Group #18018071 — subgroups

Subgroups — C₁₉×#12112 #18018071

Order 4864.

390 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 74 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×#3202	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2188	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2020	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1350	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1315	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉×#137	—	2	1	no	—
7	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#536	—	2	1	no	—
9	C₂×C₁₉×Q₃₂	—	2	2	no	—
10	C₁₉×#485	—	2	2	no	—
11	C₁₉×#470	—	2	1	no	—
12	C₁₉×#467	C₂²	1	2	yes	—
13	C₁₉×#451	—	2	2	no	—
14	C₂×C₁₉×#101	—	2	1	no	—
15	C₁₉×#408	C₂²	1	1	yes	characteristic
16	C₁₉×#358	—	2	2	no	—
17	C₁₉×C₂²⋊C₁₆	C₂²	1	2	yes	—
18	C₁₉×#341	C₂²	1	1	yes	characteristic
19	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
20	C₂²×Q₈×C₁₉	—	2	1	no	—
21	C₂²×Q₈×C₁₉	—	2	1	no	—
22	C₁₉×#137	—	4	2	no	—
23	C₁₉×#137	—	4	2	no	—
24	C₂×Q₁₆×C₁₉	—	2	1	no	—
25	C₂×Q₁₆×C₁₉	—	2	2	no	—
26	C₂×Q₁₆×C₁₉	—	4	2	no	—
27	C₂×Q₁₆×C₁₉	—	4	1	no	—
28	C₂×Q₁₆×C₁₉	D₄	1	2	yes	—
29	C₂×SD₁₆×C₁₉	—	4	1	no	—
30	C₂×M₁₆×C₁₉	—	2	1	no	—
31	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
33	C₁₉×C₄⋊Q₈	—	4	1	no	—
34	C₁₉×#124	—	4	1	no	—
35	C₁₉×#123	—	4	1	no	—
36	C₁₉×#123	—	4	1	no	—
37	C₁₉×C₂²⋊Q₈	—	2	2	no	—
38	C₁₉×C₂²⋊Q₈	—	2	2	no	—
39	C₁₉×#117	—	2	1	no	—
40	C₁₉×Q₃₂	—	4	4	no	—
41	C₂×C₁₆×C₁₉	—	2	2	no	—
42	C₁₉×#107	D₄	1	2	yes	—
43	C₁₉×#106	—	2	1	no	—
44	C₁₉×#103	—	2	2	no	—
45	C₁₉×#103	—	2	2	no	—
46	C₁₉×#101	—	4	2	no	—
47	C₁₉×C₂²⋊C₈	—	2	2	no	—
48	#41×C₁₉	—	4	1	no	—
49	#41×C₁₉	—	4	1	no	—
50	C₂×Q₈×C₁₉	—	2	2	no	—
51	C₂×Q₈×C₁₉	—	2	2	no	—
52	C₂×Q₈×C₁₉	—	4	1	no	—
53	C₂×Q₈×C₁₉	—	4	1	no	—
54	C₂×Q₈×C₁₉	—	4	1	no	—
55	C₂×Q₈×C₁₉	—	4	1	no	—
56	C₂×Q₈×C₁₉	—	4	1	no	—
57	C₂×Q₈×C₁₉	—	4	1	no	—
58	C₂×Q₈×C₁₉	—	8	1	no	—
59	C₂×Q₈×C₁₉	—	8	1	no	—
60	C₂×Q₈×C₁₉	D₈	1	1	yes	characteristic
61	C₂×D₄×C₁₉	—	2	1	no	—
62	C₂×D₄×C₁₉	D₈	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	—	2	1	no	—
64	C₂²×C₄×C₁₉	—	4	1	no	—
65	C₂²×C₄×C₁₉	—	4	1	no	—
66	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
67	Q₁₆×C₁₉	—	2	4	no	—
68	Q₁₆×C₁₉	—	4	2	no	—
69	Q₁₆×C₁₉	—	4	2	no	—
70	Q₁₆×C₁₉	—	4	4	no	—
71	Q₁₆×C₁₉	—	8	1	no	—
72	SD₁₆×C₁₉	—	4	4	no	—
73	M₁₆×C₁₉	—	2	2	no	—
74	M₁₆×C₁₉	—	4	1	no	—
75	M₁₆×C₁₉	—	4	1	no	—
76	C₂×C₈×C₁₉	—	2	1	no	—
77	C₂×C₈×C₁₉	—	4	1	no	—
78	C₂×C₈×C₁₉	—	4	1	no	—
79	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
80	C₄⋊C₄×C₁₉	—	2	2	no	—
81	C₄⋊C₄×C₁₉	—	4	2	no	—
82	C₄⋊C₄×C₁₉	—	4	2	no	—
83	C₂²⋊C₄×C₁₉	—	4	1	no	—
84	C₂²⋊C₄×C₁₉	—	4	2	no	—
85	C₂²⋊C₄×C₁₉	—	4	2	no	—
86	C₄²×C₁₉	—	4	1	no	—
87	C₁₆×C₁₉	—	4	2	no	—
88	#12112	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂³×C₁₉	—	2	1	no	—
90	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
91	Q₈×C₁₉	—	4	1	no	—
92	Q₈×C₁₉	—	4	2	no	—
93	Q₈×C₁₉	—	4	2	no	—
94	Q₈×C₁₉	—	4	2	no	—
95	Q₈×C₁₉	—	4	2	no	—
96	Q₈×C₁₉	—	8	1	no	—
97	Q₈×C₁₉	—	8	2	no	—
98	Q₈×C₁₉	—	8	1	no	—
99	D₄×C₁₉	—	4	1	no	—
100	D₄×C₁₉	—	8	1	no	—
101	C₂×C₄×C₁₉	—	2	1	no	—
102	C₂×C₄×C₁₉	—	2	1	no	—
103	C₂×C₄×C₁₉	—	2	1	no	—
104	C₂×C₄×C₁₉	—	4	1	no	—
105	C₂×C₄×C₁₉	—	4	1	no	—
106	C₂×C₄×C₁₉	—	4	2	no	—
107	C₂×C₄×C₁₉	—	4	2	no	—
108	C₂×C₄×C₁₉	—	4	2	no	—
109	C₂×C₄×C₁₉	—	8	1	no	—
110	C₂×C₄×C₁₉	—	8	2	no	—
111	C₂×C₄×C₁₉	—	8	1	no	—
112	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
113	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
114	C₈×C₁₉	—	2	2	no	—
115	C₈×C₁₉	—	4	2	no	—
116	C₈×C₁₉	—	4	1	no	—
117	#3202	C₂×C₁₉	1	1	yes	characteristic
118	#2188	C₂×C₁₉	1	2	yes	complemented
119	#2020	C₂×C₁₉	1	1	yes	characteristic
120	#1350	C₂×C₁₉	1	2	yes	complemented
121	#1315	C₂×C₁₉	1	1	yes	characteristic
122	C₂²×C₁₉	—	2	1	no	—
123	C₂²×C₁₉	—	2	2	no	—
124	C₂²×C₁₉	—	4	1	no	—
125	C₂²×C₁₉	—	4	2	no	—
126	C₂²×C₁₉	#447	1	1	yes	characteristic
127	C₄×C₁₉	—	2	1	no	—
128	C₄×C₁₉	—	4	1	no	—
129	C₄×C₁₉	—	8	2	no	—
130	C₄×C₁₉	—	8	2	no	—
131	C₄×C₁₉	—	8	2	no	—
132	C₄×C₁₉	#453	1	1	yes	characteristic
133	C₄×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
134	C₂×#137	—	2	1	no	—
135	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
136	#536	—	2	1	no	—
137	C₂×Q₃₂	—	2	2	no	—
138	#485	—	2	2	no	—
139	#470	—	2	1	no	—
140	#467	C₂²×C₁₉	1	2	yes	—
141	#451	—	2	2	no	—
142	C₂×#101	—	2	1	no	—
143	#408	C₂²×C₁₉	1	1	yes	characteristic
144	#358	—	2	2	no	—
145	C₂²⋊C₁₆	C₂²×C₁₉	1	2	yes	—
146	#341	C₂²×C₁₉	1	1	yes	characteristic
147	C₂×C₁₉	—	4	1	no	—
148	C₂×C₁₉	—	8	1	no	—
149	C₂×C₁₉	#1595	1	1	yes	characteristic
150	C₂×C₁₉	#2195	1	2	yes	—
151	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
152	C₂²×Q₈	—	2	1	no	—
153	C₂²×Q₈	—	2	1	no	—
154	#137	—	4	2	no	—
155	#137	—	4	2	no	—
156	C₂×Q₁₆	—	2	1	no	—
157	C₂×Q₁₆	—	2	2	no	—
158	C₂×Q₁₆	—	4	2	no	—
159	C₂×Q₁₆	—	4	1	no	—
160	C₂×Q₁₆	D₄×C₁₉	1	2	yes	—
161	C₂×SD₁₆	—	4	1	no	—
162	C₂×M₁₆	—	2	1	no	—
163	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
164	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
165	C₄⋊Q₈	—	4	1	no	—
166	#124	—	4	1	no	—
167	#123	—	4	1	no	—
168	#123	—	4	1	no	—
169	C₂²⋊Q₈	—	2	2	no	—
170	C₂²⋊Q₈	—	2	2	no	—
171	#117	—	2	1	no	—
172	Q₃₂	—	4	4	no	—
173	C₂×C₁₆	—	2	2	no	—
174	#107	D₄×C₁₉	1	2	yes	—
175	#106	—	2	1	no	—
176	#103	—	2	2	no	—
177	#103	—	2	2	no	—
178	#101	—	4	2	no	—
179	C₂²⋊C₈	—	2	2	no	—
180	C₁₉	#12112	1	1	yes	characteristic, direct product factor, Sylow
181	#41	—	4	1	no	—
182	#41	—	4	1	no	—
183	C₂×Q₈	—	2	2	no	—
184	C₂×Q₈	—	2	2	no	—
185	C₂×Q₈	—	4	1	no	—
186	C₂×Q₈	—	4	1	no	—
187	C₂×Q₈	—	4	1	no	—
188	C₂×Q₈	—	4	1	no	—
189	C₂×Q₈	—	4	1	no	—
190	C₂×Q₈	—	4	1	no	—
191	C₂×Q₈	—	8	1	no	—
192	C₂×Q₈	—	8	1	no	—
193	C₂×Q₈	D₈×C₁₉	1	1	yes	characteristic
194	C₂×D₄	—	2	1	no	—
195	C₂×D₄	D₈×C₁₉	1	1	yes	characteristic
196	C₂²×C₄	—	2	1	no	—
197	C₂²×C₄	—	4	1	no	—
198	C₂²×C₄	—	4	1	no	—
199	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
200	Q₁₆	—	2	4	no	—
201	Q₁₆	—	4	2	no	—
202	Q₁₆	—	4	2	no	—
203	Q₁₆	—	4	4	no	—
204	Q₁₆	—	8	1	no	—
205	SD₁₆	—	4	4	no	—
206	M₁₆	—	2	2	no	—
207	M₁₆	—	4	1	no	—
208	M₁₆	—	4	1	no	—
209	C₂×C₈	—	2	1	no	—
210	C₂×C₈	—	4	1	no	—
211	C₂×C₈	—	4	1	no	—
212	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
213	C₄⋊C₄	—	2	2	no	—
214	C₄⋊C₄	—	4	2	no	—
215	C₄⋊C₄	—	4	2	no	—
216	C₂²⋊C₄	—	4	1	no	—
217	C₂²⋊C₄	—	4	2	no	—
218	C₂²⋊C₄	—	4	2	no	—
219	C₄²	—	4	1	no	—
220	C₁₆	—	4	2	no	—
221	C₂³	—	2	1	no	—
222	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
223	Q₈	—	4	1	no	—
224	Q₈	—	4	2	no	—
225	Q₈	—	4	2	no	—
226	Q₈	—	4	2	no	—
227	Q₈	—	4	2	no	—
228	Q₈	—	8	1	no	—
229	Q₈	—	8	2	no	—
230	Q₈	—	8	1	no	—
231	D₄	—	4	1	no	—
232	D₄	—	8	1	no	—
233	C₂×C₄	—	2	1	no	—
234	C₂×C₄	—	2	1	no	—
235	C₂×C₄	—	2	1	no	—
236	C₂×C₄	—	4	1	no	—
237	C₂×C₄	—	4	1	no	—
238	C₂×C₄	—	4	2	no	—
239	C₂×C₄	—	4	2	no	—
240	C₂×C₄	—	4	2	no	—
241	C₂×C₄	—	8	1	no	—
242	C₂×C₄	—	8	2	no	—
243	C₂×C₄	—	8	1	no	—
244	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
245	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
246	C₈	—	2	2	no	—
247	C₈	—	4	2	no	—
248	C₈	—	4	1	no	—
249	C₂²	—	2	2	no	—
250	C₂²	—	2	1	no	—
251	C₂²	—	4	2	no	—
252	C₂²	—	4	1	no	—
253	C₂²	C₁₉×#447	1	1	yes	characteristic
254	C₄	—	2	1	no	—
255	C₄	—	4	1	no	—
256	C₄	—	8	2	no	—
257	C₄	—	8	2	no	—
258	C₄	—	8	2	no	—
259	C₄	C₁₉×#453	1	1	yes	characteristic
260	C₄	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
261	C₂	—	4	1	no	—
262	C₂	—	8	1	no	—
263	C₂	C₁₉×#1595	1	1	yes	characteristic
264	C₂	C₁₉×#2195	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#3202

C₂

yes

maximal, characteristic

C₁₉×#2188

C₂

yes

maximal, complemented

C₁₉×#2020

C₂

yes

maximal, characteristic

C₁₉×#1350

C₂

yes

maximal, complemented

C₁₉×#1315

C₂

yes

maximal, characteristic

C₂×C₁₉×#137

—

C₂²×Q₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#536

—

C₂×C₁₉×Q₃₂

—

C₁₉×#485

—

C₁₉×#470

—

C₁₉×#467

C₂²

yes

—

C₁₉×#451

—

C₂×C₁₉×#101

—

C₁₉×#408

C₂²

yes

characteristic

C₁₉×#358

—

C₁₉×C₂²⋊C₁₆

C₂²

yes

—

C₁₉×#341

C₂²

yes

characteristic

C₂×#41×C₁₉

D₄

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₁₉×#137

—

C₁₉×#137

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

D₄

yes

—

C₂×SD₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

C₂³

yes

characteristic

C₁₉×C₄⋊Q₈

—

C₁₉×#124

—

C₁₉×#123

—

C₁₉×#123

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₁₉×#117

—

C₁₉×Q₃₂

—

C₂×C₁₆×C₁₉

—

C₁₉×#107

D₄

yes

—

C₁₉×#106

—

C₁₉×#103

—

C₁₉×#103

—

C₁₉×#101

—

C₁₉×C₂²⋊C₈

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₈

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

D₈

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

SD₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₁₆×C₁₉

—

#12112

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

AGL(1,ℤ/8)

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

100

D₄×C₁₉

—

101

C₂×C₄×C₁₉

—

102

C₂×C₄×C₁₉

—

103

C₂×C₄×C₁₉

—

104

C₂×C₄×C₁₉

—

105

C₂×C₄×C₁₉

—

106

C₂×C₄×C₁₉

—

107

C₂×C₄×C₁₉

—

108

C₂×C₄×C₁₉

—

109

C₂×C₄×C₁₉

—

110

C₂×C₄×C₁₉

—

111

C₂×C₄×C₁₉

—

112

C₂×C₄×C₁₉

#120

yes

characteristic

113

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

114

C₈×C₁₉

—

115

C₈×C₁₉

—

116

C₈×C₁₉

—

117

#3202

C₂×C₁₉

yes

characteristic

118

#2188

C₂×C₁₉

yes

complemented

119

#2020

C₂×C₁₉

yes

characteristic

120

#1350

C₂×C₁₉

yes

complemented

121

#1315

C₂×C₁₉

yes

characteristic

122

C₂²×C₁₉

—

123

C₂²×C₁₉

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

—

126

C₂²×C₁₉

#447

yes

characteristic

127

C₄×C₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

#453

yes

characteristic

133

C₄×C₁₉

B(4,𝔽₂)

yes

characteristic

134

C₂×#137

—

135

C₂²×Q₁₆

C₂²×C₁₉

yes

characteristic

136

#536

—

137

C₂×Q₃₂

—

138

#485

—

139

#470

—

140

#467

C₂²×C₁₉

yes

—

141

#451

—

142

C₂×#101

—

143

#408

C₂²×C₁₉

yes

characteristic

144

#358

—

145

C₂²⋊C₁₆

C₂²×C₁₉

yes

—

146

#341

C₂²×C₁₉

yes

characteristic

147

C₂×C₁₉

—

148

C₂×C₁₉

—

149

C₂×C₁₉

#1595

yes

characteristic

150

C₂×C₁₉

#2195

yes

—

151

C₂×#41

D₄×C₁₉

yes

characteristic

152

C₂²×Q₈

—

153

C₂²×Q₈

—

154

#137

—

155

#137

—

156

C₂×Q₁₆

—

157

C₂×Q₁₆

—

158

C₂×Q₁₆

—

159

C₂×Q₁₆

—

160

C₂×Q₁₆

D₄×C₁₉

yes

—

161

C₂×SD₁₆

—

162

C₂×M₁₆

—

163

C₂×M₁₆

D₄×C₁₉

yes

characteristic

164

C₂²×C₈

C₂³×C₁₉

yes

characteristic

165

C₄⋊Q₈

—

166

#124

—

167

#123

—

168

#123

—

169

C₂²⋊Q₈

—

170

C₂²⋊Q₈

—

171

#117

—

172

Q₃₂

—

173

C₂×C₁₆

—

174

#107

D₄×C₁₉

yes

—

175

#106

—

176

#103

—

177

#103

—

178

#101

—

179

C₂²⋊C₈

—

180

C₁₉

#12112

yes

characteristic, direct product factor, Sylow

181

#41

—

182

#41

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×Q₈

—

188

C₂×Q₈

—

189

C₂×Q₈

—

190

C₂×Q₈

—

191

C₂×Q₈

—

192

C₂×Q₈

—

193

C₂×Q₈

D₈×C₁₉

yes

characteristic

194

C₂×D₄

—

195

C₂×D₄

D₈×C₁₉

yes

characteristic

196

C₂²×C₄

—

197

C₂²×C₄

—

198

C₂²×C₄

—

199

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

200

Q₁₆

—

201

Q₁₆

—

202

Q₁₆

—

203

Q₁₆

—

204

Q₁₆

—

205

SD₁₆

—

206

M₁₆

—

207

M₁₆

—

208

M₁₆

—

209

C₂×C₈

—

210

C₂×C₈

—

211

C₂×C₈

—

212

C₂×C₈

C₂×D₄×C₁₉

yes

—

213

C₄⋊C₄

—

214

C₄⋊C₄

—

215

C₄⋊C₄

—

216

C₂²⋊C₄

—

217

C₂²⋊C₄

—

218

C₂²⋊C₄

—

219

C₄²

—

220

C₁₆

—

221

C₂³

—

222

C₂³

C₁₉×AGL(1,ℤ/8)

yes

characteristic

223

Q₈

—

224

Q₈

—

225

Q₈

—

226

Q₈

—

227

Q₈

—

228

Q₈

—

229

Q₈

—

230

Q₈

—

231

D₄

—

232

D₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

243

C₂×C₄

—

244

C₂×C₄

C₁₉×#120

yes

characteristic

245

C₂×C₄

C₂×D₈×C₁₉

yes

characteristic

246

C₈

—

247

C₈

—

248

C₈

—

249

C₂²

—

250

C₂²

—

251

C₂²

—

252

C₂²

—

253

C₂²

C₁₉×#447

yes

characteristic

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

C₁₉×#453

yes

characteristic

260

C₄

C₁₉×B(4,𝔽₂)

yes

characteristic

261

C₂

—

262

C₂

—

263

C₂

C₁₉×#1595

yes

characteristic

264

C₂

C₁₉×#2195

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₉	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₂×#41×C₁₉	D₄
LCS	G ▷ C₂²×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₁₉×#408 ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#447

commutator, Frattini, cosocle

C₂²×C₈

C₂³×C₁₉

prime radical

C₂×#41×C₁₉

D₄

LCS

G ▷ C₂²×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₁₉×#408 ◁ G

N	H ≅ G/N	type
2. C₁₉×#2188	C₂	semidirect
4. C₁₉×#1350	C₂	semidirect
88. #12112	C₁₉	direct (N × H)
118. #2188	C₂×C₁₉	semidirect
120. #1350	C₂×C₁₉	semidirect
180. C₁₉	#12112	direct (N × H)

H ≅ G/N

type

2. C₁₉×#2188

C₂

semidirect

4. C₁₉×#1350

C₂

semidirect

88. #12112

C₁₉

direct (N × H)

118. #2188

C₂×C₁₉

semidirect

120. #1350

C₂×C₁₉

semidirect

180. C₁₉

#12112

direct (N × H)

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

subgroup	index
C₁₉×#3202	2
C₁₉×#2188	2
C₁₉×#2020	2
C₁₉×#1350	2
C₁₉×#1315	2
#12112	19

subgroup

index

C₁₉×#3202

C₁₉×#2188

C₁₉×#2020

C₁₉×#1350

C₁₉×#1315

#12112

Subgroups — C₁₉×#12112 #18018071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#12112 #18018071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#12112 #18018071