Group #18015989 — subgroups

Subgroups — C₁₉×#10030 #18015989

Order 4864.

520 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 102 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, complemented
2	C₁₉×#3110	C₂	1	2	yes	maximal
3	C₁₉×#1955	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1531	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1290	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#533	C₂²	1	2	yes	—
7	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#484	—	2	2	no	—
9	C₁₉×#477	—	2	2	no	—
10	C₁₉×#474	—	2	2	no	—
11	C₁₉×#467	—	2	2	no	—
12	C₁₉×#462	—	2	2	no	—
13	C₁₉×#461	—	2	2	no	—
14	C₁₉×#450	—	2	2	no	—
15	C₁₉×#440	—	2	4	no	—
16	C₁₉×#432	C₂²	1	2	yes	—
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
19	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
20	C₁₉×#330	—	2	4	no	—
21	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₉	—	2	1	no	—
23	C₂×Q₁₆×C₁₉	—	2	2	no	—
24	C₂×SD₁₆×C₁₉	—	2	4	no	—
25	C₂²×C₈×C₁₉	—	2	1	no	—
26	C₂²×C₈×C₁₉	D₄	1	2	yes	—
27	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
28	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
29	C₁₉×#125	—	2	2	no	—
30	C₁₉×C₂²⋊Q₈	—	2	2	no	—
31	C₁₉×C₂²⋊Q₈	—	2	2	no	—
32	C₄×Q₈×C₁₉	—	2	2	no	—
33	C₄×Q₈×C₁₉	—	2	2	no	—
34	C₄×D₄×C₁₉	—	2	2	no	—
35	C₄×D₄×C₁₉	—	2	2	no	—
36	C₁₉×#117	—	2	2	no	—
37	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
38	C₂×C₂²⋊C₄×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×C₄⋊C₈	—	2	2	no	—
43	C₁₉×C₄⋊C₈	—	2	2	no	—
44	C₁₉×#103	—	2	4	no	—
45	C₁₉×#103	—	2	4	no	—
46	C₁₉×#102	—	2	4	no	—
47	C₁₉×C₂²⋊C₈	—	2	2	no	—
48	C₁₉×C₂²⋊C₈	—	4	4	no	—
49	C₁₉×#97	—	2	2	no	—
50	C₁₉×#97	D₄	1	4	yes	—
51	C₂⁴×C₁₉	—	2	1	no	—
52	C₂×Q₈×C₁₉	—	2	2	no	—
53	C₂×Q₈×C₁₉	—	2	2	no	—
54	C₂×D₄×C₁₉	—	2	2	no	—
55	C₂×D₄×C₁₉	—	4	2	no	—
56	C₂²×C₄×C₁₉	—	2	1	no	—
57	C₂²×C₄×C₁₉	—	4	2	no	—
58	C₂²×C₄×C₁₉	—	4	2	no	—
59	C₂²×C₄×C₁₉	—	4	1	no	—
60	C₂²×C₄×C₁₉	—	4	1	no	—
61	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
64	Q₁₆×C₁₉	—	8	2	no	—
65	SD₁₆×C₁₉	—	4	8	no	—
66	C₂×C₈×C₁₉	—	2	2	no	—
67	C₂×C₈×C₁₉	—	2	2	no	—
68	C₂×C₈×C₁₉	—	2	4	no	—
69	C₂×C₈×C₁₉	—	4	1	no	—
70	C₂×C₈×C₁₉	—	4	1	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	—	2	2	no	—
75	C₄⋊C₄×C₁₉	—	2	2	no	—
76	C₄⋊C₄×C₁₉	—	2	2	no	—
77	C₄⋊C₄×C₁₉	—	4	2	no	—
78	C₄⋊C₄×C₁₉	—	4	2	no	—
79	C₂²⋊C₄×C₁₉	—	4	2	no	—
80	C₂²⋊C₄×C₁₉	—	4	2	no	—
81	C₄²×C₁₉	—	4	2	no	—
82	C₄²×C₁₉	C₂×D₄	1	2	yes	—
83	C₄²×C₁₉	C₂×D₄	1	2	yes	—
84	#10030	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
85	C₂³×C₁₉	—	2	2	no	—
86	C₂³×C₁₉	—	4	2	no	—
87	C₂³×C₁₉	—	4	1	no	—
88	C₂³×C₁₉	—	4	1	no	—
89	C₂³×C₁₉	—	4	2	no	—
90	C₂³×C₁₉	#121	1	1	yes	characteristic
91	Q₈×C₁₉	—	4	4	no	—
92	Q₈×C₁₉	—	4	2	no	—
93	Q₈×C₁₉	—	4	2	no	—
94	D₄×C₁₉	—	2	4	no	—
95	D₄×C₁₉	—	4	2	no	—
96	C₂×C₄×C₁₉	—	2	2	no	—
97	C₂×C₄×C₁₉	—	2	1	no	—
98	C₂×C₄×C₁₉	—	2	1	no	—
99	C₂×C₄×C₁₉	—	4	1	no	—
100	C₂×C₄×C₁₉	—	4	2	no	—
101	C₂×C₄×C₁₉	—	4	2	no	—
102	C₂×C₄×C₁₉	—	4	2	no	—
103	C₂×C₄×C₁₉	—	4	1	no	—
104	C₂×C₄×C₁₉	—	8	2	no	—
105	C₂×C₄×C₁₉	—	8	1	no	—
106	C₂×C₄×C₁₉	—	8	1	no	—
107	C₂×C₄×C₁₉	#120	1	2	yes	—
108	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
109	C₂×C₄×C₁₉	#121	1	2	yes	—
110	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
111	C₈×C₁₉	—	4	2	no	—
112	C₈×C₁₉	—	4	4	no	—
113	C₈×C₁₉	—	4	2	no	—
114	#3249	C₂×C₁₉	1	1	yes	characteristic, complemented
115	#3110	C₂×C₁₉	1	2	yes	—
116	#1955	C₂×C₁₉	1	1	yes	characteristic
117	#1531	C₂×C₁₉	1	2	yes	complemented
118	#1290	C₂×C₁₉	1	1	yes	characteristic, complemented
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	#392	1	1	yes	characteristic
127	C₂²×C₁₉	#473	1	2	yes	—
128	C₄×C₁₉	—	2	1	no	—
129	C₄×C₁₉	—	2	2	no	—
130	C₄×C₁₉	—	2	2	no	—
131	C₄×C₁₉	—	8	1	no	—
132	C₄×C₁₉	—	8	2	no	—
133	C₄×C₁₉	—	8	2	no	—
134	C₄×C₁₉	#453	1	1	yes	characteristic
135	C₄×C₁₉	#454	1	1	yes	characteristic
136	#533	C₂²×C₁₉	1	2	yes	—
137	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
138	#484	—	2	2	no	—
139	#477	—	2	2	no	—
140	#474	—	2	2	no	—
141	#467	—	2	2	no	—
142	#462	—	2	2	no	—
143	#461	—	2	2	no	—
144	#450	—	2	2	no	—
145	#440	—	2	4	no	—
146	#432	C₂²×C₁₉	1	2	yes	—
147	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
148	C₂×C₂²⋊C₈	—	2	2	no	—
149	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
150	#330	—	2	4	no	—
151	C₂×C₁₉	—	2	2	no	—
152	C₂×C₁₉	—	8	2	no	—
153	C₂×C₁₉	#2006	1	1	yes	characteristic
154	C₂×C₁₉	#2010	1	1	yes	characteristic
155	C₂×C₁₉	#2020	1	1	yes	characteristic
156	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
157	C₂³×C₄	—	2	1	no	—
158	C₂×Q₁₆	—	2	2	no	—
159	C₂×SD₁₆	—	2	4	no	—
160	C₂²×C₈	—	2	1	no	—
161	C₂²×C₈	D₄×C₁₉	1	2	yes	—
162	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
163	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
164	#125	—	2	2	no	—
165	C₂²⋊Q₈	—	2	2	no	—
166	C₂²⋊Q₈	—	2	2	no	—
167	C₄×Q₈	—	2	2	no	—
168	C₄×Q₈	—	2	2	no	—
169	C₄×D₄	—	2	2	no	—
170	C₄×D₄	—	2	2	no	—
171	#117	—	2	2	no	—
172	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
173	C₂×C₂²⋊C₄	—	2	1	no	—
174	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
175	#107	—	2	4	no	—
176	#107	—	2	2	no	—
177	C₄⋊C₈	—	2	2	no	—
178	C₄⋊C₈	—	2	2	no	—
179	#103	—	2	4	no	—
180	#103	—	2	4	no	—
181	#102	—	2	4	no	—
182	C₂²⋊C₈	—	2	2	no	—
183	C₂²⋊C₈	—	4	4	no	—
184	#97	—	2	2	no	—
185	#97	D₄×C₁₉	1	4	yes	—
186	C₁₉	#10030	1	1	yes	characteristic, direct product factor, Sylow
187	C₂⁴	—	2	1	no	—
188	C₂×Q₈	—	2	2	no	—
189	C₂×Q₈	—	2	2	no	—
190	C₂×D₄	—	2	2	no	—
191	C₂×D₄	—	4	2	no	—
192	C₂²×C₄	—	2	1	no	—
193	C₂²×C₄	—	4	2	no	—
194	C₂²×C₄	—	4	2	no	—
195	C₂²×C₄	—	4	1	no	—
196	C₂²×C₄	—	4	1	no	—
197	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
198	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
199	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
200	Q₁₆	—	8	2	no	—
201	SD₁₆	—	4	8	no	—
202	C₂×C₈	—	2	2	no	—
203	C₂×C₈	—	2	4	no	—
204	C₂×C₈	—	2	2	no	—
205	C₂×C₈	—	4	1	no	—
206	C₂×C₈	—	4	1	no	—
207	C₂×C₈	—	4	2	no	—
208	C₄⋊C₄	—	2	2	no	—
209	C₄⋊C₄	—	2	2	no	—
210	C₄⋊C₄	—	2	2	no	—
211	C₄⋊C₄	—	2	2	no	—
212	C₄⋊C₄	—	2	2	no	—
213	C₄⋊C₄	—	4	2	no	—
214	C₄⋊C₄	—	4	2	no	—
215	C₂²⋊C₄	—	4	2	no	—
216	C₂²⋊C₄	—	4	2	no	—
217	C₄²	—	4	2	no	—
218	C₄²	C₂×D₄×C₁₉	1	2	yes	—
219	C₄²	C₂×D₄×C₁₉	1	2	yes	—
220	C₂³	—	2	2	no	—
221	C₂³	—	4	2	no	—
222	C₂³	—	4	1	no	—
223	C₂³	—	4	1	no	—
224	C₂³	—	4	2	no	—
225	C₂³	C₁₉×#121	1	1	yes	characteristic
226	Q₈	—	4	4	no	—
227	Q₈	—	4	2	no	—
228	Q₈	—	4	2	no	—
229	D₄	—	2	4	no	—
230	D₄	—	4	2	no	—
231	C₂×C₄	—	2	2	no	—
232	C₂×C₄	—	2	1	no	—
233	C₂×C₄	—	2	1	no	—
234	C₂×C₄	—	4	1	no	—
235	C₂×C₄	—	4	2	no	—
236	C₂×C₄	—	4	2	no	—
237	C₂×C₄	—	4	2	no	—
238	C₂×C₄	—	4	1	no	—
239	C₂×C₄	—	8	2	no	—
240	C₂×C₄	—	8	1	no	—
241	C₂×C₄	—	8	1	no	—
242	C₂×C₄	C₁₉×#120	1	2	yes	—
243	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
244	C₂×C₄	C₁₉×#121	1	2	yes	—
245	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
246	C₈	—	4	2	no	—
247	C₈	—	4	4	no	—
248	C₈	—	4	2	no	—
249	C₂²	—	2	1	no	—
250	C₂²	—	2	1	no	—
251	C₂²	—	4	4	no	—
252	C₂²	—	4	2	no	—
253	C₂²	—	8	2	no	—
254	C₂²	—	8	1	no	—
255	C₂²	—	8	1	no	—
256	C₂²	C₁₉×#392	1	1	yes	characteristic
257	C₂²	C₁₉×#473	1	2	yes	—
258	C₄	—	2	1	no	—
259	C₄	—	2	2	no	—
260	C₄	—	2	2	no	—
261	C₄	—	8	1	no	—
262	C₄	—	8	2	no	—
263	C₄	—	8	2	no	—
264	C₄	C₁₉×#453	1	1	yes	characteristic
265	C₄	C₁₉×#454	1	1	yes	characteristic
266	C₂	—	2	2	no	—
267	C₂	—	8	2	no	—
268	C₂	C₁₉×#2006	1	1	yes	characteristic
269	C₂	C₁₉×#2010	1	1	yes	characteristic
270	C₂	C₁₉×#2020	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#3249

C₂

yes

maximal, characteristic, complemented

C₁₉×#3110

C₂

yes

maximal

C₁₉×#1955

C₂

yes

maximal, characteristic

C₁₉×#1531

C₂

yes

maximal, complemented

C₁₉×#1290

C₂

yes

maximal, characteristic, complemented

C₁₉×#533

C₂²

yes

—

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₁₉×#484

—

C₁₉×#477

—

C₁₉×#474

—

C₁₉×#467

—

C₁₉×#462

—

C₁₉×#461

—

C₁₉×#450

—

C₁₉×#440

—

C₁₉×#432

C₂²

yes

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂×C₁₉×C₂²⋊C₈

—

C₂×C₁₉×#97

C₂²

yes

characteristic

C₁₉×#330

—

C₂²×D₄×C₁₉

D₄

yes

characteristic

C₂³×C₄×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×SD₁₆×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×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×#107

—

C₁₉×#107

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#103

—

C₁₉×#103

—

C₁₉×#102

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₁₉×#97

D₄

yes

—

C₂⁴×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

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

Q₁₆×C₁₉

—

SD₁₆×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

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

#10030

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#121

yes

characteristic

Q₈×C₁₉

—

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

#120

yes

—

108

C₂×C₄×C₁₉

#120

yes

characteristic

109

C₂×C₄×C₁₉

#121

yes

—

110

C₂×C₄×C₁₉

#127

yes

characteristic

111

C₈×C₁₉

—

112

C₈×C₁₉

—

113

C₈×C₁₉

—

114

#3249

C₂×C₁₉

yes

characteristic, complemented

115

#3110

C₂×C₁₉

yes

—

116

#1955

C₂×C₁₉

yes

characteristic

117

#1531

C₂×C₁₉

yes

complemented

118

#1290

C₂×C₁₉

yes

characteristic, complemented

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

—

122

C₂²×C₁₉

—

123

C₂²×C₁₉

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

—

126

C₂²×C₁₉

#392

yes

characteristic

127

C₂²×C₁₉

#473

yes

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

—

134

C₄×C₁₉

#453

yes

characteristic

135

C₄×C₁₉

#454

yes

characteristic

136

#533

C₂²×C₁₉

yes

—

137

C₂×C₄×D₄

C₂²×C₁₉

yes

characteristic

138

#484

—

139

#477

—

140

#474

—

141

#467

—

142

#462

—

143

#461

—

144

#450

—

145

#440

—

146

#432

C₂²×C₁₉

yes

—

147

C₂×C₄⋊C₈

C₂²×C₁₉

yes

characteristic

148

C₂×C₂²⋊C₈

—

149

C₂×#97

C₂²×C₁₉

yes

characteristic

150

#330

—

151

C₂×C₁₉

—

152

C₂×C₁₉

—

153

C₂×C₁₉

#2006

yes

characteristic

154

C₂×C₁₉

#2010

yes

characteristic

155

C₂×C₁₉

#2020

yes

characteristic

156

C₂²×D₄

D₄×C₁₉

yes

characteristic

157

C₂³×C₄

—

158

C₂×Q₁₆

—

159

C₂×SD₁₆

—

160

C₂²×C₈

—

161

C₂²×C₈

D₄×C₁₉

yes

—

162

C₄⋊Q₈

D₄×C₁₉

yes

—

163

C₄⋊Q₈

D₄×C₁₉

yes

—

164

#125

—

165

C₂²⋊Q₈

—

166

C₂²⋊Q₈

—

167

C₄×Q₈

—

168

C₄×Q₈

—

169

C₄×D₄

—

170

C₄×D₄

—

171

#117

—

172

C₂×C₄⋊C₄

D₄×C₁₉

yes

characteristic

173

C₂×C₂²⋊C₄

—

174

C₂×C₄²

C₂³×C₁₉

yes

characteristic

175

#107

—

176

#107

—

177

C₄⋊C₈

—

178

C₄⋊C₈

—

179

#103

—

180

#103

—

181

#102

—

182

C₂²⋊C₈

—

183

C₂²⋊C₈

—

184

#97

—

185

#97

D₄×C₁₉

yes

—

186

C₁₉

#10030

yes

characteristic, direct product factor, Sylow

187

C₂⁴

—

188

C₂×Q₈

—

189

C₂×Q₈

—

190

C₂×D₄

—

191

C₂×D₄

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

—

196

C₂²×C₄

—

197

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

198

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

199

C₂²×C₄

#41×C₁₉

yes

characteristic

200

Q₁₆

—

201

SD₁₆

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₄⋊C₄

—

212

C₄⋊C₄

—

213

C₄⋊C₄

—

214

C₄⋊C₄

—

215

C₂²⋊C₄

—

216

C₂²⋊C₄

—

217

C₄²

—

218

C₄²

C₂×D₄×C₁₉

yes

—

219

C₄²

C₂×D₄×C₁₉

yes

—

220

C₂³

—

221

C₂³

—

222

C₂³

—

223

C₂³

—

224

C₂³

—

225

C₂³

C₁₉×#121

yes

characteristic

226

Q₈

—

227

Q₈

—

228

Q₈

—

229

D₄

—

230

D₄

—

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

C₁₉×#120

yes

—

243

C₂×C₄

C₁₉×#120

yes

characteristic

244

C₂×C₄

C₁₉×#121

yes

—

245

C₂×C₄

C₁₉×#127

yes

characteristic

246

C₈

—

247

C₈

—

248

C₈

—

249

C₂²

—

250

C₂²

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

—

255

C₂²

—

256

C₂²

C₁₉×#392

yes

characteristic

257

C₂²

C₁₉×#473

yes

—

258

C₄

—

259

C₄

—

260

C₄

—

261

C₄

—

262

C₄

—

263

C₄

—

264

C₄

C₁₉×#453

yes

characteristic

265

C₄

C₁₉×#454

yes

characteristic

266

C₂

—

267

C₂

—

268

C₂

C₁₉×#2006

yes

characteristic

269

C₂

C₁₉×#2010

yes

characteristic

270

C₂

C₁₉×#2020

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂²×D₄×C₁₉	D₄
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

C₂²×D₄×C₁₉

D₄

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
1. C₁₉×#3249	C₂	semidirect
4. C₁₉×#1531	C₂	semidirect
5. C₁₉×#1290	C₂	semidirect
84. #10030	C₁₉	direct (N × H)
114. #3249	C₂×C₁₉	semidirect
117. #1531	C₂×C₁₉	semidirect
118. #1290	C₂×C₁₉	semidirect
186. C₁₉	#10030	direct (N × H)

H ≅ G/N

type

1. C₁₉×#3249

C₂

semidirect

4. C₁₉×#1531

C₂

semidirect

5. C₁₉×#1290

C₂

semidirect

84. #10030

C₁₉

direct (N × H)

114. #3249

C₂×C₁₉

semidirect

117. #1531

C₂×C₁₉

semidirect

118. #1290

C₂×C₁₉

semidirect

186. C₁₉

#10030

direct (N × H)

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

subgroup	index
C₁₉×#3249	2
C₁₉×#3110	2
C₁₉×#1955	2
C₁₉×#1531	2
C₁₉×#1290	2
#10030	19

subgroup

index

C₁₉×#3249

C₁₉×#3110

C₁₉×#1955

C₁₉×#1531

C₁₉×#1290

#10030

Subgroups — C₁₉×#10030 #18015989

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#10030 #18015989

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10030 #18015989