Group #18019261 — subgroups

Subgroups — C₁₉×#13302 #18019261

Order 4864.

420 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2567	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1801	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₉×#101	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1394	C₂	1	4	yes	maximal
5	C₂×C₁₉×C₄⋊Q₈	C₄	1	1	yes	characteristic
6	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₁₉×#423	—	2	1	no	—
8	C₂×C₁₉×#101	C₂²	1	2	yes	—
9	C₂×C₁₉×#101	C₂²	1	2	yes	—
10	C₄×M₁₆×C₁₉	—	2	1	no	—
11	C₁₉×#395	—	2	1	no	—
12	C₁₉×#395	—	2	1	no	—
13	C₁₉×#391	C₂²	1	2	yes	—
14	C₁₉×#389	—	2	1	no	—
15	C₁₉×#389	—	2	1	no	—
16	C₁₉×#384	C₄	1	2	yes	—
17	C₄×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
18	C₁₉×#343	—	2	1	no	—
19	C₁₉×#343	—	2	1	no	—
20	C₂²×Q₈×C₁₉	—	2	1	no	—
21	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
22	C₂×M₁₆×C₁₉	—	2	2	no	—
23	C₂×M₁₆×C₁₉	—	2	2	no	—
24	C₁₉×C₄⋊Q₈	—	4	1	no	—
25	C₁₉×C₄⋊Q₈	—	4	1	no	—
26	C₄×Q₈×C₁₉	—	4	1	no	—
27	C₄×Q₈×C₁₉	—	4	1	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
32	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
33	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
35	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
38	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
40	C₁₉×C₄⋊C₈	—	4	1	no	—
41	C₁₉×C₄⋊C₈	—	4	1	no	—
42	C₁₉×#101	—	2	2	no	—
43	C₁₉×#101	—	2	4	no	—
44	C₁₉×#101	Q₈	1	4	yes	complemented
45	C₁₉×#97	—	4	1	no	—
46	C₄×C₈×C₁₉	—	4	1	no	—
47	C₁₉×#95	—	2	1	no	—
48	C₁₉×#95	—	2	2	no	—
49	C₁₉×#95	—	2	2	no	—
50	C₂×Q₈×C₁₉	—	4	1	no	—
51	C₂×Q₈×C₁₉	—	4	1	no	—
52	C₂×Q₈×C₁₉	—	4	2	no	—
53	C₂×Q₈×C₁₉	—	8	2	no	—
54	C₂×Q₈×C₁₉	C₂×Q₈	1	2	yes	—
55	C₂×Q₈×C₁₉	#41	1	2	yes	—
56	C₂²×C₄×C₁₉	—	2	2	no	—
57	C₂²×C₄×C₁₉	—	2	2	no	—
58	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
65	M₁₆×C₁₉	—	2	4	no	—
66	M₁₆×C₁₉	—	4	2	no	—
67	M₁₆×C₁₉	—	4	2	no	—
68	M₁₆×C₁₉	—	4	2	no	—
69	C₂×C₈×C₁₉	—	4	2	no	—
70	C₂×C₈×C₁₉	—	4	2	no	—
71	C₄⋊C₄×C₁₉	—	2	4	no	—
72	C₄⋊C₄×C₁₉	—	4	1	no	—
73	C₄⋊C₄×C₁₉	—	4	1	no	—
74	C₄⋊C₄×C₁₉	—	4	1	no	—
75	C₄⋊C₄×C₁₉	—	4	2	no	—
76	C₄⋊C₄×C₁₉	—	4	1	no	—
77	C₄⋊C₄×C₁₉	—	4	1	no	—
78	C₄⋊C₄×C₁₉	—	8	2	no	—
79	C₄⋊C₄×C₁₉	—	8	2	no	—
80	C₄²×C₁₉	—	2	1	no	—
81	C₄²×C₁₉	—	2	1	no	—
82	C₄²×C₁₉	—	2	1	no	—
83	C₄²×C₁₉	—	2	1	no	—
84	C₄²×C₁₉	—	2	1	no	—
85	C₄²×C₁₉	—	2	1	no	—
86	C₄²×C₁₉	—	4	2	no	—
87	#13302	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
88	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
89	Q₈×C₁₉	—	4	2	no	—
90	Q₈×C₁₉	—	4	2	no	—
91	Q₈×C₁₉	—	8	4	no	—
92	C₂×C₄×C₁₉	—	2	1	no	—
93	C₂×C₄×C₁₉	—	2	1	no	—
94	C₂×C₄×C₁₉	—	2	1	no	—
95	C₂×C₄×C₁₉	—	2	1	no	—
96	C₂×C₄×C₁₉	—	2	1	no	—
97	C₂×C₄×C₁₉	—	2	1	no	—
98	C₂×C₄×C₁₉	—	2	2	no	—
99	C₂×C₄×C₁₉	—	2	4	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	2	no	—
104	C₂×C₄×C₁₉	—	4	2	no	—
105	C₂×C₄×C₁₉	—	4	1	no	—
106	C₂×C₄×C₁₉	—	4	1	no	—
107	C₂×C₄×C₁₉	—	4	1	no	—
108	C₂×C₄×C₁₉	—	4	2	no	—
109	C₂×C₄×C₁₉	—	4	2	no	—
110	C₂×C₄×C₁₉	—	4	2	no	—
111	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
112	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
113	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
114	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
115	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
116	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
117	C₈×C₁₉	—	4	4	no	—
118	C₈×C₁₉	—	8	2	no	—
119	#2567	C₂×C₁₉	1	1	yes	characteristic
120	#1801	C₂×C₁₉	1	1	yes	characteristic
121	C₄×#101	C₂×C₁₉	1	1	yes	characteristic
122	#1394	C₂×C₁₉	1	4	yes	—
123	C₂²×C₁₉	—	2	1	no	—
124	C₂²×C₁₉	—	2	1	no	—
125	C₂²×C₁₉	#391	1	1	yes	characteristic
126	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
127	C₂²×C₁₉	#410	1	1	yes	characteristic
128	C₄×C₁₉	—	2	1	no	—
129	C₄×C₁₉	—	2	2	no	—
130	C₄×C₁₉	—	2	1	no	—
131	C₄×C₁₉	—	2	2	no	—
132	C₄×C₁₉	—	2	1	no	—
133	C₄×C₁₉	—	4	4	no	—
134	C₄×C₁₉	—	4	1	no	—
135	C₄×C₁₉	—	4	1	no	—
136	C₄×C₁₉	—	4	1	no	—
137	C₄×C₁₉	—	8	2	no	—
138	C₄×C₁₉	#356	1	2	yes	—
139	C₂×C₄⋊Q₈	C₄×C₁₉	1	1	yes	characteristic
140	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
141	#423	—	2	1	no	—
142	C₂×#101	C₂²×C₁₉	1	2	yes	—
143	C₂×#101	C₂²×C₁₉	1	2	yes	—
144	C₄×M₁₆	—	2	1	no	—
145	#395	—	2	1	no	—
146	#395	—	2	1	no	—
147	#391	C₂²×C₁₉	1	2	yes	—
148	#389	—	2	1	no	—
149	#389	—	2	1	no	—
150	#384	C₄×C₁₉	1	2	yes	—
151	C₄×C₄⋊C₄	C₄×C₁₉	1	1	yes	characteristic
152	#343	—	2	1	no	—
153	#343	—	2	1	no	—
154	C₂×C₁₉	—	2	1	no	—
155	C₂×C₁₉	—	2	1	no	—
156	C₂×C₁₉	#1996	1	1	yes	characteristic
157	C₂×C₁₉	C₂×#356	1	1	yes	characteristic
158	C₂×C₁₉	#2134	1	1	yes	characteristic
159	C₂²×Q₈	—	2	1	no	—
160	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
161	C₂×M₁₆	—	2	2	no	—
162	C₂×M₁₆	—	2	2	no	—
163	C₄⋊Q₈	—	4	1	no	—
164	C₄⋊Q₈	—	4	1	no	—
165	C₄×Q₈	—	4	1	no	—
166	C₄×Q₈	—	4	1	no	—
167	C₂×C₄⋊C₄	—	2	1	no	—
168	C₂×C₄⋊C₄	—	2	1	no	—
169	C₂×C₄⋊C₄	—	2	2	no	—
170	C₂×C₄⋊C₄	—	2	2	no	—
171	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
172	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
173	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
174	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
175	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
176	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
177	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
178	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
179	C₄⋊C₈	—	4	1	no	—
180	C₄⋊C₈	—	4	1	no	—
181	#101	—	2	2	no	—
182	#101	—	2	4	no	—
183	#101	Q₈×C₁₉	1	4	yes	complemented
184	#97	—	4	1	no	—
185	C₄×C₈	—	4	1	no	—
186	#95	—	2	1	no	—
187	#95	—	2	2	no	—
188	#95	—	2	2	no	—
189	C₁₉	#13302	1	1	yes	characteristic, direct product factor, Sylow
190	C₂×Q₈	—	4	1	no	—
191	C₂×Q₈	—	4	1	no	—
192	C₂×Q₈	—	4	2	no	—
193	C₂×Q₈	—	8	2	no	—
194	C₂×Q₈	C₂×Q₈×C₁₉	1	2	yes	—
195	C₂×Q₈	#41×C₁₉	1	2	yes	—
196	C₂²×C₄	—	2	2	no	—
197	C₂²×C₄	—	2	2	no	—
198	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
199	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
200	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
201	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
202	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
203	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
204	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
205	M₁₆	—	2	4	no	—
206	M₁₆	—	4	2	no	—
207	M₁₆	—	4	2	no	—
208	M₁₆	—	4	2	no	—
209	C₂×C₈	—	4	2	no	—
210	C₂×C₈	—	4	2	no	—
211	C₄⋊C₄	—	2	4	no	—
212	C₄⋊C₄	—	4	1	no	—
213	C₄⋊C₄	—	4	1	no	—
214	C₄⋊C₄	—	4	1	no	—
215	C₄⋊C₄	—	4	2	no	—
216	C₄⋊C₄	—	4	1	no	—
217	C₄⋊C₄	—	4	1	no	—
218	C₄⋊C₄	—	8	2	no	—
219	C₄⋊C₄	—	8	2	no	—
220	C₄²	—	2	1	no	—
221	C₄²	—	2	1	no	—
222	C₄²	—	2	1	no	—
223	C₄²	—	2	1	no	—
224	C₄²	—	2	1	no	—
225	C₄²	—	2	1	no	—
226	C₄²	—	4	2	no	—
227	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
228	Q₈	—	4	2	no	—
229	Q₈	—	4	2	no	—
230	Q₈	—	8	4	no	—
231	C₂×C₄	—	2	1	no	—
232	C₂×C₄	—	2	1	no	—
233	C₂×C₄	—	2	1	no	—
234	C₂×C₄	—	2	1	no	—
235	C₂×C₄	—	2	1	no	—
236	C₂×C₄	—	2	1	no	—
237	C₂×C₄	—	2	2	no	—
238	C₂×C₄	—	2	4	no	—
239	C₂×C₄	—	2	1	no	—
240	C₂×C₄	—	2	1	no	—
241	C₂×C₄	—	2	1	no	—
242	C₂×C₄	—	4	2	no	—
243	C₂×C₄	—	4	2	no	—
244	C₂×C₄	—	4	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	—	4	2	no	—
250	C₂×C₄	C₁₉×#99	1	1	yes	characteristic
251	C₂×C₄	C₁₉×#99	1	1	yes	characteristic
252	C₂×C₄	C₄×Q₈×C₁₉	1	2	yes	—
253	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
254	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
255	C₂×C₄	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
256	C₈	—	4	4	no	—
257	C₈	—	8	2	no	—
258	C₂²	—	2	1	no	—
259	C₂²	—	2	1	no	—
260	C₂²	C₁₉×#391	1	1	yes	characteristic
261	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
262	C₂²	C₁₉×#410	1	1	yes	characteristic
263	C₄	—	2	2	no	—
264	C₄	—	2	1	no	—
265	C₄	—	2	2	no	—
266	C₄	—	2	1	no	—
267	C₄	—	2	1	no	—
268	C₄	—	4	4	no	—
269	C₄	—	4	1	no	—
270	C₄	—	4	1	no	—
271	C₄	—	4	1	no	—
272	C₄	—	8	2	no	—
273	C₄	C₁₉×#356	1	2	yes	—
274	C₂	—	2	1	no	—
275	C₂	—	2	1	no	—
276	C₂	C₁₉×#1996	1	1	yes	characteristic
277	C₂	C₂×C₁₉×#356	1	1	yes	characteristic
278	C₂	C₁₉×#2134	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2567

C₂

yes

maximal, characteristic

C₁₉×#1801

C₂

yes

maximal, characteristic

C₄×C₁₉×#101

C₂

yes

maximal, characteristic

C₁₉×#1394

C₂

yes

maximal

C₂×C₁₉×C₄⋊Q₈

C₄

yes

characteristic

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×#423

—

C₂×C₁₉×#101

C₂²

yes

—

C₂×C₁₉×#101

C₂²

yes

—

C₄×M₁₆×C₁₉

—

C₁₉×#395

—

C₁₉×#395

—

C₁₉×#391

C₂²

yes

—

C₁₉×#389

—

C₁₉×#389

—

C₁₉×#384

C₄

yes

—

C₄×C₄⋊C₄×C₁₉

C₄

yes

characteristic

C₁₉×#343

—

C₁₉×#343

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

C₂³

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#101

—

C₁₉×#101

—

C₁₉×#101

Q₈

yes

complemented

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₁₉×#95

—

C₁₉×#95

—

C₁₉×#95

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂×Q₈

yes

—

C₂×Q₈×C₁₉

#41

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×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

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

#13302

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×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

—

104

C₂×C₄×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

#99

yes

characteristic

112

C₂×C₄×C₁₉

#99

yes

characteristic

113

C₂×C₄×C₁₉

C₄×Q₈

yes

—

114

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

115

C₂×C₄×C₁₉

#124

yes

characteristic

116

C₂×C₄×C₁₉

C₄⋊Q₈

yes

characteristic

117

C₈×C₁₉

—

118

C₈×C₁₉

—

119

#2567

C₂×C₁₉

yes

characteristic

120

#1801

C₂×C₁₉

yes

characteristic

121

C₄×#101

C₂×C₁₉

yes

characteristic

122

#1394

C₂×C₁₉

yes

—

123

C₂²×C₁₉

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

#391

yes

characteristic

126

C₂²×C₁₉

C₂×#99

yes

characteristic

127

C₂²×C₁₉

#410

yes

characteristic

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

—

134

C₄×C₁₉

—

135

C₄×C₁₉

—

136

C₄×C₁₉

—

137

C₄×C₁₉

—

138

C₄×C₁₉

#356

yes

—

139

C₂×C₄⋊Q₈

C₄×C₁₉

yes

characteristic

140

C₂×C₄×Q₈

C₂²×C₁₉

yes

characteristic

141

#423

—

142

C₂×#101

C₂²×C₁₉

yes

—

143

C₂×#101

C₂²×C₁₉

yes

—

144

C₄×M₁₆

—

145

#395

—

146

#395

—

147

#391

C₂²×C₁₉

yes

—

148

#389

—

149

#389

—

150

#384

C₄×C₁₉

yes

—

151

C₄×C₄⋊C₄

C₄×C₁₉

yes

characteristic

152

#343

—

153

#343

—

154

C₂×C₁₉

—

155

C₂×C₁₉

—

156

C₂×C₁₉

#1996

yes

characteristic

157

C₂×C₁₉

C₂×#356

yes

characteristic

158

C₂×C₁₉

#2134

yes

characteristic

159

C₂²×Q₈

—

160

C₂²×Q₈

C₂³×C₁₉

yes

characteristic

161

C₂×M₁₆

—

162

C₂×M₁₆

—

163

C₄⋊Q₈

—

164

C₄⋊Q₈

—

165

C₄×Q₈

—

166

C₄×Q₈

—

167

C₂×C₄⋊C₄

—

168

C₂×C₄⋊C₄

—

169

C₂×C₄⋊C₄

—

170

C₂×C₄⋊C₄

—

171

C₂×C₄⋊C₄

C₂×C₄×C₁₉

yes

—

172

C₂×C₄⋊C₄

C₂×C₄×C₁₉

yes

characteristic

173

C₂×C₄⋊C₄

D₄×C₁₉

yes

characteristic

174

C₂×C₄⋊C₄

D₄×C₁₉

yes

characteristic

175

C₂×C₄²

C₂×C₄×C₁₉

yes

characteristic

176

C₂×C₄²

C₂×C₄×C₁₉

yes

—

177

C₂×C₄²

D₄×C₁₉

yes

characteristic

178

C₂×C₄²

D₄×C₁₉

yes

characteristic

179

C₄⋊C₈

—

180

C₄⋊C₈

—

181

#101

—

182

#101

—

183

#101

Q₈×C₁₉

yes

complemented

184

#97

—

185

C₄×C₈

—

186

#95

—

187

#95

—

188

#95

—

189

C₁₉

#13302

yes

characteristic, direct product factor, Sylow

190

C₂×Q₈

—

191

C₂×Q₈

—

192

C₂×Q₈

—

193

C₂×Q₈

—

194

C₂×Q₈

C₂×Q₈×C₁₉

yes

—

195

C₂×Q₈

#41×C₁₉

yes

—

196

C₂²×C₄

—

197

C₂²×C₄

—

198

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

199

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

200

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

201

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

202

C₂²×C₄

C₂²×C₄×C₁₉

yes

characteristic

203

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

204

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

205

M₁₆

—

206

M₁₆

—

207

M₁₆

—

208

M₁₆

—

209

C₂×C₈

—

210

C₂×C₈

—

211

C₄⋊C₄

—

212

C₄⋊C₄

—

213

C₄⋊C₄

—

214

C₄⋊C₄

—

215

C₄⋊C₄

—

216

C₄⋊C₄

—

217

C₄⋊C₄

—

218

C₄⋊C₄

—

219

C₄⋊C₄

—

220

C₄²

—

221

C₄²

—

222

C₄²

—

223

C₄²

—

224

C₄²

—

225

C₄²

—

226

C₄²

—

227

C₂³

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

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

—

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×#99

yes

characteristic

251

C₂×C₄

C₁₉×#99

yes

characteristic

252

C₂×C₄

C₄×Q₈×C₁₉

yes

—

253

C₂×C₄

C₁₉×C₂²⋊Q₈

yes

—

254

C₂×C₄

C₁₉×#124

yes

characteristic

255

C₂×C₄

C₁₉×C₄⋊Q₈

yes

characteristic

256

C₈

—

257

C₈

—

258

C₂²

—

259

C₂²

—

260

C₂²

C₁₉×#391

yes

characteristic

261

C₂²

C₂×C₁₉×#99

yes

characteristic

262

C₂²

C₁₉×#410

yes

characteristic

263

C₄

—

264

C₄

—

265

C₄

—

266

C₄

—

267

C₄

—

268

C₄

—

269

C₄

—

270

C₄

—

271

C₄

—

272

C₄

—

273

C₄

C₁₉×#356

yes

—

274

C₂

—

275

C₂

—

276

C₂

C₁₉×#1996

yes

characteristic

277

C₂

C₂×C₁₉×#356

yes

characteristic

278

C₂

C₁₉×#2134

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#99
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×Q₈	C₂³×C₁₉
prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

C₂×#99

commutator

C₂²×C₄

C₂²×C₄×C₁₉

Frattini, cosocle

C₂²×Q₈

C₂³×C₁₉

prime radical

C₂³×C₁₉

C₂×C₂²⋊C₄

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

N	H ≅ G/N	type
44. C₁₉×#101	Q₈	semidirect
87. #13302	C₁₉	direct (N × H)
183. #101	Q₈×C₁₉	semidirect
189. C₁₉	#13302	direct (N × H)

H ≅ G/N

type

44. C₁₉×#101

Q₈

semidirect

87. #13302

C₁₉

direct (N × H)

183. #101

Q₈×C₁₉

semidirect

189. C₁₉

#13302

direct (N × H)

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

subgroup	index
C₁₉×#2567	2
C₁₉×#1801	2
C₄×C₁₉×#101	2
C₁₉×#1394	2
#13302	19

subgroup

index

C₁₉×#2567

C₁₉×#1801

C₄×C₁₉×#101

C₁₉×#1394

#13302

Subgroups — C₁₉×#13302 #18019261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#13302 #18019261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13302 #18019261