Group #18016171 — subgroups

Subgroups — C₁₉×#10212 #18016171

Order 4864.

536 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 98 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×#3253	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3214	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1963	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1505	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1307	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#532	C₂²	1	1	yes	characteristic
7	C₁₉×#532	C₂²	1	2	yes	—
8	C₁₉×#496	—	2	2	no	—
9	C₁₉×#489	—	2	2	no	—
10	C₁₉×#476	—	2	2	no	—
11	C₁₉×#469	—	2	2	no	—
12	C₁₉×#461	—	2	2	no	—
13	C₁₉×#459	—	2	2	no	—
14	C₁₉×#459	—	2	2	no	—
15	C₁₉×#449	—	2	4	no	—
16	C₁₉×#432	C₂²	1	2	yes	—
17	C₁₉×#423	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#104	—	2	2	no	—
19	C₁₉×#376	C₂²	1	1	yes	characteristic
20	C₁₉×#327	—	2	4	no	—
21	C₂×#41×C₁₉	—	2	1	no	—
22	C₂×#41×C₁₉	—	2	2	no	—
23	C₂×SD₁₆×C₁₉	—	2	4	no	—
24	C₂×D₈×C₁₉	—	2	4	no	—
25	C₂×D₈×C₁₉	—	2	2	no	—
26	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
27	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
28	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
29	C₁₉×#127	D₄	1	2	yes	—
30	C₁₉×#127	D₄	1	1	yes	characteristic
31	C₁₉×#124	—	2	2	no	—
32	C₁₉×#124	—	2	1	no	—
33	C₁₉×#121	—	2	2	no	—
34	C₁₉×#121	—	2	2	no	—
35	C₁₉×#121	—	2	2	no	—
36	C₄×D₄×C₁₉	—	2	2	no	—
37	C₄×D₄×C₁₉	—	2	2	no	—
38	C₄×D₄×C₁₉	—	2	2	no	—
39	C₂×C₄²×C₁₉	—	2	1	no	—
40	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
41	C₁₉×#106	—	2	2	no	—
42	C₁₉×C₄⋊C₈	—	2	2	no	—
43	C₁₉×C₄⋊C₈	—	2	2	no	—
44	C₁₉×#104	—	4	4	no	—
45	C₁₉×#103	—	2	4	no	—
46	C₁₉×#102	—	2	4	no	—
47	C₁₉×#102	—	2	4	no	—
48	C₁₉×C₂²⋊C₈	D₄	1	4	yes	—
49	C₁₉×#97	—	2	2	no	—
50	C₁₉×#95	—	2	2	no	—
51	#41×C₁₉	—	4	2	no	—
52	#41×C₁₉	—	4	2	no	—
53	#41×C₁₉	—	8	4	no	—
54	C₂×Q₈×C₁₉	—	2	2	no	—
55	C₂×Q₈×C₁₉	—	2	1	no	—
56	C₂×D₄×C₁₉	—	2	2	no	—
57	C₂×D₄×C₁₉	—	2	2	no	—
58	C₂×D₄×C₁₉	—	2	2	no	—
59	C₂×D₄×C₁₉	—	2	1	no	—
60	C₂×D₄×C₁₉	—	2	2	no	—
61	C₂×D₄×C₁₉	—	4	1	no	—
62	C₂×D₄×C₁₉	—	4	2	no	—
63	C₂²×C₄×C₁₉	—	4	1	no	—
64	C₂²×C₄×C₁₉	—	4	1	no	—
65	C₂²×C₄×C₁₉	—	4	2	no	—
66	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
68	SD₁₆×C₁₉	—	8	4	no	—
69	D₈×C₁₉	—	8	4	no	—
70	D₈×C₁₉	—	8	2	no	—
71	M₁₆×C₁₉	—	4	2	no	—
72	C₂×C₈×C₁₉	—	2	2	no	—
73	C₂×C₈×C₁₉	—	2	4	no	—
74	C₄⋊C₄×C₁₉	—	2	2	no	—
75	C₄⋊C₄×C₁₉	—	2	2	no	—
76	C₄⋊C₄×C₁₉	—	2	2	no	—
77	C₂²⋊C₄×C₁₉	—	4	2	no	—
78	C₂²⋊C₄×C₁₉	—	4	2	no	—
79	C₂²⋊C₄×C₁₉	—	4	2	no	—
80	C₄²×C₁₉	—	2	2	no	—
81	C₄²×C₁₉	—	4	1	no	—
82	C₄²×C₁₉	C₂×D₄	1	2	yes	—
83	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
84	C₄²×C₁₉	#41	1	1	yes	characteristic
85	#10212	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂³×C₁₉	—	4	1	no	—
87	C₂³×C₁₉	—	4	2	no	—
88	C₂³×C₁₉	#127	1	1	yes	characteristic
89	Q₈×C₁₉	—	4	4	no	—
90	Q₈×C₁₉	—	4	2	no	—
91	D₄×C₁₉	—	4	2	no	—
92	D₄×C₁₉	—	4	4	no	—
93	D₄×C₁₉	—	4	2	no	—
94	D₄×C₁₉	—	4	2	no	—
95	D₄×C₁₉	—	4	2	no	—
96	D₄×C₁₉	—	4	2	no	—
97	D₄×C₁₉	—	8	2	no	—
98	D₄×C₁₉	—	8	2	no	—
99	D₄×C₁₉	—	8	4	no	—
100	C₂×C₄×C₁₉	—	2	1	no	—
101	C₂×C₄×C₁₉	—	2	1	no	—
102	C₂×C₄×C₁₉	—	4	2	no	—
103	C₂×C₄×C₁₉	—	4	2	no	—
104	C₂×C₄×C₁₉	—	4	1	no	—
105	C₂×C₄×C₁₉	—	4	2	no	—
106	C₂×C₄×C₁₉	—	8	4	no	—
107	C₂×C₄×C₁₉	—	8	2	no	—
108	C₂×C₄×C₁₉	—	8	1	no	—
109	C₂×C₄×C₁₉	—	8	1	no	—
110	C₂×C₄×C₁₉	#120	1	2	yes	—
111	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
112	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
113	C₂×C₄×C₁₉	#121	1	2	yes	—
114	C₈×C₁₉	—	4	4	no	—
115	C₈×C₁₉	—	4	2	no	—
116	#3253	C₂×C₁₉	1	1	yes	characteristic, complemented
117	#3214	C₂×C₁₉	1	2	yes	complemented
118	#1963	C₂×C₁₉	1	1	yes	characteristic, complemented
119	#1505	C₂×C₁₉	1	2	yes	complemented
120	#1307	C₂×C₁₉	1	1	yes	characteristic, complemented
121	C₂²×C₁₉	—	2	1	no	—
122	C₂²×C₁₉	—	2	2	no	—
123	C₂²×C₁₉	—	8	1	no	—
124	C₂²×C₁₉	—	8	2	no	—
125	C₂²×C₁₉	—	8	2	no	—
126	C₂²×C₁₉	—	8	2	no	—
127	C₂²×C₁₉	—	8	2	no	—
128	C₂²×C₁₉	#392	1	1	yes	characteristic
129	C₄×C₁₉	—	2	1	no	—
130	C₄×C₁₉	—	2	2	no	—
131	C₄×C₁₉	—	2	2	no	—
132	C₄×C₁₉	—	8	2	no	—
133	C₄×C₁₉	—	8	1	no	—
134	C₄×C₁₉	—	8	2	no	—
135	C₄×C₁₉	#453	1	1	yes	characteristic
136	C₄×C₁₉	#454	1	1	yes	characteristic
137	#532	C₂²×C₁₉	1	1	yes	characteristic
138	#532	C₂²×C₁₉	1	2	yes	—
139	#496	—	2	2	no	—
140	#489	—	2	2	no	—
141	#476	—	2	2	no	—
142	#469	—	2	2	no	—
143	#461	—	2	2	no	—
144	#459	—	2	2	no	—
145	#459	—	2	2	no	—
146	#449	—	2	4	no	—
147	#432	C₂²×C₁₉	1	2	yes	—
148	#423	C₂²×C₁₉	1	1	yes	characteristic
149	C₂×#104	—	2	2	no	—
150	#376	C₂²×C₁₉	1	1	yes	characteristic
151	#327	—	2	4	no	—
152	C₂×C₁₉	—	4	1	no	—
153	C₂×C₁₉	—	16	1	no	—
154	C₂×C₁₉	—	16	2	no	—
155	C₂×C₁₉	#2006	1	1	yes	characteristic
156	C₂×C₁₉	#2008	1	2	yes	—
157	C₂×#41	—	2	1	no	—
158	C₂×#41	—	2	2	no	—
159	C₂×SD₁₆	—	2	4	no	—
160	C₂×D₈	—	2	4	no	—
161	C₂×D₈	—	2	2	no	—
162	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
163	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
164	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
165	#127	D₄×C₁₉	1	2	yes	—
166	#127	D₄×C₁₉	1	1	yes	characteristic
167	#124	—	2	2	no	—
168	#124	—	2	1	no	—
169	#121	—	2	2	no	—
170	#121	—	2	2	no	—
171	#121	—	2	2	no	—
172	C₄×D₄	—	2	2	no	—
173	C₄×D₄	—	2	2	no	—
174	C₄×D₄	—	2	2	no	—
175	C₂×C₄²	—	2	1	no	—
176	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
177	#106	—	2	2	no	—
178	C₄⋊C₈	—	2	2	no	—
179	C₄⋊C₈	—	2	2	no	—
180	#104	—	4	4	no	—
181	#103	—	2	4	no	—
182	#102	—	2	4	no	—
183	#102	—	2	4	no	—
184	C₂²⋊C₈	D₄×C₁₉	1	4	yes	—
185	#97	—	2	2	no	—
186	#95	—	2	2	no	—
187	C₁₉	#10212	1	1	yes	characteristic, direct product factor, Sylow
188	#41	—	4	2	no	—
189	#41	—	4	2	no	—
190	#41	—	8	4	no	—
191	C₂×Q₈	—	2	2	no	—
192	C₂×Q₈	—	2	1	no	—
193	C₂×D₄	—	2	2	no	—
194	C₂×D₄	—	2	2	no	—
195	C₂×D₄	—	2	2	no	—
196	C₂×D₄	—	2	1	no	—
197	C₂×D₄	—	2	2	no	—
198	C₂×D₄	—	4	1	no	—
199	C₂×D₄	—	4	2	no	—
200	C₂²×C₄	—	4	1	no	—
201	C₂²×C₄	—	4	1	no	—
202	C₂²×C₄	—	4	2	no	—
203	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
204	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
205	SD₁₆	—	8	4	no	—
206	D₈	—	8	4	no	—
207	D₈	—	8	2	no	—
208	M₁₆	—	4	2	no	—
209	C₂×C₈	—	2	4	no	—
210	C₂×C₈	—	2	2	no	—
211	C₄⋊C₄	—	2	2	no	—
212	C₄⋊C₄	—	2	2	no	—
213	C₄⋊C₄	—	2	2	no	—
214	C₂²⋊C₄	—	4	2	no	—
215	C₂²⋊C₄	—	4	2	no	—
216	C₂²⋊C₄	—	4	2	no	—
217	C₄²	—	2	2	no	—
218	C₄²	—	4	1	no	—
219	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
220	C₄²	C₂×D₄×C₁₉	1	2	yes	—
221	C₄²	#41×C₁₉	1	1	yes	characteristic
222	C₂³	—	4	1	no	—
223	C₂³	—	4	2	no	—
224	C₂³	C₁₉×#127	1	1	yes	characteristic
225	Q₈	—	4	4	no	—
226	Q₈	—	4	2	no	—
227	D₄	—	4	2	no	—
228	D₄	—	4	4	no	—
229	D₄	—	4	2	no	—
230	D₄	—	4	2	no	—
231	D₄	—	4	2	no	—
232	D₄	—	4	2	no	—
233	D₄	—	8	2	no	—
234	D₄	—	8	2	no	—
235	D₄	—	8	4	no	—
236	C₂×C₄	—	2	1	no	—
237	C₂×C₄	—	2	1	no	—
238	C₂×C₄	—	4	2	no	—
239	C₂×C₄	—	4	2	no	—
240	C₂×C₄	—	4	1	no	—
241	C₂×C₄	—	4	2	no	—
242	C₂×C₄	—	8	4	no	—
243	C₂×C₄	—	8	2	no	—
244	C₂×C₄	—	8	1	no	—
245	C₂×C₄	—	8	1	no	—
246	C₂×C₄	C₁₉×#120	1	2	yes	—
247	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
248	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
249	C₂×C₄	C₁₉×#121	1	2	yes	—
250	C₈	—	4	4	no	—
251	C₈	—	4	2	no	—
252	C₂²	—	2	1	no	—
253	C₂²	—	2	2	no	—
254	C₂²	—	8	1	no	—
255	C₂²	—	8	2	no	—
256	C₂²	—	8	2	no	—
257	C₂²	—	8	2	no	—
258	C₂²	—	8	2	no	—
259	C₂²	C₁₉×#392	1	1	yes	characteristic
260	C₄	—	2	1	no	—
261	C₄	—	2	2	no	—
262	C₄	—	2	2	no	—
263	C₄	—	8	2	no	—
264	C₄	—	8	1	no	—
265	C₄	—	8	2	no	—
266	C₄	C₁₉×#453	1	1	yes	characteristic
267	C₄	C₁₉×#454	1	1	yes	characteristic
268	C₂	—	4	1	no	—
269	C₂	—	16	1	no	—
270	C₂	—	16	2	no	—
271	C₂	C₁₉×#2006	1	1	yes	characteristic
272	C₂	C₁₉×#2008	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#3253

C₂

yes

maximal, characteristic, complemented

C₁₉×#3214

C₂

yes

maximal, complemented

C₁₉×#1963

C₂

yes

maximal, characteristic, complemented

C₁₉×#1505

C₂

yes

maximal, complemented

C₁₉×#1307

C₂

yes

maximal, characteristic, complemented

C₁₉×#532

C₂²

yes

characteristic

C₁₉×#532

C₂²

yes

—

C₁₉×#496

—

C₁₉×#489

—

C₁₉×#476

—

C₁₉×#469

—

C₁₉×#461

—

C₁₉×#459

—

C₁₉×#459

—

C₁₉×#449

—

C₁₉×#432

C₂²

yes

—

C₁₉×#423

C₂²

yes

characteristic

C₂×C₁₉×#104

—

C₁₉×#376

C₂²

yes

characteristic

C₁₉×#327

—

C₂×#41×C₁₉

—

C₂×#41×C₁₉

—

C₂×SD₁₆×C₁₉

—

C₂×D₈×C₁₉

—

C₂×D₈×C₁₉

—

C₂×M₁₆×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

characteristic

C₁₉×#127

D₄

yes

—

C₁₉×#127

D₄

yes

characteristic

C₁₉×#124

—

C₁₉×#124

—

C₁₉×#121

—

C₁₉×#121

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×#106

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#104

—

C₁₉×#103

—

C₁₉×#102

—

C₁₉×#102

—

C₁₉×C₂²⋊C₈

D₄

yes

—

C₁₉×#97

—

C₁₉×#95

—

#41×C₁₉

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

SD₁₆×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#127

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

100

C₂×C₄×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

#120

yes

—

111

C₂×C₄×C₁₉

#120

yes

characteristic

112

C₂×C₄×C₁₉

#121

yes

characteristic

113

C₂×C₄×C₁₉

#121

yes

—

114

C₈×C₁₉

—

115

C₈×C₁₉

—

116

#3253

C₂×C₁₉

yes

characteristic, complemented

117

#3214

C₂×C₁₉

yes

complemented

118

#1963

C₂×C₁₉

yes

characteristic, complemented

119

#1505

C₂×C₁₉

yes

complemented

120

#1307

C₂×C₁₉

yes

characteristic, complemented

121

C₂²×C₁₉

—

122

C₂²×C₁₉

—

123

C₂²×C₁₉

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

—

126

C₂²×C₁₉

—

127

C₂²×C₁₉

—

128

C₂²×C₁₉

#392

yes

characteristic

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

—

134

C₄×C₁₉

—

135

C₄×C₁₉

#453

yes

characteristic

136

C₄×C₁₉

#454

yes

characteristic

137

#532

C₂²×C₁₉

yes

characteristic

138

#532

C₂²×C₁₉

yes

—

139

#496

—

140

#489

—

141

#476

—

142

#469

—

143

#461

—

144

#459

—

145

#459

—

146

#449

—

147

#432

C₂²×C₁₉

yes

—

148

#423

C₂²×C₁₉

yes

characteristic

149

C₂×#104

—

150

#376

C₂²×C₁₉

yes

characteristic

151

#327

—

152

C₂×C₁₉

—

153

C₂×C₁₉

—

154

C₂×C₁₉

—

155

C₂×C₁₉

#2006

yes

characteristic

156

C₂×C₁₉

#2008

yes

—

157

C₂×#41

—

158

C₂×#41

—

159

C₂×SD₁₆

—

160

C₂×D₈

—

161

C₂×D₈

—

162

C₂×M₁₆

D₄×C₁₉

yes

—

163

C₄⋊Q₈

D₄×C₁₉

yes

—

164

C₄⋊Q₈

D₄×C₁₉

yes

characteristic

165

#127

D₄×C₁₉

yes

—

166

#127

D₄×C₁₉

yes

characteristic

167

#124

—

168

#124

—

169

#121

—

170

#121

—

171

#121

—

172

C₄×D₄

—

173

C₄×D₄

—

174

C₄×D₄

—

175

C₂×C₄²

—

176

C₂×C₄²

C₂³×C₁₉

yes

characteristic

177

#106

—

178

C₄⋊C₈

—

179

C₄⋊C₈

—

180

#104

—

181

#103

—

182

#102

—

183

#102

—

184

C₂²⋊C₈

D₄×C₁₉

yes

—

185

#97

—

186

#95

—

187

C₁₉

#10212

yes

characteristic, direct product factor, Sylow

188

#41

—

189

#41

—

190

#41

—

191

C₂×Q₈

—

192

C₂×Q₈

—

193

C₂×D₄

—

194

C₂×D₄

—

195

C₂×D₄

—

196

C₂×D₄

—

197

C₂×D₄

—

198

C₂×D₄

—

199

C₂×D₄

—

200

C₂²×C₄

—

201

C₂²×C₄

—

202

C₂²×C₄

—

203

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

204

C₂²×C₄

C₂×D₄×C₁₉

yes

—

205

SD₁₆

—

206

D₈

—

207

D₈

—

208

M₁₆

—

209

C₂×C₈

—

210

C₂×C₈

—

211

C₄⋊C₄

—

212

C₄⋊C₄

—

213

C₄⋊C₄

—

214

C₂²⋊C₄

—

215

C₂²⋊C₄

—

216

C₂²⋊C₄

—

217

C₄²

—

218

C₄²

—

219

C₄²

C₂×D₄×C₁₉

yes

characteristic

220

C₄²

C₂×D₄×C₁₉

yes

—

221

C₄²

#41×C₁₉

yes

characteristic

222

C₂³

—

223

C₂³

—

224

C₂³

C₁₉×#127

yes

characteristic

225

Q₈

—

226

Q₈

—

227

D₄

—

228

D₄

—

229

D₄

—

230

D₄

—

231

D₄

—

232

D₄

—

233

D₄

—

234

D₄

—

235

D₄

—

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

—

245

C₂×C₄

—

246

C₂×C₄

C₁₉×#120

yes

—

247

C₂×C₄

C₁₉×#120

yes

characteristic

248

C₂×C₄

C₁₉×#121

yes

characteristic

249

C₂×C₄

C₁₉×#121

yes

—

250

C₈

—

251

C₈

—

252

C₂²

—

253

C₂²

—

254

C₂²

—

255

C₂²

—

256

C₂²

—

257

C₂²

—

258

C₂²

—

259

C₂²

C₁₉×#392

yes

characteristic

260

C₄

—

261

C₄

—

262

C₄

—

263

C₄

—

264

C₄

—

265

C₄

—

266

C₄

C₁₉×#453

yes

characteristic

267

C₄

C₁₉×#454

yes

characteristic

268

C₂

—

269

C₂

—

270

C₂

—

271

C₂

C₁₉×#2006

yes

characteristic

272

C₂

C₁₉×#2008

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#392

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₁₉

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
1. C₁₉×#3253	C₂	semidirect
2. C₁₉×#3214	C₂	semidirect
3. C₁₉×#1963	C₂	semidirect
4. C₁₉×#1505	C₂	semidirect
5. C₁₉×#1307	C₂	semidirect
85. #10212	C₁₉	direct (N × H)
116. #3253	C₂×C₁₉	semidirect
117. #3214	C₂×C₁₉	semidirect
118. #1963	C₂×C₁₉	semidirect
119. #1505	C₂×C₁₉	semidirect
120. #1307	C₂×C₁₉	semidirect
187. C₁₉	#10212	direct (N × H)

H ≅ G/N

type

1. C₁₉×#3253

C₂

semidirect

2. C₁₉×#3214

C₂

semidirect

3. C₁₉×#1963

C₂

semidirect

4. C₁₉×#1505

C₂

semidirect

5. C₁₉×#1307

C₂

semidirect

85. #10212

C₁₉

direct (N × H)

116. #3253

C₂×C₁₉

semidirect

117. #3214

C₂×C₁₉

semidirect

118. #1963

C₂×C₁₉

semidirect

119. #1505

C₂×C₁₉

semidirect

120. #1307

C₂×C₁₉

semidirect

187. C₁₉

#10212

direct (N × H)

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

subgroup	index
C₁₉×#3253	2
C₁₉×#3214	2
C₁₉×#1963	2
C₁₉×#1505	2
C₁₉×#1307	2
#10212	19

subgroup

index

C₁₉×#3253

C₁₉×#3214

C₁₉×#1963

C₁₉×#1505

C₁₉×#1307

#10212

Subgroups — C₁₉×#10212 #18016171

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#10212 #18016171

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10212 #18016171