD₁₆

—

145

C₂²×C₈

—

146

C₂²×C₈

C₂×D₁₉

yes

characteristic

147

C₄×Q₈

—

148

C₄×Q₈

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

152

C₂×C₂²⋊C₄

—

153

C₂×C₂²⋊C₄

—

154

C₂×C₄²

—

155

C₂×C₄²

—

156

#103

—

157

#102

—

158

C₁₉

#1880

yes

characteristic, complemented, Sylow

159

C₂⁴

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×D₄

—

167

C₂×D₄

—

168

C₂×D₄

—

169

C₂×D₄

—

170

C₂×D₄

—

171

C₂×D₄

C₄×D₁₉

yes

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

C₂²×D₁₉

yes

characteristic

178

SD₁₆

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

C₂²⋊D₁₉

yes

—

190

C₂²⋊C₄

—

191

C₂²⋊C₄

—

192

C₄²

—

193

C₄²

—

194

C₄²

—

195

C₂³

—

196

C₂³

—

197

C₂³

—

198

C₂³

—

199

C₂³

—

200

C₂³

—

201

C₂³

—

202

C₂³

D₄×D₁₉

yes

characteristic

203

Q₈

—

204

Q₈

—

205

Q₈

—

206

Q₈

—

207

D₄

—

208

D₄

—

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

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

227

C₂×C₄

#64541

yes

characteristic

228

C₂×C₄

D₄×D₁₉

yes

characteristic

229

C₂×C₄

D₄×D₁₉

yes

characteristic

230

C₂×C₄

#64543

yes

characteristic

231

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

232

C₈

—

233

C₈

—

234

C₂²

—

235

C₂²

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

241

C₂²

(C₂²⋊D₁₉)⋊C₄

yes

characteristic

242

C₂²

#10597330

yes

characteristic

243

C₂²

#10597357

yes

characteristic

244

C₂²

#10597358

yes

characteristic

245

C₂²

SD₁₆×D₁₉

yes

characteristic

246

C₂²

#10597361

yes

characteristic

247

C₂²

#10597383

yes

characteristic

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

—

152

—

253

C₄

C₂²⋊C₄×D₁₉

yes

characteristic

254

C₄

#10597329

yes

characteristic

255

C₄

C₄×C₂²⋊D₁₉

yes

characteristic

256

C₄

#10597384

yes

characteristic

257

C₂

—

258

C₂

#11926420

yes

characteristic

259

C₂

#11926635

yes

characteristic

260

C₂

#11926641

yes

characteristic

261

C₂

#11926681

yes

characteristic

262

C₂

#11926686

yes

characteristic

263

C₂

#11926743

yes

characteristic

264

C₂

#11926765

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#102	C₂
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂²×D₄×C₁₉	C₂²
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×#102	D₁₉
hypocenter	C₁₉	#1880
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#102

subgroup

G/H

center

C₂³

D₄×D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#102

C₂

socle

C₂³×C₁₉

C₂×D₄

prime radical

C₂²×D₄×C₁₉

C₂²

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#102

N	H ≅ G/N	type
2. C₂×#10597333	C₂	semidirect
3. C₂×#10597273	C₂	semidirect
5. #11926306	C₂	semidirect
6. #11926298	C₂	semidirect
16. C₂×#64526	C₄	semidirect
94. C₂×Dic₁₉	SD₁₆	semidirect
98. Dic₃₈	C₂²⋊C₄	semidirect
158. C₁₉	#1880	semidirect

H ≅ G/N

type

2. C₂×#10597333

C₂

semidirect

3. C₂×#10597273

C₂

semidirect

5. #11926306

C₂

semidirect

6. #11926298

C₂

semidirect

16. C₂×#64526

C₄

semidirect

94. C₂×Dic₁₉

SD₁₆

semidirect

98. Dic₃₈

C₂²⋊C₄

semidirect

158. C₁₉

#1880

semidirect

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

subgroup	index
C₂²×#64526	2
C₂×#10597333	2
C₂×#10597273	2
#11926447	2
#11926306	2
#11926298	2
C₂×C₁₉×#102	2
#1880	19

subgroup

index

C₂²×#64526

C₂×C₁₉×#102

Subgroups — #14563987

Conjugacy classes of subgroups

Complements

Maximal subgroups