Group #18015446 — subgroups

Subgroups — C₁₉×#9487 #18015446

Order 4864.

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

normal subgroups only

This group has 518 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×#2975	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2580	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1800	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1487	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1286	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#436	—	2	4	no	—
9	C₁₉×#431	C₂²	1	2	yes	—
10	C₁₉×#423	C₂²	1	2	yes	—
11	C₂×C₁₉×#100	—	2	1	no	—
12	C₁₉×#407	—	2	2	no	—
13	C₁₉×#399	C₄	1	2	yes	—
14	C₁₉×#393	C₄	1	2	yes	—
15	C₁₉×#390	—	2	1	no	—
16	C₁₉×#389	—	2	1	no	—
17	C₁₉×#385	—	2	2	no	—
18	C₁₉×#382	C₂²	1	1	yes	characteristic
19	C₁₉×#343	—	2	1	no	—
20	C₁₉×Q₈⋊C₈	—	2	4	no	—
21	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₉	D₄	1	2	yes	—
24	C₂×M₁₆×C₁₉	—	2	4	no	—
25	C₂×M₁₆×C₁₉	—	2	2	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	1	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
33	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
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	C₂×C₄	1	2	yes	—
38	C₂×C₄²×C₁₉	—	2	1	no	—
39	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
40	C₁₉×C₄⋊C₈	—	2	2	no	—
41	C₁₉×C₄⋊C₈	—	2	2	no	—
42	C₁₉×C₄⋊C₈	—	2	2	no	—
43	C₁₉×#100	—	4	2	no	—
44	C₁₉×C₂²⋊C₈	—	2	4	no	—
45	C₁₉×C₂²⋊C₈	—	2	2	no	—
46	C₄×C₈×C₁₉	D₄	1	4	yes	—
47	C₁₉×#95	—	2	2	no	—
48	C₁₉×#95	—	2	1	no	—
49	C₁₉×#95	C₂×C₄	1	2	yes	—
50	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
51	C₂×Q₈×C₁₉	—	2	2	no	—
52	C₂×Q₈×C₁₉	—	4	2	no	—
53	C₂×D₄×C₁₉	—	2	2	no	—
54	C₂×D₄×C₁₉	—	2	1	no	—
55	C₂×D₄×C₁₉	—	2	2	no	—
56	C₂×D₄×C₁₉	—	2	1	no	—
57	C₂²×C₄×C₁₉	—	2	1	no	—
58	C₂²×C₄×C₁₉	—	2	2	no	—
59	C₂²×C₄×C₁₉	—	2	2	no	—
60	C₂²×C₄×C₁₉	—	2	1	no	—
61	C₂²×C₄×C₁₉	—	2	2	no	—
62	C₂²×C₄×C₁₉	—	8	2	no	—
63	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
64	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
67	M₁₆×C₁₉	—	4	2	no	—
68	M₁₆×C₁₉	—	4	2	no	—
69	M₁₆×C₁₉	—	8	4	no	—
70	C₂×C₈×C₁₉	—	2	4	no	—
71	C₂×C₈×C₁₉	—	4	2	no	—
72	C₄⋊C₄×C₁₉	—	2	2	no	—
73	C₄⋊C₄×C₁₉	—	2	2	no	—
74	C₄⋊C₄×C₁₉	—	4	1	no	—
75	C₄⋊C₄×C₁₉	—	4	1	no	—
76	C₄⋊C₄×C₁₉	—	4	1	no	—
77	C₄⋊C₄×C₁₉	—	4	1	no	—
78	C₄⋊C₄×C₁₉	—	8	2	no	—
79	C₂²⋊C₄×C₁₉	—	2	4	no	—
80	C₂²⋊C₄×C₁₉	—	4	4	no	—
81	C₂²⋊C₄×C₁₉	—	8	2	no	—
82	C₄²×C₁₉	—	4	2	no	—
83	C₄²×C₁₉	C₂×D₄	1	2	yes	—
84	C₄²×C₁₉	#41	1	2	yes	—
85	#9487	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂³×C₁₉	—	2	2	no	—
87	C₂³×C₁₉	—	2	2	no	—
88	C₂³×C₁₉	—	2	2	no	—
89	C₂³×C₁₉	—	4	2	no	—
90	C₂³×C₁₉	—	4	2	no	—
91	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
92	Q₈×C₁₉	—	2	4	no	—
93	Q₈×C₁₉	—	4	2	no	—
94	D₄×C₁₉	—	4	2	no	—
95	D₄×C₁₉	—	4	2	no	—
96	C₂×C₄×C₁₉	—	2	2	no	—
97	C₂×C₄×C₁₉	—	2	2	no	—
98	C₂×C₄×C₁₉	—	4	1	no	—
99	C₂×C₄×C₁₉	—	4	1	no	—
100	C₂×C₄×C₁₉	—	4	4	no	—
101	C₂×C₄×C₁₉	—	4	1	no	—
102	C₂×C₄×C₁₉	—	4	1	no	—
103	C₂×C₄×C₁₉	—	4	2	no	—
104	C₂×C₄×C₁₉	—	4	2	no	—
105	C₂×C₄×C₁₉	—	4	1	no	—
106	C₂×C₄×C₁₉	—	4	2	no	—
107	C₂×C₄×C₁₉	—	4	1	no	—
108	C₂×C₄×C₁₉	—	4	1	no	—
109	C₂×C₄×C₁₉	—	4	2	no	—
110	C₂×C₄×C₁₉	—	8	2	no	—
111	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
112	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
113	C₂×C₄×C₁₉	#121	1	2	yes	—
114	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
115	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
116	C₂×C₄×C₁₉	#137	1	2	yes	—
117	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
118	C₈×C₁₉	—	4	4	no	—
119	C₈×C₁₉	—	8	2	no	—
120	#2975	C₂×C₁₉	1	1	yes	characteristic
121	#2580	C₂×C₁₉	1	1	yes	characteristic
122	#1800	C₂×C₁₉	1	1	yes	characteristic
123	#1487	C₂×C₁₉	1	2	yes	complemented
124	#1286	C₂×C₁₉	1	2	yes	complemented
125	C₂²×C₁₉	—	2	1	no	—
126	C₂²×C₁₉	—	2	1	no	—
127	C₂²×C₁₉	—	4	4	no	—
128	C₂²×C₁₉	—	4	2	no	—
129	C₂²×C₁₉	—	4	2	no	—
130	C₂²×C₁₉	—	4	2	no	—
131	C₂²×C₁₉	—	8	2	no	—
132	C₂²×C₁₉	#386	1	1	yes	characteristic
133	C₂²×C₁₉	#417	1	1	yes	characteristic
134	C₂²×C₁₉	#419	1	1	yes	characteristic
135	C₄×C₁₉	—	2	2	no	—
136	C₄×C₁₉	—	2	1	no	—
137	C₄×C₁₉	—	2	1	no	—
138	C₄×C₁₉	—	4	2	no	—
139	C₄×C₁₉	—	4	2	no	—
140	C₄×C₁₉	—	8	2	no	—
141	C₄×C₁₉	—	8	1	no	—
142	C₄×C₁₉	#468	1	2	yes	—
143	C₄×C₁₉	#470	1	2	yes	—
144	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
145	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
146	#436	—	2	4	no	—
147	#431	C₂²×C₁₉	1	2	yes	—
148	#423	C₂²×C₁₉	1	2	yes	—
149	C₂×#100	—	2	1	no	—
150	#407	—	2	2	no	—
151	#399	C₄×C₁₉	1	2	yes	—
152	#393	C₄×C₁₉	1	2	yes	—
153	#390	—	2	1	no	—
154	#389	—	2	1	no	—
155	#385	—	2	2	no	—
156	#382	C₂²×C₁₉	1	1	yes	characteristic
157	#343	—	2	1	no	—
158	Q₈⋊C₈	—	2	4	no	—
159	C₂×C₁₉	—	2	1	no	—
160	C₂×C₁₉	—	2	1	no	—
161	C₂×C₁₉	—	8	2	no	—
162	C₂×C₁₉	#1891	1	1	yes	characteristic
163	C₂×C₁₉	#1894	1	1	yes	characteristic
164	C₂×C₁₉	#1911	1	1	yes	characteristic
165	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
166	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
167	C₂³×C₄	D₄×C₁₉	1	2	yes	—
168	C₂×M₁₆	—	2	4	no	—
169	C₂×M₁₆	—	2	2	no	—
170	C₄×Q₈	—	2	2	no	—
171	C₄×Q₈	—	2	2	no	—
172	C₄×D₄	—	2	2	no	—
173	C₄×D₄	—	2	2	no	—
174	C₂×C₄⋊C₄	—	2	1	no	—
175	C₂×C₄⋊C₄	—	2	1	no	—
176	C₂×C₄⋊C₄	—	2	2	no	—
177	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
178	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
179	C₂×C₂²⋊C₄	—	2	2	no	—
180	C₂×C₂²⋊C₄	—	2	2	no	—
181	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
182	C₂×C₄²	—	2	1	no	—
183	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
184	C₄⋊C₈	—	2	2	no	—
185	C₄⋊C₈	—	2	2	no	—
186	C₄⋊C₈	—	2	2	no	—
187	#100	—	4	2	no	—
188	C₂²⋊C₈	—	2	4	no	—
189	C₂²⋊C₈	—	2	2	no	—
190	C₄×C₈	D₄×C₁₉	1	4	yes	—
191	#95	—	2	2	no	—
192	#95	—	2	1	no	—
193	#95	C₂×C₄×C₁₉	1	2	yes	—
194	C₁₉	#9487	1	1	yes	characteristic, direct product factor, Sylow
195	C₂⁴	C₂²⋊C₄×C₁₉	1	2	yes	—
196	C₂×Q₈	—	2	2	no	—
197	C₂×Q₈	—	4	2	no	—
198	C₂×D₄	—	2	2	no	—
199	C₂×D₄	—	2	1	no	—
200	C₂×D₄	—	2	2	no	—
201	C₂×D₄	—	2	1	no	—
202	C₂²×C₄	—	2	1	no	—
203	C₂²×C₄	—	2	2	no	—
204	C₂²×C₄	—	2	2	no	—
205	C₂²×C₄	—	2	2	no	—
206	C₂²×C₄	—	2	1	no	—
207	C₂²×C₄	—	8	2	no	—
208	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
209	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
210	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
211	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
212	M₁₆	—	4	2	no	—
213	M₁₆	—	4	2	no	—
214	M₁₆	—	8	4	no	—
215	C₂×C₈	—	2	4	no	—
216	C₂×C₈	—	4	2	no	—
217	C₄⋊C₄	—	2	2	no	—
218	C₄⋊C₄	—	2	2	no	—
219	C₄⋊C₄	—	4	1	no	—
220	C₄⋊C₄	—	4	1	no	—
221	C₄⋊C₄	—	4	1	no	—
222	C₄⋊C₄	—	4	1	no	—
223	C₄⋊C₄	—	8	2	no	—
224	C₂²⋊C₄	—	2	4	no	—
225	C₂²⋊C₄	—	4	4	no	—
226	C₂²⋊C₄	—	8	2	no	—
227	C₄²	—	4	2	no	—
228	C₄²	C₂×D₄×C₁₉	1	2	yes	—
229	C₄²	#41×C₁₉	1	2	yes	—
230	C₂³	—	2	2	no	—
231	C₂³	—	2	2	no	—
232	C₂³	—	2	2	no	—
233	C₂³	—	4	2	no	—
234	C₂³	—	4	2	no	—
235	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
236	Q₈	—	2	4	no	—
237	Q₈	—	4	2	no	—
238	D₄	—	4	2	no	—
239	D₄	—	4	2	no	—
240	C₂×C₄	—	2	2	no	—
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	4	1	no	—
243	C₂×C₄	—	4	1	no	—
244	C₂×C₄	—	4	4	no	—
245	C₂×C₄	—	4	1	no	—
246	C₂×C₄	—	4	1	no	—
247	C₂×C₄	—	4	2	no	—
248	C₂×C₄	—	4	2	no	—
249	C₂×C₄	—	4	1	no	—
250	C₂×C₄	—	4	2	no	—
251	C₂×C₄	—	4	1	no	—
252	C₂×C₄	—	4	1	no	—
253	C₂×C₄	—	4	2	no	—
254	C₂×C₄	—	8	2	no	—
255	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
256	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
257	C₂×C₄	C₁₉×#121	1	2	yes	—
258	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
259	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
260	C₂×C₄	C₁₉×#137	1	2	yes	—
261	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
262	C₈	—	4	4	no	—
263	C₈	—	8	2	no	—
264	C₂²	—	2	1	no	—
265	C₂²	—	2	1	no	—
266	C₂²	—	4	4	no	—
267	C₂²	—	4	2	no	—
268	C₂²	—	4	2	no	—
269	C₂²	—	4	2	no	—
270	C₂²	—	8	2	no	—
271	C₂²	C₁₉×#386	1	1	yes	characteristic
272	C₂²	C₁₉×#417	1	1	yes	characteristic
273	C₂²	C₁₉×#419	1	1	yes	characteristic
274	C₄	—	2	2	no	—
275	C₄	—	2	1	no	—
276	C₄	—	2	1	no	—
277	C₄	—	4	2	no	—
278	C₄	—	4	2	no	—
279	C₄	—	8	2	no	—
280	C₄	—	8	1	no	—
281	C₄	C₁₉×#468	1	2	yes	—
282	C₄	C₁₉×#470	1	2	yes	—
283	C₂	—	2	1	no	—
284	C₂	—	2	1	no	—
285	C₂	—	8	2	no	—
286	C₂	C₁₉×#1891	1	1	yes	characteristic
287	C₂	C₁₉×#1894	1	1	yes	characteristic
288	C₂	C₁₉×#1911	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2975

C₂

yes

maximal, characteristic

C₁₉×#2580

C₂

yes

maximal, characteristic

C₁₉×#1800

C₂

yes

maximal, characteristic

C₁₉×#1487

C₂

yes

maximal, complemented

C₁₉×#1286

C₂

yes

maximal, complemented

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₁₉×#436

—

C₁₉×#431

C₂²

yes

—

C₁₉×#423

C₂²

yes

—

C₂×C₁₉×#100

—

C₁₉×#407

—

C₁₉×#399

C₄

yes

—

C₁₉×#393

C₄

yes

—

C₁₉×#390

—

C₁₉×#389

—

C₁₉×#385

—

C₁₉×#382

C₂²

yes

characteristic

C₁₉×#343

—

C₁₉×Q₈⋊C₈

—

C₂²×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×D₄×C₁₉

D₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

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⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#100

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

D₄

yes

—

C₁₉×#95

—

C₁₉×#95

—

C₁₉×#95

C₂×C₄

yes

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×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

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

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

—

M₁₆×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

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

#9487

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

—

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

C₄×D₄

yes

—

112

C₂×C₄×C₁₉

#120

yes

characteristic

113

C₂×C₄×C₁₉

#121

yes

—

114

C₂×C₄×C₁₉

#123

yes

characteristic

115

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

characteristic

116

C₂×C₄×C₁₉

#137

yes

—

117

C₂×C₄×C₁₉

#137

yes

characteristic

118

C₈×C₁₉

—

119

C₈×C₁₉

—

120

#2975

C₂×C₁₉

yes

characteristic

121

#2580

C₂×C₁₉

yes

characteristic

122

#1800

C₂×C₁₉

yes

characteristic

123

#1487

C₂×C₁₉

yes

complemented

124

#1286

C₂×C₁₉

yes

complemented

125

C₂²×C₁₉

—

126

C₂²×C₁₉

—

127

C₂²×C₁₉

—

128

C₂²×C₁₉

—

129

C₂²×C₁₉

—

130

C₂²×C₁₉

—

131

C₂²×C₁₉

—

132

C₂²×C₁₉

#386

yes

characteristic

133

C₂²×C₁₉

#417

yes

characteristic

134

C₂²×C₁₉

#419

yes

characteristic

135

C₄×C₁₉

—

136

C₄×C₁₉

—

137

C₄×C₁₉

—

138

C₄×C₁₉

—

139

C₄×C₁₉

—

140

C₄×C₁₉

—

141

C₄×C₁₉

—

142

C₄×C₁₉

#468

yes

—

143

C₄×C₁₉

#470

yes

—

144

C₂×C₄×Q₈

C₂²×C₁₉

yes

characteristic

145

C₂×C₄×D₄

C₂²×C₁₉

yes

characteristic

146

#436

—

147

#431

C₂²×C₁₉

yes

—

148

#423

C₂²×C₁₉

yes

—

149

C₂×#100

—

150

#407

—

151

#399

C₄×C₁₉

yes

—

152

#393

C₄×C₁₉

yes

—

153

#390

—

154

#389

—

155

#385

—

156

#382

C₂²×C₁₉

yes

characteristic

157

#343

—

158

Q₈⋊C₈

—

159

C₂×C₁₉

—

160

C₂×C₁₉

—

161

C₂×C₁₉

—

162

C₂×C₁₉

#1891

yes

characteristic

163

C₂×C₁₉

#1894

yes

characteristic

164

C₂×C₁₉

#1911

yes

characteristic

165

C₂²×Q₈

C₂×C₄×C₁₉

yes

characteristic

166

C₂²×D₄

D₄×C₁₉

yes

characteristic

167

C₂³×C₄

D₄×C₁₉

yes

—

168

C₂×M₁₆

—

169

C₂×M₁₆

—

170

C₄×Q₈

—

171

C₄×Q₈

—

172

C₄×D₄

—

173

C₄×D₄

—

174

C₂×C₄⋊C₄

—

175

C₂×C₄⋊C₄

—

176

C₂×C₄⋊C₄

—

177

C₂×C₄⋊C₄

C₂×C₄×C₁₉

yes

characteristic

178

C₂×C₄⋊C₄

D₄×C₁₉

yes

characteristic

179

C₂×C₂²⋊C₄

—

180

C₂×C₂²⋊C₄

—

181

C₂×C₂²⋊C₄

C₂×C₄×C₁₉

yes

—

182

C₂×C₄²

—

183

C₂×C₄²

C₂³×C₁₉

yes

characteristic

184

C₄⋊C₈

—

185

C₄⋊C₈

—

186

C₄⋊C₈

—

187

#100

—

188

C₂²⋊C₈

—

189

C₂²⋊C₈

—

190

C₄×C₈

D₄×C₁₉

yes

—

191

#95

—

192

#95

—

193

#95

C₂×C₄×C₁₉

yes

—

194

C₁₉

#9487

yes

characteristic, direct product factor, Sylow

195

C₂⁴

C₂²⋊C₄×C₁₉

yes

—

196

C₂×Q₈

—

197

C₂×Q₈

—

198

C₂×D₄

—

199

C₂×D₄

—

200

C₂×D₄

—

201

C₂×D₄

—

202

C₂²×C₄

—

203

C₂²×C₄

—

204

C₂²×C₄

—

205

C₂²×C₄

—

206

C₂²×C₄

—

207

C₂²×C₄

—

208

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

—

209

C₂²×C₄

C₂²×C₄×C₁₉

yes

characteristic

210

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

211

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

212

M₁₆

—

213

M₁₆

—

214

M₁₆

—

215

C₂×C₈

—

216

C₂×C₈

—

217

C₄⋊C₄

—

218

C₄⋊C₄

—

219

C₄⋊C₄

—

220

C₄⋊C₄

—

221

C₄⋊C₄

—

222

C₄⋊C₄

—

223

C₄⋊C₄

—

224

C₂²⋊C₄

—

225

C₂²⋊C₄

—

226

C₂²⋊C₄

—

227

C₄²

—

228

C₄²

C₂×D₄×C₁₉

yes

—

229

C₄²

#41×C₁₉

yes

—

230

C₂³

—

231

C₂³

—

232

C₂³

—

233

C₂³

—

234

C₂³

—

235

C₂³

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

236

Q₈

—

237

Q₈

—

238

D₄

—

239

D₄

—

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

—

251

C₂×C₄

—

252

C₂×C₄

—

253

C₂×C₄

—

254

C₂×C₄

—

255

C₂×C₄

C₄×D₄×C₁₉

yes

—

256

C₂×C₄

C₁₉×#120

yes

characteristic

257

C₂×C₄

C₁₉×#121

yes

—

258

C₂×C₄

C₁₉×#123

yes

characteristic

259

C₂×C₄

C₁₉×AGL(1,ℤ/8)

yes

characteristic

260

C₂×C₄

C₁₉×#137

yes

—

261

C₂×C₄

C₁₉×#137

yes

characteristic

262

C₈

—

263

C₈

—

264

C₂²

—

265

C₂²

—

266

C₂²

—

267

C₂²

—

268

C₂²

—

269

C₂²

—

270

C₂²

—

271

C₂²

C₁₉×#386

yes

characteristic

272

C₂²

C₁₉×#417

yes

characteristic

273

C₂²

C₁₉×#419

yes

characteristic

274

C₄

—

275

C₄

—

276

C₄

—

277

C₄

—

278

C₄

—

279

C₄

—

280

C₄

—

281

C₄

C₁₉×#468

yes

—

282

C₄

C₁₉×#470

yes

—

283

C₂

—

284

C₂

—

285

C₂

—

286

C₂

C₁₉×#1891

yes

characteristic

287

C₂

C₁₉×#1894

yes

characteristic

288

C₂

C₁₉×#1911

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	D₄
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

D₄

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
4. C₁₉×#1487	C₂	semidirect
5. C₁₉×#1286	C₂	semidirect
85. #9487	C₁₉	direct (N × H)
123. #1487	C₂×C₁₉	semidirect
124. #1286	C₂×C₁₉	semidirect
194. C₁₉	#9487	direct (N × H)

H ≅ G/N

type

4. C₁₉×#1487

C₂

semidirect

5. C₁₉×#1286

C₂

semidirect

85. #9487

C₁₉

direct (N × H)

123. #1487

C₂×C₁₉

semidirect

124. #1286

C₂×C₁₉

semidirect

194. C₁₉

#9487

direct (N × H)

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

subgroup	index
C₁₉×#2975	2
C₁₉×#2580	2
C₁₉×#1800	2
C₁₉×#1487	2
C₁₉×#1286	2
#9487	19

subgroup

index

C₁₉×#2975

C₁₉×#2580

C₁₉×#1800

C₁₉×#1487

C₁₉×#1286

#9487

Subgroups — C₁₉×#9487 #18015446

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#9487 #18015446

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9487 #18015446