Group #18016218 — subgroups

Subgroups — C₁₉×#10259 #18016218

Order 4864.

474 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 122 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×#3249	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3078	C₂	1	2	yes	maximal
3	C₁₉×#1984	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1493	C₂	1	2	yes	maximal
5	C₁₉×#1292	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#533	C₂²	1	2	yes	—
7	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#479	—	2	4	no	—
9	C₁₉×#477	—	2	2	no	—
10	C₁₉×#477	—	2	2	no	—
11	C₁₉×#475	—	2	2	no	—
12	C₁₉×#467	—	2	2	no	—
13	C₁₉×#462	—	2	2	no	—
14	C₁₉×#428	—	2	2	no	—
15	C₁₉×#423	C₂²	1	2	yes	—
16	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₁₉×#419	—	2	2	no	—
18	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#336	—	2	2	no	—
20	C₁₉×Q₈⋊C₈	—	2	4	no	—
21	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
22	C₂×Q₁₆×C₁₉	—	2	2	no	—
23	C₂×M₁₆×C₁₉	—	2	2	no	—
24	C₂²×C₈×C₁₉	—	2	1	no	—
25	C₂²×C₈×C₁₉	D₄	1	2	yes	—
26	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
27	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
28	C₁₉×#125	—	2	2	no	—
29	C₁₉×C₂²⋊Q₈	—	2	2	no	—
30	C₁₉×C₂²⋊Q₈	—	2	2	no	—
31	C₄×Q₈×C₁₉	—	2	2	no	—
32	C₄×Q₈×C₁₉	—	2	2	no	—
33	C₄×Q₈×C₁₉	—	2	2	no	—
34	C₄×Q₈×C₁₉	—	2	2	no	—
35	C₁₉×#117	—	2	2	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₉	—	2	1	no	—
39	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
40	C₁₉×#107	—	2	4	no	—
41	C₁₉×#107	—	2	2	no	—
42	C₁₉×#106	—	2	4	no	—
43	C₁₉×C₄⋊C₈	—	2	2	no	—
44	C₁₉×C₄⋊C₈	—	2	2	no	—
45	C₁₉×C₄⋊C₈	D₄	1	4	yes	—
46	C₁₉×#103	—	2	4	no	—
47	C₁₉×#103	—	2	4	no	—
48	C₁₉×#103	—	2	4	no	—
49	C₄×C₈×C₁₉	—	2	2	no	—
50	C₂×Q₈×C₁₉	—	2	1	no	—
51	C₂×Q₈×C₁₉	—	2	2	no	—
52	C₂×Q₈×C₁₉	—	2	2	no	—
53	C₂×Q₈×C₁₉	—	2	2	no	—
54	C₂×Q₈×C₁₉	—	2	2	no	—
55	C₂×Q₈×C₁₉	Q₁₆	1	2	yes	complemented
56	C₂²×C₄×C₁₉	—	2	1	no	—
57	C₂²×C₄×C₁₉	—	2	1	no	—
58	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
61	Q₁₆×C₁₉	—	8	2	no	—
62	M₁₆×C₁₉	—	4	2	no	—
63	M₁₆×C₁₉	—	4	2	no	—
64	C₂×C₈×C₁₉	—	2	2	no	—
65	C₂×C₈×C₁₉	—	2	2	no	—
66	C₂×C₈×C₁₉	—	2	4	no	—
67	C₂×C₈×C₁₉	—	4	1	no	—
68	C₂×C₈×C₁₉	—	4	1	no	—
69	C₂×C₈×C₁₉	—	4	2	no	—
70	C₄⋊C₄×C₁₉	—	2	2	no	—
71	C₄⋊C₄×C₁₉	—	2	2	no	—
72	C₄⋊C₄×C₁₉	—	2	2	no	—
73	C₄⋊C₄×C₁₉	—	2	2	no	—
74	C₄⋊C₄×C₁₉	—	2	2	no	—
75	C₄⋊C₄×C₁₉	—	4	2	no	—
76	C₄⋊C₄×C₁₉	—	4	2	no	—
77	C₄⋊C₄×C₁₉	—	4	2	no	—
78	C₂²⋊C₄×C₁₉	—	4	2	no	—
79	C₄²×C₁₉	—	4	1	no	—
80	C₄²×C₁₉	—	4	2	no	—
81	C₄²×C₁₉	—	4	1	no	—
82	C₄²×C₁₉	C₂×D₄	1	2	yes	—
83	C₄²×C₁₉	C₂×D₄	1	2	yes	—
84	#10259	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
85	C₂³×C₁₉	#121	1	1	yes	characteristic
86	Q₈×C₁₉	—	2	4	no	—
87	Q₈×C₁₉	—	4	4	no	—
88	Q₈×C₁₉	—	4	2	no	—
89	Q₈×C₁₉	—	4	2	no	—
90	Q₈×C₁₉	—	4	2	no	—
91	C₂×C₄×C₁₉	—	2	1	no	—
92	C₂×C₄×C₁₉	—	2	1	no	—
93	C₂×C₄×C₁₉	—	2	2	no	—
94	C₂×C₄×C₁₉	—	4	1	no	—
95	C₂×C₄×C₁₉	—	4	1	no	—
96	C₂×C₄×C₁₉	—	4	1	no	—
97	C₂×C₄×C₁₉	—	4	2	no	—
98	C₂×C₄×C₁₉	—	4	1	no	—
99	C₂×C₄×C₁₉	—	4	2	no	—
100	C₂×C₄×C₁₉	—	4	2	no	—
101	C₂×C₄×C₁₉	#120	1	2	yes	—
102	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
103	C₂×C₄×C₁₉	#121	1	2	yes	—
104	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
105	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
106	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
107	C₂×C₄×C₁₉	#137	1	2	yes	—
108	C₈×C₁₉	—	4	2	no	—
109	C₈×C₁₉	—	4	4	no	—
110	C₈×C₁₉	—	4	2	no	—
111	#3249	C₂×C₁₉	1	1	yes	characteristic
112	#3078	C₂×C₁₉	1	2	yes	—
113	#1984	C₂×C₁₉	1	1	yes	characteristic
114	#1493	C₂×C₁₉	1	2	yes	—
115	#1292	C₂×C₁₉	1	1	yes	characteristic
116	C₂²×C₁₉	—	2	1	no	—
117	C₂²×C₁₉	—	2	1	no	—
118	C₂²×C₁₉	#392	1	1	yes	characteristic
119	C₂²×C₁₉	#467	1	1	yes	characteristic
120	C₂²×C₁₉	#470	1	1	yes	characteristic
121	C₄×C₁₉	—	2	1	no	—
122	C₄×C₁₉	—	2	2	no	—
123	C₄×C₁₉	—	4	2	no	—
124	C₄×C₁₉	—	8	2	no	—
125	C₄×C₁₉	—	8	1	no	—
126	C₄×C₁₉	—	8	2	no	—
127	C₄×C₁₉	#451	1	2	yes	—
128	C₄×C₁₉	#452	1	2	yes	—
129	C₄×C₁₉	#455	1	1	yes	characteristic
130	C₄×C₁₉	#456	1	1	yes	characteristic
131	#533	C₂²×C₁₉	1	2	yes	—
132	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
133	#479	—	2	4	no	—
134	#477	—	2	2	no	—
135	#477	—	2	2	no	—
136	#475	—	2	2	no	—
137	#467	—	2	2	no	—
138	#462	—	2	2	no	—
139	#428	—	2	2	no	—
140	#423	C₂²×C₁₉	1	2	yes	—
141	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
142	#419	—	2	2	no	—
143	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
144	#336	—	2	2	no	—
145	Q₈⋊C₈	—	2	4	no	—
146	C₂×C₁₉	—	2	1	no	—
147	C₂×C₁₉	—	2	1	no	—
148	C₂×C₁₉	#2001	1	1	yes	characteristic
149	C₂×C₁₉	#2007	1	1	yes	characteristic
150	C₂×C₁₉	#2017	1	1	yes	characteristic
151	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
152	C₂×Q₁₆	—	2	2	no	—
153	C₂×M₁₆	—	2	2	no	—
154	C₂²×C₈	—	2	1	no	—
155	C₂²×C₈	D₄×C₁₉	1	2	yes	—
156	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
157	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
158	#125	—	2	2	no	—
159	C₂²⋊Q₈	—	2	2	no	—
160	C₂²⋊Q₈	—	2	2	no	—
161	C₄×Q₈	—	2	2	no	—
162	C₄×Q₈	—	2	2	no	—
163	C₄×Q₈	—	2	2	no	—
164	C₄×Q₈	—	2	2	no	—
165	#117	—	2	2	no	—
166	C₂×C₄⋊C₄	—	2	1	no	—
167	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
168	C₂×C₄²	—	2	1	no	—
169	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
170	#107	—	2	4	no	—
171	#107	—	2	2	no	—
172	#106	—	2	4	no	—
173	C₄⋊C₈	—	2	2	no	—
174	C₄⋊C₈	—	2	2	no	—
175	C₄⋊C₈	D₄×C₁₉	1	4	yes	—
176	#103	—	2	4	no	—
177	#103	—	2	4	no	—
178	#103	—	2	4	no	—
179	C₄×C₈	—	2	2	no	—
180	C₁₉	#10259	1	1	yes	characteristic, direct product factor, Sylow
181	C₂×Q₈	—	2	1	no	—
182	C₂×Q₈	—	2	2	no	—
183	C₂×Q₈	—	2	2	no	—
184	C₂×Q₈	—	2	2	no	—
185	C₂×Q₈	—	2	2	no	—
186	C₂×Q₈	Q₁₆×C₁₉	1	2	yes	complemented
187	C₂²×C₄	—	2	1	no	—
188	C₂²×C₄	—	2	1	no	—
189	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
190	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
191	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
192	Q₁₆	—	8	2	no	—
193	M₁₆	—	4	2	no	—
194	M₁₆	—	4	2	no	—
195	C₂×C₈	—	2	2	no	—
196	C₂×C₈	—	2	2	no	—
197	C₂×C₈	—	2	4	no	—
198	C₂×C₈	—	4	1	no	—
199	C₂×C₈	—	4	1	no	—
200	C₂×C₈	—	4	2	no	—
201	C₄⋊C₄	—	2	2	no	—
202	C₄⋊C₄	—	2	2	no	—
203	C₄⋊C₄	—	2	2	no	—
204	C₄⋊C₄	—	2	2	no	—
205	C₄⋊C₄	—	2	2	no	—
206	C₄⋊C₄	—	4	2	no	—
207	C₄⋊C₄	—	4	2	no	—
208	C₄⋊C₄	—	4	2	no	—
209	C₂²⋊C₄	—	4	2	no	—
210	C₄²	—	4	1	no	—
211	C₄²	—	4	2	no	—
212	C₄²	—	4	1	no	—
213	C₄²	C₂×D₄×C₁₉	1	2	yes	—
214	C₄²	C₂×D₄×C₁₉	1	2	yes	—
215	C₂³	C₁₉×#121	1	1	yes	characteristic
216	Q₈	—	2	4	no	—
217	Q₈	—	4	4	no	—
218	Q₈	—	4	2	no	—
219	Q₈	—	4	2	no	—
220	Q₈	—	4	2	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	4	1	no	—
225	C₂×C₄	—	4	1	no	—
226	C₂×C₄	—	4	1	no	—
227	C₂×C₄	—	4	2	no	—
228	C₂×C₄	—	4	1	no	—
229	C₂×C₄	—	4	2	no	—
230	C₂×C₄	—	4	2	no	—
231	C₂×C₄	C₁₉×#120	1	2	yes	—
232	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
233	C₂×C₄	C₁₉×#121	1	2	yes	—
234	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
235	C₂×C₄	C₂×Q₁₆×C₁₉	1	1	yes	characteristic
236	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
237	C₂×C₄	C₁₉×#137	1	2	yes	—
238	C₈	—	4	2	no	—
239	C₈	—	4	4	no	—
240	C₈	—	4	2	no	—
241	C₂²	—	2	1	no	—
242	C₂²	—	2	1	no	—
243	C₂²	C₁₉×#392	1	1	yes	characteristic
244	C₂²	C₁₉×#467	1	1	yes	characteristic
245	C₂²	C₁₉×#470	1	1	yes	characteristic
246	C₄	—	2	1	no	—
247	C₄	—	2	2	no	—
248	C₄	—	4	2	no	—
249	C₄	—	8	2	no	—
250	C₄	—	8	1	no	—
251	C₄	—	8	2	no	—
252	C₄	C₁₉×#451	1	2	yes	—
253	C₄	C₁₉×#452	1	2	yes	—
254	C₄	C₁₉×#455	1	1	yes	characteristic
255	C₄	C₁₉×#456	1	1	yes	characteristic
256	C₂	—	2	1	no	—
257	C₂	—	2	1	no	—
258	C₂	C₁₉×#2001	1	1	yes	characteristic
259	C₂	C₁₉×#2007	1	1	yes	characteristic
260	C₂	C₁₉×#2017	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#3249

C₂

yes

maximal, characteristic

C₁₉×#3078

C₂

yes

maximal

C₁₉×#1984

C₂

yes

maximal, characteristic

C₁₉×#1493

C₂

yes

maximal

C₁₉×#1292

C₂

yes

maximal, characteristic

C₁₉×#533

C₂²

yes

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×#479

—

C₁₉×#477

—

C₁₉×#477

—

C₁₉×#475

—

C₁₉×#467

—

C₁₉×#462

—

C₁₉×#428

—

C₁₉×#423

C₂²

yes

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₁₉×#419

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#336

—

C₁₉×Q₈⋊C₈

—

C₂²×Q₈×C₁₉

D₄

yes

characteristic

C₂×Q₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×#125

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×#107

—

C₁₉×#107

—

C₁₉×#106

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉×#103

—

C₁₉×#103

—

C₁₉×#103

—

C₄×C₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

Q₁₆

yes

complemented

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

Q₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

#10259

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

#121

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×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

#120

yes

—

102

C₂×C₄×C₁₉

#120

yes

characteristic

103

C₂×C₄×C₁₉

#121

yes

—

104

C₂×C₄×C₁₉

#127

yes

characteristic

105

C₂×C₄×C₁₉

C₂×Q₁₆

yes

characteristic

106

C₂×C₄×C₁₉

#135

yes

characteristic

107

C₂×C₄×C₁₉

#137

yes

—

108

C₈×C₁₉

—

109

C₈×C₁₉

—

110

C₈×C₁₉

—

111

#3249

C₂×C₁₉

yes

characteristic

112

#3078

C₂×C₁₉

yes

—

113

#1984

C₂×C₁₉

yes

characteristic

114

#1493

C₂×C₁₉

yes

—

115

#1292

C₂×C₁₉

yes

characteristic

116

C₂²×C₁₉

—

117

C₂²×C₁₉

—

118

C₂²×C₁₉

#392

yes

characteristic

119

C₂²×C₁₉

#467

yes

characteristic

120

C₂²×C₁₉

#470

yes

characteristic

121

C₄×C₁₉

—

122

C₄×C₁₉

—

123

C₄×C₁₉

—

124

C₄×C₁₉

—

125

C₄×C₁₉

—

126

C₄×C₁₉

—

127

C₄×C₁₉

#451

yes

—

128

C₄×C₁₉

#452

yes

—

129

C₄×C₁₉

#455

yes

characteristic

130

C₄×C₁₉

#456

yes

characteristic

131

#533

C₂²×C₁₉

yes

—

132

C₂×C₄×Q₈

C₂²×C₁₉

yes

characteristic

133

#479

—

134

#477

—

135

#477

—

136

#475

—

137

#467

—

138

#462

—

139

#428

—

140

#423

C₂²×C₁₉

yes

—

141

C₂×C₄⋊C₈

C₂²×C₁₉

yes

characteristic

142

#419

—

143

C₂×C₄×C₈

C₂²×C₁₉

yes

characteristic

144

#336

—

145

Q₈⋊C₈

—

146

C₂×C₁₉

—

147

C₂×C₁₉

—

148

C₂×C₁₉

#2001

yes

characteristic

149

C₂×C₁₉

#2007

yes

characteristic

150

C₂×C₁₉

#2017

yes

characteristic

151

C₂²×Q₈

D₄×C₁₉

yes

characteristic

152

C₂×Q₁₆

—

153

C₂×M₁₆

—

154

C₂²×C₈

—

155

C₂²×C₈

D₄×C₁₉

yes

—

156

C₄⋊Q₈

D₄×C₁₉

yes

—

157

C₄⋊Q₈

D₄×C₁₉

yes

—

158

#125

—

159

C₂²⋊Q₈

—

160

C₂²⋊Q₈

—

161

C₄×Q₈

—

162

C₄×Q₈

—

163

C₄×Q₈

—

164

C₄×Q₈

—

165

#117

—

166

C₂×C₄⋊C₄

—

167

C₂×C₄⋊C₄

D₄×C₁₉

yes

characteristic

168

C₂×C₄²

—

169

C₂×C₄²

C₂³×C₁₉

yes

characteristic

170

#107

—

171

#107

—

172

#106

—

173

C₄⋊C₈

—

174

C₄⋊C₈

—

175

C₄⋊C₈

D₄×C₁₉

yes

—

176

#103

—

177

#103

—

178

#103

—

179

C₄×C₈

—

180

C₁₉

#10259

yes

characteristic, direct product factor, Sylow

181

C₂×Q₈

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×Q₈

Q₁₆×C₁₉

yes

complemented

187

C₂²×C₄

—

188

C₂²×C₄

—

189

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

190

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

191

C₂²×C₄

#41×C₁₉

yes

characteristic

192

Q₁₆

—

193

M₁₆

—

194

M₁₆

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₂²⋊C₄

—

210

C₄²

—

211

C₄²

—

212

C₄²

—

213

C₄²

C₂×D₄×C₁₉

yes

—

214

C₄²

C₂×D₄×C₁₉

yes

—

215

C₂³

C₁₉×#121

yes

characteristic

216

Q₈

—

217

Q₈

—

218

Q₈

—

219

Q₈

—

220

Q₈

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

C₁₉×#120

yes

—

232

C₂×C₄

C₁₉×#120

yes

characteristic

233

C₂×C₄

C₁₉×#121

yes

—

234

C₂×C₄

C₁₉×#127

yes

characteristic

235

C₂×C₄

C₂×Q₁₆×C₁₉

yes

characteristic

236

C₂×C₄

C₁₉×#135

yes

characteristic

237

C₂×C₄

C₁₉×#137

yes

—

238

C₈

—

239

C₈

—

240

C₈

—

241

C₂²

—

242

C₂²

—

243

C₂²

C₁₉×#392

yes

characteristic

244

C₂²

C₁₉×#467

yes

characteristic

245

C₂²

C₁₉×#470

yes

characteristic

246

C₄

—

247

C₄

—

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

C₁₉×#451

yes

—

253

C₄

C₁₉×#452

yes

—

254

C₄

C₁₉×#455

yes

characteristic

255

C₄

C₁₉×#456

yes

characteristic

256

C₂

—

257

C₂

—

258

C₂

C₁₉×#2001

yes

characteristic

259

C₂

C₁₉×#2007

yes

characteristic

260

C₂

C₁₉×#2017

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂³×C₁₉	#121
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

prime radical

C₂³×C₁₉

#121

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
55. C₂×Q₈×C₁₉	Q₁₆	semidirect
84. #10259	C₁₉	direct (N × H)
180. C₁₉	#10259	direct (N × H)
186. C₂×Q₈	Q₁₆×C₁₉	semidirect

H ≅ G/N

type

55. C₂×Q₈×C₁₉

Q₁₆

semidirect

84. #10259

C₁₉

direct (N × H)

180. C₁₉

#10259

direct (N × H)

186. C₂×Q₈

Q₁₆×C₁₉

semidirect

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

subgroup	index
C₁₉×#3249	2
C₁₉×#3078	2
C₁₉×#1984	2
C₁₉×#1493	2
C₁₉×#1292	2
#10259	19

subgroup

index

C₁₉×#3249

C₁₉×#3078

C₁₉×#1984

C₁₉×#1493

C₁₉×#1292

#10259

Subgroups — C₁₉×#10259 #18016218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#10259 #18016218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10259 #18016218