Group #18019289 — subgroups

Subgroups — C₁₉×#13330 #18019289

Order 4864.

558 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 146 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	C₂²×C₁₉×Q₃₂	C₂	1	2	yes	maximal
2	C₂×C₁₉×#494	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#358	C₂	1	2	yes	maximal
4	C₁₉×#1969	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1374	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₁₆×C₁₉	—	2	1	no	—
7	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×Q₁₆×C₁₉	C₂²	1	2	yes	—
9	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
10	C₂×C₁₉×Q₃₂	—	2	4	no	—
11	C₂×C₁₉×Q₃₂	—	2	4	no	—
12	C₂×C₁₉×Q₃₂	—	2	4	no	—
13	C₂²×C₁₆×C₁₉	C₂²	1	2	yes	—
14	C₁₉×#494	—	2	4	no	—
15	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#103	—	2	1	no	—
17	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#391	—	2	1	no	—
19	C₁₉×#358	—	2	4	no	—
20	C₂²×Q₈×C₁₉	—	2	1	no	—
21	C₂²×Q₈×C₁₉	—	2	2	no	—
22	C₂×Q₁₆×C₁₉	—	2	4	no	—
23	C₂×Q₁₆×C₁₉	—	2	2	no	—
24	C₂×Q₁₆×C₁₉	—	2	2	no	—
25	C₂×Q₁₆×C₁₉	—	2	2	no	—
26	C₂×Q₁₆×C₁₉	—	2	2	no	—
27	C₂×Q₁₆×C₁₉	—	2	2	no	—
28	C₂×Q₁₆×C₁₉	—	2	2	no	—
29	C₂×Q₁₆×C₁₉	—	2	2	no	—
30	C₂×Q₁₆×C₁₉	—	2	1	no	—
31	C₂×Q₁₆×C₁₉	—	4	2	no	—
32	C₂×Q₁₆×C₁₉	—	4	2	no	—
33	C₂×Q₁₆×C₁₉	D₄	1	4	yes	—
34	C₂×Q₁₆×C₁₉	D₄	1	2	yes	—
35	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
37	C₁₉×C₄⋊Q₈	—	2	4	no	—
38	C₁₉×C₄⋊Q₈	—	4	2	no	—
39	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
40	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
41	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
42	C₁₉×Q₃₂	—	2	16	no	—
43	C₂×C₁₆×C₁₉	—	2	2	no	—
44	C₂×C₁₆×C₁₉	—	2	2	no	—
45	C₂×C₁₆×C₁₉	D₄	1	4	yes	—
46	C₁₉×#107	—	2	2	no	—
47	C₁₉×#103	—	4	2	no	—
48	C₄×C₈×C₁₉	—	2	2	no	—
49	C₁₉×#95	—	4	2	no	—
50	C₂×Q₈×C₁₉	—	2	4	no	—
51	C₂×Q₈×C₁₉	—	2	2	no	—
52	C₂×Q₈×C₁₉	—	4	2	no	—
53	C₂×Q₈×C₁₉	—	4	1	no	—
54	C₂×Q₈×C₁₉	—	4	1	no	—
55	C₂×Q₈×C₁₉	—	4	2	no	—
56	C₂×Q₈×C₁₉	—	4	2	no	—
57	C₂×Q₈×C₁₉	—	4	1	no	—
58	C₂×Q₈×C₁₉	—	4	2	no	—
59	C₂×Q₈×C₁₉	—	4	1	no	—
60	C₂×Q₈×C₁₉	—	4	2	no	—
61	C₂×Q₈×C₁₉	—	4	1	no	—
62	C₂²×C₄×C₁₉	—	4	2	no	—
63	C₂²×C₄×C₁₉	—	4	1	no	—
64	C₂²×C₄×C₁₉	—	4	1	no	—
65	C₂²×C₄×C₁₉	D₈	1	2	yes	—
66	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
67	Q₁₆×C₁₉	—	2	4	no	—
68	Q₁₆×C₁₉	—	2	4	no	—
69	Q₁₆×C₁₉	—	2	4	no	—
70	Q₁₆×C₁₉	—	4	8	no	—
71	Q₁₆×C₁₉	—	4	2	no	—
72	Q₁₆×C₁₉	—	4	2	no	—
73	Q₁₆×C₁₉	—	4	2	no	—
74	C₂×C₈×C₁₉	—	2	1	no	—
75	C₂×C₈×C₁₉	—	2	1	no	—
76	C₂×C₈×C₁₉	D₈	1	2	yes	—
77	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
79	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
80	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
81	C₄⋊C₄×C₁₉	—	4	8	no	—
82	C₄⋊C₄×C₁₉	—	4	1	no	—
83	C₄⋊C₄×C₁₉	—	4	1	no	—
84	C₄²×C₁₉	—	2	1	no	—
85	C₄²×C₁₉	—	2	1	no	—
86	C₁₆×C₁₉	—	2	4	no	—
87	#13330	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
88	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
89	Q₈×C₁₉	—	4	2	no	—
90	Q₈×C₁₉	—	4	4	no	—
91	Q₈×C₁₉	—	4	4	no	—
92	Q₈×C₁₉	—	4	2	no	—
93	Q₈×C₁₉	—	8	1	no	—
94	Q₈×C₁₉	—	8	2	no	—
95	Q₈×C₁₉	—	8	2	no	—
96	Q₈×C₁₉	—	8	1	no	—
97	C₂×C₄×C₁₉	—	2	2	no	—
98	C₂×C₄×C₁₉	—	2	2	no	—
99	C₂×C₄×C₁₉	—	4	4	no	—
100	C₂×C₄×C₁₉	—	4	2	no	—
101	C₂×C₄×C₁₉	—	8	1	no	—
102	C₂×C₄×C₁₉	—	8	2	no	—
103	C₂×C₄×C₁₉	—	8	2	no	—
104	C₂×C₄×C₁₉	—	8	1	no	—
105	C₂×C₄×C₁₉	—	8	1	no	—
106	C₂×C₄×C₁₉	—	8	2	no	—
107	C₂×C₄×C₁₉	Q₃₂	1	4	yes	complemented
108	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
109	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
110	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
111	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
112	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
113	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
114	C₈×C₁₉	—	2	2	no	—
115	C₈×C₁₉	#120	1	2	yes	—
116	C₈×C₁₉	#121	1	2	yes	—
117	C₂²×Q₃₂	C₂×C₁₉	1	2	yes	—
118	C₂×#494	C₂×C₁₉	1	1	yes	characteristic
119	C₂×#358	C₂×C₁₉	1	2	yes	—
120	#1969	C₂×C₁₉	1	1	yes	characteristic
121	#1374	C₂×C₁₉	1	1	yes	characteristic
122	C₂²×C₁₉	#447	1	1	yes	characteristic
123	C₂²×C₁₉	#459	1	1	yes	characteristic
124	C₂²×C₁₉	#493	1	1	yes	characteristic
125	C₂²×C₁₉	C₂×Q₃₂	1	2	yes	—
126	C₂²×C₁₉	#510	1	2	yes	—
127	C₄×C₁₉	—	2	4	no	—
128	C₄×C₁₉	—	8	4	no	—
129	C₄×C₁₉	—	8	2	no	—
130	C₄×C₁₉	—	16	1	no	—
131	C₄×C₁₉	#392	1	1	yes	characteristic
132	C₄×C₁₉	#447	1	1	yes	characteristic
133	C₄×C₁₉	#459	1	1	yes	characteristic
134	C₄×C₁₉	#496	1	1	yes	characteristic
135	C₂²×Q₁₆	—	2	1	no	—
136	C₂²×Q₁₆	C₂²×C₁₉	1	2	yes	—
137	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
138	C₂×C₄⋊Q₈	—	2	1	no	—
139	C₂×Q₃₂	—	2	4	no	—
140	C₂×Q₃₂	—	2	4	no	—
141	C₂×Q₃₂	—	2	4	no	—
142	C₂²×C₁₆	C₂²×C₁₉	1	2	yes	—
143	#494	—	2	4	no	—
144	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
145	C₂×#103	—	2	1	no	—
146	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
147	#391	—	2	1	no	—
148	#358	—	2	4	no	—
149	C₂×C₁₉	#2011	1	1	yes	characteristic
150	C₂×C₁₉	#2188	1	2	yes	—
151	C₂×C₁₉	#2209	1	2	yes	—
152	C₂×C₁₉	#2247	1	1	yes	characteristic
153	C₂×C₁₉	#2251	1	1	yes	characteristic
154	C₂²×Q₈	—	2	2	no	—
155	C₂²×Q₈	—	2	1	no	—
156	C₂×Q₁₆	—	2	4	no	—
157	C₂×Q₁₆	—	2	2	no	—
158	C₂×Q₁₆	—	2	2	no	—
159	C₂×Q₁₆	—	2	2	no	—
160	C₂×Q₁₆	—	2	2	no	—
161	C₂×Q₁₆	—	2	2	no	—
162	C₂×Q₁₆	—	2	2	no	—
163	C₂×Q₁₆	—	2	2	no	—
164	C₂×Q₁₆	—	2	1	no	—
165	C₂×Q₁₆	—	4	2	no	—
166	C₂×Q₁₆	—	4	2	no	—
167	C₂×Q₁₆	D₄×C₁₉	1	4	yes	—
168	C₂×Q₁₆	D₄×C₁₉	1	2	yes	—
169	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
170	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
171	C₄⋊Q₈	—	2	4	no	—
172	C₄⋊Q₈	—	4	2	no	—
173	C₂×C₄⋊C₄	—	2	1	no	—
174	C₂×C₄⋊C₄	—	4	2	no	—
175	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
176	Q₃₂	—	2	16	no	—
177	C₂×C₁₆	—	2	2	no	—
178	C₂×C₁₆	—	2	2	no	—
179	C₂×C₁₆	D₄×C₁₉	1	4	yes	—
180	#107	—	2	2	no	—
181	#103	—	4	2	no	—
182	C₄×C₈	—	2	2	no	—
183	#95	—	4	2	no	—
184	C₁₉	#13330	1	1	yes	characteristic, direct product factor, Sylow
185	C₂×Q₈	—	2	4	no	—
186	C₂×Q₈	—	2	2	no	—
187	C₂×Q₈	—	4	2	no	—
188	C₂×Q₈	—	4	1	no	—
189	C₂×Q₈	—	4	1	no	—
190	C₂×Q₈	—	4	2	no	—
191	C₂×Q₈	—	4	2	no	—
192	C₂×Q₈	—	4	1	no	—
193	C₂×Q₈	—	4	1	no	—
194	C₂×Q₈	—	4	2	no	—
195	C₂×Q₈	—	4	2	no	—
196	C₂×Q₈	—	4	1	no	—
197	C₂²×C₄	—	4	1	no	—
198	C₂²×C₄	—	4	2	no	—
199	C₂²×C₄	—	4	1	no	—
200	C₂²×C₄	D₈×C₁₉	1	2	yes	—
201	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
202	Q₁₆	—	2	4	no	—
203	Q₁₆	—	2	4	no	—
204	Q₁₆	—	2	4	no	—
205	Q₁₆	—	4	8	no	—
206	Q₁₆	—	4	2	no	—
207	Q₁₆	—	4	2	no	—
208	Q₁₆	—	4	2	no	—
209	C₂×C₈	—	2	1	no	—
210	C₂×C₈	—	2	1	no	—
211	C₂×C₈	D₈×C₁₉	1	2	yes	—
212	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
213	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
214	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
215	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
216	C₄⋊C₄	—	4	8	no	—
217	C₄⋊C₄	—	4	1	no	—
218	C₄⋊C₄	—	4	1	no	—
219	C₄²	—	2	1	no	—
220	C₄²	—	2	1	no	—
221	C₁₆	—	2	4	no	—
222	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
223	Q₈	—	4	2	no	—
224	Q₈	—	4	4	no	—
225	Q₈	—	4	4	no	—
226	Q₈	—	4	2	no	—
227	Q₈	—	8	1	no	—
228	Q₈	—	8	2	no	—
229	Q₈	—	8	2	no	—
230	Q₈	—	8	1	no	—
231	C₂×C₄	—	2	2	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	4	4	no	—
234	C₂×C₄	—	4	2	no	—
235	C₂×C₄	—	8	1	no	—
236	C₂×C₄	—	8	2	no	—
237	C₂×C₄	—	8	1	no	—
238	C₂×C₄	—	8	2	no	—
239	C₂×C₄	—	8	1	no	—
240	C₂×C₄	—	8	2	no	—
241	C₂×C₄	C₁₉×Q₃₂	1	4	yes	complemented
242	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
243	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
244	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
245	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
246	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
247	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
248	C₈	—	2	2	no	—
249	C₈	C₁₉×#120	1	2	yes	—
250	C₈	C₁₉×#121	1	2	yes	—
251	C₂²	C₁₉×#447	1	1	yes	characteristic
252	C₂²	C₁₉×#459	1	1	yes	characteristic
253	C₂²	C₁₉×#493	1	1	yes	characteristic
254	C₂²	C₂×C₁₉×Q₃₂	1	2	yes	—
255	C₂²	C₁₉×#510	1	2	yes	—
256	C₄	—	2	4	no	—
257	C₄	—	8	4	no	—
258	C₄	—	8	2	no	—
259	C₄	—	16	1	no	—
260	C₄	C₁₉×#392	1	1	yes	characteristic
261	C₄	C₁₉×#447	1	1	yes	characteristic
262	C₄	C₁₉×#459	1	1	yes	characteristic
263	C₄	C₁₉×#496	1	1	yes	characteristic
264	C₂	C₁₉×#2011	1	1	yes	characteristic
265	C₂	C₁₉×#2188	1	2	yes	—
266	C₂	C₁₉×#2209	1	2	yes	—
267	C₂	C₁₉×#2247	1	1	yes	characteristic
268	C₂	C₁₉×#2251	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₁₉×Q₃₂

C₂

yes

maximal

C₂×C₁₉×#494

C₂

yes

maximal, characteristic

C₂×C₁₉×#358

C₂

yes

maximal

C₁₉×#1969

C₂

yes

maximal, characteristic

C₁₉×#1374

C₂

yes

maximal, characteristic

C₂²×Q₁₆×C₁₉

—

C₂²×Q₁₆×C₁₉

C₂²

yes

characteristic

C₂²×Q₁₆×C₁₉

C₂²

yes

—

C₂×C₁₉×C₄⋊Q₈

—

C₂×C₁₉×Q₃₂

—

C₂×C₁₉×Q₃₂

—

C₂×C₁₉×Q₃₂

—

C₂²×C₁₆×C₁₉

C₂²

yes

—

C₁₉×#494

—

C₂×C₁₉×#107

C₂²

yes

characteristic

C₂×C₁₉×#103

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#391

—

C₁₉×#358

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

D₄

yes

—

C₂×Q₁₆×C₁₉

D₄

yes

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

C₂³

yes

characteristic

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₁₉×Q₃₂

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

D₄

yes

—

C₁₉×#107

—

C₁₉×#103

—

C₄×C₈×C₁₉

—

C₁₉×#95

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₈

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

—

C₂×C₈×C₁₉

C₂×D₄

yes

characteristic

C₂×C₈×C₁₉

C₂×D₄

yes

—

C₂×C₈×C₁₉

C₂×D₄

yes

—

C₂×C₈×C₁₉

#41

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₁₆×C₁₉

—

#13330

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

C₂×D₈

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×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

Q₃₂

yes

complemented

108

C₂×C₄×C₁₉

#120

yes

characteristic

109

C₂×C₄×C₁₉

#121

yes

characteristic

110

C₂×C₄×C₁₉

#127

yes

characteristic

111

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

112

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

characteristic

113

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

characteristic

114

C₈×C₁₉

—

115

C₈×C₁₉

#120

yes

—

116

C₈×C₁₉

#121

yes

—

117

C₂²×Q₃₂

C₂×C₁₉

yes

—

118

C₂×#494

C₂×C₁₉

yes

characteristic

119

C₂×#358

C₂×C₁₉

yes

—

120

#1969

C₂×C₁₉

yes

characteristic

121

#1374

C₂×C₁₉

yes

characteristic

122

C₂²×C₁₉

#447

yes

characteristic

123

C₂²×C₁₉

#459

yes

characteristic

124

C₂²×C₁₉

#493

yes

characteristic

125

C₂²×C₁₉

C₂×Q₃₂

yes

—

126

C₂²×C₁₉

#510

yes

—

127

C₄×C₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

#392

yes

characteristic

132

C₄×C₁₉

#447

yes

characteristic

133

C₄×C₁₉

#459

yes

characteristic

134

C₄×C₁₉

#496

yes

characteristic

135

C₂²×Q₁₆

—

136

C₂²×Q₁₆

C₂²×C₁₉

yes

—

137

C₂²×Q₁₆

C₂²×C₁₉

yes

characteristic

138

C₂×C₄⋊Q₈

—

139

C₂×Q₃₂

—

140

C₂×Q₃₂

—

141

C₂×Q₃₂

—

142

C₂²×C₁₆

C₂²×C₁₉

yes

—

143

#494

—

144

C₂×#107

C₂²×C₁₉

yes

characteristic

145

C₂×#103

—

146

C₂×C₄×C₈

C₂²×C₁₉

yes

characteristic

147

#391

—

148

#358

—

149

C₂×C₁₉

#2011

yes

characteristic

150

C₂×C₁₉

#2188

yes

—

151

C₂×C₁₉

#2209

yes

—

152

C₂×C₁₉

#2247

yes

characteristic

153

C₂×C₁₉

#2251

yes

characteristic

154

C₂²×Q₈

—

155

C₂²×Q₈

—

156

C₂×Q₁₆

—

157

C₂×Q₁₆

—

158

C₂×Q₁₆

—

159

C₂×Q₁₆

—

160

C₂×Q₁₆

—

161

C₂×Q₁₆

—

162

C₂×Q₁₆

—

163

C₂×Q₁₆

—

164

C₂×Q₁₆

—

165

C₂×Q₁₆

—

166

C₂×Q₁₆

—

167

C₂×Q₁₆

D₄×C₁₉

yes

—

168

C₂×Q₁₆

D₄×C₁₉

yes

—

169

C₂²×C₈

D₄×C₁₉

yes

characteristic

170

C₂²×C₈

C₂³×C₁₉

yes

characteristic

171

C₄⋊Q₈

—

172

C₄⋊Q₈

—

173

C₂×C₄⋊C₄

—

174

C₂×C₄⋊C₄

—

175

C₂×C₄²

D₄×C₁₉

yes

characteristic

176

Q₃₂

—

177

C₂×C₁₆

—

178

C₂×C₁₆

—

179

C₂×C₁₆

D₄×C₁₉

yes

—

180

#107

—

181

#103

—

182

C₄×C₈

—

183

#95

—

184

C₁₉

#13330

yes

characteristic, direct product factor, Sylow

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×Q₈

—

188

C₂×Q₈

—

189

C₂×Q₈

—

190

C₂×Q₈

—

191

C₂×Q₈

—

192

C₂×Q₈

—

193

C₂×Q₈

—

194

C₂×Q₈

—

195

C₂×Q₈

—

196

C₂×Q₈

—

197

C₂²×C₄

—

198

C₂²×C₄

—

199

C₂²×C₄

—

200

C₂²×C₄

D₈×C₁₉

yes

—

201

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

202

Q₁₆

—

203

Q₁₆

—

204

Q₁₆

—

205

Q₁₆

—

206

Q₁₆

—

207

Q₁₆

—

208

Q₁₆

—

209

C₂×C₈

—

210

C₂×C₈

—

211

C₂×C₈

D₈×C₁₉

yes

—

212

C₂×C₈

C₂×D₄×C₁₉

yes

characteristic

213

C₂×C₈

C₂×D₄×C₁₉

yes

—

214

C₂×C₈

C₂×D₄×C₁₉

yes

—

215

C₂×C₈

#41×C₁₉

yes

characteristic

216

C₄⋊C₄

—

217

C₄⋊C₄

—

218

C₄⋊C₄

—

219

C₄²

—

220

C₄²

—

221

C₁₆

—

222

C₂³

C₂×D₈×C₁₉

yes

characteristic

223

Q₈

—

224

Q₈

—

225

Q₈

—

226

Q₈

—

227

Q₈

—

228

Q₈

—

229

Q₈

—

230

Q₈

—

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

C₁₉×Q₃₂

yes

complemented

242

C₂×C₄

C₁₉×#120

yes

characteristic

243

C₂×C₄

C₁₉×#121

yes

characteristic

244

C₂×C₄

C₁₉×#127

yes

characteristic

245

C₂×C₄

C₂×D₈×C₁₉

yes

characteristic

246

C₂×C₄

C₁₉×AGL(1,ℤ/8)

yes

characteristic

247

C₂×C₄

C₁₉×AGL(1,ℤ/8)

yes

characteristic

248

C₈

—

249

C₈

C₁₉×#120

yes

—

250

C₈

C₁₉×#121

yes

—

251

C₂²

C₁₉×#447

yes

characteristic

252

C₂²

C₁₉×#459

yes

characteristic

253

C₂²

C₁₉×#493

yes

characteristic

254

C₂²

C₂×C₁₉×Q₃₂

yes

—

255

C₂²

C₁₉×#510

yes

—

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

260

C₄

C₁₉×#392

yes

characteristic

261

C₄

C₁₉×#447

yes

characteristic

262

C₄

C₁₉×#459

yes

characteristic

263

C₄

C₁₉×#496

yes

characteristic

264

C₂

C₁₉×#2011

yes

characteristic

265

C₂

C₁₉×#2188

yes

—

266

C₂

C₁₉×#2209

yes

—

267

C₂

C₁₉×#2247

yes

characteristic

268

C₂

C₁₉×#2251

yes

characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂×D₈
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₁₉

C₂×D₈

commutator, Frattini, cosocle

C₂²×C₈

C₂³×C₁₉

LCS

G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

N	H ≅ G/N	type
87. #13330	C₁₉	direct (N × H)
107. C₂×C₄×C₁₉	Q₃₂	semidirect
184. C₁₉	#13330	direct (N × H)
241. C₂×C₄	C₁₉×Q₃₂	semidirect

H ≅ G/N

type

87. #13330

C₁₉

direct (N × H)

107. C₂×C₄×C₁₉

Q₃₂

semidirect

184. C₁₉

#13330

direct (N × H)

241. C₂×C₄

C₁₉×Q₃₂

semidirect

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

subgroup	index
C₂²×C₁₉×Q₃₂	2
C₂×C₁₉×#494	2
C₂×C₁₉×#358	2
C₁₉×#1969	2
C₁₉×#1374	2
#13330	19

subgroup

index

C₂²×C₁₉×Q₃₂

C₂×C₁₉×#494

C₂×C₁₉×#358

C₁₉×#1969

C₁₉×#1374

#13330

Subgroups — C₁₉×#13330 #18019289

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#13330 #18019289

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13330 #18019289