Group #18015449 — subgroups

Subgroups — C₁₉×#9490 #18015449

Order 4864.

522 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 134 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×#2983	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2536	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1801	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1486	C₂	1	2	yes	maximal
5	C₁₉×#1286	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
7	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#446	—	2	4	no	—
10	C₁₉×#432	—	2	2	no	—
11	C₁₉×#431	C₂²	1	2	yes	—
12	C₁₉×#423	C₂²	1	2	yes	—
13	C₂×C₁₉×#101	—	2	1	no	—
14	C₁₉×#398	C₄	1	2	yes	—
15	C₁₉×#394	C₄	1	2	yes	—
16	C₁₉×#388	—	2	2	no	—
17	C₁₉×#382	C₂²	1	1	yes	characteristic
18	C₁₉×#380	—	2	1	no	—
19	C₁₉×#343	—	2	1	no	—
20	C₁₉×D₄⋊C₈	—	2	4	no	—
21	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
22	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₉	—	2	1	no	—
24	C₂×M₁₆×C₁₉	—	2	2	no	—
25	C₁₉×C₂²⋊Q₈	—	4	4	no	—
26	C₄×Q₈×C₁₉	—	2	2	no	—
27	C₄×Q₈×C₁₉	—	2	2	no	—
28	C₄×D₄×C₁₉	—	2	2	no	—
29	C₄×D₄×C₁₉	—	2	2	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
34	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
35	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
36	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
37	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄²×C₁₉	D₄	1	2	yes	—
39	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
40	C₁₉×C₄⋊C₈	—	2	4	no	—
41	C₁₉×C₄⋊C₈	—	2	2	no	—
42	C₁₉×C₄⋊C₈	—	2	2	no	—
43	C₁₉×C₄⋊C₈	—	2	2	no	—
44	C₁₉×#101	—	4	2	no	—
45	C₁₉×C₂²⋊C₈	—	2	2	no	—
46	C₁₉×#97	—	2	4	no	—
47	C₄×C₈×C₁₉	D₄	1	4	yes	—
48	C₁₉×#95	—	2	2	no	—
49	C₁₉×#95	—	2	1	no	—
50	C₁₉×#95	C₂×C₄	1	2	yes	—
51	C₂⁴×C₁₉	—	2	1	no	—
52	C₂×Q₈×C₁₉	—	2	2	no	—
53	C₂×Q₈×C₁₉	—	2	2	no	—
54	C₂×Q₈×C₁₉	—	2	1	no	—
55	C₂×Q₈×C₁₉	—	2	1	no	—
56	C₂×D₄×C₁₉	—	2	2	no	—
57	C₂×D₄×C₁₉	—	4	2	no	—
58	C₂²×C₄×C₁₉	—	2	2	no	—
59	C₂²×C₄×C₁₉	—	2	1	no	—
60	C₂²×C₄×C₁₉	—	4	2	no	—
61	C₂²×C₄×C₁₉	—	4	2	no	—
62	C₂²×C₄×C₁₉	—	4	1	no	—
63	C₂²×C₄×C₁₉	—	4	1	no	—
64	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
65	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
66	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
69	M₁₆×C₁₉	—	4	2	no	—
70	M₁₆×C₁₉	—	4	2	no	—
71	C₂×C₈×C₁₉	—	2	4	no	—
72	C₂×C₈×C₁₉	—	4	2	no	—
73	C₄⋊C₄×C₁₉	—	2	4	no	—
74	C₄⋊C₄×C₁₉	—	2	2	no	—
75	C₄⋊C₄×C₁₉	—	2	2	no	—
76	C₄⋊C₄×C₁₉	—	4	4	no	—
77	C₄⋊C₄×C₁₉	—	4	2	no	—
78	C₂²⋊C₄×C₁₉	—	4	4	no	—
79	C₂²⋊C₄×C₁₉	—	4	4	no	—
80	C₂²⋊C₄×C₁₉	—	4	1	no	—
81	C₂²⋊C₄×C₁₉	—	4	1	no	—
82	C₄²×C₁₉	—	2	2	no	—
83	C₄²×C₁₉	—	2	2	no	—
84	C₄²×C₁₉	C₂×D₄	1	2	yes	—
85	C₄²×C₁₉	#41	1	2	yes	—
86	#9490	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂³×C₁₉	—	2	2	no	—
88	C₂³×C₁₉	—	4	1	no	—
89	C₂³×C₁₉	—	4	1	no	—
90	C₂³×C₁₉	—	4	1	no	—
91	C₂³×C₁₉	—	4	1	no	—
92	C₂³×C₁₉	—	4	1	no	—
93	C₂³×C₁₉	—	4	1	no	—
94	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
95	Q₈×C₁₉	—	4	2	no	—
96	Q₈×C₁₉	—	4	2	no	—
97	D₄×C₁₉	—	2	4	no	—
98	D₄×C₁₉	—	4	2	no	—
99	C₂×C₄×C₁₉	—	2	2	no	—
100	C₂×C₄×C₁₉	—	2	2	no	—
101	C₂×C₄×C₁₉	—	2	2	no	—
102	C₂×C₄×C₁₉	—	2	2	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	2	no	—
108	C₂×C₄×C₁₉	—	4	1	no	—
109	C₂×C₄×C₁₉	—	4	1	no	—
110	C₂×C₄×C₁₉	—	4	2	no	—
111	C₂×C₄×C₁₉	—	4	1	no	—
112	C₂×C₄×C₁₉	—	8	2	no	—
113	C₂×C₄×C₁₉	—	8	2	no	—
114	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
115	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
116	C₂×C₄×C₁₉	#121	1	2	yes	—
117	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
118	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
119	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
120	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
121	C₈×C₁₉	—	4	4	no	—
122	C₈×C₁₉	—	8	2	no	—
123	#2983	C₂×C₁₉	1	1	yes	characteristic, complemented
124	#2536	C₂×C₁₉	1	1	yes	characteristic
125	#1801	C₂×C₁₉	1	1	yes	characteristic, complemented
126	#1486	C₂×C₁₉	1	2	yes	—
127	#1286	C₂×C₁₉	1	2	yes	complemented
128	C₂²×C₁₉	—	2	1	no	—
129	C₂²×C₁₉	—	2	1	no	—
130	C₂²×C₁₉	—	4	2	no	—
131	C₂²×C₁₉	—	4	2	no	—
132	C₂²×C₁₉	—	4	2	no	—
133	C₂²×C₁₉	—	8	1	no	—
134	C₂²×C₁₉	—	8	1	no	—
135	C₂²×C₁₉	—	8	1	no	—
136	C₂²×C₁₉	—	8	1	no	—
137	C₂²×C₁₉	#386	1	1	yes	characteristic
138	C₂²×C₁₉	#417	1	1	yes	characteristic
139	C₂²×C₁₉	#418	1	1	yes	characteristic
140	C₄×C₁₉	—	2	2	no	—
141	C₄×C₁₉	—	2	1	no	—
142	C₄×C₁₉	—	2	1	no	—
143	C₄×C₁₉	—	4	2	no	—
144	C₄×C₁₉	—	4	2	no	—
145	C₄×C₁₉	—	8	2	no	—
146	C₄×C₁₉	—	8	1	no	—
147	C₄×C₁₉	#468	1	2	yes	—
148	C₄×C₁₉	#469	1	2	yes	—
149	C₂×C₂²⋊Q₈	—	2	1	no	—
150	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
151	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
152	#446	—	2	4	no	—
153	#432	—	2	2	no	—
154	#431	C₂²×C₁₉	1	2	yes	—
155	#423	C₂²×C₁₉	1	2	yes	—
156	C₂×#101	—	2	1	no	—
157	#398	C₄×C₁₉	1	2	yes	—
158	#394	C₄×C₁₉	1	2	yes	—
159	#388	—	2	2	no	—
160	#382	C₂²×C₁₉	1	1	yes	characteristic
161	#380	—	2	1	no	—
162	#343	—	2	1	no	—
163	D₄⋊C₈	—	2	4	no	—
164	C₂×C₁₉	—	2	1	no	—
165	C₂×C₁₉	—	2	1	no	—
166	C₂×C₁₉	—	8	2	no	—
167	C₂×C₁₉	#1891	1	1	yes	characteristic
168	C₂×C₁₉	#1895	1	1	yes	characteristic
169	C₂×C₁₉	#1912	1	1	yes	characteristic
170	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
171	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
172	C₂³×C₄	—	2	1	no	—
173	C₂×M₁₆	—	2	2	no	—
174	C₂²⋊Q₈	—	4	4	no	—
175	C₄×Q₈	—	2	2	no	—
176	C₄×Q₈	—	2	2	no	—
177	C₄×D₄	—	2	2	no	—
178	C₄×D₄	—	2	2	no	—
179	C₂×C₄⋊C₄	—	2	2	no	—
180	C₂×C₄⋊C₄	—	2	1	no	—
181	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
182	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
183	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
184	C₂×C₂²⋊C₄	—	2	2	no	—
185	C₂×C₂²⋊C₄	—	2	2	no	—
186	C₂×C₂²⋊C₄	—	2	1	no	—
187	C₂×C₄²	D₄×C₁₉	1	2	yes	—
188	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
189	C₄⋊C₈	—	2	4	no	—
190	C₄⋊C₈	—	2	2	no	—
191	C₄⋊C₈	—	2	2	no	—
192	C₄⋊C₈	—	2	2	no	—
193	#101	—	4	2	no	—
194	C₂²⋊C₈	—	2	2	no	—
195	#97	—	2	4	no	—
196	C₄×C₈	D₄×C₁₉	1	4	yes	—
197	#95	—	2	2	no	—
198	#95	—	2	1	no	—
199	#95	C₂×C₄×C₁₉	1	2	yes	—
200	C₁₉	#9490	1	1	yes	characteristic, direct product factor, Sylow
201	C₂⁴	—	2	1	no	—
202	C₂×Q₈	—	2	2	no	—
203	C₂×Q₈	—	2	1	no	—
204	C₂×Q₈	—	2	2	no	—
205	C₂×Q₈	—	2	1	no	—
206	C₂×D₄	—	2	2	no	—
207	C₂×D₄	—	4	2	no	—
208	C₂²×C₄	—	2	2	no	—
209	C₂²×C₄	—	2	1	no	—
210	C₂²×C₄	—	4	2	no	—
211	C₂²×C₄	—	4	2	no	—
212	C₂²×C₄	—	4	1	no	—
213	C₂²×C₄	—	4	1	no	—
214	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
215	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
216	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
217	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
218	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
219	M₁₆	—	4	2	no	—
220	M₁₆	—	4	2	no	—
221	C₂×C₈	—	2	4	no	—
222	C₂×C₈	—	4	2	no	—
223	C₄⋊C₄	—	2	4	no	—
224	C₄⋊C₄	—	2	2	no	—
225	C₄⋊C₄	—	2	2	no	—
226	C₄⋊C₄	—	4	4	no	—
227	C₄⋊C₄	—	4	2	no	—
228	C₂²⋊C₄	—	4	4	no	—
229	C₂²⋊C₄	—	4	4	no	—
230	C₂²⋊C₄	—	4	1	no	—
231	C₂²⋊C₄	—	4	1	no	—
232	C₄²	—	2	2	no	—
233	C₄²	—	2	2	no	—
234	C₄²	C₂×D₄×C₁₉	1	2	yes	—
235	C₄²	#41×C₁₉	1	2	yes	—
236	C₂³	—	2	2	no	—
237	C₂³	—	4	1	no	—
238	C₂³	—	4	1	no	—
239	C₂³	—	4	1	no	—
240	C₂³	—	4	1	no	—
241	C₂³	—	4	1	no	—
242	C₂³	—	4	1	no	—
243	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
244	Q₈	—	4	2	no	—
245	Q₈	—	4	2	no	—
246	D₄	—	2	4	no	—
247	D₄	—	4	2	no	—
248	C₂×C₄	—	2	2	no	—
249	C₂×C₄	—	2	2	no	—
250	C₂×C₄	—	2	2	no	—
251	C₂×C₄	—	2	2	no	—
252	C₂×C₄	—	4	1	no	—
253	C₂×C₄	—	4	1	no	—
254	C₂×C₄	—	4	2	no	—
255	C₂×C₄	—	4	2	no	—
256	C₂×C₄	—	4	2	no	—
257	C₂×C₄	—	4	1	no	—
258	C₂×C₄	—	4	1	no	—
259	C₂×C₄	—	4	2	no	—
260	C₂×C₄	—	4	1	no	—
261	C₂×C₄	—	8	2	no	—
262	C₂×C₄	—	8	2	no	—
263	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
264	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
265	C₂×C₄	C₁₉×#121	1	2	yes	—
266	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
267	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
268	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
269	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
270	C₈	—	4	4	no	—
271	C₈	—	8	2	no	—
272	C₂²	—	2	1	no	—
273	C₂²	—	2	1	no	—
274	C₂²	—	4	2	no	—
275	C₂²	—	4	2	no	—
276	C₂²	—	4	2	no	—
277	C₂²	—	8	1	no	—
278	C₂²	—	8	1	no	—
279	C₂²	—	8	1	no	—
280	C₂²	—	8	1	no	—
281	C₂²	C₁₉×#386	1	1	yes	characteristic
282	C₂²	C₁₉×#417	1	1	yes	characteristic
283	C₂²	C₁₉×#418	1	1	yes	characteristic
284	C₄	—	2	2	no	—
285	C₄	—	2	1	no	—
286	C₄	—	2	1	no	—
287	C₄	—	4	2	no	—
288	C₄	—	4	2	no	—
289	C₄	—	8	2	no	—
290	C₄	—	8	1	no	—
291	C₄	C₁₉×#468	1	2	yes	—
292	C₄	C₁₉×#469	1	2	yes	—
293	C₂	—	2	1	no	—
294	C₂	—	2	1	no	—
295	C₂	—	8	2	no	—
296	C₂	C₁₉×#1891	1	1	yes	characteristic
297	C₂	C₁₉×#1895	1	1	yes	characteristic
298	C₂	C₁₉×#1912	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2983

C₂

yes

maximal, characteristic, complemented

C₁₉×#2536

C₂

yes

maximal, characteristic

C₁₉×#1801

C₂

yes

maximal, characteristic, complemented

C₁₉×#1486

C₂

yes

maximal

C₁₉×#1286

C₂

yes

maximal, complemented

C₂×C₁₉×C₂²⋊Q₈

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₁₉×#446

—

C₁₉×#432

—

C₁₉×#431

C₂²

yes

—

C₁₉×#423

C₂²

yes

—

C₂×C₁₉×#101

—

C₁₉×#398

C₄

yes

—

C₁₉×#394

C₄

yes

—

C₁₉×#388

—

C₁₉×#382

C₂²

yes

characteristic

C₁₉×#380

—

C₁₉×#343

—

C₁₉×D₄⋊C₈

—

C₂²×Q₈×C₁₉

D₄

yes

characteristic

C₂²×D₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

—

C₂×M₁₆×C₁₉

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#101

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₄×C₈×C₁₉

D₄

yes

—

C₁₉×#95

—

C₁₉×#95

—

C₁₉×#95

C₂×C₄

yes

—

C₂⁴×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

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

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

#9490

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

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

—

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

—

111

C₂×C₄×C₁₉

—

112

C₂×C₄×C₁₉

—

113

C₂×C₄×C₁₉

—

114

C₂×C₄×C₁₉

C₄×D₄

yes

—

115

C₂×C₄×C₁₉

#120

yes

characteristic

116

C₂×C₄×C₁₉

#121

yes

—

117

C₂×C₄×C₁₉

#123

yes

characteristic

118

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

119

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

characteristic

120

C₂×C₄×C₁₉

#137

yes

characteristic

121

C₈×C₁₉

—

122

C₈×C₁₉

—

123

#2983

C₂×C₁₉

yes

characteristic, complemented

124

#2536

C₂×C₁₉

yes

characteristic

125

#1801

C₂×C₁₉

yes

characteristic, complemented

126

#1486

C₂×C₁₉

yes

—

127

#1286

C₂×C₁₉

yes

complemented

128

C₂²×C₁₉

—

129

C₂²×C₁₉

—

130

C₂²×C₁₉

—

131

C₂²×C₁₉

—

132

C₂²×C₁₉

—

133

C₂²×C₁₉

—

134

C₂²×C₁₉

—

135

C₂²×C₁₉

—

136

C₂²×C₁₉

—

137

C₂²×C₁₉

#386

yes

characteristic

138

C₂²×C₁₉

#417

yes

characteristic

139

C₂²×C₁₉

#418

yes

characteristic

140

C₄×C₁₉

—

141

C₄×C₁₉

—

142

C₄×C₁₉

—

143

C₄×C₁₉

—

144

C₄×C₁₉

—

145

C₄×C₁₉

—

146

C₄×C₁₉

—

147

C₄×C₁₉

#468

yes

—

148

C₄×C₁₉

#469

yes

—

149

C₂×C₂²⋊Q₈

—

150

C₂×C₄×Q₈

C₂²×C₁₉

yes

characteristic

151

C₂×C₄×D₄

C₂²×C₁₉

yes

characteristic

152

#446

—

153

#432

—

154

#431

C₂²×C₁₉

yes

—

155

#423

C₂²×C₁₉

yes

—

156

C₂×#101

—

157

#398

C₄×C₁₉

yes

—

158

#394

C₄×C₁₉

yes

—

159

#388

—

160

#382

C₂²×C₁₉

yes

characteristic

161

#380

—

162

#343

—

163

D₄⋊C₈

—

164

C₂×C₁₉

—

165

C₂×C₁₉

—

166

C₂×C₁₉

—

167

C₂×C₁₉

#1891

yes

characteristic

168

C₂×C₁₉

#1895

yes

characteristic

169

C₂×C₁₉

#1912

yes

characteristic

170

C₂²×Q₈

D₄×C₁₉

yes

characteristic

171

C₂²×D₄

C₂×C₄×C₁₉

yes

characteristic

172

C₂³×C₄

—

173

C₂×M₁₆

—

174

C₂²⋊Q₈

—

175

C₄×Q₈

—

176

C₄×Q₈

—

177

C₄×D₄

—

178

C₄×D₄

—

179

C₂×C₄⋊C₄

—

180

C₂×C₄⋊C₄

—

181

C₂×C₄⋊C₄

C₂×C₄×C₁₉

yes

characteristic

182

C₂×C₄⋊C₄

C₂×C₄×C₁₉

yes

—

183

C₂×C₄⋊C₄

D₄×C₁₉

yes

characteristic

184

C₂×C₂²⋊C₄

—

185

C₂×C₂²⋊C₄

—

186

C₂×C₂²⋊C₄

—

187

C₂×C₄²

D₄×C₁₉

yes

—

188

C₂×C₄²

C₂³×C₁₉

yes

characteristic

189

C₄⋊C₈

—

190

C₄⋊C₈

—

191

C₄⋊C₈

—

192

C₄⋊C₈

—

193

#101

—

194

C₂²⋊C₈

—

195

#97

—

196

C₄×C₈

D₄×C₁₉

yes

—

197

#95

—

198

#95

—

199

#95

C₂×C₄×C₁₉

yes

—

200

C₁₉

#9490

yes

characteristic, direct product factor, Sylow

201

C₂⁴

—

202

C₂×Q₈

—

203

C₂×Q₈

—

204

C₂×Q₈

—

205

C₂×Q₈

—

206

C₂×D₄

—

207

C₂×D₄

—

208

C₂²×C₄

—

209

C₂²×C₄

—

210

C₂²×C₄

—

211

C₂²×C₄

—

212

C₂²×C₄

—

213

C₂²×C₄

—

214

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

—

215

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

—

216

C₂²×C₄

C₂²×C₄×C₁₉

yes

characteristic

217

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

218

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

219

M₁₆

—

220

M₁₆

—

221

C₂×C₈

—

222

C₂×C₈

—

223

C₄⋊C₄

—

224

C₄⋊C₄

—

225

C₄⋊C₄

—

226

C₄⋊C₄

—

227

C₄⋊C₄

—

228

C₂²⋊C₄

—

229

C₂²⋊C₄

—

230

C₂²⋊C₄

—

231

C₂²⋊C₄

—

232

C₄²

—

233

C₄²

—

234

C₄²

C₂×D₄×C₁₉

yes

—

235

C₄²

#41×C₁₉

yes

—

236

C₂³

—

237

C₂³

—

238

C₂³

—

239

C₂³

—

240

C₂³

—

241

C₂³

—

242

C₂³

—

243

C₂³

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

244

Q₈

—

245

Q₈

—

246

D₄

—

247

D₄

—

248

C₂×C₄

—

249

C₂×C₄

—

250

C₂×C₄

—

251

C₂×C₄

—

252

C₂×C₄

—

253

C₂×C₄

—

254

C₂×C₄

—

255

C₂×C₄

—

256

C₂×C₄

—

257

C₂×C₄

—

258

C₂×C₄

—

259

C₂×C₄

—

260

C₂×C₄

—

261

C₂×C₄

—

262

C₂×C₄

—

263

C₂×C₄

C₄×D₄×C₁₉

yes

—

264

C₂×C₄

C₁₉×#120

yes

characteristic

265

C₂×C₄

C₁₉×#121

yes

—

266

C₂×C₄

C₁₉×#123

yes

characteristic

267

C₂×C₄

C₁₉×AGL(1,ℤ/8)

yes

—

268

C₂×C₄

C₁₉×AGL(1,ℤ/8)

yes

characteristic

269

C₂×C₄

C₁₉×#137

yes

characteristic

270

C₈

—

271

C₈

—

272

C₂²

—

273

C₂²

—

274

C₂²

—

275

C₂²

—

276

C₂²

—

277

C₂²

—

278

C₂²

—

279

C₂²

—

280

C₂²

—

281

C₂²

C₁₉×#386

yes

characteristic

282

C₂²

C₁₉×#417

yes

characteristic

283

C₂²

C₁₉×#418

yes

characteristic

284

C₄

—

285

C₄

—

286

C₄

—

287

C₄

—

288

C₄

—

289

C₄

—

290

C₄

—

291

C₄

C₁₉×#468

yes

—

292

C₄

C₁₉×#469

yes

—

293

C₂

—

294

C₂

—

295

C₂

—

296

C₂

C₁₉×#1891

yes

characteristic

297

C₂

C₁₉×#1895

yes

characteristic

298

C₂

C₁₉×#1912

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂²×D₄×C₁₉	C₂×C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#386

commutator

C₂²×C₄

C₂²×C₄×C₁₉

Frattini, cosocle

C₂×C₄²

C₂³×C₁₉

prime radical

C₂²×D₄×C₁₉

C₂×C₄

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
1. C₁₉×#2983	C₂	semidirect
3. C₁₉×#1801	C₂	semidirect
5. C₁₉×#1286	C₂	semidirect
86. #9490	C₁₉	direct (N × H)
123. #2983	C₂×C₁₉	semidirect
125. #1801	C₂×C₁₉	semidirect
127. #1286	C₂×C₁₉	semidirect
200. C₁₉	#9490	direct (N × H)

H ≅ G/N

type

1. C₁₉×#2983

C₂

semidirect

3. C₁₉×#1801

C₂

semidirect

5. C₁₉×#1286

C₂

semidirect

86. #9490

C₁₉

direct (N × H)

123. #2983

C₂×C₁₉

semidirect

125. #1801

C₂×C₁₉

semidirect

127. #1286

C₂×C₁₉

semidirect

200. C₁₉

#9490

direct (N × H)

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

subgroup	index
C₁₉×#2983	2
C₁₉×#2536	2
C₁₉×#1801	2
C₁₉×#1486	2
C₁₉×#1286	2
#9490	19

subgroup

index

C₁₉×#2983

C₁₉×#2536

C₁₉×#1801

C₁₉×#1486

C₁₉×#1286

#9490

Subgroups — C₁₉×#9490 #18015449

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#9490 #18015449

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9490 #18015449