Group #18013608 — subgroups

Subgroups — C₁₉×#7649 #18013608

Order 4864.

468 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 130 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	C₄×C₁₉×#124	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1839	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1272	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1270	C₂	1	2	yes	maximal
5	C₂×C₁₉×#124	C₄	1	1	yes	characteristic
6	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic
7	C₂×C₄×D₄×C₁₉	C₄	1	1	yes	characteristic
8	C₁₉×#391	C₂²	1	1	yes	characteristic
9	C₁₉×#390	C₂²	1	1	yes	characteristic
10	C₁₉×#388	—	2	2	no	—
11	C₁₉×#382	C₄	1	1	yes	characteristic
12	C₄×C₂²⋊C₄×C₁₉	—	2	2	no	—
13	C₄³×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#336	—	2	2	no	—
15	C₁₉×#336	—	2	2	no	—
16	C₁₉×#336	C₂²	1	4	yes	—
17	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂³×C₄×C₁₉	—	2	1	no	—
20	C₂²×C₈×C₁₉	—	2	4	no	—
21	C₁₉×#124	—	2	2	no	—
22	C₁₉×#124	—	2	2	no	—
23	C₄×Q₈×C₁₉	—	4	2	no	—
24	C₄×D₄×C₁₉	—	4	2	no	—
25	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
26	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
29	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
30	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
31	C₂×C₄²×C₁₉	—	2	1	no	—
32	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₉	D₄	1	2	yes	—
35	C₂×C₄²×C₁₉	D₄	1	2	yes	—
36	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
37	C₁₉×#95	—	2	2	no	—
38	C₁₉×#95	—	2	2	no	—
39	C₂⁴×C₁₉	—	2	1	no	—
40	C₂×Q₈×C₁₉	—	2	1	no	—
41	C₂×Q₈×C₁₉	—	4	1	no	—
42	C₂×Q₈×C₁₉	—	4	1	no	—
43	C₂×Q₈×C₁₉	M₁₆	1	2	yes	—
44	C₂×D₄×C₁₉	—	2	1	no	—
45	C₂×D₄×C₁₉	—	4	1	no	—
46	C₂×D₄×C₁₉	—	4	1	no	—
47	C₂×D₄×C₁₉	M₁₆	1	2	yes	—
48	C₂²×C₄×C₁₉	—	2	1	no	—
49	C₂²×C₄×C₁₉	—	2	1	no	—
50	C₂²×C₄×C₁₉	—	2	1	no	—
51	C₂²×C₄×C₁₉	—	4	4	no	—
52	C₂²×C₄×C₁₉	—	4	2	no	—
53	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
55	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
58	C₂×C₈×C₁₉	—	4	4	no	—
59	C₂×C₈×C₁₉	—	4	4	no	—
60	C₂×C₈×C₁₉	—	4	4	no	—
61	C₄⋊C₄×C₁₉	—	4	1	no	—
62	C₄⋊C₄×C₁₉	—	4	1	no	—
63	C₄⋊C₄×C₁₉	—	4	2	no	—
64	C₂²⋊C₄×C₁₉	—	2	8	no	—
65	C₂²⋊C₄×C₁₉	—	4	2	no	—
66	C₂²⋊C₄×C₁₉	—	4	4	no	—
67	C₄²×C₁₉	—	2	2	no	—
68	C₄²×C₁₉	—	2	1	no	—
69	C₄²×C₁₉	—	2	1	no	—
70	C₄²×C₁₉	—	2	4	no	—
71	C₄²×C₁₉	—	4	2	no	—
72	C₄²×C₁₉	—	4	1	no	—
73	C₄²×C₁₉	—	4	2	no	—
74	#7649	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
75	C₂³×C₁₉	—	2	2	no	—
76	C₂³×C₁₉	—	4	1	no	—
77	C₂³×C₁₉	—	4	1	no	—
78	C₂³×C₁₉	—	4	2	no	—
79	C₂³×C₁₉	—	4	2	no	—
80	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	Q₈×C₁₉	—	4	2	no	—
82	Q₈×C₁₉	—	4	2	no	—
83	D₄×C₁₉	—	4	2	no	—
84	D₄×C₁₉	—	4	2	no	—
85	C₂×C₄×C₁₉	—	2	2	no	—
86	C₂×C₄×C₁₉	—	2	1	no	—
87	C₂×C₄×C₁₉	—	2	1	no	—
88	C₂×C₄×C₁₉	—	2	2	no	—
89	C₂×C₄×C₁₉	—	2	2	no	—
90	C₂×C₄×C₁₉	—	2	2	no	—
91	C₂×C₄×C₁₉	—	2	2	no	—
92	C₂×C₄×C₁₉	—	2	1	no	—
93	C₂×C₄×C₁₉	—	2	2	no	—
94	C₂×C₄×C₁₉	—	2	2	no	—
95	C₂×C₄×C₁₉	—	2	2	no	—
96	C₂×C₄×C₁₉	—	4	1	no	—
97	C₂×C₄×C₁₉	—	4	1	no	—
98	C₂×C₄×C₁₉	—	4	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	—	8	4	no	—
103	C₂×C₄×C₁₉	#100	1	2	yes	—
104	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
105	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
106	C₂×C₄×C₁₉	#135	1	4	yes	—
107	C₈×C₁₉	—	8	4	no	—
108	C₄×#124	C₂×C₁₉	1	1	yes	characteristic
109	#1839	C₂×C₁₉	1	2	yes	complemented
110	#1272	C₂×C₁₉	1	2	yes	complemented
111	#1270	C₂×C₁₉	1	2	yes	—
112	C₂²×C₁₉	—	4	2	no	—
113	C₂²×C₁₉	—	4	4	no	—
114	C₂²×C₁₉	—	8	1	no	—
115	C₂²×C₁₉	—	8	2	no	—
116	C₂²×C₁₉	—	8	1	no	—
117	C₂²×C₁₉	#407	1	1	yes	characteristic
118	C₂²×C₁₉	#410	1	1	yes	characteristic
119	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
120	C₂²×C₁₉	#416	1	2	yes	—
121	C₂²×C₁₉	#421	1	2	yes	—
122	C₄×C₁₉	—	2	1	no	—
123	C₄×C₁₉	—	2	1	no	—
124	C₄×C₁₉	—	2	4	no	—
125	C₄×C₁₉	—	2	2	no	—
126	C₄×C₁₉	—	4	1	no	—
127	C₄×C₁₉	—	4	2	no	—
128	C₄×C₁₉	—	4	2	no	—
129	C₄×C₁₉	—	8	1	no	—
130	C₄×C₁₉	—	8	1	no	—
131	C₂×#124	C₄×C₁₉	1	1	yes	characteristic
132	C₂×C₄×Q₈	C₄×C₁₉	1	1	yes	characteristic
133	C₂×C₄×D₄	C₄×C₁₉	1	1	yes	characteristic
134	#391	C₂²×C₁₉	1	1	yes	characteristic
135	#390	C₂²×C₁₉	1	1	yes	characteristic
136	#388	—	2	2	no	—
137	#382	C₄×C₁₉	1	1	yes	characteristic
138	C₄×C₂²⋊C₄	—	2	2	no	—
139	C₄³	C₂²×C₁₉	1	1	yes	characteristic
140	#336	—	2	2	no	—
141	#336	—	2	2	no	—
142	#336	C₂²×C₁₉	1	4	yes	—
143	C₂×C₁₉	—	8	2	no	—
144	C₂×C₁₉	#1466	1	1	yes	characteristic
145	C₂×C₁₉	#1488	1	2	yes	—
146	C₂×C₁₉	#1521	1	2	yes	—
147	C₂×C₁₉	#1533	1	1	yes	characteristic
148	C₂×C₁₉	#1543	1	1	yes	characteristic
149	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
150	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
151	C₂³×C₄	—	2	1	no	—
152	C₂²×C₈	—	2	4	no	—
153	#124	—	2	2	no	—
154	#124	—	2	2	no	—
155	C₄×Q₈	—	4	2	no	—
156	C₄×D₄	—	4	2	no	—
157	C₂×C₄⋊C₄	—	2	1	no	—
158	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
159	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
160	C₂×C₂²⋊C₄	—	2	2	no	—
161	C₂×C₂²⋊C₄	—	2	1	no	—
162	C₂×C₂²⋊C₄	—	2	2	no	—
163	C₂×C₄²	—	2	1	no	—
164	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
165	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
166	C₂×C₄²	D₄×C₁₉	1	2	yes	—
167	C₂×C₄²	D₄×C₁₉	1	2	yes	—
168	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
169	#95	—	2	2	no	—
170	#95	—	2	2	no	—
171	C₁₉	#7649	1	1	yes	characteristic, direct product factor, Sylow
172	C₂⁴	—	2	1	no	—
173	C₂×Q₈	—	2	1	no	—
174	C₂×Q₈	—	4	1	no	—
175	C₂×Q₈	—	4	1	no	—
176	C₂×Q₈	M₁₆×C₁₉	1	2	yes	—
177	C₂×D₄	—	2	1	no	—
178	C₂×D₄	—	4	1	no	—
179	C₂×D₄	—	4	1	no	—
180	C₂×D₄	M₁₆×C₁₉	1	2	yes	—
181	C₂²×C₄	—	2	1	no	—
182	C₂²×C₄	—	2	1	no	—
183	C₂²×C₄	—	2	1	no	—
184	C₂²×C₄	—	4	4	no	—
185	C₂²×C₄	—	4	2	no	—
186	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
187	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
188	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
189	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
190	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
191	C₂×C₈	—	4	4	no	—
192	C₂×C₈	—	4	4	no	—
193	C₂×C₈	—	4	4	no	—
194	C₄⋊C₄	—	4	1	no	—
195	C₄⋊C₄	—	4	1	no	—
196	C₄⋊C₄	—	4	2	no	—
197	C₂²⋊C₄	—	2	8	no	—
198	C₂²⋊C₄	—	4	2	no	—
199	C₂²⋊C₄	—	4	4	no	—
200	C₄²	—	2	1	no	—
201	C₄²	—	2	1	no	—
202	C₄²	—	2	4	no	—
203	C₄²	—	2	2	no	—
204	C₄²	—	4	2	no	—
205	C₄²	—	4	1	no	—
206	C₄²	—	4	2	no	—
207	C₂³	—	2	2	no	—
208	C₂³	—	4	1	no	—
209	C₂³	—	4	1	no	—
210	C₂³	—	4	2	no	—
211	C₂³	—	4	2	no	—
212	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
213	Q₈	—	4	2	no	—
214	Q₈	—	4	2	no	—
215	D₄	—	4	2	no	—
216	D₄	—	4	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	2	2	no	—
222	C₂×C₄	—	2	2	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	2	2	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	4	1	no	—
229	C₂×C₄	—	4	1	no	—
230	C₂×C₄	—	4	1	no	—
231	C₂×C₄	—	4	1	no	—
232	C₂×C₄	—	4	2	no	—
233	C₂×C₄	—	4	2	no	—
234	C₂×C₄	—	8	4	no	—
235	C₂×C₄	C₁₉×#100	1	2	yes	—
236	C₂×C₄	C₂×M₁₆×C₁₉	1	1	yes	characteristic
237	C₂×C₄	C₂×M₁₆×C₁₉	1	1	yes	characteristic
238	C₂×C₄	C₁₉×#135	1	4	yes	—
239	C₈	—	8	4	no	—
240	C₂²	—	4	2	no	—
241	C₂²	—	4	4	no	—
242	C₂²	—	8	2	no	—
243	C₂²	—	8	1	no	—
244	C₂²	—	8	1	no	—
245	C₂²	C₁₉×#407	1	1	yes	characteristic
246	C₂²	C₁₉×#410	1	1	yes	characteristic
247	C₂²	C₂×C₁₉×#100	1	1	yes	characteristic
248	C₂²	C₁₉×#416	1	2	yes	—
249	C₂²	C₁₉×#421	1	2	yes	—
250	C₄	—	2	1	no	—
251	C₄	—	2	1	no	—
252	C₄	—	2	4	no	—
253	C₄	—	2	2	no	—
254	C₄	—	4	2	no	—
255	C₄	—	4	2	no	—
256	C₄	—	4	1	no	—
257	C₄	—	8	1	no	—
258	C₄	—	8	1	no	—
259	C₂	—	8	2	no	—
260	C₂	C₁₉×#1466	1	1	yes	characteristic
261	C₂	C₁₉×#1488	1	2	yes	—
262	C₂	C₁₉×#1521	1	2	yes	—
263	C₂	C₁₉×#1533	1	1	yes	characteristic
264	C₂	C₁₉×#1543	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×C₁₉×#124

C₂

yes

maximal, characteristic

C₁₉×#1839

C₂

yes

maximal, complemented

C₁₉×#1272

C₂

yes

maximal, complemented

C₁₉×#1270

C₂

yes

maximal

C₂×C₁₉×#124

C₄

yes

characteristic

C₂×C₄×Q₈×C₁₉

C₄

yes

characteristic

C₂×C₄×D₄×C₁₉

C₄

yes

characteristic

C₁₉×#391

C₂²

yes

characteristic

C₁₉×#390

C₂²

yes

characteristic

C₁₉×#388

—

C₁₉×#382

C₄

yes

characteristic

C₄×C₂²⋊C₄×C₁₉

—

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#336

—

C₁₉×#336

—

C₁₉×#336

C₂²

yes

—

C₂²×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×D₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

—

C₂²×C₈×C₁₉

—

C₁₉×#124

—

C₁₉×#124

—

C₄×Q₈×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×#95

—

C₁₉×#95

—

C₂⁴×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

M₁₆

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

M₁₆

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×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

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

#7649

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×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

#100

yes

—

104

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

105

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

106

C₂×C₄×C₁₉

#135

yes

—

107

C₈×C₁₉

—

108

C₄×#124

C₂×C₁₉

yes

characteristic

109

#1839

C₂×C₁₉

yes

complemented

110

#1272

C₂×C₁₉

yes

complemented

111

#1270

C₂×C₁₉

yes

—

112

C₂²×C₁₉

—

113

C₂²×C₁₉

—

114

C₂²×C₁₉

—

115

C₂²×C₁₉

—

116

C₂²×C₁₉

—

117

C₂²×C₁₉

#407

yes

characteristic

118

C₂²×C₁₉

#410

yes

characteristic

119

C₂²×C₁₉

C₂×#100

yes

characteristic

120

C₂²×C₁₉

#416

yes

—

121

C₂²×C₁₉

#421

yes

—

122

C₄×C₁₉

—

123

C₄×C₁₉

—

124

C₄×C₁₉

—

125

C₄×C₁₉

—

126

C₄×C₁₉

—

127

C₄×C₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₂×#124

C₄×C₁₉

yes

characteristic

132

C₂×C₄×Q₈

C₄×C₁₉

yes

characteristic

133

C₂×C₄×D₄

C₄×C₁₉

yes

characteristic

134

#391

C₂²×C₁₉

yes

characteristic

135

#390

C₂²×C₁₉

yes

characteristic

136

#388

—

137

#382

C₄×C₁₉

yes

characteristic

138

C₄×C₂²⋊C₄

—

139

C₄³

C₂²×C₁₉

yes

characteristic

140

#336

—

141

#336

—

142

#336

C₂²×C₁₉

yes

—

143

C₂×C₁₉

—

144

C₂×C₁₉

#1466

yes

characteristic

145

C₂×C₁₉

#1488

yes

—

146

C₂×C₁₉

#1521

yes

—

147

C₂×C₁₉

#1533

yes

characteristic

148

C₂×C₁₉

#1543

yes

characteristic

149

C₂²×Q₈

C₂×C₄×C₁₉

yes

characteristic

150

C₂²×D₄

C₂×C₄×C₁₉

yes

characteristic

151

C₂³×C₄

—

152

C₂²×C₈

—

153

#124

—

154

#124

—

155

C₄×Q₈

—

156

C₄×D₄

—

157

C₂×C₄⋊C₄

—

158

C₂×C₄⋊C₄

C₂×C₄×C₁₉

yes

characteristic

159

C₂×C₄⋊C₄

C₂×C₄×C₁₉

yes

characteristic

160

C₂×C₂²⋊C₄

—

161

C₂×C₂²⋊C₄

—

162

C₂×C₂²⋊C₄

—

163

C₂×C₄²

—

164

C₂×C₄²

C₂×C₄×C₁₉

yes

characteristic

165

C₂×C₄²

C₂×C₄×C₁₉

yes

characteristic

166

C₂×C₄²

D₄×C₁₉

yes

—

167

C₂×C₄²

D₄×C₁₉

yes

—

168

C₂×C₄²

C₂³×C₁₉

yes

characteristic

169

#95

—

170

#95

—

171

C₁₉

#7649

yes

characteristic, direct product factor, Sylow

172

C₂⁴

—

173

C₂×Q₈

—

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂×Q₈

M₁₆×C₁₉

yes

—

177

C₂×D₄

—

178

C₂×D₄

—

179

C₂×D₄

—

180

C₂×D₄

M₁₆×C₁₉

yes

—

181

C₂²×C₄

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

—

187

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

188

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

189

C₂²×C₄

C₂²×C₄×C₁₉

yes

characteristic

190

C₂²×C₄

C₂×D₄×C₁₉

yes

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₂²⋊C₄

—

198

C₂²⋊C₄

—

199

C₂²⋊C₄

—

200

C₄²

—

201

C₄²

—

202

C₄²

—

203

C₄²

—

204

C₄²

—

205

C₄²

—

206

C₄²

—

207

C₂³

—

208

C₂³

—

209

C₂³

—

210

C₂³

—

211

C₂³

—

212

C₂³

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

213

Q₈

—

214

Q₈

—

215

D₄

—

216

D₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

C₁₉×#100

yes

—

236

C₂×C₄

C₂×M₁₆×C₁₉

yes

characteristic

237

C₂×C₄

C₂×M₁₆×C₁₉

yes

characteristic

238

C₂×C₄

C₁₉×#135

yes

—

239

C₈

—

240

C₂²

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

—

245

C₂²

C₁₉×#407

yes

characteristic

246

C₂²

C₁₉×#410

yes

characteristic

247

C₂²

C₂×C₁₉×#100

yes

characteristic

248

C₂²

C₁₉×#416

yes

—

249

C₂²

C₁₉×#421

yes

—

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

—

259

C₂

—

260

C₂

C₁₉×#1466

yes

characteristic

261

C₂

C₁₉×#1488

yes

—

262

C₂

C₁₉×#1521

yes

—

263

C₂

C₁₉×#1533

yes

characteristic

264

C₂

C₁₉×#1543

yes

characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂²×D₄×C₁₉	C₂×C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄³×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂³×C₁₉

C₂×C₂²⋊C₄

commutator

C₂²×C₄

C₂²×C₄×C₁₉

Frattini, cosocle

C₂×C₄²

C₂³×C₁₉

prime radical

C₂²×D₄×C₁₉

C₂×C₄

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₁₉ ◁ C₄³×C₁₉ ◁ G

N	H ≅ G/N	type
2. C₁₉×#1839	C₂	semidirect
3. C₁₉×#1272	C₂	semidirect
74. #7649	C₁₉	direct (N × H)
109. #1839	C₂×C₁₉	semidirect
110. #1272	C₂×C₁₉	semidirect
171. C₁₉	#7649	direct (N × H)

H ≅ G/N

type

2. C₁₉×#1839

C₂

semidirect

3. C₁₉×#1272

C₂

semidirect

74. #7649

C₁₉

direct (N × H)

109. #1839

C₂×C₁₉

semidirect

110. #1272

C₂×C₁₉

semidirect

171. C₁₉

#7649

direct (N × H)

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

subgroup	index
C₄×C₁₉×#124	2
C₁₉×#1839	2
C₁₉×#1272	2
C₁₉×#1270	2
#7649	19

subgroup

index

C₄×C₁₉×#124

C₁₉×#1839

C₁₉×#1272

C₁₉×#1270

#7649

Subgroups — C₁₉×#7649 #18013608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#7649 #18013608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#7649 #18013608