Group #18018068 — subgroups

Subgroups — C₁₉×#12109 #18018068

Order 4864.

410 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 74 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×#3202	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2187	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2018	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1350	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1315	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
7	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#536	—	2	1	no	—
9	C₂×C₁₉×SD₃₂	—	2	2	no	—
10	C₁₉×#485	—	2	2	no	—
11	C₁₉×#470	—	2	1	no	—
12	C₁₉×#467	C₂²	1	2	yes	—
13	C₁₉×#451	—	2	2	no	—
14	C₂×C₁₉×#100	—	2	1	no	—
15	C₁₉×#408	C₂²	1	1	yes	characteristic
16	C₁₉×#357	—	2	2	no	—
17	C₁₉×C₂²⋊C₁₆	C₂²	1	2	yes	—
18	C₁₉×#341	C₂²	1	1	yes	characteristic
19	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
20	C₂²×Q₈×C₁₉	—	2	1	no	—
21	C₂²×D₄×C₁₉	—	2	1	no	—
22	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
23	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
24	C₂×Q₁₆×C₁₉	—	2	1	no	—
25	C₂×Q₁₆×C₁₉	D₄	1	2	yes	—
26	C₂×SD₁₆×C₁₉	—	4	1	no	—
27	C₂×D₈×C₁₉	—	2	2	no	—
28	C₂×D₈×C₁₉	—	4	2	no	—
29	C₂×D₈×C₁₉	—	4	1	no	—
30	C₂×M₁₆×C₁₉	—	2	1	no	—
31	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
33	C₁₉×C₄⋊Q₈	—	4	1	no	—
34	C₁₉×#124	—	4	1	no	—
35	C₁₉×#123	—	4	1	no	—
36	C₁₉×#123	—	4	1	no	—
37	C₁₉×C₂²⋊Q₈	—	2	2	no	—
38	C₁₉×C₂²⋊Q₈	—	2	2	no	—
39	C₁₉×#117	—	2	1	no	—
40	C₁₉×SD₃₂	—	4	4	no	—
41	C₂×C₁₆×C₁₉	—	2	2	no	—
42	C₁₉×#107	D₄	1	2	yes	—
43	C₁₉×#106	—	2	1	no	—
44	C₁₉×#103	—	2	2	no	—
45	C₁₉×#103	—	2	2	no	—
46	C₁₉×#100	—	4	2	no	—
47	C₁₉×C₂²⋊C₈	—	2	2	no	—
48	C₂⁴×C₁₉	—	4	1	no	—
49	#41×C₁₉	—	4	1	no	—
50	#41×C₁₉	—	4	1	no	—
51	C₂×Q₈×C₁₉	—	2	2	no	—
52	C₂×Q₈×C₁₉	—	4	1	no	—
53	C₂×Q₈×C₁₉	—	8	1	no	—
54	C₂×Q₈×C₁₉	—	8	1	no	—
55	C₂×Q₈×C₁₉	D₈	1	1	yes	characteristic
56	C₂×D₄×C₁₉	—	2	2	no	—
57	C₂×D₄×C₁₉	—	2	1	no	—
58	C₂×D₄×C₁₉	—	4	1	no	—
59	C₂×D₄×C₁₉	—	4	1	no	—
60	C₂×D₄×C₁₉	—	4	1	no	—
61	C₂×D₄×C₁₉	—	4	1	no	—
62	C₂×D₄×C₁₉	—	4	1	no	—
63	C₂×D₄×C₁₉	D₈	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	—	2	1	no	—
65	C₂²×C₄×C₁₉	—	4	1	no	—
66	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
67	Q₁₆×C₁₉	—	4	2	no	—
68	Q₁₆×C₁₉	—	8	1	no	—
69	SD₁₆×C₁₉	—	4	4	no	—
70	D₈×C₁₉	—	2	4	no	—
71	D₈×C₁₉	—	4	2	no	—
72	D₈×C₁₉	—	4	4	no	—
73	M₁₆×C₁₉	—	2	2	no	—
74	M₁₆×C₁₉	—	4	1	no	—
75	M₁₆×C₁₉	—	4	1	no	—
76	C₂×C₈×C₁₉	—	2	1	no	—
77	C₂×C₈×C₁₉	—	4	1	no	—
78	C₂×C₈×C₁₉	—	4	1	no	—
79	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
80	C₄⋊C₄×C₁₉	—	2	2	no	—
81	C₄⋊C₄×C₁₉	—	4	2	no	—
82	C₄⋊C₄×C₁₉	—	4	2	no	—
83	C₂²⋊C₄×C₁₉	—	4	1	no	—
84	C₂²⋊C₄×C₁₉	—	4	2	no	—
85	C₂²⋊C₄×C₁₉	—	4	2	no	—
86	C₄²×C₁₉	—	4	1	no	—
87	C₁₆×C₁₉	—	4	2	no	—
88	#12109	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂³×C₁₉	—	2	1	no	—
90	C₂³×C₁₉	—	4	2	no	—
91	C₂³×C₁₉	—	8	1	no	—
92	C₂³×C₁₉	—	8	1	no	—
93	C₂³×C₁₉	—	16	2	no	—
94	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
95	Q₈×C₁₉	—	4	1	no	—
96	Q₈×C₁₉	—	4	2	no	—
97	Q₈×C₁₉	—	4	2	no	—
98	Q₈×C₁₉	—	8	2	no	—
99	D₄×C₁₉	—	4	1	no	—
100	D₄×C₁₉	—	4	2	no	—
101	D₄×C₁₉	—	4	2	no	—
102	D₄×C₁₉	—	8	1	no	—
103	D₄×C₁₉	—	8	1	no	—
104	D₄×C₁₉	—	8	1	no	—
105	C₂×C₄×C₁₉	—	2	1	no	—
106	C₂×C₄×C₁₉	—	2	1	no	—
107	C₂×C₄×C₁₉	—	2	1	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	2	no	—
112	C₂×C₄×C₁₉	—	8	2	no	—
113	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
114	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
115	C₈×C₁₉	—	2	2	no	—
116	C₈×C₁₉	—	4	2	no	—
117	C₈×C₁₉	—	4	1	no	—
118	#3202	C₂×C₁₉	1	1	yes	characteristic, complemented
119	#2187	C₂×C₁₉	1	2	yes	complemented
120	#2018	C₂×C₁₉	1	1	yes	characteristic
121	#1350	C₂×C₁₉	1	2	yes	complemented
122	#1315	C₂×C₁₉	1	1	yes	characteristic, complemented
123	C₂²×C₁₉	—	2	1	no	—
124	C₂²×C₁₉	—	2	2	no	—
125	C₂²×C₁₉	—	4	1	no	—
126	C₂²×C₁₉	—	4	2	no	—
127	C₂²×C₁₉	—	8	2	no	—
128	C₂²×C₁₉	—	16	2	no	—
129	C₂²×C₁₉	—	16	2	no	—
130	C₂²×C₁₉	—	16	2	no	—
131	C₂²×C₁₉	#447	1	1	yes	characteristic
132	C₄×C₁₉	—	2	1	no	—
133	C₄×C₁₉	—	4	1	no	—
134	C₄×C₁₉	—	8	2	no	—
135	C₄×C₁₉	—	8	2	no	—
136	C₄×C₁₉	#453	1	1	yes	characteristic
137	C₄×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
138	C₂×AGL(1,ℤ/8)	—	2	1	no	—
139	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
140	#536	—	2	1	no	—
141	C₂×SD₃₂	—	2	2	no	—
142	#485	—	2	2	no	—
143	#470	—	2	1	no	—
144	#467	C₂²×C₁₉	1	2	yes	—
145	#451	—	2	2	no	—
146	C₂×#100	—	2	1	no	—
147	#408	C₂²×C₁₉	1	1	yes	characteristic
148	#357	—	2	2	no	—
149	C₂²⋊C₁₆	C₂²×C₁₉	1	2	yes	—
150	#341	C₂²×C₁₉	1	1	yes	characteristic
151	C₂×C₁₉	—	4	1	no	—
152	C₂×C₁₉	—	8	1	no	—
153	C₂×C₁₉	—	16	2	no	—
154	C₂×C₁₉	#1595	1	1	yes	characteristic
155	C₂×C₁₉	#2193	1	2	yes	—
156	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
157	C₂²×Q₈	—	2	1	no	—
158	C₂²×D₄	—	2	1	no	—
159	AGL(1,ℤ/8)	—	4	2	no	—
160	AGL(1,ℤ/8)	—	4	2	no	—
161	C₂×Q₁₆	—	2	1	no	—
162	C₂×Q₁₆	D₄×C₁₉	1	2	yes	—
163	C₂×SD₁₆	—	4	1	no	—
164	C₂×D₈	—	2	2	no	—
165	C₂×D₈	—	4	2	no	—
166	C₂×D₈	—	4	1	no	—
167	C₂×M₁₆	—	2	1	no	—
168	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
169	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
170	C₄⋊Q₈	—	4	1	no	—
171	#124	—	4	1	no	—
172	#123	—	4	1	no	—
173	#123	—	4	1	no	—
174	C₂²⋊Q₈	—	2	2	no	—
175	C₂²⋊Q₈	—	2	2	no	—
176	#117	—	2	1	no	—
177	SD₃₂	—	4	4	no	—
178	C₂×C₁₆	—	2	2	no	—
179	#107	D₄×C₁₉	1	2	yes	—
180	#106	—	2	1	no	—
181	#103	—	2	2	no	—
182	#103	—	2	2	no	—
183	#100	—	4	2	no	—
184	C₂²⋊C₈	—	2	2	no	—
185	C₁₉	#12109	1	1	yes	characteristic, direct product factor, Sylow
186	C₂⁴	—	4	1	no	—
187	#41	—	4	1	no	—
188	#41	—	4	1	no	—
189	C₂×Q₈	—	2	2	no	—
190	C₂×Q₈	—	4	1	no	—
191	C₂×Q₈	—	8	1	no	—
192	C₂×Q₈	—	8	1	no	—
193	C₂×Q₈	D₈×C₁₉	1	1	yes	characteristic
194	C₂×D₄	—	2	2	no	—
195	C₂×D₄	—	2	1	no	—
196	C₂×D₄	—	4	1	no	—
197	C₂×D₄	—	4	1	no	—
198	C₂×D₄	—	4	1	no	—
199	C₂×D₄	—	4	1	no	—
200	C₂×D₄	—	4	1	no	—
201	C₂×D₄	D₈×C₁₉	1	1	yes	characteristic
202	C₂²×C₄	—	2	1	no	—
203	C₂²×C₄	—	4	1	no	—
204	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
205	Q₁₆	—	4	2	no	—
206	Q₁₆	—	8	1	no	—
207	SD₁₆	—	4	4	no	—
208	D₈	—	2	4	no	—
209	D₈	—	4	2	no	—
210	D₈	—	4	4	no	—
211	M₁₆	—	2	2	no	—
212	M₁₆	—	4	1	no	—
213	M₁₆	—	4	1	no	—
214	C₂×C₈	—	2	1	no	—
215	C₂×C₈	—	4	1	no	—
216	C₂×C₈	—	4	1	no	—
217	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
218	C₄⋊C₄	—	2	2	no	—
219	C₄⋊C₄	—	4	2	no	—
220	C₄⋊C₄	—	4	2	no	—
221	C₂²⋊C₄	—	4	1	no	—
222	C₂²⋊C₄	—	4	2	no	—
223	C₂²⋊C₄	—	4	2	no	—
224	C₄²	—	4	1	no	—
225	C₁₆	—	4	2	no	—
226	C₂³	—	2	1	no	—
227	C₂³	—	4	2	no	—
228	C₂³	—	8	1	no	—
229	C₂³	—	8	1	no	—
230	C₂³	—	16	2	no	—
231	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
232	Q₈	—	4	1	no	—
233	Q₈	—	4	2	no	—
234	Q₈	—	4	2	no	—
235	Q₈	—	8	2	no	—
236	D₄	—	4	1	no	—
237	D₄	—	4	2	no	—
238	D₄	—	4	2	no	—
239	D₄	—	8	1	no	—
240	D₄	—	8	1	no	—
241	D₄	—	8	1	no	—
242	C₂×C₄	—	2	1	no	—
243	C₂×C₄	—	2	1	no	—
244	C₂×C₄	—	2	1	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	—	8	2	no	—
250	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
251	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
252	C₈	—	2	2	no	—
253	C₈	—	4	2	no	—
254	C₈	—	4	1	no	—
255	C₂²	—	2	2	no	—
256	C₂²	—	2	1	no	—
257	C₂²	—	4	2	no	—
258	C₂²	—	4	1	no	—
259	C₂²	—	8	2	no	—
260	C₂²	—	16	2	no	—
261	C₂²	—	16	2	no	—
262	C₂²	—	16	2	no	—
263	C₂²	C₁₉×#447	1	1	yes	characteristic
264	C₄	—	2	1	no	—
265	C₄	—	4	1	no	—
266	C₄	—	8	2	no	—
267	C₄	—	8	2	no	—
268	C₄	C₁₉×#453	1	1	yes	characteristic
269	C₄	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
270	C₂	—	4	1	no	—
271	C₂	—	8	1	no	—
272	C₂	—	16	2	no	—
273	C₂	C₁₉×#1595	1	1	yes	characteristic
274	C₂	C₁₉×#2193	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#3202

C₂

yes

maximal, characteristic, complemented

C₁₉×#2187

C₂

yes

maximal, complemented

C₁₉×#2018

C₂

yes

maximal, characteristic

C₁₉×#1350

C₂

yes

maximal, complemented

C₁₉×#1315

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×AGL(1,ℤ/8)

—

C₂²×D₈×C₁₉

C₂²

yes

characteristic

C₁₉×#536

—

C₂×C₁₉×SD₃₂

—

C₁₉×#485

—

C₁₉×#470

—

C₁₉×#467

C₂²

yes

—

C₁₉×#451

—

C₂×C₁₉×#100

—

C₁₉×#408

C₂²

yes

characteristic

C₁₉×#357

—

C₁₉×C₂²⋊C₁₆

C₂²

yes

—

C₁₉×#341

C₂²

yes

characteristic

C₂×#41×C₁₉

D₄

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂²×D₄×C₁₉

—

C₁₉×AGL(1,ℤ/8)

—

C₁₉×AGL(1,ℤ/8)

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

D₄

yes

—

C₂×SD₁₆×C₁₉

—

C₂×D₈×C₁₉

—

C₂×D₈×C₁₉

—

C₂×D₈×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

C₂³

yes

characteristic

C₁₉×C₄⋊Q₈

—

C₁₉×#124

—

C₁₉×#123

—

C₁₉×#123

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₁₉×#117

—

C₁₉×SD₃₂

—

C₂×C₁₆×C₁₉

—

C₁₉×#107

D₄

yes

—

C₁₉×#106

—

C₁₉×#103

—

C₁₉×#103

—

C₁₉×#100

—

C₁₉×C₂²⋊C₈

—

C₂⁴×C₁₉

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₈

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

D₈

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

SD₁₆×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×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

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₁₆×C₁₉

—

#12109

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

AGL(1,ℤ/8)

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

100

D₄×C₁₉

—

101

D₄×C₁₉

—

102

D₄×C₁₉

—

103

D₄×C₁₉

—

104

D₄×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

#120

yes

characteristic

114

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

115

C₈×C₁₉

—

116

C₈×C₁₉

—

117

C₈×C₁₉

—

118

#3202

C₂×C₁₉

yes

characteristic, complemented

119

#2187

C₂×C₁₉

yes

complemented

120

#2018

C₂×C₁₉

yes

characteristic

121

#1350

C₂×C₁₉

yes

complemented

122

#1315

C₂×C₁₉

yes

characteristic, complemented

123

C₂²×C₁₉

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

—

126

C₂²×C₁₉

—

127

C₂²×C₁₉

—

128

C₂²×C₁₉

—

129

C₂²×C₁₉

—

130

C₂²×C₁₉

—

131

C₂²×C₁₉

#447

yes

characteristic

132

C₄×C₁₉

—

133

C₄×C₁₉

—

134

C₄×C₁₉

—

135

C₄×C₁₉

—

136

C₄×C₁₉

#453

yes

characteristic

137

C₄×C₁₉

B(4,𝔽₂)

yes

characteristic

138

C₂×AGL(1,ℤ/8)

—

139

C₂²×D₈

C₂²×C₁₉

yes

characteristic

140

#536

—

141

C₂×SD₃₂

—

142

#485

—

143

#470

—

144

#467

C₂²×C₁₉

yes

—

145

#451

—

146

C₂×#100

—

147

#408

C₂²×C₁₉

yes

characteristic

148

#357

—

149

C₂²⋊C₁₆

C₂²×C₁₉

yes

—

150

#341

C₂²×C₁₉

yes

characteristic

151

C₂×C₁₉

—

152

C₂×C₁₉

—

153

C₂×C₁₉

—

154

C₂×C₁₉

#1595

yes

characteristic

155

C₂×C₁₉

#2193

yes

—

156

C₂×#41

D₄×C₁₉

yes

characteristic

157

C₂²×Q₈

—

158

C₂²×D₄

—

159

AGL(1,ℤ/8)

—

160

AGL(1,ℤ/8)

—

161

C₂×Q₁₆

—

162

C₂×Q₁₆

D₄×C₁₉

yes

—

163

C₂×SD₁₆

—

164

C₂×D₈

—

165

C₂×D₈

—

166

C₂×D₈

—

167

C₂×M₁₆

—

168

C₂×M₁₆

D₄×C₁₉

yes

characteristic

169

C₂²×C₈

C₂³×C₁₉

yes

characteristic

170

C₄⋊Q₈

—

171

#124

—

172

#123

—

173

#123

—

174

C₂²⋊Q₈

—

175

C₂²⋊Q₈

—

176

#117

—

177

SD₃₂

—

178

C₂×C₁₆

—

179

#107

D₄×C₁₉

yes

—

180

#106

—

181

#103

—

182

#103

—

183

#100

—

184

C₂²⋊C₈

—

185

C₁₉

#12109

yes

characteristic, direct product factor, Sylow

186

C₂⁴

—

187

#41

—

188

#41

—

189

C₂×Q₈

—

190

C₂×Q₈

—

191

C₂×Q₈

—

192

C₂×Q₈

—

193

C₂×Q₈

D₈×C₁₉

yes

characteristic

194

C₂×D₄

—

195

C₂×D₄

—

196

C₂×D₄

—

197

C₂×D₄

—

198

C₂×D₄

—

199

C₂×D₄

—

200

C₂×D₄

—

201

C₂×D₄

D₈×C₁₉

yes

characteristic

202

C₂²×C₄

—

203

C₂²×C₄

—

204

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

205

Q₁₆

—

206

Q₁₆

—

207

SD₁₆

—

208

D₈

—

209

D₈

—

210

D₈

—

211

M₁₆

—

212

M₁₆

—

213

M₁₆

—

214

C₂×C₈

—

215

C₂×C₈

—

216

C₂×C₈

—

217

C₂×C₈

C₂×D₄×C₁₉

yes

—

218

C₄⋊C₄

—

219

C₄⋊C₄

—

220

C₄⋊C₄

—

221

C₂²⋊C₄

—

222

C₂²⋊C₄

—

223

C₂²⋊C₄

—

224

C₄²

—

225

C₁₆

—

226

C₂³

—

227

C₂³

—

228

C₂³

—

229

C₂³

—

230

C₂³

—

231

C₂³

C₁₉×AGL(1,ℤ/8)

yes

characteristic

232

Q₈

—

233

Q₈

—

234

Q₈

—

235

Q₈

—

236

D₄

—

237

D₄

—

238

D₄

—

239

D₄

—

240

D₄

—

241

D₄

—

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

C₁₉×#120

yes

characteristic

251

C₂×C₄

C₂×D₈×C₁₉

yes

characteristic

252

C₈

—

253

C₈

—

254

C₈

—

255

C₂²

—

256

C₂²

—

257

C₂²

—

258

C₂²

—

259

C₂²

—

260

C₂²

—

261

C₂²

—

262

C₂²

—

263

C₂²

C₁₉×#447

yes

characteristic

264

C₄

—

265

C₄

—

266

C₄

—

267

C₄

—

268

C₄

C₁₉×#453

yes

characteristic

269

C₄

C₁₉×B(4,𝔽₂)

yes

characteristic

270

C₂

—

271

C₂

—

272

C₂

—

273

C₂

C₁₉×#1595

yes

characteristic

274

C₂

C₁₉×#2193

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₉	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₁₉×#2018	C₂
LCS	G ▷ C₂²×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₁₉×#408 ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#447

commutator, Frattini, cosocle

C₂²×C₈

C₂³×C₁₉

prime radical

C₁₉×#2018

C₂

LCS

G ▷ C₂²×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₁₉×#408 ◁ G

N	H ≅ G/N	type
1. C₁₉×#3202	C₂	semidirect
2. C₁₉×#2187	C₂	semidirect
4. C₁₉×#1350	C₂	semidirect
5. C₁₉×#1315	C₂	semidirect
88. #12109	C₁₉	direct (N × H)
118. #3202	C₂×C₁₉	semidirect
119. #2187	C₂×C₁₉	semidirect
121. #1350	C₂×C₁₉	semidirect
122. #1315	C₂×C₁₉	semidirect
185. C₁₉	#12109	direct (N × H)

H ≅ G/N

type

1. C₁₉×#3202

C₂

semidirect

2. C₁₉×#2187

C₂

semidirect

4. C₁₉×#1350

C₂

semidirect

5. C₁₉×#1315

C₂

semidirect

88. #12109

C₁₉

direct (N × H)

118. #3202

C₂×C₁₉

semidirect

119. #2187

C₂×C₁₉

semidirect

121. #1350

C₂×C₁₉

semidirect

122. #1315

C₂×C₁₉

semidirect

185. C₁₉

#12109

direct (N × H)

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

subgroup	index
C₁₉×#3202	2
C₁₉×#2187	2
C₁₉×#2018	2
C₁₉×#1350	2
C₁₉×#1315	2
#12109	19

subgroup

index

C₁₉×#3202

C₁₉×#2187

C₁₉×#2018

C₁₉×#1350

C₁₉×#1315

#12109

Subgroups — C₁₉×#12109 #18018068

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#12109 #18018068

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#12109 #18018068