Group #18017919 — subgroups

Subgroups — C₁₉×#11960 #18017919

Order 4864.

392 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 118 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	C₁₉×#3147	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2163	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1568	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1360	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₉×#135	—	2	1	no	—
6	C₂×C₁₉×#135	C₄	1	2	yes	—
7	C₁₉×#532	—	2	1	no	—
8	C₁₉×#495	—	2	1	no	—
9	C₁₉×#495	C₂²	1	2	yes	—
10	C₁₉×#494	C₄	1	1	yes	characteristic
11	C₁₉×#493	C₄	1	1	yes	characteristic
12	C₁₉×#492	—	2	1	no	—
13	C₁₉×#432	—	2	1	no	—
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×C₄⋊C₁₆	C₂²	1	2	yes	—
16	C₁₉×C₂²⋊C₁₆	—	2	1	no	—
17	C₁₉×#346	—	2	1	no	—
18	C₁₉×#335	—	2	1	no	—
19	C₁₉×#334	C₂²	1	2	yes	—
20	C₂×#41×C₁₉	—	2	2	no	—
21	C₁₉×#135	—	4	4	no	—
22	C₁₉×#135	—	4	4	no	—
23	C₂×Q₁₆×C₁₉	—	2	1	no	—
24	C₂×Q₁₆×C₁₉	C₂×C₄	1	2	yes	—
25	C₂×SD₁₆×C₁₉	—	2	2	no	—
26	C₂×SD₁₆×C₁₉	—	2	2	no	—
27	C₂×D₈×C₁₉	—	2	1	no	—
28	C₂×D₈×C₁₉	C₂×C₄	1	2	yes	—
29	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
31	C₁₉×C₄⋊Q₈	—	2	1	no	—
32	C₁₉×#127	—	2	1	no	—
33	C₁₉×#124	—	2	2	no	—
34	C₁₉×#121	—	4	1	no	—
35	C₁₉×#121	—	4	1	no	—
36	C₄×D₄×C₁₉	—	4	1	no	—
37	C₄×D₄×C₁₉	—	4	1	no	—
38	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
39	C₂×C₁₆×C₁₉	—	2	2	no	—
40	C₁₉×C₄⋊C₈	—	2	2	no	—
41	C₁₉×C₂²⋊C₈	—	4	1	no	—
42	C₁₉×#97	—	4	1	no	—
43	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
45	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
46	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
47	#41×C₁₉	—	4	4	no	—
48	#41×C₁₉	—	4	4	no	—
49	C₂×Q₈×C₁₉	—	2	2	no	—
50	C₂×D₄×C₁₉	—	2	2	no	—
51	C₂×D₄×C₁₉	—	4	2	no	—
52	C₂×D₄×C₁₉	—	4	1	no	—
53	C₂×D₄×C₁₉	—	4	1	no	—
54	C₂²×C₄×C₁₉	—	4	2	no	—
55	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
58	Q₁₆×C₁₉	—	4	2	no	—
59	Q₁₆×C₁₉	—	4	2	no	—
60	SD₁₆×C₁₉	—	4	4	no	—
61	SD₁₆×C₁₉	—	4	4	no	—
62	D₈×C₁₉	—	4	2	no	—
63	D₈×C₁₉	—	4	2	no	—
64	C₂×C₈×C₁₉	—	2	2	no	—
65	C₂×C₈×C₁₉	—	2	2	no	—
66	C₂×C₈×C₁₉	—	4	2	no	—
67	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
68	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
70	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₄⋊C₄×C₁₉	—	4	1	no	—
72	C₄⋊C₄×C₁₉	—	4	1	no	—
73	C₂²⋊C₄×C₁₉	—	4	2	no	—
74	C₂²⋊C₄×C₁₉	—	4	2	no	—
75	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
76	C₄²×C₁₉	D₈	1	1	yes	characteristic
77	C₄²×C₁₉	SD₁₆	1	1	yes	characteristic
78	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₁₆×C₁₉	—	4	2	no	—
80	#11960	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
81	C₂³×C₁₉	—	4	2	no	—
82	C₂³×C₁₉	#102	1	1	yes	characteristic
83	Q₈×C₁₉	—	4	2	no	—
84	Q₈×C₁₉	—	4	2	no	—
85	D₄×C₁₉	—	4	2	no	—
86	D₄×C₁₉	—	4	2	no	—
87	D₄×C₁₉	—	8	2	no	—
88	D₄×C₁₉	—	8	2	no	—
89	D₄×C₁₉	—	8	4	no	—
90	C₂×C₄×C₁₉	—	2	1	no	—
91	C₂×C₄×C₁₉	—	2	1	no	—
92	C₂×C₄×C₁₉	—	4	1	no	—
93	C₂×C₄×C₁₉	—	4	1	no	—
94	C₂×C₄×C₁₉	—	4	2	no	—
95	C₂×C₄×C₁₉	—	8	4	no	—
96	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
97	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
98	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
99	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
101	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
102	C₈×C₁₉	—	2	1	no	—
103	C₈×C₁₉	—	2	1	no	—
104	C₈×C₁₉	—	8	2	no	—
105	C₈×C₁₉	#100	1	2	yes	—
106	C₈×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
107	#3147	C₂×C₁₉	1	1	yes	characteristic
108	#2163	C₂×C₁₉	1	1	yes	characteristic, complemented
109	#1568	C₂×C₁₉	1	1	yes	characteristic, complemented
110	#1360	C₂×C₁₉	1	4	yes	complemented
111	C₂²×C₁₉	—	2	1	no	—
112	C₂²×C₁₉	—	2	1	no	—
113	C₂²×C₁₉	—	2	1	no	—
114	C₂²×C₁₉	—	8	2	no	—
115	C₂²×C₁₉	—	8	2	no	—
116	C₂²×C₁₉	—	8	2	no	—
117	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
118	C₄×C₁₉	—	2	1	no	—
119	C₄×C₁₉	—	2	1	no	—
120	C₄×C₁₉	—	2	1	no	—
121	C₄×C₁₉	—	2	1	no	—
122	C₄×C₁₉	—	2	1	no	—
123	C₄×C₁₉	—	8	2	no	—
124	C₄×C₁₉	C₂×#100	1	1	yes	characteristic
125	C₄×C₁₉	#418	1	1	yes	characteristic
126	C₂×#135	—	2	1	no	—
127	C₂×#135	C₄×C₁₉	1	2	yes	—
128	#532	—	2	1	no	—
129	#495	—	2	1	no	—
130	#495	C₂²×C₁₉	1	2	yes	—
131	#494	C₄×C₁₉	1	1	yes	characteristic
132	#493	C₄×C₁₉	1	1	yes	characteristic
133	#492	—	2	1	no	—
134	#432	—	2	1	no	—
135	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
136	C₄⋊C₁₆	C₂²×C₁₉	1	2	yes	—
137	C₂²⋊C₁₆	—	2	1	no	—
138	#346	—	2	1	no	—
139	#335	—	2	1	no	—
140	#334	C₂²×C₁₉	1	2	yes	—
141	C₂×C₁₉	—	4	1	no	—
142	C₂×C₁₉	—	16	2	no	—
143	C₂×C₁₉	#1545	1	1	yes	characteristic
144	C₂×C₁₉	#2143	1	1	yes	characteristic
145	C₂×C₁₉	#2145	1	1	yes	characteristic
146	C₂×#41	—	2	2	no	—
147	#135	—	4	4	no	—
148	#135	—	4	4	no	—
149	C₂×Q₁₆	—	2	1	no	—
150	C₂×Q₁₆	C₂×C₄×C₁₉	1	2	yes	—
151	C₂×SD₁₆	—	2	2	no	—
152	C₂×SD₁₆	—	2	2	no	—
153	C₂×D₈	—	2	1	no	—
154	C₂×D₈	C₂×C₄×C₁₉	1	2	yes	—
155	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
156	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
157	C₄⋊Q₈	—	2	1	no	—
158	#127	—	2	1	no	—
159	#124	—	2	2	no	—
160	#121	—	4	1	no	—
161	#121	—	4	1	no	—
162	C₄×D₄	—	4	1	no	—
163	C₄×D₄	—	4	1	no	—
164	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
165	C₂×C₁₆	—	2	2	no	—
166	C₄⋊C₈	—	2	2	no	—
167	C₂²⋊C₈	—	4	1	no	—
168	#97	—	4	1	no	—
169	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
170	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
171	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
172	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
173	C₁₉	#11960	1	1	yes	characteristic, direct product factor, Sylow
174	#41	—	4	4	no	—
175	#41	—	4	4	no	—
176	C₂×Q₈	—	2	2	no	—
177	C₂×D₄	—	2	2	no	—
178	C₂×D₄	—	4	2	no	—
179	C₂×D₄	—	4	1	no	—
180	C₂×D₄	—	4	1	no	—
181	C₂²×C₄	—	4	2	no	—
182	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
183	C₂²×C₄	D₈×C₁₉	1	1	yes	characteristic
184	C₂²×C₄	SD₁₆×C₁₉	1	1	yes	characteristic
185	Q₁₆	—	4	2	no	—
186	Q₁₆	—	4	2	no	—
187	SD₁₆	—	4	4	no	—
188	SD₁₆	—	4	4	no	—
189	D₈	—	4	2	no	—
190	D₈	—	4	2	no	—
191	C₂×C₈	—	2	2	no	—
192	C₂×C₈	—	2	2	no	—
193	C₂×C₈	—	4	2	no	—
194	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
195	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
196	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
197	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
198	C₄⋊C₄	—	4	1	no	—
199	C₄⋊C₄	—	4	1	no	—
200	C₂²⋊C₄	—	4	2	no	—
201	C₂²⋊C₄	—	4	2	no	—
202	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
203	C₄²	D₈×C₁₉	1	1	yes	characteristic
204	C₄²	SD₁₆×C₁₉	1	1	yes	characteristic
205	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
206	C₁₆	—	4	2	no	—
207	C₂³	—	4	2	no	—
208	C₂³	C₁₉×#102	1	1	yes	characteristic
209	Q₈	—	4	2	no	—
210	Q₈	—	4	2	no	—
211	D₄	—	4	2	no	—
212	D₄	—	4	2	no	—
213	D₄	—	8	2	no	—
214	D₄	—	8	2	no	—
215	D₄	—	8	4	no	—
216	C₂×C₄	—	2	1	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	4	1	no	—
219	C₂×C₄	—	4	1	no	—
220	C₂×C₄	—	4	2	no	—
221	C₂×C₄	—	8	4	no	—
222	C₂×C₄	C₁₉×#102	1	1	yes	characteristic
223	C₂×C₄	C₁₉×#102	1	1	yes	characteristic
224	C₂×C₄	C₁₉×#102	1	1	yes	characteristic
225	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
226	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
227	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
228	C₈	—	2	1	no	—
229	C₈	—	2	1	no	—
230	C₈	—	8	2	no	—
231	C₈	C₁₉×#100	1	2	yes	—
232	C₈	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
233	C₂²	—	2	1	no	—
234	C₂²	—	2	1	no	—
235	C₂²	—	2	1	no	—
236	C₂²	—	8	2	no	—
237	C₂²	—	8	2	no	—
238	C₂²	—	8	2	no	—
239	C₂²	C₂×C₁₉×#102	1	1	yes	characteristic
240	C₄	—	2	1	no	—
241	C₄	—	2	1	no	—
242	C₄	—	2	1	no	—
243	C₄	—	2	1	no	—
244	C₄	—	2	1	no	—
245	C₄	—	8	2	no	—
246	C₄	C₂×C₁₉×#100	1	1	yes	characteristic
247	C₄	C₁₉×#418	1	1	yes	characteristic
248	C₂	—	4	1	no	—
249	C₂	—	16	2	no	—
250	C₂	C₁₉×#1545	1	1	yes	characteristic
251	C₂	C₁₉×#2143	1	1	yes	characteristic
252	C₂	C₁₉×#2145	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#3147

C₂

yes

maximal, characteristic

C₁₉×#2163

C₂

yes

maximal, characteristic, complemented

C₁₉×#1568

C₂

yes

maximal, characteristic, complemented

C₁₉×#1360

C₂

yes

maximal, complemented

C₂×C₁₉×#135

—

C₂×C₁₉×#135

C₄

yes

—

C₁₉×#532

—

C₁₉×#495

—

C₁₉×#495

C₂²

yes

—

C₁₉×#494

C₄

yes

characteristic

C₁₉×#493

C₄

yes

characteristic

C₁₉×#492

—

C₁₉×#432

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×C₄⋊C₁₆

C₂²

yes

—

C₁₉×C₂²⋊C₁₆

—

C₁₉×#346

—

C₁₉×#335

—

C₁₉×#334

C₂²

yes

—

C₂×#41×C₁₉

—

C₁₉×#135

—

C₁₉×#135

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

C₂×C₄

yes

—

C₂×SD₁₆×C₁₉

—

C₂×SD₁₆×C₁₉

—

C₂×D₈×C₁₉

—

C₂×D₈×C₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₁₉×C₄⋊Q₈

—

C₁₉×#127

—

C₁₉×#124

—

C₁₉×#121

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₁₆×C₁₉

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

C₂³

yes

characteristic

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

D₈

yes

characteristic

C₂²×C₄×C₁₉

SD₁₆

yes

characteristic

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

SD₁₆×C₁₉

—

SD₁₆×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×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

C₂×D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₄²×C₁₉

D₈

yes

characteristic

C₄²×C₁₉

SD₁₆

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₁₆×C₁₉

—

#11960

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#102

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

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

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

100

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

101

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

102

C₈×C₁₉

—

103

C₈×C₁₉

—

104

C₈×C₁₉

—

105

C₈×C₁₉

#100

yes

—

106

C₈×C₁₉

AGL(1,ℤ/8)

yes

—

107

#3147

C₂×C₁₉

yes

characteristic

108

#2163

C₂×C₁₉

yes

characteristic, complemented

109

#1568

C₂×C₁₉

yes

characteristic, complemented

110

#1360

C₂×C₁₉

yes

complemented

111

C₂²×C₁₉

—

112

C₂²×C₁₉

—

113

C₂²×C₁₉

—

114

C₂²×C₁₉

—

115

C₂²×C₁₉

—

116

C₂²×C₁₉

—

117

C₂²×C₁₉

C₂×#102

yes

characteristic

118

C₄×C₁₉

—

119

C₄×C₁₉

—

120

C₄×C₁₉

—

121

C₄×C₁₉

—

122

C₄×C₁₉

—

123

C₄×C₁₉

—

124

C₄×C₁₉

C₂×#100

yes

characteristic

125

C₄×C₁₉

#418

yes

characteristic

126

C₂×#135

—

127

C₂×#135

C₄×C₁₉

yes

—

128

#532

—

129

#495

—

130

#495

C₂²×C₁₉

yes

—

131

#494

C₄×C₁₉

yes

characteristic

132

#493

C₄×C₁₉

yes

characteristic

133

#492

—

134

#432

—

135

C₂×C₄×C₈

C₂²×C₁₉

yes

characteristic

136

C₄⋊C₁₆

C₂²×C₁₉

yes

—

137

C₂²⋊C₁₆

—

138

#346

—

139

#335

—

140

#334

C₂²×C₁₉

yes

—

141

C₂×C₁₉

—

142

C₂×C₁₉

—

143

C₂×C₁₉

#1545

yes

characteristic

144

C₂×C₁₉

#2143

yes

characteristic

145

C₂×C₁₉

#2145

yes

characteristic

146

C₂×#41

—

147

#135

—

148

#135

—

149

C₂×Q₁₆

—

150

C₂×Q₁₆

C₂×C₄×C₁₉

yes

—

151

C₂×SD₁₆

—

152

C₂×SD₁₆

—

153

C₂×D₈

—

154

C₂×D₈

C₂×C₄×C₁₉

yes

—

155

C₂²×C₈

C₂×C₄×C₁₉

yes

characteristic

156

C₂²×C₈

D₄×C₁₉

yes

characteristic

157

C₄⋊Q₈

—

158

#127

—

159

#124

—

160

#121

—

161

#121

—

162

C₄×D₄

—

163

C₄×D₄

—

164

C₂×C₄²

D₄×C₁₉

yes

characteristic

165

C₂×C₁₆

—

166

C₄⋊C₈

—

167

C₂²⋊C₈

—

168

#97

—

169

C₄×C₈

C₂×C₄×C₁₉

yes

characteristic

170

C₄×C₈

D₄×C₁₉

yes

characteristic

171

C₄×C₈

D₄×C₁₉

yes

characteristic

172

C₄×C₈

C₂³×C₁₉

yes

characteristic

173

C₁₉

#11960

yes

characteristic, direct product factor, Sylow

174

#41

—

175

#41

—

176

C₂×Q₈

—

177

C₂×D₄

—

178

C₂×D₄

—

179

C₂×D₄

—

180

C₂×D₄

—

181

C₂²×C₄

—

182

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

183

C₂²×C₄

D₈×C₁₉

yes

characteristic

184

C₂²×C₄

SD₁₆×C₁₉

yes

characteristic

185

Q₁₆

—

186

Q₁₆

—

187

SD₁₆

—

188

SD₁₆

—

189

D₈

—

190

D₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

C₂²⋊C₄×C₁₉

yes

characteristic

195

C₂×C₈

C₂²⋊C₄×C₁₉

yes

characteristic

196

C₂×C₈

C₂²×C₄×C₁₉

yes

characteristic

197

C₂×C₈

C₂×D₄×C₁₉

yes

characteristic

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₂²⋊C₄

—

201

C₂²⋊C₄

—

202

C₄²

C₂²⋊C₄×C₁₉

yes

characteristic

203

C₄²

D₈×C₁₉

yes

characteristic

204

C₄²

SD₁₆×C₁₉

yes

characteristic

205

C₄²

C₂×D₄×C₁₉

yes

characteristic

206

C₁₆

—

207

C₂³

—

208

C₂³

C₁₉×#102

yes

characteristic

209

Q₈

—

210

Q₈

—

211

D₄

—

212

D₄

—

213

D₄

—

214

D₄

—

215

D₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

C₁₉×#102

yes

characteristic

223

C₂×C₄

C₁₉×#102

yes

characteristic

224

C₂×C₄

C₁₉×#102

yes

characteristic

225

C₂×C₄

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

226

C₂×C₄

C₂×D₈×C₁₉

yes

characteristic

227

C₂×C₄

C₂×SD₁₆×C₁₉

yes

characteristic

228

C₈

—

229

C₈

—

230

C₈

—

231

C₈

C₁₉×#100

yes

—

232

C₈

C₁₉×AGL(1,ℤ/8)

yes

—

233

C₂²

—

234

C₂²

—

235

C₂²

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

C₂×C₁₉×#102

yes

characteristic

240

C₄

—

241

C₄

—

242

C₄

—

243

C₄

—

244

C₄

—

245

C₄

—

246

C₄

C₂×C₁₉×#100

yes

characteristic

247

C₄

C₁₉×#418

yes

characteristic

248

C₂

—

249

C₂

—

250

C₂

C₁₉×#1545

yes

characteristic

251

C₂

C₁₉×#2143

yes

characteristic

252

C₂

C₁₉×#2145

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₄×C₈	C₂³×C₁₉
prime radical	C₁₉×#3147	C₂
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

C₂×#102

commutator

C₂×C₈

C₂²×C₄×C₁₉

Frattini, cosocle

C₄×C₈

C₂³×C₁₉

prime radical

C₁₉×#3147

C₂

LCS

G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

N	H ≅ G/N	type
2. C₁₉×#2163	C₂	semidirect
3. C₁₉×#1568	C₂	semidirect
4. C₁₉×#1360	C₂	semidirect
80. #11960	C₁₉	direct (N × H)
108. #2163	C₂×C₁₉	semidirect
109. #1568	C₂×C₁₉	semidirect
110. #1360	C₂×C₁₉	semidirect
173. C₁₉	#11960	direct (N × H)

H ≅ G/N

type

2. C₁₉×#2163

C₂

semidirect

3. C₁₉×#1568

C₂

semidirect

4. C₁₉×#1360

C₂

semidirect

80. #11960

C₁₉

direct (N × H)

108. #2163

C₂×C₁₉

semidirect

109. #1568

C₂×C₁₉

semidirect

110. #1360

C₂×C₁₉

semidirect

173. C₁₉

#11960

direct (N × H)

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

subgroup	index
C₁₉×#3147	2
C₁₉×#2163	2
C₁₉×#1568	2
C₁₉×#1360	2
#11960	19

subgroup

index

C₁₉×#3147

C₁₉×#2163

C₁₉×#1568

C₁₉×#1360

#11960

Subgroups — C₁₉×#11960 #18017919

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#11960 #18017919

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11960 #18017919