Group #18014485 — subgroups

Subgroups — C₁₉×#8526 #18014485

Order 4864.

784 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 142 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×C₁₉×#540	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1555	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1534	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1464	C₂	1	2	yes	maximal, complemented
5	C₁₉×#540	—	2	4	no	—
6	C₁₉×#540	—	2	4	no	—
7	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
8	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×#123	—	2	2	no	—
10	C₂×C₁₉×#121	—	2	2	no	—
11	C₂×C₁₉×#121	C₄	1	2	yes	—
12	C₂×C₄×D₄×C₁₉	C₄	1	2	yes	—
13	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
14	C₁₉×#432	C₂²	1	4	yes	—
15	C₁₉×#331	—	2	4	no	—
16	C₁₉×#330	—	2	4	no	—
17	C₁₉×#324	—	2	2	no	—
18	C₁₉×#323	—	2	2	no	—
19	C₂²×D₄×C₁₉	—	2	2	no	—
20	C₂²×D₄×C₁₉	—	2	2	no	—
21	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
22	C₂³×C₄×C₁₉	—	2	2	no	—
23	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₁₉×#127	—	2	2	no	—
25	C₁₉×#127	D₄	1	4	yes	—
26	C₁₉×#125	—	2	2	no	—
27	C₁₉×#125	D₄	1	4	yes	—
28	C₁₉×#123	—	2	16	no	—
29	C₁₉×#121	—	2	16	no	—
30	C₁₉×#121	—	2	4	no	—
31	C₁₉×#121	—	2	4	no	—
32	C₄×D₄×C₁₉	—	2	4	no	—
33	C₄×D₄×C₁₉	—	2	4	no	—
34	C₁₉×#117	—	2	2	no	—
35	C₁₉×#117	—	2	2	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
37	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
38	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
39	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
40	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
41	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
42	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
44	C₁₉×C₄⋊C₈	—	2	4	no	—
45	C₁₉×C₂²⋊C₈	—	2	4	no	—
46	C₁₉×#97	—	2	4	no	—
47	C₂⁴×C₁₉	—	2	2	no	—
48	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
49	C₂×D₄×C₁₉	—	2	8	no	—
50	C₂×D₄×C₁₉	—	2	2	no	—
51	C₂×D₄×C₁₉	—	2	8	no	—
52	C₂×D₄×C₁₉	—	4	4	no	—
53	C₂×D₄×C₁₉	—	8	4	no	—
54	C₂×D₄×C₁₉	—	8	4	no	—
55	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
56	C₂²×C₄×C₁₉	—	2	2	no	—
57	C₂²×C₄×C₁₉	—	2	8	no	—
58	C₂²×C₄×C₁₉	—	2	1	no	—
59	C₂²×C₄×C₁₉	—	2	1	no	—
60	C₂²×C₄×C₁₉	—	4	2	no	—
61	C₂²×C₄×C₁₉	—	8	4	no	—
62	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
64	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
66	C₂×C₈×C₁₉	—	4	4	no	—
67	C₄⋊C₄×C₁₉	—	2	2	no	—
68	C₄⋊C₄×C₁₉	—	2	8	no	—
69	C₄⋊C₄×C₁₉	—	2	4	no	—
70	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
71	C₂²⋊C₄×C₁₉	—	2	8	no	—
72	C₂²⋊C₄×C₁₉	—	2	8	no	—
73	C₂²⋊C₄×C₁₉	—	2	4	no	—
74	C₄²×C₁₉	—	2	1	no	—
75	C₄²×C₁₉	—	2	1	no	—
76	C₄²×C₁₉	C₂×D₄	1	2	yes	—
77	C₄²×C₁₉	C₂×D₄	1	2	yes	—
78	#8526	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
79	C₂³×C₁₉	—	2	1	no	—
80	C₂³×C₁₉	—	2	4	no	—
81	C₂³×C₁₉	—	2	2	no	—
82	C₂³×C₁₉	—	4	4	no	—
83	C₂³×C₁₉	—	4	4	no	—
84	C₂³×C₁₉	—	4	2	no	—
85	C₂³×C₁₉	—	4	4	no	—
86	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
87	D₄×C₁₉	—	4	4	no	—
88	D₄×C₁₉	—	4	4	no	—
89	D₄×C₁₉	—	8	8	no	—
90	D₄×C₁₉	—	8	8	no	—
91	C₂×C₄×C₁₉	—	2	2	no	—
92	C₂×C₄×C₁₉	—	2	2	no	—
93	C₂×C₄×C₁₉	—	2	1	no	—
94	C₂×C₄×C₁₉	—	2	4	no	—
95	C₂×C₄×C₁₉	—	2	2	no	—
96	C₂×C₄×C₁₉	—	4	2	no	—
97	C₂×C₄×C₁₉	—	4	2	no	—
98	C₂×C₄×C₁₉	—	4	2	no	—
99	C₂×C₄×C₁₉	—	4	4	no	—
100	C₂×C₄×C₁₉	—	4	2	no	—
101	C₂×C₄×C₁₉	—	8	8	no	—
102	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₄×C₁₉	#120	1	4	yes	—
105	C₈×C₁₉	—	8	4	no	—
106	C₂×#540	C₂×C₁₉	1	1	yes	characteristic
107	#1555	C₂×C₁₉	1	2	yes	complemented
108	#1534	C₂×C₁₉	1	2	yes	complemented
109	#1464	C₂×C₁₉	1	2	yes	complemented
110	C₂²×C₁₉	—	2	2	no	—
111	C₂²×C₁₉	—	4	4	no	—
112	C₂²×C₁₉	—	4	2	no	—
113	C₂²×C₁₉	—	4	4	no	—
114	C₂²×C₁₉	—	4	1	no	—
115	C₂²×C₁₉	—	4	4	no	—
116	C₂²×C₁₉	—	8	2	no	—
117	C₂²×C₁₉	—	8	8	no	—
118	C₂²×C₁₉	#379	1	1	yes	characteristic
119	C₂²×C₁₉	#413	1	2	yes	—
120	C₄×C₁₉	—	2	4	no	—
121	C₄×C₁₉	—	2	1	no	—
122	C₄×C₁₉	—	2	1	no	—
123	C₄×C₁₉	—	4	4	no	—
124	C₄×C₁₉	—	4	2	no	—
125	C₄×C₁₉	—	4	1	no	—
126	#540	—	2	4	no	—
127	#540	—	2	4	no	—
128	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
129	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
130	C₂×#123	—	2	2	no	—
131	C₂×#121	—	2	2	no	—
132	C₂×#121	C₄×C₁₉	1	2	yes	—
133	C₂×C₄×D₄	C₄×C₁₉	1	2	yes	—
134	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
135	#432	C₂²×C₁₉	1	4	yes	—
136	#331	—	2	4	no	—
137	#330	—	2	4	no	—
138	#324	—	2	2	no	—
139	#323	—	2	2	no	—
140	C₂×C₁₉	—	2	2	no	—
141	C₂×C₁₉	—	8	1	no	—
142	C₂×C₁₉	—	8	4	no	—
143	C₂×C₁₉	#1785	1	1	yes	characteristic
144	C₂×C₁₉	#1795	1	2	yes	—
145	C₂²×D₄	—	2	2	no	—
146	C₂²×D₄	—	2	2	no	—
147	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
148	C₂³×C₄	—	2	2	no	—
149	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
150	#127	—	2	2	no	—
151	#127	D₄×C₁₉	1	4	yes	—
152	#125	—	2	2	no	—
153	#125	D₄×C₁₉	1	4	yes	—
154	#123	—	2	16	no	—
155	#121	—	2	16	no	—
156	#121	—	2	4	no	—
157	#121	—	2	4	no	—
158	C₄×D₄	—	2	4	no	—
159	C₄×D₄	—	2	4	no	—
160	#117	—	2	2	no	—
161	#117	—	2	2	no	—
162	C₂×C₄⋊C₄	—	2	2	no	—
163	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
164	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
165	C₂×C₂²⋊C₄	—	2	2	no	—
166	C₂×C₂²⋊C₄	—	2	2	no	—
167	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
168	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
169	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
170	C₄⋊C₈	—	2	4	no	—
171	C₂²⋊C₈	—	2	4	no	—
172	#97	—	2	4	no	—
173	C₁₉	#8526	1	1	yes	characteristic, direct product factor, Sylow
174	C₂⁴	—	2	2	no	—
175	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
176	C₂×D₄	—	2	8	no	—
177	C₂×D₄	—	2	2	no	—
178	C₂×D₄	—	2	8	no	—
179	C₂×D₄	—	4	4	no	—
180	C₂×D₄	—	8	4	no	—
181	C₂×D₄	—	8	4	no	—
182	C₂×D₄	C₂²⋊C₄×C₁₉	1	4	yes	—
183	C₂²×C₄	—	2	2	no	—
184	C₂²×C₄	—	2	8	no	—
185	C₂²×C₄	—	2	1	no	—
186	C₂²×C₄	—	2	1	no	—
187	C₂²×C₄	—	4	2	no	—
188	C₂²×C₄	—	8	4	no	—
189	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
190	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
191	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
192	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
193	C₂×C₈	—	4	4	no	—
194	C₄⋊C₄	—	2	2	no	—
195	C₄⋊C₄	—	2	8	no	—
196	C₄⋊C₄	—	2	4	no	—
197	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
198	C₂²⋊C₄	—	2	8	no	—
199	C₂²⋊C₄	—	2	8	no	—
200	C₂²⋊C₄	—	2	4	no	—
201	C₄²	—	2	1	no	—
202	C₄²	—	2	1	no	—
203	C₄²	C₂×D₄×C₁₉	1	2	yes	—
204	C₄²	C₂×D₄×C₁₉	1	2	yes	—
205	C₂³	—	2	1	no	—
206	C₂³	—	2	4	no	—
207	C₂³	—	2	2	no	—
208	C₂³	—	4	4	no	—
209	C₂³	—	4	4	no	—
210	C₂³	—	4	2	no	—
211	C₂³	—	4	4	no	—
212	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
213	D₄	—	4	4	no	—
214	D₄	—	4	4	no	—
215	D₄	—	8	8	no	—
216	D₄	—	8	8	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	2	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	4	no	—
221	C₂×C₄	—	2	2	no	—
222	C₂×C₄	—	4	2	no	—
223	C₂×C₄	—	4	2	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	—	4	4	no	—
226	C₂×C₄	—	4	2	no	—
227	C₂×C₄	—	8	8	no	—
228	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
229	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
230	C₂×C₄	C₁₉×#120	1	4	yes	—
231	C₈	—	8	4	no	—
232	C₂²	—	2	2	no	—
233	C₂²	—	4	1	no	—
234	C₂²	—	4	4	no	—
235	C₂²	—	4	4	no	—
236	C₂²	—	4	4	no	—
237	C₂²	—	4	2	no	—
238	C₂²	—	8	2	no	—
239	C₂²	—	8	8	no	—
240	C₂²	C₁₉×#379	1	1	yes	characteristic
241	C₂²	C₁₉×#413	1	2	yes	—
242	C₄	—	2	1	no	—
243	C₄	—	2	1	no	—
244	C₄	—	2	4	no	—
245	C₄	—	4	1	no	—
246	C₄	—	4	4	no	—
247	C₄	—	4	2	no	—
248	C₂	—	2	2	no	—
249	C₂	—	8	4	no	—
250	C₂	—	8	1	no	—
251	C₂	C₁₉×#1785	1	1	yes	characteristic
252	C₂	C₁₉×#1795	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×#540

C₂

yes

maximal, characteristic

C₁₉×#1555

C₂

yes

maximal, complemented

C₁₉×#1534

C₂

yes

maximal, complemented

C₁₉×#1464

C₂

yes

maximal, complemented

C₁₉×#540

—

C₁₉×#540

—

C₂×C₁₉×#127

C₂²

yes

characteristic

C₂×C₁₉×#125

C₂²

yes

characteristic

C₂×C₁₉×#123

—

C₂×C₁₉×#121

—

C₂×C₁₉×#121

C₄

yes

—

C₂×C₄×D₄×C₁₉

C₄

yes

—

C₂×C₁₉×#117

C₂²

yes

characteristic

C₁₉×#432

C₂²

yes

—

C₁₉×#331

—

C₁₉×#330

—

C₁₉×#324

—

C₁₉×#323

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₁₉×#127

—

C₁₉×#127

D₄

yes

—

C₁₉×#125

—

C₁₉×#125

D₄

yes

—

C₁₉×#123

—

C₁₉×#121

—

C₁₉×#121

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₁₉×#117

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

#8526

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

100

C₂×C₄×C₁₉

—

101

C₂×C₄×C₁₉

—

102

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

103

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

104

C₂×C₄×C₁₉

#120

yes

—

105

C₈×C₁₉

—

106

C₂×#540

C₂×C₁₉

yes

characteristic

107

#1555

C₂×C₁₉

yes

complemented

108

#1534

C₂×C₁₉

yes

complemented

109

#1464

C₂×C₁₉

yes

complemented

110

C₂²×C₁₉

—

111

C₂²×C₁₉

—

112

C₂²×C₁₉

—

113

C₂²×C₁₉

—

114

C₂²×C₁₉

—

115

C₂²×C₁₉

—

116

C₂²×C₁₉

—

117

C₂²×C₁₉

—

118

C₂²×C₁₉

#379

yes

characteristic

119

C₂²×C₁₉

#413

yes

—

120

C₄×C₁₉

—

121

C₄×C₁₉

—

122

C₄×C₁₉

—

123

C₄×C₁₉

—

124

C₄×C₁₉

—

125

C₄×C₁₉

—

126

#540

—

127

#540

—

128

C₂×#127

C₂²×C₁₉

yes

characteristic

129

C₂×#125

C₂²×C₁₉

yes

characteristic

130

C₂×#123

—

131

C₂×#121

—

132

C₂×#121

C₄×C₁₉

yes

—

133

C₂×C₄×D₄

C₄×C₁₉

yes

—

134

C₂×#117

C₂²×C₁₉

yes

characteristic

135

#432

C₂²×C₁₉

yes

—

136

#331

—

137

#330

—

138

#324

—

139

#323

—

140

C₂×C₁₉

—

141

C₂×C₁₉

—

142

C₂×C₁₉

—

143

C₂×C₁₉

#1785

yes

characteristic

144

C₂×C₁₉

#1795

yes

—

145

C₂²×D₄

—

146

C₂²×D₄

—

147

C₂²×D₄

C₂×C₄×C₁₉

yes

—

148

C₂³×C₄

—

149

C₂³×C₄

C₂×C₄×C₁₉

yes

characteristic

150

#127

—

151

#127

D₄×C₁₉

yes

—

152

#125

—

153

#125

D₄×C₁₉

yes

—

154

#123

—

155

#121

—

156

#121

—

157

#121

—

158

C₄×D₄

—

159

C₄×D₄

—

160

#117

—

161

#117

—

162

C₂×C₄⋊C₄

—

163

C₂×C₄⋊C₄

C₂×C₄×C₁₉

yes

—

164

C₂×C₄⋊C₄

D₄×C₁₉

yes

—

165

C₂×C₂²⋊C₄

—

166

C₂×C₂²⋊C₄

—

167

C₂×C₂²⋊C₄

D₄×C₁₉

yes

—

168

C₂×C₄²

C₂×C₄×C₁₉

yes

characteristic

169

C₂×C₄²

C₂³×C₁₉

yes

characteristic

170

C₄⋊C₈

—

171

C₂²⋊C₈

—

172

#97

—

173

C₁₉

#8526

yes

characteristic, direct product factor, Sylow

174

C₂⁴

—

175

C₂⁴

C₂²⋊C₄×C₁₉

yes

characteristic

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂×D₄

—

179

C₂×D₄

—

180

C₂×D₄

—

181

C₂×D₄

—

182

C₂×D₄

C₂²⋊C₄×C₁₉

yes

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

—

188

C₂²×C₄

—

189

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

190

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

—

191

C₂²×C₄

C₂²×C₄×C₁₉

yes

characteristic

192

C₂²×C₄

C₂×D₄×C₁₉

yes

—

193

C₂×C₈

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

C₂²⋊C₄×C₁₉

yes

—

198

C₂²⋊C₄

—

199

C₂²⋊C₄

—

200

C₂²⋊C₄

—

201

C₄²

—

202

C₄²

—

203

C₄²

C₂×D₄×C₁₉

yes

—

204

C₄²

C₂×D₄×C₁₉

yes

—

205

C₂³

—

206

C₂³

—

207

C₂³

—

208

C₂³

—

209

C₂³

—

210

C₂³

—

211

C₂³

—

212

C₂³

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

213

D₄

—

214

D₄

—

215

D₄

—

216

D₄

—

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

—

227

C₂×C₄

—

228

C₂×C₄

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

229

C₂×C₄

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

230

C₂×C₄

C₁₉×#120

yes

—

231

C₈

—

232

C₂²

—

233

C₂²

—

234

C₂²

—

235

C₂²

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

—

240

C₂²

C₁₉×#379

yes

characteristic

241

C₂²

C₁₉×#413

yes

—

242

C₄

—

243

C₄

—

244

C₄

—

245

C₄

—

246

C₄

—

247

C₄

—

248

C₂

—

249

C₂

—

250

C₂

—

251

C₂

C₁₉×#1785

yes

characteristic

252

C₂

C₁₉×#1795

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂×C₁₉×#540	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#379

commutator

C₂²×C₄

C₂²×C₄×C₁₉

Frattini, cosocle

C₂×C₄²

C₂³×C₁₉

prime radical

C₂×C₁₉×#540

C₂

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
2. C₁₉×#1555	C₂	semidirect
3. C₁₉×#1534	C₂	semidirect
4. C₁₉×#1464	C₂	semidirect
78. #8526	C₁₉	direct (N × H)
107. #1555	C₂×C₁₉	semidirect
108. #1534	C₂×C₁₉	semidirect
109. #1464	C₂×C₁₉	semidirect
173. C₁₉	#8526	direct (N × H)

H ≅ G/N

type

2. C₁₉×#1555

C₂

semidirect

3. C₁₉×#1534

C₂

semidirect

4. C₁₉×#1464

C₂

semidirect

78. #8526

C₁₉

direct (N × H)

107. #1555

C₂×C₁₉

semidirect

108. #1534

C₂×C₁₉

semidirect

109. #1464

C₂×C₁₉

semidirect

173. C₁₉

#8526

direct (N × H)

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

subgroup	index
C₂×C₁₉×#540	2
C₁₉×#1555	2
C₁₉×#1534	2
C₁₉×#1464	2
#8526	19

subgroup

index

C₂×C₁₉×#540

C₁₉×#1555

C₁₉×#1534

C₁₉×#1464

#8526

Subgroups — C₁₉×#8526 #18014485

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#8526 #18014485

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8526 #18014485