Group #18017867 — subgroups

Subgroups — C₁₉×#11908 #18017867

Order 4864.

388 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 118 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	C₁₉×#1461	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1354	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×#431	—	2	1	no	—
8	C₁₉×#423	—	2	1	no	—
9	C₂×C₁₉×#101	—	2	1	no	—
10	C₁₉×#395	C₄	1	2	yes	—
11	C₁₉×#395	C₂²	1	2	yes	—
12	C₁₉×#391	—	2	1	no	—
13	C₁₉×#389	—	2	1	no	—
14	C₁₉×#389	—	2	1	no	—
15	C₁₉×#384	—	2	1	no	—
16	C₄×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
17	C₁₉×#343	C₂²	1	2	yes	—
18	C₁₉×#324	—	2	1	no	—
19	C₁₉×#324	C₂²	1	2	yes	—
20	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
21	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
22	C₂×M₁₆×C₁₉	—	2	2	no	—
23	C₁₉×C₄⋊Q₈	—	4	1	no	—
24	C₁₉×C₄⋊Q₈	—	4	1	no	—
25	C₄×Q₈×C₁₉	—	4	1	no	—
26	C₄×Q₈×C₁₉	—	4	1	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	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	1	yes	characteristic
33	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
34	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
35	C₂×C₄²×C₁₉	—	2	1	no	—
36	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
39	C₁₉×C₄⋊C₈	—	4	1	no	—
40	C₁₉×C₄⋊C₈	—	4	1	no	—
41	C₁₉×C₄⋊C₈	—	4	1	no	—
42	C₁₉×#101	—	4	2	no	—
43	C₁₉×C₂²⋊C₈	—	2	2	no	—
44	C₄×C₈×C₁₉	—	4	1	no	—
45	C₁₉×#95	—	2	2	no	—
46	C₁₉×#95	—	2	2	no	—
47	C₁₉×#95	C₂×C₄	1	2	yes	—
48	C₂×Q₈×C₁₉	—	4	1	no	—
49	C₂×Q₈×C₁₉	—	4	1	no	—
50	C₂×Q₈×C₁₉	—	4	2	no	—
51	C₂×Q₈×C₁₉	—	8	2	no	—
52	C₂×Q₈×C₁₉	SD₁₆	1	2	yes	—
53	C₂×Q₈×C₁₉	Q₁₆	1	2	yes	—
54	C₂²×C₄×C₁₉	—	2	2	no	—
55	C₂²×C₄×C₁₉	—	2	2	no	—
56	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
63	M₁₆×C₁₉	—	4	2	no	—
64	M₁₆×C₁₉	—	4	2	no	—
65	C₂×C₈×C₁₉	—	4	2	no	—
66	C₂×C₈×C₁₉	—	4	2	no	—
67	C₄⋊C₄×C₁₉	—	2	4	no	—
68	C₄⋊C₄×C₁₉	—	4	1	no	—
69	C₄⋊C₄×C₁₉	—	4	1	no	—
70	C₄⋊C₄×C₁₉	—	4	1	no	—
71	C₄⋊C₄×C₁₉	—	4	2	no	—
72	C₄⋊C₄×C₁₉	—	4	1	no	—
73	C₄⋊C₄×C₁₉	—	4	1	no	—
74	C₄⋊C₄×C₁₉	—	8	2	no	—
75	C₄⋊C₄×C₁₉	—	8	2	no	—
76	C₄²×C₁₉	—	2	1	no	—
77	C₄²×C₁₉	—	2	1	no	—
78	C₄²×C₁₉	—	2	1	no	—
79	C₄²×C₁₉	—	2	1	no	—
80	C₄²×C₁₉	—	2	1	no	—
81	C₄²×C₁₉	—	2	1	no	—
82	C₄²×C₁₉	—	4	2	no	—
83	#11908	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	Q₈×C₁₉	—	4	2	no	—
86	Q₈×C₁₉	—	4	2	no	—
87	Q₈×C₁₉	—	8	4	no	—
88	C₂×C₄×C₁₉	—	2	1	no	—
89	C₂×C₄×C₁₉	—	2	1	no	—
90	C₂×C₄×C₁₉	—	2	1	no	—
91	C₂×C₄×C₁₉	—	2	1	no	—
92	C₂×C₄×C₁₉	—	2	1	no	—
93	C₂×C₄×C₁₉	—	2	1	no	—
94	C₂×C₄×C₁₉	—	2	2	no	—
95	C₂×C₄×C₁₉	—	2	4	no	—
96	C₂×C₄×C₁₉	—	2	1	no	—
97	C₂×C₄×C₁₉	—	2	1	no	—
98	C₂×C₄×C₁₉	—	2	1	no	—
99	C₂×C₄×C₁₉	—	4	2	no	—
100	C₂×C₄×C₁₉	—	4	2	no	—
101	C₂×C₄×C₁₉	—	4	1	no	—
102	C₂×C₄×C₁₉	—	4	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	—	4	2	no	—
107	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
108	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
109	C₂×C₄×C₁₉	#103	1	2	yes	—
110	C₂×C₄×C₁₉	#103	1	2	yes	—
111	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
112	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
113	C₈×C₁₉	—	8	2	no	—
114	C₈×C₁₉	—	8	2	no	—
115	#2567	C₂×C₁₉	1	1	yes	characteristic
116	#1801	C₂×C₁₉	1	1	yes	characteristic
117	#1461	C₂×C₁₉	1	1	yes	characteristic
118	#1354	C₂×C₁₉	1	4	yes	—
119	C₂²×C₁₉	—	2	1	no	—
120	C₂²×C₁₉	—	2	1	no	—
121	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
122	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
123	C₂²×C₁₉	#421	1	1	yes	characteristic
124	C₄×C₁₉	—	2	1	no	—
125	C₄×C₁₉	—	2	1	no	—
126	C₄×C₁₉	—	2	2	no	—
127	C₄×C₁₉	—	2	2	no	—
128	C₄×C₁₉	—	2	1	no	—
129	C₄×C₁₉	—	4	4	no	—
130	C₄×C₁₉	—	4	1	no	—
131	C₄×C₁₉	—	4	1	no	—
132	C₄×C₁₉	—	4	1	no	—
133	C₄×C₁₉	—	8	2	no	—
134	C₄×C₁₉	#356	1	2	yes	—
135	C₂×C₄⋊Q₈	C₄×C₁₉	1	1	yes	characteristic
136	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
137	#431	—	2	1	no	—
138	#423	—	2	1	no	—
139	C₂×#101	—	2	1	no	—
140	#395	C₄×C₁₉	1	2	yes	—
141	#395	C₂²×C₁₉	1	2	yes	—
142	#391	—	2	1	no	—
143	#389	—	2	1	no	—
144	#389	—	2	1	no	—
145	#384	—	2	1	no	—
146	C₄×C₄⋊C₄	C₄×C₁₉	1	1	yes	characteristic
147	#343	C₂²×C₁₉	1	2	yes	—
148	#324	—	2	1	no	—
149	#324	C₂²×C₁₉	1	2	yes	—
150	C₂×C₁₉	—	2	1	no	—
151	C₂×C₁₉	—	2	1	no	—
152	C₂×C₁₉	#1520	1	1	yes	characteristic
153	C₂×C₁₉	#2122	1	1	yes	characteristic
154	C₂×C₁₉	C₂×#356	1	1	yes	characteristic
155	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
156	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
157	C₂×M₁₆	—	2	2	no	—
158	C₄⋊Q₈	—	4	1	no	—
159	C₄⋊Q₈	—	4	1	no	—
160	C₄×Q₈	—	4	1	no	—
161	C₄×Q₈	—	4	1	no	—
162	C₂×C₄⋊C₄	—	2	1	no	—
163	C₂×C₄⋊C₄	—	2	1	no	—
164	C₂×C₄⋊C₄	—	2	1	no	—
165	C₂×C₄⋊C₄	—	2	2	no	—
166	C₂×C₄⋊C₄	—	2	2	no	—
167	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
168	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
169	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
170	C₂×C₄²	—	2	1	no	—
171	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
172	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
173	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
174	C₄⋊C₈	—	4	1	no	—
175	C₄⋊C₈	—	4	1	no	—
176	C₄⋊C₈	—	4	1	no	—
177	#101	—	4	2	no	—
178	C₂²⋊C₈	—	2	2	no	—
179	C₄×C₈	—	4	1	no	—
180	#95	—	2	2	no	—
181	#95	—	2	2	no	—
182	#95	C₂×C₄×C₁₉	1	2	yes	—
183	C₁₉	#11908	1	1	yes	characteristic, direct product factor, Sylow
184	C₂×Q₈	—	4	1	no	—
185	C₂×Q₈	—	4	1	no	—
186	C₂×Q₈	—	4	2	no	—
187	C₂×Q₈	—	8	2	no	—
188	C₂×Q₈	SD₁₆×C₁₉	1	2	yes	—
189	C₂×Q₈	Q₁₆×C₁₉	1	2	yes	—
190	C₂²×C₄	—	2	2	no	—
191	C₂²×C₄	—	2	2	no	—
192	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
193	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
194	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
195	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
196	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
197	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
198	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
199	M₁₆	—	4	2	no	—
200	M₁₆	—	4	2	no	—
201	C₂×C₈	—	4	2	no	—
202	C₂×C₈	—	4	2	no	—
203	C₄⋊C₄	—	2	4	no	—
204	C₄⋊C₄	—	4	1	no	—
205	C₄⋊C₄	—	4	1	no	—
206	C₄⋊C₄	—	4	1	no	—
207	C₄⋊C₄	—	4	2	no	—
208	C₄⋊C₄	—	4	1	no	—
209	C₄⋊C₄	—	4	1	no	—
210	C₄⋊C₄	—	8	2	no	—
211	C₄⋊C₄	—	8	2	no	—
212	C₄²	—	2	1	no	—
213	C₄²	—	2	1	no	—
214	C₄²	—	2	1	no	—
215	C₄²	—	2	1	no	—
216	C₄²	—	2	1	no	—
217	C₄²	—	2	1	no	—
218	C₄²	—	4	2	no	—
219	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
220	Q₈	—	4	2	no	—
221	Q₈	—	4	2	no	—
222	Q₈	—	8	4	no	—
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	2	1	no	—
226	C₂×C₄	—	2	1	no	—
227	C₂×C₄	—	2	1	no	—
228	C₂×C₄	—	2	1	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	2	4	no	—
231	C₂×C₄	—	2	1	no	—
232	C₂×C₄	—	2	1	no	—
233	C₂×C₄	—	2	1	no	—
234	C₂×C₄	—	4	2	no	—
235	C₂×C₄	—	4	2	no	—
236	C₂×C₄	—	4	1	no	—
237	C₂×C₄	—	4	1	no	—
238	C₂×C₄	—	4	1	no	—
239	C₂×C₄	—	4	2	no	—
240	C₂×C₄	—	4	2	no	—
241	C₂×C₄	—	4	2	no	—
242	C₂×C₄	C₁₉×#99	1	1	yes	characteristic
243	C₂×C₄	C₁₉×#99	1	1	yes	characteristic
244	C₂×C₄	C₁₉×#103	1	2	yes	—
245	C₂×C₄	C₁₉×#103	1	2	yes	—
246	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
247	C₂×C₄	C₂×Q₁₆×C₁₉	1	1	yes	characteristic
248	C₈	—	8	2	no	—
249	C₈	—	8	2	no	—
250	C₂²	—	2	1	no	—
251	C₂²	—	2	1	no	—
252	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
253	C₂²	C₂×C₁₉×#103	1	1	yes	characteristic
254	C₂²	C₁₉×#421	1	1	yes	characteristic
255	C₄	—	2	1	no	—
256	C₄	—	2	1	no	—
257	C₄	—	2	2	no	—
258	C₄	—	2	2	no	—
259	C₄	—	2	1	no	—
260	C₄	—	4	4	no	—
261	C₄	—	4	1	no	—
262	C₄	—	4	1	no	—
263	C₄	—	4	1	no	—
264	C₄	—	8	2	no	—
265	C₄	C₁₉×#356	1	2	yes	—
266	C₂	—	2	1	no	—
267	C₂	—	2	1	no	—
268	C₂	C₁₉×#1520	1	1	yes	characteristic
269	C₂	C₁₉×#2122	1	1	yes	characteristic
270	C₂	C₂×C₁₉×#356	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2567

C₂

yes

maximal, characteristic

C₁₉×#1801

C₂

yes

maximal, characteristic

C₁₉×#1461

C₂

yes

maximal, characteristic

C₁₉×#1354

C₂

yes

maximal

C₂×C₁₉×C₄⋊Q₈

C₄

yes

characteristic

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×#431

—

C₁₉×#423

—

C₂×C₁₉×#101

—

C₁₉×#395

C₄

yes

—

C₁₉×#395

C₂²

yes

—

C₁₉×#391

—

C₁₉×#389

—

C₁₉×#389

—

C₁₉×#384

—

C₄×C₄⋊C₄×C₁₉

C₄

yes

characteristic

C₁₉×#343

C₂²

yes

—

C₁₉×#324

—

C₁₉×#324

C₂²

yes

—

C₂²×Q₈×C₁₉

C₂×C₄

yes

—

C₂²×Q₈×C₁₉

D₄

yes

characteristic

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⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂³

yes

characteristic

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#101

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₁₉×#95

—

C₁₉×#95

—

C₁₉×#95

C₂×C₄

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

SD₁₆

yes

—

C₂×Q₈×C₁₉

Q₁₆

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

—

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

—

#11908

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

—

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

#99

yes

characteristic

108

C₂×C₄×C₁₉

#99

yes

characteristic

109

C₂×C₄×C₁₉

#103

yes

—

110

C₂×C₄×C₁₉

#103

yes

—

111

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

112

C₂×C₄×C₁₉

C₂×Q₁₆

yes

characteristic

113

C₈×C₁₉

—

114

C₈×C₁₉

—

115

#2567

C₂×C₁₉

yes

characteristic

116

#1801

C₂×C₁₉

yes

characteristic

117

#1461

C₂×C₁₉

yes

characteristic

118

#1354

C₂×C₁₉

yes

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

C₂×#99

yes

characteristic

122

C₂²×C₁₉

C₂×#103

yes

characteristic

123

C₂²×C₁₉

#421

yes

characteristic

124

C₄×C₁₉

—

125

C₄×C₁₉

—

126

C₄×C₁₉

—

127

C₄×C₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

—

134

C₄×C₁₉

#356

yes

—

135

C₂×C₄⋊Q₈

C₄×C₁₉

yes

characteristic

136

C₂×C₄×Q₈

C₂²×C₁₉

yes

characteristic

137

#431

—

138

#423

—

139

C₂×#101

—

140

#395

C₄×C₁₉

yes

—

141

#395

C₂²×C₁₉

yes

—

142

#391

—

143

#389

—

144

#389

—

145

#384

—

146

C₄×C₄⋊C₄

C₄×C₁₉

yes

characteristic

147

#343

C₂²×C₁₉

yes

—

148

#324

—

149

#324

C₂²×C₁₉

yes

—

150

C₂×C₁₉

—

151

C₂×C₁₉

—

152

C₂×C₁₉

#1520

yes

characteristic

153

C₂×C₁₉

#2122

yes

characteristic

154

C₂×C₁₉

C₂×#356

yes

characteristic

155

C₂²×Q₈

C₂×C₄×C₁₉

yes

—

156

C₂²×Q₈

D₄×C₁₉

yes

characteristic

157

C₂×M₁₆

—

158

C₄⋊Q₈

—

159

C₄⋊Q₈

—

160

C₄×Q₈

—

161

C₄×Q₈

—

162

C₂×C₄⋊C₄

—

163

C₂×C₄⋊C₄

—

164

C₂×C₄⋊C₄

—

165

C₂×C₄⋊C₄

—

166

C₂×C₄⋊C₄

—

167

C₂×C₄⋊C₄

C₂×C₄×C₁₉

yes

characteristic

168

C₂×C₄⋊C₄

D₄×C₁₉

yes

characteristic

169

C₂×C₄⋊C₄

C₂³×C₁₉

yes

characteristic

170

C₂×C₄²

—

171

C₂×C₄²

C₂×C₄×C₁₉

yes

characteristic

172

C₂×C₄²

D₄×C₁₉

yes

characteristic

173

C₂×C₄²

D₄×C₁₉

yes

characteristic

174

C₄⋊C₈

—

175

C₄⋊C₈

—

176

C₄⋊C₈

—

177

#101

—

178

C₂²⋊C₈

—

179

C₄×C₈

—

180

#95

—

181

#95

—

182

#95

C₂×C₄×C₁₉

yes

—

183

C₁₉

#11908

yes

characteristic, direct product factor, Sylow

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×Q₈

—

188

C₂×Q₈

SD₁₆×C₁₉

yes

—

189

C₂×Q₈

Q₁₆×C₁₉

yes

—

190

C₂²×C₄

—

191

C₂²×C₄

—

192

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

193

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

194

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

195

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

196

C₂²×C₄

C₂²×C₄×C₁₉

yes

characteristic

197

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

198

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

199

M₁₆

—

200

M₁₆

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₄⋊C₄

—

212

C₄²

—

213

C₄²

—

214

C₄²

—

215

C₄²

—

216

C₄²

—

217

C₄²

—

218

C₄²

—

219

C₂³

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

220

Q₈

—

221

Q₈

—

222

Q₈

—

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

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

C₁₉×#99

yes

characteristic

243

C₂×C₄

C₁₉×#99

yes

characteristic

244

C₂×C₄

C₁₉×#103

yes

—

245

C₂×C₄

C₁₉×#103

yes

—

246

C₂×C₄

C₂×SD₁₆×C₁₉

yes

characteristic

247

C₂×C₄

C₂×Q₁₆×C₁₉

yes

characteristic

248

C₈

—

249

C₈

—

250

C₂²

—

251

C₂²

—

252

C₂²

C₂×C₁₉×#99

yes

characteristic

253

C₂²

C₂×C₁₉×#103

yes

characteristic

254

C₂²

C₁₉×#421

yes

characteristic

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

260

C₄

—

261

C₄

—

262

C₄

—

263

C₄

—

264

C₄

—

265

C₄

C₁₉×#356

yes

—

266

C₂

—

267

C₂

—

268

C₂

C₁₉×#1520

yes

characteristic

269

C₂

C₁₉×#2122

yes

characteristic

270

C₂

C₂×C₁₉×#356

yes

characteristic

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

C₂×C₄⋊C₄

C₂³×C₁₉

prime radical

C₂³×C₁₉

C₂×C₂²⋊C₄

LCS

G ▷ C₂²×C₄ ▷ C₂³ ▷ C₂ ▷ C₁

UCS

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

N	H ≅ G/N	type
83. #11908	C₁₉	direct (N × H)
183. C₁₉	#11908	direct (N × H)

H ≅ G/N

type

83. #11908

C₁₉

direct (N × H)

183. C₁₉

#11908

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
C₁₉×#1461	2
C₁₉×#1354	2
#11908	19

subgroup

index

C₁₉×#2567

C₁₉×#1801

C₁₉×#1461

C₁₉×#1354

#11908

Subgroups — C₁₉×#11908 #18017867

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#11908 #18017867

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11908 #18017867