Group #18018118 — subgroups

Subgroups — C₁₉×#12159 #18018118

Order 4864.

390 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 82 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×#2187	C₂	1	2	yes	maximal
3	C₁₉×#2054	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1348	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1322	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₁₉×#533	—	2	1	no	—
8	C₂×C₁₉×SD₃₂	—	2	2	no	—
9	C₁₉×#477	—	2	2	no	—
10	C₁₉×#467	—	2	1	no	—
11	C₁₉×#467	C₂²	1	2	yes	—
12	C₁₉×#462	—	2	2	no	—
13	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#102	—	2	1	no	—
15	C₁₉×#390	—	2	1	no	—
16	C₁₉×#357	—	2	2	no	—
17	C₁₉×C₂²⋊C₁₆	C₂²	1	2	yes	—
18	C₁₉×#340	C₂²	1	1	yes	characteristic
19	C₂²×D₄×C₁₉	—	2	1	no	—
20	C₂×Q₁₆×C₁₉	—	2	1	no	—
21	C₂×Q₁₆×C₁₉	D₄	1	2	yes	—
22	C₂×D₈×C₁₉	—	2	2	no	—
23	C₂×D₈×C₁₉	—	4	2	no	—
24	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
26	C₁₉×C₄⋊Q₈	—	2	1	no	—
27	C₁₉×C₄⋊Q₈	—	2	1	no	—
28	C₁₉×#125	—	4	1	no	—
29	C₁₉×C₂²⋊Q₈	—	2	2	no	—
30	C₁₉×C₂²⋊Q₈	—	4	1	no	—
31	C₄×Q₈×C₁₉	—	2	2	no	—
32	C₄×Q₈×C₁₉	—	4	1	no	—
33	C₁₉×#117	—	4	1	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
36	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
37	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
38	C₁₉×SD₃₂	—	4	4	no	—
39	C₂×C₁₆×C₁₉	—	2	2	no	—
40	C₁₉×#107	—	2	1	no	—
41	C₁₉×#107	D₄	1	2	yes	—
42	C₁₉×C₄⋊C₈	—	2	2	no	—
43	C₁₉×#103	—	2	2	no	—
44	C₁₉×#103	—	2	2	no	—
45	C₁₉×#102	—	4	2	no	—
46	C₂⁴×C₁₉	—	4	1	no	—
47	C₂×Q₈×C₁₉	—	2	2	no	—
48	C₂×Q₈×C₁₉	—	4	1	no	—
49	C₂×D₄×C₁₉	—	2	2	no	—
50	C₂×D₄×C₁₉	—	4	1	no	—
51	C₂×D₄×C₁₉	—	4	1	no	—
52	C₂×D₄×C₁₉	—	4	1	no	—
53	C₂×D₄×C₁₉	—	4	1	no	—
54	C₂×D₄×C₁₉	—	4	1	no	—
55	C₂²×C₄×C₁₉	—	4	1	no	—
56	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
59	Q₁₆×C₁₉	—	4	2	no	—
60	Q₁₆×C₁₉	—	8	1	no	—
61	D₈×C₁₉	—	2	4	no	—
62	D₈×C₁₉	—	4	2	no	—
63	C₂×C₈×C₁₉	—	2	1	no	—
64	C₂×C₈×C₁₉	—	4	1	no	—
65	C₂×C₈×C₁₉	—	4	1	no	—
66	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
67	C₄⋊C₄×C₁₉	—	2	2	no	—
68	C₄⋊C₄×C₁₉	—	4	1	no	—
69	C₄⋊C₄×C₁₉	—	4	1	no	—
70	C₄⋊C₄×C₁₉	—	4	2	no	—
71	C₄⋊C₄×C₁₉	—	4	1	no	—
72	C₄⋊C₄×C₁₉	—	4	1	no	—
73	C₄⋊C₄×C₁₉	—	4	1	no	—
74	C₄⋊C₄×C₁₉	—	4	2	no	—
75	C₂²⋊C₄×C₁₉	—	4	2	no	—
76	C₂²⋊C₄×C₁₉	—	8	2	no	—
77	C₂²⋊C₄×C₁₉	—	8	2	no	—
78	C₄²×C₁₉	—	2	1	no	—
79	C₄²×C₁₉	—	2	1	no	—
80	C₄²×C₁₉	—	4	2	no	—
81	C₁₆×C₁₉	—	4	2	no	—
82	#12159	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
83	C₂³×C₁₉	—	4	2	no	—
84	C₂³×C₁₉	—	8	1	no	—
85	C₂³×C₁₉	—	8	1	no	—
86	C₂³×C₁₉	—	8	1	no	—
87	C₂³×C₁₉	—	8	1	no	—
88	C₂³×C₁₉	—	8	1	no	—
89	C₂³×C₁₉	—	8	1	no	—
90	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
91	Q₈×C₁₉	—	4	2	no	—
92	Q₈×C₁₉	—	4	2	no	—
93	Q₈×C₁₉	—	8	2	no	—
94	D₄×C₁₉	—	4	2	no	—
95	D₄×C₁₉	—	4	2	no	—
96	D₄×C₁₉	—	8	1	no	—
97	D₄×C₁₉	—	8	1	no	—
98	C₂×C₄×C₁₉	—	2	1	no	—
99	C₂×C₄×C₁₉	—	2	1	no	—
100	C₂×C₄×C₁₉	—	2	1	no	—
101	C₂×C₄×C₁₉	—	2	1	no	—
102	C₂×C₄×C₁₉	—	2	1	no	—
103	C₂×C₄×C₁₉	—	4	1	no	—
104	C₂×C₄×C₁₉	—	4	2	no	—
105	C₂×C₄×C₁₉	—	4	2	no	—
106	C₂×C₄×C₁₉	—	8	1	no	—
107	C₂×C₄×C₁₉	—	8	1	no	—
108	C₂×C₄×C₁₉	—	8	1	no	—
109	C₂×C₄×C₁₉	SD₃₂	1	2	yes	complemented
110	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
111	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
112	C₈×C₁₉	—	2	2	no	—
113	C₈×C₁₉	—	4	1	no	—
114	#3249	C₂×C₁₉	1	1	yes	characteristic, complemented
115	#2187	C₂×C₁₉	1	2	yes	—
116	#2054	C₂×C₁₉	1	1	yes	characteristic
117	#1348	C₂×C₁₉	1	2	yes	complemented
118	#1322	C₂×C₁₉	1	1	yes	characteristic, complemented
119	C₂²×C₁₉	—	2	1	no	—
120	C₂²×C₁₉	—	2	1	no	—
121	C₂²×C₁₉	—	8	2	no	—
122	C₂²×C₁₉	—	8	2	no	—
123	C₂²×C₁₉	—	8	2	no	—
124	C₂²×C₁₉	—	16	1	no	—
125	C₂²×C₁₉	—	16	1	no	—
126	C₂²×C₁₉	—	16	1	no	—
127	C₂²×C₁₉	—	16	1	no	—
128	C₂²×C₁₉	#447	1	1	yes	characteristic
129	C₂²×C₁₉	C₂×SD₃₂	1	1	yes	characteristic
130	C₂²×C₁₉	#510	1	1	yes	characteristic
131	C₄×C₁₉	—	2	1	no	—
132	C₄×C₁₉	—	2	2	no	—
133	C₄×C₁₉	—	4	1	no	—
134	C₄×C₁₉	—	8	2	no	—
135	C₄×C₁₉	—	8	2	no	—
136	C₄×C₁₉	—	16	1	no	—
137	C₄×C₁₉	#454	1	1	yes	characteristic
138	C₄×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
139	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
140	#533	—	2	1	no	—
141	C₂×SD₃₂	—	2	2	no	—
142	#477	—	2	2	no	—
143	#467	—	2	1	no	—
144	#467	C₂²×C₁₉	1	2	yes	—
145	#462	—	2	2	no	—
146	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
147	C₂×#102	—	2	1	no	—
148	#390	—	2	1	no	—
149	#357	—	2	2	no	—
150	C₂²⋊C₁₆	C₂²×C₁₉	1	2	yes	—
151	#340	C₂²×C₁₉	1	1	yes	characteristic
152	C₂×C₁₉	—	2	1	no	—
153	C₂×C₁₉	—	2	1	no	—
154	C₂×C₁₉	—	16	2	no	—
155	C₂×C₁₉	#1598	1	1	yes	characteristic
156	C₂×C₁₉	#2185	1	1	yes	characteristic
157	C₂×C₁₉	#2190	1	1	yes	characteristic
158	C₂²×D₄	—	2	1	no	—
159	C₂×Q₁₆	—	2	1	no	—
160	C₂×Q₁₆	D₄×C₁₉	1	2	yes	—
161	C₂×D₈	—	2	2	no	—
162	C₂×D₈	—	4	2	no	—
163	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
164	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
165	C₄⋊Q₈	—	2	1	no	—
166	C₄⋊Q₈	—	2	1	no	—
167	#125	—	4	1	no	—
168	C₂²⋊Q₈	—	2	2	no	—
169	C₂²⋊Q₈	—	4	1	no	—
170	C₄×Q₈	—	2	2	no	—
171	C₄×Q₈	—	4	1	no	—
172	#117	—	4	1	no	—
173	C₂×C₄⋊C₄	—	2	1	no	—
174	C₂×C₂²⋊C₄	—	4	1	no	—
175	C₂×C₂²⋊C₄	—	4	1	no	—
176	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
177	SD₃₂	—	4	4	no	—
178	C₂×C₁₆	—	2	2	no	—
179	#107	—	2	1	no	—
180	#107	D₄×C₁₉	1	2	yes	—
181	C₄⋊C₈	—	2	2	no	—
182	#103	—	2	2	no	—
183	#103	—	2	2	no	—
184	#102	—	4	2	no	—
185	C₁₉	#12159	1	1	yes	characteristic, direct product factor, Sylow
186	C₂⁴	—	4	1	no	—
187	C₂×Q₈	—	2	2	no	—
188	C₂×Q₈	—	4	1	no	—
189	C₂×D₄	—	2	2	no	—
190	C₂×D₄	—	4	1	no	—
191	C₂×D₄	—	4	1	no	—
192	C₂×D₄	—	4	1	no	—
193	C₂×D₄	—	4	1	no	—
194	C₂×D₄	—	4	1	no	—
195	C₂²×C₄	—	4	1	no	—
196	C₂²×C₄	D₈×C₁₉	1	1	yes	characteristic
197	C₂²×C₄	D₈×C₁₉	1	1	yes	characteristic
198	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
199	Q₁₆	—	4	2	no	—
200	Q₁₆	—	8	1	no	—
201	D₈	—	2	4	no	—
202	D₈	—	4	2	no	—
203	C₂×C₈	—	2	1	no	—
204	C₂×C₈	—	4	1	no	—
205	C₂×C₈	—	4	1	no	—
206	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
207	C₄⋊C₄	—	2	2	no	—
208	C₄⋊C₄	—	4	1	no	—
209	C₄⋊C₄	—	4	1	no	—
210	C₄⋊C₄	—	4	2	no	—
211	C₄⋊C₄	—	4	1	no	—
212	C₄⋊C₄	—	4	1	no	—
213	C₄⋊C₄	—	4	1	no	—
214	C₄⋊C₄	—	4	2	no	—
215	C₂²⋊C₄	—	4	2	no	—
216	C₂²⋊C₄	—	8	2	no	—
217	C₂²⋊C₄	—	8	2	no	—
218	C₄²	—	2	1	no	—
219	C₄²	—	2	1	no	—
220	C₄²	—	4	2	no	—
221	C₁₆	—	4	2	no	—
222	C₂³	—	4	2	no	—
223	C₂³	—	8	1	no	—
224	C₂³	—	8	1	no	—
225	C₂³	—	8	1	no	—
226	C₂³	—	8	1	no	—
227	C₂³	—	8	1	no	—
228	C₂³	—	8	1	no	—
229	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
230	Q₈	—	4	2	no	—
231	Q₈	—	4	2	no	—
232	Q₈	—	8	2	no	—
233	D₄	—	4	2	no	—
234	D₄	—	4	2	no	—
235	D₄	—	8	1	no	—
236	D₄	—	8	1	no	—
237	C₂×C₄	—	2	1	no	—
238	C₂×C₄	—	2	1	no	—
239	C₂×C₄	—	2	1	no	—
240	C₂×C₄	—	2	1	no	—
241	C₂×C₄	—	2	1	no	—
242	C₂×C₄	—	4	1	no	—
243	C₂×C₄	—	4	2	no	—
244	C₂×C₄	—	4	2	no	—
245	C₂×C₄	—	8	1	no	—
246	C₂×C₄	—	8	1	no	—
247	C₂×C₄	—	8	1	no	—
248	C₂×C₄	C₁₉×SD₃₂	1	2	yes	complemented
249	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
250	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
251	C₈	—	2	2	no	—
252	C₈	—	4	1	no	—
253	C₂²	—	2	1	no	—
254	C₂²	—	2	1	no	—
255	C₂²	—	8	2	no	—
256	C₂²	—	8	2	no	—
257	C₂²	—	8	2	no	—
258	C₂²	—	16	1	no	—
259	C₂²	—	16	1	no	—
260	C₂²	—	16	1	no	—
261	C₂²	—	16	1	no	—
262	C₂²	C₁₉×#447	1	1	yes	characteristic
263	C₂²	C₂×C₁₉×SD₃₂	1	1	yes	characteristic
264	C₂²	C₁₉×#510	1	1	yes	characteristic
265	C₄	—	2	2	no	—
266	C₄	—	2	1	no	—
267	C₄	—	4	1	no	—
268	C₄	—	8	2	no	—
269	C₄	—	8	2	no	—
270	C₄	—	16	1	no	—
271	C₄	C₁₉×#454	1	1	yes	characteristic
272	C₄	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
273	C₂	—	2	1	no	—
274	C₂	—	2	1	no	—
275	C₂	—	16	2	no	—
276	C₂	C₁₉×#1598	1	1	yes	characteristic
277	C₂	C₁₉×#2185	1	1	yes	characteristic
278	C₂	C₁₉×#2190	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#3249

C₂

yes

maximal, characteristic, complemented

C₁₉×#2187

C₂

yes

maximal

C₁₉×#2054

C₂

yes

maximal, characteristic

C₁₉×#1348

C₂

yes

maximal, complemented

C₁₉×#1322

C₂

yes

maximal, characteristic, complemented

C₂²×D₈×C₁₉

C₂²

yes

characteristic

C₁₉×#533

—

C₂×C₁₉×SD₃₂

—

C₁₉×#477

—

C₁₉×#467

—

C₁₉×#467

C₂²

yes

—

C₁₉×#462

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂×C₁₉×#102

—

C₁₉×#390

—

C₁₉×#357

—

C₁₉×C₂²⋊C₁₆

C₂²

yes

—

C₁₉×#340

C₂²

yes

characteristic

C₂²×D₄×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

D₄

yes

—

C₂×D₈×C₁₉

—

C₂×D₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

C₂³

yes

characteristic

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×#125

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₁₉×SD₃₂

—

C₂×C₁₆×C₁₉

—

C₁₉×#107

—

C₁₉×#107

D₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×#103

—

C₁₉×#103

—

C₁₉×#102

—

C₂⁴×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₈

yes

characteristic

C₂²×C₄×C₁₉

D₈

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×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

—

C₄²×C₁₉

—

C₁₆×C₁₉

—

#12159

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×D₈

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×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

SD₃₂

yes

complemented

110

C₂×C₄×C₁₉

#120

yes

characteristic

111

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

characteristic

112

C₈×C₁₉

—

113

C₈×C₁₉

—

114

#3249

C₂×C₁₉

yes

characteristic, complemented

115

#2187

C₂×C₁₉

yes

—

116

#2054

C₂×C₁₉

yes

characteristic

117

#1348

C₂×C₁₉

yes

complemented

118

#1322

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

—

127

C₂²×C₁₉

—

128

C₂²×C₁₉

#447

yes

characteristic

129

C₂²×C₁₉

C₂×SD₃₂

yes

characteristic

130

C₂²×C₁₉

#510

yes

characteristic

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

—

134

C₄×C₁₉

—

135

C₄×C₁₉

—

136

C₄×C₁₉

—

137

C₄×C₁₉

#454

yes

characteristic

138

C₄×C₁₉

B(4,𝔽₂)

yes

characteristic

139

C₂²×D₈

C₂²×C₁₉

yes

characteristic

140

#533

—

141

C₂×SD₃₂

—

142

#477

—

143

#467

—

144

#467

C₂²×C₁₉

yes

—

145

#462

—

146

C₂×C₄⋊C₈

C₂²×C₁₉

yes

characteristic

147

C₂×#102

—

148

#390

—

149

#357

—

150

C₂²⋊C₁₆

C₂²×C₁₉

yes

—

151

#340

C₂²×C₁₉

yes

characteristic

152

C₂×C₁₉

—

153

C₂×C₁₉

—

154

C₂×C₁₉

—

155

C₂×C₁₉

#1598

yes

characteristic

156

C₂×C₁₉

#2185

yes

characteristic

157

C₂×C₁₉

#2190

yes

characteristic

158

C₂²×D₄

—

159

C₂×Q₁₆

—

160

C₂×Q₁₆

D₄×C₁₉

yes

—

161

C₂×D₈

—

162

C₂×D₈

—

163

C₂²×C₈

D₄×C₁₉

yes

characteristic

164

C₂²×C₈

C₂³×C₁₉

yes

characteristic

165

C₄⋊Q₈

—

166

C₄⋊Q₈

—

167

#125

—

168

C₂²⋊Q₈

—

169

C₂²⋊Q₈

—

170

C₄×Q₈

—

171

C₄×Q₈

—

172

#117

—

173

C₂×C₄⋊C₄

—

174

C₂×C₂²⋊C₄

—

175

C₂×C₂²⋊C₄

—

176

C₂×C₄²

D₄×C₁₉

yes

characteristic

177

SD₃₂

—

178

C₂×C₁₆

—

179

#107

—

180

#107

D₄×C₁₉

yes

—

181

C₄⋊C₈

—

182

#103

—

183

#103

—

184

#102

—

185

C₁₉

#12159

yes

characteristic, direct product factor, Sylow

186

C₂⁴

—

187

C₂×Q₈

—

188

C₂×Q₈

—

189

C₂×D₄

—

190

C₂×D₄

—

191

C₂×D₄

—

192

C₂×D₄

—

193

C₂×D₄

—

194

C₂×D₄

—

195

C₂²×C₄

—

196

C₂²×C₄

D₈×C₁₉

yes

characteristic

197

C₂²×C₄

D₈×C₁₉

yes

characteristic

198

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

199

Q₁₆

—

200

Q₁₆

—

201

D₈

—

202

D₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

C₂×D₄×C₁₉

yes

—

207

C₄⋊C₄

—

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

C₂²⋊C₄

—

218

C₄²

—

219

C₄²

—

220

C₄²

—

221

C₁₆

—

222

C₂³

—

223

C₂³

—

224

C₂³

—

225

C₂³

—

226

C₂³

—

227

C₂³

—

228

C₂³

—

229

C₂³

C₂×D₈×C₁₉

yes

characteristic

230

Q₈

—

231

Q₈

—

232

Q₈

—

233

D₄

—

234

D₄

—

235

D₄

—

236

D₄

—

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

C₁₉×SD₃₂

yes

complemented

249

C₂×C₄

C₁₉×#120

yes

characteristic

250

C₂×C₄

C₁₉×AGL(1,ℤ/8)

yes

characteristic

251

C₈

—

252

C₈

—

253

C₂²

—

254

C₂²

—

255

C₂²

—

256

C₂²

—

257

C₂²

—

258

C₂²

—

259

C₂²

—

260

C₂²

—

261

C₂²

—

262

C₂²

C₁₉×#447

yes

characteristic

263

C₂²

C₂×C₁₉×SD₃₂

yes

characteristic

264

C₂²

C₁₉×#510

yes

characteristic

265

C₄

—

266

C₄

—

267

C₄

—

268

C₄

—

269

C₄

—

270

C₄

—

271

C₄

C₁₉×#454

yes

characteristic

272

C₄

C₁₉×B(4,𝔽₂)

yes

characteristic

273

C₂

—

274

C₂

—

275

C₂

—

276

C₂

C₁₉×#1598

yes

characteristic

277

C₂

C₁₉×#2185

yes

characteristic

278

C₂

C₁₉×#2190

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₂²×D₈×C₁₉	C₂²
LCS	G ▷ C₂²×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×C₄⋊C₈ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#447

commutator, Frattini, cosocle

C₂²×C₈

C₂³×C₁₉

prime radical

C₂²×D₈×C₁₉

C₂²

LCS

G ▷ C₂²×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×C₄⋊C₈ ◁ G

N	H ≅ G/N	type
1. C₁₉×#3249	C₂	semidirect
4. C₁₉×#1348	C₂	semidirect
5. C₁₉×#1322	C₂	semidirect
82. #12159	C₁₉	direct (N × H)
109. C₂×C₄×C₁₉	SD₃₂	semidirect
114. #3249	C₂×C₁₉	semidirect
117. #1348	C₂×C₁₉	semidirect
118. #1322	C₂×C₁₉	semidirect
185. C₁₉	#12159	direct (N × H)
248. C₂×C₄	C₁₉×SD₃₂	semidirect

H ≅ G/N

type

1. C₁₉×#3249

C₂

semidirect

4. C₁₉×#1348

C₂

semidirect

5. C₁₉×#1322

C₂

semidirect

82. #12159

C₁₉

direct (N × H)

109. C₂×C₄×C₁₉

SD₃₂

semidirect

114. #3249

C₂×C₁₉

semidirect

117. #1348

C₂×C₁₉

semidirect

118. #1322

C₂×C₁₉

semidirect

185. C₁₉

#12159

direct (N × H)

248. C₂×C₄

C₁₉×SD₃₂

semidirect

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

subgroup	index
C₁₉×#3249	2
C₁₉×#2187	2
C₁₉×#2054	2
C₁₉×#1348	2
C₁₉×#1322	2
#12159	19

subgroup

index

C₁₉×#3249

C₁₉×#2187

C₁₉×#2054

C₁₉×#1348

C₁₉×#1322

#12159

Subgroups — C₁₉×#12159 #18018118

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#12159 #18018118

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#12159 #18018118