Group #18016293 — subgroups

Subgroups — C₁₉×#10334 #18016293

Order 4864.

754 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 754 conjugacy classes of subgroups — too many to draw. Only its 106 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×#3195	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2434	C₂	1	2	yes	maximal
3	C₁₉×#1784	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1508	C₂	1	2	yes	maximal
5	C₁₉×#1297	C₂	1	1	yes	maximal, characteristic
6	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₉×C₄⋊Q₈	—	2	2	no	—
8	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
9	C₁₉×#483	—	2	2	no	—
10	C₁₉×#470	—	2	2	no	—
11	C₁₉×#451	—	2	2	no	—
12	C₂×C₁₉×#101	—	2	2	no	—
13	C₁₉×#407	C₂²	1	1	yes	characteristic
14	C₁₉×#407	C₂²	1	1	yes	characteristic
15	C₁₉×#395	—	2	4	no	—
16	C₁₉×#391	—	2	2	no	—
17	C₁₉×#385	—	2	4	no	—
18	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
19	C₁₉×#328	—	2	4	no	—
20	C₂²×Q₈×C₁₉	—	2	2	no	—
21	C₂²×Q₈×C₁₉	—	2	1	no	—
22	C₂²×Q₈×C₁₉	—	2	2	no	—
23	C₂²×Q₈×C₁₉	—	2	1	no	—
24	C₂²×Q₈×C₁₉	—	4	4	no	—
25	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
26	C₂³×C₄×C₁₉	D₄	1	2	yes	—
27	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂×Q₁₆×C₁₉	—	2	2	no	—
29	C₂×M₁₆×C₁₉	—	2	1	no	—
30	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
31	C₁₉×C₄⋊Q₈	—	4	8	no	—
32	C₁₉×C₂²⋊Q₈	—	2	2	no	—
33	C₁₉×C₂²⋊Q₈	—	2	2	no	—
34	C₁₉×C₂²⋊Q₈	—	2	2	no	—
35	C₁₉×C₂²⋊Q₈	—	2	2	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
38	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
39	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
40	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
41	C₂×C₄²×C₁₉	—	2	2	no	—
42	C₁₉×#106	—	2	2	no	—
43	C₁₉×#103	—	2	4	no	—
44	C₁₉×#101	—	4	4	no	—
45	C₁₉×C₂²⋊C₈	—	2	2	no	—
46	C₁₉×C₂²⋊C₈	—	2	2	no	—
47	C₁₉×#95	—	2	8	no	—
48	C₁₉×#95	D₄	1	4	yes	—
49	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂×Q₈×C₁₉	—	2	8	no	—
51	C₂×Q₈×C₁₉	—	2	4	no	—
52	C₂×Q₈×C₁₉	—	2	2	no	—
53	C₂×Q₈×C₁₉	—	2	2	no	—
54	C₂×Q₈×C₁₉	—	4	4	no	—
55	C₂×Q₈×C₁₉	—	4	2	no	—
56	C₂×Q₈×C₁₉	—	4	8	no	—
57	C₂×Q₈×C₁₉	—	4	4	no	—
58	C₂×Q₈×C₁₉	—	4	4	no	—
59	C₂×Q₈×C₁₉	—	4	1	no	—
60	C₂×Q₈×C₁₉	—	4	2	no	—
61	C₂×Q₈×C₁₉	—	4	1	no	—
62	C₂²×C₄×C₁₉	—	2	4	no	—
63	C₂²×C₄×C₁₉	—	2	4	no	—
64	C₂²×C₄×C₁₉	—	2	2	no	—
65	C₂²×C₄×C₁₉	—	2	2	no	—
66	C₂²×C₄×C₁₉	—	2	2	no	—
67	C₂²×C₄×C₁₉	—	4	4	no	—
68	C₂²×C₄×C₁₉	—	4	2	no	—
69	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
70	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
72	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
73	Q₁₆×C₁₉	—	8	2	no	—
74	M₁₆×C₁₉	—	4	2	no	—
75	M₁₆×C₁₉	—	4	2	no	—
76	C₂×C₈×C₁₉	—	2	2	no	—
77	C₂×C₈×C₁₉	—	4	1	no	—
78	C₄⋊C₄×C₁₉	—	2	2	no	—
79	C₄⋊C₄×C₁₉	—	2	2	no	—
80	C₄⋊C₄×C₁₉	—	4	16	no	—
81	C₄⋊C₄×C₁₉	—	4	2	no	—
82	C₄⋊C₄×C₁₉	—	4	2	no	—
83	C₂²⋊C₄×C₁₉	—	2	8	no	—
84	C₂²⋊C₄×C₁₉	—	4	2	no	—
85	C₂²⋊C₄×C₁₉	—	4	2	no	—
86	C₄²×C₁₉	—	4	4	no	—
87	#10334	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
88	C₂³×C₁₉	—	2	4	no	—
89	C₂³×C₁₉	—	4	1	no	—
90	C₂³×C₁₉	#120	1	2	yes	—
91	C₂³×C₁₉	#121	1	1	yes	characteristic
92	Q₈×C₁₉	—	4	4	no	—
93	Q₈×C₁₉	—	4	8	no	—
94	Q₈×C₁₉	—	4	4	no	—
95	Q₈×C₁₉	—	4	4	no	—
96	Q₈×C₁₉	—	8	2	no	—
97	C₂×C₄×C₁₉	—	2	4	no	—
98	C₂×C₄×C₁₉	—	2	2	no	—
99	C₂×C₄×C₁₉	—	2	8	no	—
100	C₂×C₄×C₁₉	—	2	8	no	—
101	C₂×C₄×C₁₉	—	2	4	no	—
102	C₂×C₄×C₁₉	—	4	2	no	—
103	C₂×C₄×C₁₉	—	4	1	no	—
104	C₂×C₄×C₁₉	—	4	4	no	—
105	C₂×C₄×C₁₉	—	4	4	no	—
106	C₂×C₄×C₁₉	—	4	2	no	—
107	C₂×C₄×C₁₉	—	4	2	no	—
108	C₂×C₄×C₁₉	—	4	4	no	—
109	C₂×C₄×C₁₉	—	4	4	no	—
110	C₂×C₄×C₁₉	—	4	2	no	—
111	C₂×C₄×C₁₉	—	4	2	no	—
112	C₂×C₄×C₁₉	—	4	4	no	—
113	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
114	C₂×C₄×C₁₉	#121	1	2	yes	—
115	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
116	C₈×C₁₉	—	4	2	no	—
117	C₈×C₁₉	—	8	1	no	—
118	#3195	C₂×C₁₉	1	1	yes	characteristic
119	#2434	C₂×C₁₉	1	2	yes	—
120	#1784	C₂×C₁₉	1	1	yes	characteristic
121	#1508	C₂×C₁₉	1	2	yes	—
122	#1297	C₂×C₁₉	1	1	yes	characteristic
123	C₂²×C₁₉	—	2	2	no	—
124	C₂²×C₁₉	—	2	2	no	—
125	C₂²×C₁₉	—	2	2	no	—
126	C₂²×C₁₉	—	2	1	no	—
127	C₂²×C₁₉	—	4	4	no	—
128	C₂²×C₁₉	#392	1	1	yes	characteristic
129	C₂²×C₁₉	#456	1	4	yes	—
130	C₄×C₁₉	—	2	1	no	—
131	C₄×C₁₉	—	2	2	no	—
132	C₄×C₁₉	—	4	8	no	—
133	C₄×C₁₉	—	4	4	no	—
134	C₄×C₁₉	—	8	2	no	—
135	C₄×C₁₉	—	8	2	no	—
136	C₄×C₁₉	B(4,𝔽₂)	1	2	yes	—
137	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
138	C₂×C₄⋊Q₈	—	2	2	no	—
139	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
140	#483	—	2	2	no	—
141	#470	—	2	2	no	—
142	#451	—	2	2	no	—
143	C₂×#101	—	2	2	no	—
144	#407	C₂²×C₁₉	1	1	yes	characteristic
145	#407	C₂²×C₁₉	1	1	yes	characteristic
146	#395	—	2	4	no	—
147	#391	—	2	2	no	—
148	#385	—	2	4	no	—
149	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
150	#328	—	2	4	no	—
151	C₂×C₁₉	—	2	4	no	—
152	C₂×C₁₉	—	4	1	no	—
153	C₂×C₁₉	#2005	1	2	yes	—
154	C₂×C₁₉	#2021	1	1	yes	characteristic
155	C₂²×Q₈	—	2	2	no	—
156	C₂²×Q₈	—	2	1	no	—
157	C₂²×Q₈	—	2	2	no	—
158	C₂²×Q₈	—	2	1	no	—
159	C₂²×Q₈	—	4	4	no	—
160	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
161	C₂³×C₄	D₄×C₁₉	1	2	yes	—
162	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
163	C₂×Q₁₆	—	2	2	no	—
164	C₂×M₁₆	—	2	1	no	—
165	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
166	C₄⋊Q₈	—	4	8	no	—
167	C₂²⋊Q₈	—	2	2	no	—
168	C₂²⋊Q₈	—	2	2	no	—
169	C₂²⋊Q₈	—	2	2	no	—
170	C₂²⋊Q₈	—	2	2	no	—
171	C₂×C₄⋊C₄	—	2	8	no	—
172	C₂×C₄⋊C₄	—	2	2	no	—
173	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
174	C₂×C₂²⋊C₄	—	2	2	no	—
175	C₂×C₂²⋊C₄	—	2	2	no	—
176	C₂×C₄²	—	2	2	no	—
177	#106	—	2	2	no	—
178	#103	—	2	4	no	—
179	#101	—	4	4	no	—
180	C₂²⋊C₈	—	2	2	no	—
181	C₂²⋊C₈	—	2	2	no	—
182	#95	—	2	8	no	—
183	#95	D₄×C₁₉	1	4	yes	—
184	C₁₉	#10334	1	1	yes	characteristic, direct product factor, Sylow
185	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
186	C₂×Q₈	—	2	4	no	—
187	C₂×Q₈	—	2	8	no	—
188	C₂×Q₈	—	2	2	no	—
189	C₂×Q₈	—	2	2	no	—
190	C₂×Q₈	—	4	4	no	—
191	C₂×Q₈	—	4	2	no	—
192	C₂×Q₈	—	4	8	no	—
193	C₂×Q₈	—	4	4	no	—
194	C₂×Q₈	—	4	4	no	—
195	C₂×Q₈	—	4	1	no	—
196	C₂×Q₈	—	4	2	no	—
197	C₂×Q₈	—	4	1	no	—
198	C₂²×C₄	—	2	4	no	—
199	C₂²×C₄	—	2	4	no	—
200	C₂²×C₄	—	2	2	no	—
201	C₂²×C₄	—	2	2	no	—
202	C₂²×C₄	—	2	2	no	—
203	C₂²×C₄	—	4	4	no	—
204	C₂²×C₄	—	4	2	no	—
205	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
206	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
207	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
208	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
209	Q₁₆	—	8	2	no	—
210	M₁₆	—	4	2	no	—
211	M₁₆	—	4	2	no	—
212	C₂×C₈	—	2	2	no	—
213	C₂×C₈	—	4	1	no	—
214	C₄⋊C₄	—	2	2	no	—
215	C₄⋊C₄	—	2	2	no	—
216	C₄⋊C₄	—	4	16	no	—
217	C₄⋊C₄	—	4	2	no	—
218	C₄⋊C₄	—	4	2	no	—
219	C₂²⋊C₄	—	2	8	no	—
220	C₂²⋊C₄	—	4	2	no	—
221	C₂²⋊C₄	—	4	2	no	—
222	C₄²	—	4	4	no	—
223	C₂³	—	2	4	no	—
224	C₂³	—	4	1	no	—
225	C₂³	C₁₉×#120	1	2	yes	—
226	C₂³	C₁₉×#121	1	1	yes	characteristic
227	Q₈	—	4	4	no	—
228	Q₈	—	4	8	no	—
229	Q₈	—	4	4	no	—
230	Q₈	—	4	4	no	—
231	Q₈	—	8	2	no	—
232	C₂×C₄	—	2	4	no	—
233	C₂×C₄	—	2	2	no	—
234	C₂×C₄	—	2	8	no	—
235	C₂×C₄	—	2	8	no	—
236	C₂×C₄	—	2	4	no	—
237	C₂×C₄	—	4	2	no	—
238	C₂×C₄	—	4	1	no	—
239	C₂×C₄	—	4	4	no	—
240	C₂×C₄	—	4	4	no	—
241	C₂×C₄	—	4	2	no	—
242	C₂×C₄	—	4	2	no	—
243	C₂×C₄	—	4	4	no	—
244	C₂×C₄	—	4	4	no	—
245	C₂×C₄	—	4	2	no	—
246	C₂×C₄	—	4	2	no	—
247	C₂×C₄	—	4	4	no	—
248	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
249	C₂×C₄	C₁₉×#121	1	2	yes	—
250	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
251	C₈	—	4	2	no	—
252	C₈	—	8	1	no	—
253	C₂²	—	2	2	no	—
254	C₂²	—	2	2	no	—
255	C₂²	—	2	2	no	—
256	C₂²	—	2	1	no	—
257	C₂²	—	4	4	no	—
258	C₂²	C₁₉×#392	1	1	yes	characteristic
259	C₂²	C₁₉×#456	1	4	yes	—
260	C₄	—	2	1	no	—
261	C₄	—	2	2	no	—
262	C₄	—	4	8	no	—
263	C₄	—	4	4	no	—
264	C₄	—	8	2	no	—
265	C₄	—	8	2	no	—
266	C₄	C₁₉×B(4,𝔽₂)	1	2	yes	—
267	C₂	—	2	4	no	—
268	C₂	—	4	1	no	—
269	C₂	C₁₉×#2005	1	2	yes	—
270	C₂	C₁₉×#2021	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#3195

C₂

yes

maximal, characteristic

C₁₉×#2434

C₂

yes

maximal

C₁₉×#1784

C₂

yes

maximal, characteristic

C₁₉×#1508

C₂

yes

maximal

C₁₉×#1297

C₂

yes

maximal, characteristic

C₂³×Q₈×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊Q₈

—

C₂×C₁₉×C₂²⋊Q₈

C₂²

yes

—

C₁₉×#483

—

C₁₉×#470

—

C₁₉×#451

—

C₂×C₁₉×#101

—

C₁₉×#407

C₂²

yes

characteristic

C₁₉×#407

C₂²

yes

characteristic

C₁₉×#395

—

C₁₉×#391

—

C₁₉×#385

—

C₄×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₁₉×#328

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

D₄

yes

—

C₂³×C₄×C₁₉

D₄

yes

—

C₂³×C₄×C₁₉

C₂³

yes

characteristic

C₂×Q₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₁₉×#106

—

C₁₉×#103

—

C₁₉×#101

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#95

—

C₁₉×#95

D₄

yes

—

C₂⁴×C₁₉

C₂×D₄

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

#41

yes

characteristic

Q₁₆×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

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

#10334

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#120

yes

—

C₂³×C₁₉

#121

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×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

—

112

C₂×C₄×C₁₉

—

113

C₂×C₄×C₁₉

#120

yes

characteristic

114

C₂×C₄×C₁₉

#121

yes

—

115

C₂×C₄×C₁₉

#127

yes

characteristic

116

C₈×C₁₉

—

117

C₈×C₁₉

—

118

#3195

C₂×C₁₉

yes

characteristic

119

#2434

C₂×C₁₉

yes

—

120

#1784

C₂×C₁₉

yes

characteristic

121

#1508

C₂×C₁₉

yes

—

122

#1297

C₂×C₁₉

yes

characteristic

123

C₂²×C₁₉

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

—

126

C₂²×C₁₉

—

127

C₂²×C₁₉

—

128

C₂²×C₁₉

#392

yes

characteristic

129

C₂²×C₁₉

#456

yes

—

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

—

134

C₄×C₁₉

—

135

C₄×C₁₉

—

136

C₄×C₁₉

B(4,𝔽₂)

yes

—

137

C₂³×Q₈

C₂²×C₁₉

yes

characteristic

138

C₂×C₄⋊Q₈

—

139

C₂×C₂²⋊Q₈

C₂²×C₁₉

yes

—

140

#483

—

141

#470

—

142

#451

—

143

C₂×#101

—

144

#407

C₂²×C₁₉

yes

characteristic

145

#407

C₂²×C₁₉

yes

characteristic

146

#395

—

147

#391

—

148

#385

—

149

C₄×C₂²⋊C₄

C₂²×C₁₉

yes

—

150

#328

—

151

C₂×C₁₉

—

152

C₂×C₁₉

—

153

C₂×C₁₉

#2005

yes

—

154

C₂×C₁₉

#2021

yes

characteristic

155

C₂²×Q₈

—

156

C₂²×Q₈

—

157

C₂²×Q₈

—

158

C₂²×Q₈

—

159

C₂²×Q₈

—

160

C₂²×Q₈

D₄×C₁₉

yes

—

161

C₂³×C₄

D₄×C₁₉

yes

—

162

C₂³×C₄

C₂³×C₁₉

yes

characteristic

163

C₂×Q₁₆

—

164

C₂×M₁₆

—

165

C₂×M₁₆

D₄×C₁₉

yes

—

166

C₄⋊Q₈

—

167

C₂²⋊Q₈

—

168

C₂²⋊Q₈

—

169

C₂²⋊Q₈

—

170

C₂²⋊Q₈

—

171

C₂×C₄⋊C₄

—

172

C₂×C₄⋊C₄

—

173

C₂×C₄⋊C₄

D₄×C₁₉

yes

—

174

C₂×C₂²⋊C₄

—

175

C₂×C₂²⋊C₄

—

176

C₂×C₄²

—

177

#106

—

178

#103

—

179

#101

—

180

C₂²⋊C₈

—

181

C₂²⋊C₈

—

182

#95

—

183

#95

D₄×C₁₉

yes

—

184

C₁₉

#10334

yes

characteristic, direct product factor, Sylow

185

C₂⁴

C₂×D₄×C₁₉

yes

characteristic

186

C₂×Q₈

—

187

C₂×Q₈

—

188

C₂×Q₈

—

189

C₂×Q₈

—

190

C₂×Q₈

—

191

C₂×Q₈

—

192

C₂×Q₈

—

193

C₂×Q₈

—

194

C₂×Q₈

—

195

C₂×Q₈

—

196

C₂×Q₈

—

197

C₂×Q₈

—

198

C₂²×C₄

—

199

C₂²×C₄

—

200

C₂²×C₄

—

201

C₂²×C₄

—

202

C₂²×C₄

—

203

C₂²×C₄

—

204

C₂²×C₄

—

205

C₂²×C₄

C₂×D₄×C₁₉

yes

—

206

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

207

C₂²×C₄

C₂×D₄×C₁₉

yes

—

208

C₂²×C₄

#41×C₁₉

yes

characteristic

209

Q₁₆

—

210

M₁₆

—

211

M₁₆

—

212

C₂×C₈

—

213

C₂×C₈

—

214

C₄⋊C₄

—

215

C₄⋊C₄

—

216

C₄⋊C₄

—

217

C₄⋊C₄

—

218

C₄⋊C₄

—

219

C₂²⋊C₄

—

220

C₂²⋊C₄

—

221

C₂²⋊C₄

—

222

C₄²

—

223

C₂³

—

224

C₂³

—

225

C₂³

C₁₉×#120

yes

—

226

C₂³

C₁₉×#121

yes

characteristic

227

Q₈

—

228

Q₈

—

229

Q₈

—

230

Q₈

—

231

Q₈

—

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

C₁₉×#120

yes

characteristic

249

C₂×C₄

C₁₉×#121

yes

—

250

C₂×C₄

C₁₉×#127

yes

characteristic

251

C₈

—

252

C₈

—

253

C₂²

—

254

C₂²

—

255

C₂²

—

256

C₂²

—

257

C₂²

—

258

C₂²

C₁₉×#392

yes

characteristic

259

C₂²

C₁₉×#456

yes

—

260

C₄

—

261

C₄

—

262

C₄

—

263

C₄

—

264

C₄

—

265

C₄

—

266

C₄

C₁₉×B(4,𝔽₂)

yes

—

267

C₂

—

268

C₂

—

269

C₂

C₁₉×#2005

yes

—

270

C₂

C₁₉×#2021

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#392

commutator, Frattini, cosocle

C₂³×C₄

C₂³×C₁₉

prime radical

C₂⁴×C₁₉

C₂×D₄

LCS

G ▷ C₂³×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

N	H ≅ G/N	type
87. #10334	C₁₉	direct (N × H)
184. C₁₉	#10334	direct (N × H)

H ≅ G/N

type

87. #10334

C₁₉

direct (N × H)

184. C₁₉

#10334

direct (N × H)

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

subgroup	index
C₁₉×#3195	2
C₁₉×#2434	2
C₁₉×#1784	2
C₁₉×#1508	2
C₁₉×#1297	2
#10334	19

subgroup

index

C₁₉×#3195

C₁₉×#2434

C₁₉×#1784

C₁₉×#1508

C₁₉×#1297

#10334

Subgroups — C₁₉×#10334 #18016293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#10334 #18016293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10334 #18016293