Group #18017489 — subgroups

Subgroups — C₁₉×#11530 #18017489

Order 4864.

444 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 110 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	C₄×C₁₉×#124	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1467	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1324	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1318	C₂	1	2	yes	maximal
5	C₂×C₁₉×#124	C₄	1	1	yes	characteristic
6	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₄×D₄×C₁₉	C₄	1	1	yes	characteristic
8	C₁₉×#432	—	2	2	no	—
9	C₁₉×#391	C₄	1	1	yes	characteristic
10	C₁₉×#390	C₂²	1	1	yes	characteristic
11	C₁₉×#388	—	2	2	no	—
12	C₁₉×#382	C₂²	1	1	yes	characteristic
13	C₄×C₂²⋊C₄×C₁₉	—	2	2	no	—
14	C₄³×C₁₉	C₄	1	1	yes	characteristic
15	C₁₉×#324	—	2	2	no	—
16	C₁₉×#324	C₂²	1	4	yes	—
17	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂³×C₄×C₁₉	—	2	1	no	—
20	C₁₉×#124	—	2	2	no	—
21	C₁₉×#124	—	2	2	no	—
22	C₄×Q₈×C₁₉	—	4	1	no	—
23	C₄×Q₈×C₁₉	—	4	1	no	—
24	C₄×D₄×C₁₉	—	4	1	no	—
25	C₄×D₄×C₁₉	—	4	1	no	—
26	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
28	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
29	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
30	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
31	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
32	C₂×C₄²×C₁₉	—	2	1	no	—
33	C₂×C₄²×C₁₉	—	2	1	no	—
34	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₉	D₄	1	2	yes	—
38	C₁₉×C₄⋊C₈	—	4	2	no	—
39	C₁₉×C₂²⋊C₈	—	2	4	no	—
40	C₁₉×#97	—	4	2	no	—
41	C₁₉×#95	—	2	2	no	—
42	C₁₉×#95	—	2	2	no	—
43	C₂⁴×C₁₉	—	2	1	no	—
44	C₂×Q₈×C₁₉	—	2	1	no	—
45	C₂×Q₈×C₁₉	—	2	1	no	—
46	C₂×Q₈×C₁₉	—	4	1	no	—
47	C₂×Q₈×C₁₉	—	4	1	no	—
48	C₂×D₄×C₁₉	—	2	1	no	—
49	C₂×D₄×C₁₉	—	4	1	no	—
50	C₂×D₄×C₁₉	—	4	1	no	—
51	C₂×D₄×C₁₉	M₁₆	1	2	yes	—
52	C₂²×C₄×C₁₉	—	2	1	no	—
53	C₂²×C₄×C₁₉	—	2	1	no	—
54	C₂²×C₄×C₁₉	—	2	1	no	—
55	C₂²×C₄×C₁₉	—	4	4	no	—
56	C₂²×C₄×C₁₉	—	4	1	no	—
57	C₂²×C₄×C₁₉	—	4	1	no	—
58	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
59	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
63	C₂×C₈×C₁₉	—	4	4	no	—
64	C₄⋊C₄×C₁₉	—	4	2	no	—
65	C₄⋊C₄×C₁₉	—	4	1	no	—
66	C₄⋊C₄×C₁₉	—	4	1	no	—
67	C₂²⋊C₄×C₁₉	—	2	8	no	—
68	C₂²⋊C₄×C₁₉	—	4	4	no	—
69	C₂²⋊C₄×C₁₉	—	4	2	no	—
70	C₄²×C₁₉	—	2	1	no	—
71	C₄²×C₁₉	—	2	1	no	—
72	C₄²×C₁₉	—	2	2	no	—
73	C₄²×C₁₉	—	2	2	no	—
74	C₄²×C₁₉	—	2	1	no	—
75	C₄²×C₁₉	—	4	1	no	—
76	C₄²×C₁₉	—	4	2	no	—
77	C₄²×C₁₉	—	4	2	no	—
78	C₄²×C₁₉	M₁₆	1	2	yes	—
79	#11530	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₂³×C₁₉	—	2	2	no	—
81	C₂³×C₁₉	—	4	2	no	—
82	C₂³×C₁₉	—	4	2	no	—
83	C₂³×C₁₉	—	4	1	no	—
84	C₂³×C₁₉	—	4	1	no	—
85	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
86	Q₈×C₁₉	—	4	2	no	—
87	Q₈×C₁₉	—	4	2	no	—
88	D₄×C₁₉	—	4	2	no	—
89	D₄×C₁₉	—	4	2	no	—
90	C₂×C₄×C₁₉	—	2	1	no	—
91	C₂×C₄×C₁₉	—	2	1	no	—
92	C₂×C₄×C₁₉	—	2	2	no	—
93	C₂×C₄×C₁₉	—	2	2	no	—
94	C₂×C₄×C₁₉	—	2	2	no	—
95	C₂×C₄×C₁₉	—	2	2	no	—
96	C₂×C₄×C₁₉	—	2	1	no	—
97	C₂×C₄×C₁₉	—	2	2	no	—
98	C₂×C₄×C₁₉	—	2	2	no	—
99	C₂×C₄×C₁₉	—	2	2	no	—
100	C₂×C₄×C₁₉	—	4	1	no	—
101	C₂×C₄×C₁₉	—	4	1	no	—
102	C₂×C₄×C₁₉	—	4	1	no	—
103	C₂×C₄×C₁₉	—	4	1	no	—
104	C₂×C₄×C₁₉	—	4	1	no	—
105	C₂×C₄×C₁₉	—	4	2	no	—
106	C₂×C₄×C₁₉	—	4	2	no	—
107	C₂×C₄×C₁₉	—	4	1	no	—
108	C₂×C₄×C₁₉	—	8	2	no	—
109	C₂×C₄×C₁₉	—	8	2	no	—
110	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
111	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
112	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
113	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
114	C₈×C₁₉	—	8	4	no	—
115	C₄×#124	C₂×C₁₉	1	1	yes	characteristic
116	#1467	C₂×C₁₉	1	2	yes	complemented
117	#1324	C₂×C₁₉	1	2	yes	complemented
118	#1318	C₂×C₁₉	1	2	yes	—
119	C₂²×C₁₉	—	2	1	no	—
120	C₂²×C₁₉	—	2	1	no	—
121	C₂²×C₁₉	—	4	4	no	—
122	C₂²×C₁₉	—	4	2	no	—
123	C₂²×C₁₉	—	8	2	no	—
124	C₂²×C₁₉	—	8	1	no	—
125	C₂²×C₁₉	—	8	1	no	—
126	C₂²×C₁₉	#407	1	1	yes	characteristic
127	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
128	C₂²×C₁₉	#413	1	1	yes	characteristic
129	C₄×C₁₉	—	2	1	no	—
130	C₄×C₁₉	—	2	1	no	—
131	C₄×C₁₉	—	2	1	no	—
132	C₄×C₁₉	—	4	2	no	—
133	C₄×C₁₉	—	4	2	no	—
134	C₄×C₁₉	—	4	2	no	—
135	C₄×C₁₉	—	4	1	no	—
136	C₄×C₁₉	—	4	2	no	—
137	C₄×C₁₉	—	8	1	no	—
138	C₄×C₁₉	#355	1	2	yes	—
139	C₂×#124	C₄×C₁₉	1	1	yes	characteristic
140	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
141	C₂×C₄×D₄	C₄×C₁₉	1	1	yes	characteristic
142	#432	—	2	2	no	—
143	#391	C₄×C₁₉	1	1	yes	characteristic
144	#390	C₂²×C₁₉	1	1	yes	characteristic
145	#388	—	2	2	no	—
146	#382	C₂²×C₁₉	1	1	yes	characteristic
147	C₄×C₂²⋊C₄	—	2	2	no	—
148	C₄³	C₄×C₁₉	1	1	yes	characteristic
149	#324	—	2	2	no	—
150	#324	C₂²×C₁₉	1	4	yes	—
151	C₂×C₁₉	—	2	1	no	—
152	C₂×C₁₉	—	2	1	no	—
153	C₂×C₁₉	—	8	2	no	—
154	C₂×C₁₉	#1465	1	1	yes	characteristic
155	C₂×C₁₉	#2126	1	1	yes	characteristic
156	C₂×C₁₉	C₂×#355	1	1	yes	characteristic
157	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
158	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
159	C₂³×C₄	—	2	1	no	—
160	#124	—	2	2	no	—
161	#124	—	2	2	no	—
162	C₄×Q₈	—	4	1	no	—
163	C₄×Q₈	—	4	1	no	—
164	C₄×D₄	—	4	1	no	—
165	C₄×D₄	—	4	1	no	—
166	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
167	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
168	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
169	C₂×C₂²⋊C₄	—	2	2	no	—
170	C₂×C₂²⋊C₄	—	2	1	no	—
171	C₂×C₂²⋊C₄	—	2	2	no	—
172	C₂×C₄²	—	2	1	no	—
173	C₂×C₄²	—	2	1	no	—
174	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
175	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
176	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
177	C₂×C₄²	D₄×C₁₉	1	2	yes	—
178	C₄⋊C₈	—	4	2	no	—
179	C₂²⋊C₈	—	2	4	no	—
180	#97	—	4	2	no	—
181	#95	—	2	2	no	—
182	#95	—	2	2	no	—
183	C₁₉	#11530	1	1	yes	characteristic, direct product factor, Sylow
184	C₂⁴	—	2	1	no	—
185	C₂×Q₈	—	2	1	no	—
186	C₂×Q₈	—	2	1	no	—
187	C₂×Q₈	—	4	1	no	—
188	C₂×Q₈	—	4	1	no	—
189	C₂×D₄	—	2	1	no	—
190	C₂×D₄	—	4	1	no	—
191	C₂×D₄	—	4	1	no	—
192	C₂×D₄	M₁₆×C₁₉	1	2	yes	—
193	C₂²×C₄	—	2	1	no	—
194	C₂²×C₄	—	2	1	no	—
195	C₂²×C₄	—	2	1	no	—
196	C₂²×C₄	—	4	4	no	—
197	C₂²×C₄	—	4	1	no	—
198	C₂²×C₄	—	4	1	no	—
199	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
200	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
201	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
202	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
203	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
204	C₂×C₈	—	4	4	no	—
205	C₄⋊C₄	—	4	2	no	—
206	C₄⋊C₄	—	4	1	no	—
207	C₄⋊C₄	—	4	1	no	—
208	C₂²⋊C₄	—	2	8	no	—
209	C₂²⋊C₄	—	4	4	no	—
210	C₂²⋊C₄	—	4	2	no	—
211	C₄²	—	2	1	no	—
212	C₄²	—	2	2	no	—
213	C₄²	—	2	2	no	—
214	C₄²	—	2	1	no	—
215	C₄²	—	2	1	no	—
216	C₄²	—	4	1	no	—
217	C₄²	—	4	2	no	—
218	C₄²	—	4	2	no	—
219	C₄²	M₁₆×C₁₉	1	2	yes	—
220	C₂³	—	2	2	no	—
221	C₂³	—	4	2	no	—
222	C₂³	—	4	2	no	—
223	C₂³	—	4	1	no	—
224	C₂³	—	4	1	no	—
225	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
226	Q₈	—	4	2	no	—
227	Q₈	—	4	2	no	—
228	D₄	—	4	2	no	—
229	D₄	—	4	2	no	—
230	C₂×C₄	—	2	1	no	—
231	C₂×C₄	—	2	1	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	2	2	no	—
234	C₂×C₄	—	2	2	no	—
235	C₂×C₄	—	2	2	no	—
236	C₂×C₄	—	2	1	no	—
237	C₂×C₄	—	2	2	no	—
238	C₂×C₄	—	2	2	no	—
239	C₂×C₄	—	2	2	no	—
240	C₂×C₄	—	4	1	no	—
241	C₂×C₄	—	4	1	no	—
242	C₂×C₄	—	4	1	no	—
243	C₂×C₄	—	4	1	no	—
244	C₂×C₄	—	4	1	no	—
245	C₂×C₄	—	4	2	no	—
246	C₂×C₄	—	4	2	no	—
247	C₂×C₄	—	4	1	no	—
248	C₂×C₄	—	8	2	no	—
249	C₂×C₄	—	8	2	no	—
250	C₂×C₄	C₁₉×#99	1	1	yes	characteristic
251	C₂×C₄	C₁₉×#99	1	1	yes	characteristic
252	C₂×C₄	C₂×M₁₆×C₁₉	1	1	yes	characteristic
253	C₂×C₄	C₂×M₁₆×C₁₉	1	1	yes	characteristic
254	C₈	—	8	4	no	—
255	C₂²	—	2	1	no	—
256	C₂²	—	2	1	no	—
257	C₂²	—	4	4	no	—
258	C₂²	—	4	2	no	—
259	C₂²	—	8	2	no	—
260	C₂²	—	8	1	no	—
261	C₂²	—	8	1	no	—
262	C₂²	C₁₉×#407	1	1	yes	characteristic
263	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
264	C₂²	C₁₉×#413	1	1	yes	characteristic
265	C₄	—	2	1	no	—
266	C₄	—	2	1	no	—
267	C₄	—	2	1	no	—
268	C₄	—	4	2	no	—
269	C₄	—	4	2	no	—
270	C₄	—	4	2	no	—
271	C₄	—	4	2	no	—
272	C₄	—	4	1	no	—
273	C₄	—	8	1	no	—
274	C₄	C₁₉×#355	1	2	yes	—
275	C₂	—	2	1	no	—
276	C₂	—	2	1	no	—
277	C₂	—	8	2	no	—
278	C₂	C₁₉×#1465	1	1	yes	characteristic
279	C₂	C₁₉×#2126	1	1	yes	characteristic
280	C₂	C₂×C₁₉×#355	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×C₁₉×#124

C₂

yes

maximal, characteristic

C₁₉×#1467

C₂

yes

maximal, complemented

C₁₉×#1324

C₂

yes

maximal, complemented

C₁₉×#1318

C₂

yes

maximal

C₂×C₁₉×#124

C₄

yes

characteristic

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₂×C₄×D₄×C₁₉

C₄

yes

characteristic

C₁₉×#432

—

C₁₉×#391

C₄

yes

characteristic

C₁₉×#390

C₂²

yes

characteristic

C₁₉×#388

—

C₁₉×#382

C₂²

yes

characteristic

C₄×C₂²⋊C₄×C₁₉

—

C₄³×C₁₉

C₄

yes

characteristic

C₁₉×#324

—

C₁₉×#324

C₂²

yes

—

C₂²×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×D₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

—

C₁₉×#124

—

C₁₉×#124

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₁₉×#95

—

C₁₉×#95

—

C₂⁴×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

M₁₆

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

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

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

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

M₁₆

yes

—

#11530

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×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

—

C₂×C₄×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

#99

yes

characteristic

111

C₂×C₄×C₁₉

#99

yes

characteristic

112

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

113

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

114

C₈×C₁₉

—

115

C₄×#124

C₂×C₁₉

yes

characteristic

116

#1467

C₂×C₁₉

yes

complemented

117

#1324

C₂×C₁₉

yes

complemented

118

#1318

C₂×C₁₉

yes

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

—

122

C₂²×C₁₉

—

123

C₂²×C₁₉

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

—

126

C₂²×C₁₉

#407

yes

characteristic

127

C₂²×C₁₉

C₂×#99

yes

characteristic

128

C₂²×C₁₉

#413

yes

characteristic

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

—

134

C₄×C₁₉

—

135

C₄×C₁₉

—

136

C₄×C₁₉

—

137

C₄×C₁₉

—

138

C₄×C₁₉

#355

yes

—

139

C₂×#124

C₄×C₁₉

yes

characteristic

140

C₂×C₄×Q₈

C₂²×C₁₉

yes

characteristic

141

C₂×C₄×D₄

C₄×C₁₉

yes

characteristic

142

#432

—

143

#391

C₄×C₁₉

yes

characteristic

144

#390

C₂²×C₁₉

yes

characteristic

145

#388

—

146

#382

C₂²×C₁₉

yes

characteristic

147

C₄×C₂²⋊C₄

—

148

C₄³

C₄×C₁₉

yes

characteristic

149

#324

—

150

#324

C₂²×C₁₉

yes

—

151

C₂×C₁₉

—

152

C₂×C₁₉

—

153

C₂×C₁₉

—

154

C₂×C₁₉

#1465

yes

characteristic

155

C₂×C₁₉

#2126

yes

characteristic

156

C₂×C₁₉

C₂×#355

yes

characteristic

157

C₂²×Q₈

C₂×C₄×C₁₉

yes

characteristic

158

C₂²×D₄

C₂×C₄×C₁₉

yes

characteristic

159

C₂³×C₄

—

160

#124

—

161

#124

—

162

C₄×Q₈

—

163

C₄×Q₈

—

164

C₄×D₄

—

165

C₄×D₄

—

166

C₂×C₄⋊C₄

C₂×C₄×C₁₉

yes

characteristic

167

C₂×C₄⋊C₄

D₄×C₁₉

yes

—

168

C₂×C₄⋊C₄

C₂³×C₁₉

yes

characteristic

169

C₂×C₂²⋊C₄

—

170

C₂×C₂²⋊C₄

—

171

C₂×C₂²⋊C₄

—

172

C₂×C₄²

—

173

C₂×C₄²

—

174

C₂×C₄²

C₂×C₄×C₁₉

yes

characteristic

175

C₂×C₄²

C₂×C₄×C₁₉

yes

characteristic

176

C₂×C₄²

C₂×C₄×C₁₉

yes

characteristic

177

C₂×C₄²

D₄×C₁₉

yes

—

178

C₄⋊C₈

—

179

C₂²⋊C₈

—

180

#97

—

181

#95

—

182

#95

—

183

C₁₉

#11530

yes

characteristic, direct product factor, Sylow

184

C₂⁴

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×Q₈

—

188

C₂×Q₈

—

189

C₂×D₄

—

190

C₂×D₄

—

191

C₂×D₄

—

192

C₂×D₄

M₁₆×C₁₉

yes

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

—

196

C₂²×C₄

—

197

C₂²×C₄

—

198

C₂²×C₄

—

199

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

—

200

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

201

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

202

C₂²×C₄

C₂²×C₄×C₁₉

yes

characteristic

203

C₂²×C₄

C₂×D₄×C₁₉

yes

—

204

C₂×C₈

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₂²⋊C₄

—

209

C₂²⋊C₄

—

210

C₂²⋊C₄

—

211

C₄²

—

212

C₄²

—

213

C₄²

—

214

C₄²

—

215

C₄²

—

216

C₄²

—

217

C₄²

—

218

C₄²

—

219

C₄²

M₁₆×C₁₉

yes

—

220

C₂³

—

221

C₂³

—

222

C₂³

—

223

C₂³

—

224

C₂³

—

225

C₂³

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

226

Q₈

—

227

Q₈

—

228

D₄

—

229

D₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

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

—

245

C₂×C₄

—

246

C₂×C₄

—

247

C₂×C₄

—

248

C₂×C₄

—

249

C₂×C₄

—

250

C₂×C₄

C₁₉×#99

yes

characteristic

251

C₂×C₄

C₁₉×#99

yes

characteristic

252

C₂×C₄

C₂×M₁₆×C₁₉

yes

characteristic

253

C₂×C₄

C₂×M₁₆×C₁₉

yes

characteristic

254

C₈

—

255

C₂²

—

256

C₂²

—

257

C₂²

—

258

C₂²

—

259

C₂²

—

260

C₂²

—

261

C₂²

—

262

C₂²

C₁₉×#407

yes

characteristic

263

C₂²

C₂×C₁₉×#99

yes

characteristic

264

C₂²

C₁₉×#413

yes

characteristic

265

C₄

—

266

C₄

—

267

C₄

—

268

C₄

—

269

C₄

—

270

C₄

—

271

C₄

—

272

C₄

—

273

C₄

—

274

C₄

C₁₉×#355

yes

—

275

C₂

—

276

C₂

—

277

C₂

—

278

C₂

C₁₉×#1465

yes

characteristic

279

C₂

C₁₉×#2126

yes

characteristic

280

C₂

C₂×C₁₉×#355

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#99
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄⋊C₄	C₂³×C₁₉
prime radical	C₂²×D₄×C₁₉	C₂×C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

C₂×#99

commutator

C₂²×C₄

C₂²×C₄×C₁₉

Frattini, cosocle

C₂×C₄⋊C₄

C₂³×C₁₉

prime radical

C₂²×D₄×C₁₉

C₂×C₄

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

N	H ≅ G/N	type
2. C₁₉×#1467	C₂	semidirect
3. C₁₉×#1324	C₂	semidirect
79. #11530	C₁₉	direct (N × H)
116. #1467	C₂×C₁₉	semidirect
117. #1324	C₂×C₁₉	semidirect
183. C₁₉	#11530	direct (N × H)

H ≅ G/N

type

2. C₁₉×#1467

C₂

semidirect

3. C₁₉×#1324

C₂

semidirect

79. #11530

C₁₉

direct (N × H)

116. #1467

C₂×C₁₉

semidirect

117. #1324

C₂×C₁₉

semidirect

183. C₁₉

#11530

direct (N × H)

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

subgroup	index
C₄×C₁₉×#124	2
C₁₉×#1467	2
C₁₉×#1324	2
C₁₉×#1318	2
#11530	19

subgroup

index

C₄×C₁₉×#124

C₁₉×#1467

C₁₉×#1324

C₁₉×#1318

#11530

Subgroups — C₁₉×#11530 #18017489

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#11530 #18017489

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11530 #18017489