Group #18017155 — subgroups

Subgroups — C₁₉×#11196 #18017155

Order 4864.

2470 conjugacy classes of subgroups; only the 254 normal subgroups are shown.

normal subgroups only

This group has 2470 conjugacy classes of subgroups — too many to draw. Only its 254 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	C₂×C₁₉×#379	C₂	1	2	yes	maximal
2	C₂×C₁₉×#379	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#342	C₂	1	4	yes	maximal, complemented
4	C₂⁶×C₁₉	C₂²	1	1	yes	characteristic
5	C₂²×C₂²⋊C₄×C₁₉	—	2	4	no	—
6	C₂²×C₂²⋊C₄×C₁₉	C₄	1	4	yes	complemented
7	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
8	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
9	C₁₉×#379	—	2	4	no	—
10	C₁₉×#379	—	2	8	no	—
11	C₁₉×#342	—	2	8	no	—
12	C₂⁵×C₁₉	—	2	4	no	—
13	C₂⁵×C₁₉	—	2	4	no	—
14	C₂⁵×C₁₉	—	2	4	no	—
15	C₂⁵×C₁₉	—	4	8	no	—
16	C₂⁵×C₁₉	C₂×C₄	1	2	yes	—
17	C₂⁵×C₁₉	D₄	1	4	yes	—
18	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
19	C₂³×C₄×C₁₉	—	2	4	no	—
20	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
21	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
22	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
23	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
24	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
25	C₂×C₂²⋊C₄×C₁₉	—	2	16	no	—
26	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
27	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
28	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
29	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
30	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
31	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
32	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
33	C₂×C₂²⋊C₄×C₁₉	—	4	16	no	—
34	C₂×C₂²⋊C₄×C₁₉	—	4	8	no	—
35	C₂×C₂²⋊C₄×C₁₉	D₄	1	8	yes	—
36	C₂⁴×C₁₉	—	2	8	no	—
37	C₂⁴×C₁₉	—	2	16	no	—
38	C₂⁴×C₁₉	—	2	4	no	—
39	C₂⁴×C₁₉	—	2	4	no	—
40	C₂⁴×C₁₉	—	2	4	no	—
41	C₂⁴×C₁₉	—	2	8	no	—
42	C₂⁴×C₁₉	—	2	8	no	—
43	C₂⁴×C₁₉	—	2	8	no	—
44	C₂⁴×C₁₉	—	4	4	no	—
45	C₂⁴×C₁₉	—	4	8	no	—
46	C₂⁴×C₁₉	—	4	4	no	—
47	C₂⁴×C₁₉	—	4	32	no	—
48	C₂⁴×C₁₉	—	4	32	no	—
49	C₂⁴×C₁₉	—	4	32	no	—
50	C₂⁴×C₁₉	—	4	4	no	—
51	C₂⁴×C₁₉	—	4	4	no	—
52	C₂⁴×C₁₉	—	4	4	no	—
53	C₂⁴×C₁₉	—	4	4	no	—
54	C₂⁴×C₁₉	C₂²⋊C₄	1	4	yes	—
55	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
56	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
57	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
58	C₂⁴×C₁₉	#41	1	4	yes	—
59	C₂⁴×C₁₉	#41	1	4	yes	—
60	C₂²×C₄×C₁₉	—	2	4	no	—
61	C₂²×C₄×C₁₉	—	2	8	no	—
62	C₂²×C₄×C₁₉	—	2	8	no	—
63	C₂²×C₄×C₁₉	—	4	16	no	—
64	C₂²×C₄×C₁₉	—	4	4	no	—
65	C₂²×C₄×C₁₉	—	4	4	no	—
66	C₂²×C₄×C₁₉	—	4	8	no	—
67	C₂²⋊C₄×C₁₉	—	2	8	no	—
68	C₂²⋊C₄×C₁₉	—	2	8	no	—
69	C₂²⋊C₄×C₁₉	—	4	32	no	—
70	C₂²⋊C₄×C₁₉	—	4	8	no	—
71	C₂²⋊C₄×C₁₉	—	4	8	no	—
72	C₂²⋊C₄×C₁₉	—	4	2	no	—
73	C₂²⋊C₄×C₁₉	—	4	4	no	—
74	C₂²⋊C₄×C₁₉	—	4	4	no	—
75	C₂²⋊C₄×C₁₉	—	4	2	no	—
76	C₂²⋊C₄×C₁₉	—	4	4	no	—
77	#11196	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂³×C₁₉	—	2	4	no	—
79	C₂³×C₁₉	—	2	8	no	—
80	C₂³×C₁₉	—	2	16	no	—
81	C₂³×C₁₉	—	2	16	no	—
82	C₂³×C₁₉	—	2	16	no	—
83	C₂³×C₁₉	—	2	4	no	—
84	C₂³×C₁₉	—	2	8	no	—
85	C₂³×C₁₉	—	2	4	no	—
86	C₂³×C₁₉	—	2	8	no	—
87	C₂³×C₁₉	—	4	8	no	—
88	C₂³×C₁₉	—	4	8	no	—
89	C₂³×C₁₉	—	4	8	no	—
90	C₂³×C₁₉	—	4	32	no	—
91	C₂³×C₁₉	—	4	32	no	—
92	C₂³×C₁₉	—	4	32	no	—
93	C₂³×C₁₉	—	4	8	no	—
94	C₂³×C₁₉	—	4	8	no	—
95	C₂³×C₁₉	—	4	8	no	—
96	C₂³×C₁₉	—	4	32	no	—
97	C₂³×C₁₉	—	4	32	no	—
98	C₂³×C₁₉	—	4	32	no	—
99	C₂³×C₁₉	—	4	32	no	—
100	C₂³×C₁₉	—	4	8	no	—
101	C₂³×C₁₉	—	4	8	no	—
102	C₂³×C₁₉	—	4	8	no	—
103	C₂³×C₁₉	#99	1	8	yes	—
104	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
105	C₂³×C₁₉	#117	1	2	yes	—
106	C₂³×C₁₉	C₄×D₄	1	4	yes	—
107	C₂³×C₁₉	#120	1	2	yes	—
108	C₂³×C₁₉	#121	1	4	yes	—
109	C₂³×C₁₉	#121	1	4	yes	—
110	C₂³×C₁₉	#123	1	4	yes	—
111	C₂³×C₁₉	#123	1	2	yes	—
112	C₂³×C₁₉	#123	1	4	yes	—
113	C₂³×C₁₉	#124	1	4	yes	—
114	C₂³×C₁₉	#126	1	4	yes	—
115	C₂×C₄×C₁₉	—	4	16	no	—
116	C₂×C₄×C₁₉	—	4	4	no	—
117	C₂×C₄×C₁₉	—	4	8	no	—
118	C₂×C₄×C₁₉	—	4	8	no	—
119	C₂×C₄×C₁₉	—	8	8	no	—
120	C₂×C₄×C₁₉	—	8	8	no	—
121	C₂×C₄×C₁₉	—	8	8	no	—
122	C₂×#379	C₂×C₁₉	1	2	yes	—
123	C₂×#379	C₂×C₁₉	1	1	yes	characteristic
124	C₂×#342	C₂×C₁₉	1	4	yes	complemented
125	C₂²×C₁₉	—	2	8	no	—
126	C₂²×C₁₉	—	2	4	no	—
127	C₂²×C₁₉	—	2	4	no	—
128	C₂²×C₁₉	—	2	8	no	—
129	C₂²×C₁₉	—	2	8	no	—
130	C₂²×C₁₉	—	2	4	no	—
131	C₂²×C₁₉	—	2	8	no	—
132	C₂²×C₁₉	—	2	16	no	—
133	C₂²×C₁₉	—	4	4	no	—
134	C₂²×C₁₉	—	4	4	no	—
135	C₂²×C₁₉	—	4	4	no	—
136	C₂²×C₁₉	—	4	4	no	—
137	C₂²×C₁₉	—	4	32	no	—
138	C₂²×C₁₉	—	4	32	no	—
139	C₂²×C₁₉	—	4	32	no	—
140	C₂²×C₁₉	—	4	4	no	—
141	C₂²×C₁₉	—	4	8	no	—
142	C₂²×C₁₉	—	4	4	no	—
143	C₂²×C₁₉	#381	1	1	yes	characteristic
144	C₂²×C₁₉	#386	1	2	yes	—
145	C₂²×C₁₉	#388	1	4	yes	—
146	C₂²×C₁₉	#394	1	4	yes	—
147	C₂²×C₁₉	#397	1	4	yes	—
148	C₂²×C₁₉	C₂×#99	1	4	yes	—
149	C₄×C₁₉	—	8	8	no	—
150	C₄×C₁₉	—	8	4	no	—
151	C₂⁶	C₂²×C₁₉	1	1	yes	characteristic
152	C₂²×C₂²⋊C₄	—	2	4	no	—
153	C₂²×C₂²⋊C₄	C₄×C₁₉	1	4	yes	complemented
154	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
155	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
156	#379	—	2	4	no	—
157	#379	—	2	8	no	—
158	#342	—	2	8	no	—
159	C₂×C₁₉	—	2	4	no	—
160	C₂×C₁₉	—	2	4	no	—
161	C₂×C₁₉	—	2	4	no	—
162	C₂×C₁₉	—	4	8	no	—
163	C₂×C₁₉	#1440	1	1	yes	characteristic
164	C₂×C₁₉	#1819	1	2	yes	—
165	C₂×C₁₉	#1898	1	4	yes	—
166	C₂⁵	—	2	4	no	—
167	C₂⁵	—	2	4	no	—
168	C₂⁵	—	2	4	no	—
169	C₂⁵	—	4	8	no	—
170	C₂⁵	C₂×C₄×C₁₉	1	2	yes	—
171	C₂⁵	D₄×C₁₉	1	4	yes	—
172	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
173	C₂³×C₄	—	2	4	no	—
174	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
175	C₂×C₂²⋊C₄	—	2	4	no	—
176	C₂×C₂²⋊C₄	—	2	4	no	—
177	C₂×C₂²⋊C₄	—	2	4	no	—
178	C₂×C₂²⋊C₄	—	2	4	no	—
179	C₂×C₂²⋊C₄	—	2	16	no	—
180	C₂×C₂²⋊C₄	—	2	4	no	—
181	C₂×C₂²⋊C₄	—	2	4	no	—
182	C₂×C₂²⋊C₄	—	2	4	no	—
183	C₂×C₂²⋊C₄	—	2	2	no	—
184	C₂×C₂²⋊C₄	—	2	2	no	—
185	C₂×C₂²⋊C₄	—	2	4	no	—
186	C₂×C₂²⋊C₄	—	2	4	no	—
187	C₂×C₂²⋊C₄	—	4	16	no	—
188	C₂×C₂²⋊C₄	—	4	8	no	—
189	C₂×C₂²⋊C₄	D₄×C₁₉	1	8	yes	—
190	C₁₉	#11196	1	1	yes	characteristic, direct product factor, Sylow
191	C₂⁴	—	2	4	no	—
192	C₂⁴	—	2	4	no	—
193	C₂⁴	—	2	4	no	—
194	C₂⁴	—	2	8	no	—
195	C₂⁴	—	2	16	no	—
196	C₂⁴	—	2	8	no	—
197	C₂⁴	—	2	8	no	—
198	C₂⁴	—	2	8	no	—
199	C₂⁴	—	4	4	no	—
200	C₂⁴	—	4	8	no	—
201	C₂⁴	—	4	4	no	—
202	C₂⁴	—	4	32	no	—
203	C₂⁴	—	4	32	no	—
204	C₂⁴	—	4	32	no	—
205	C₂⁴	—	4	4	no	—
206	C₂⁴	—	4	4	no	—
207	C₂⁴	—	4	4	no	—
208	C₂⁴	—	4	4	no	—
209	C₂⁴	C₂²⋊C₄×C₁₉	1	4	yes	—
210	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
211	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
212	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
213	C₂⁴	#41×C₁₉	1	4	yes	—
214	C₂⁴	#41×C₁₉	1	4	yes	—
215	C₂²×C₄	—	2	4	no	—
216	C₂²×C₄	—	2	8	no	—
217	C₂²×C₄	—	2	8	no	—
218	C₂²×C₄	—	4	16	no	—
219	C₂²×C₄	—	4	4	no	—
220	C₂²×C₄	—	4	4	no	—
221	C₂²×C₄	—	4	8	no	—
222	C₂²⋊C₄	—	2	8	no	—
223	C₂²⋊C₄	—	2	8	no	—
224	C₂²⋊C₄	—	4	32	no	—
225	C₂²⋊C₄	—	4	8	no	—
226	C₂²⋊C₄	—	4	2	no	—
227	C₂²⋊C₄	—	4	4	no	—
228	C₂²⋊C₄	—	4	4	no	—
229	C₂²⋊C₄	—	4	2	no	—
230	C₂²⋊C₄	—	4	4	no	—
231	C₂²⋊C₄	—	4	8	no	—
232	C₂³	—	2	4	no	—
233	C₂³	—	2	8	no	—
234	C₂³	—	2	16	no	—
235	C₂³	—	2	16	no	—
236	C₂³	—	2	16	no	—
237	C₂³	—	2	4	no	—
238	C₂³	—	2	8	no	—
239	C₂³	—	2	4	no	—
240	C₂³	—	2	8	no	—
241	C₂³	—	4	8	no	—
242	C₂³	—	4	8	no	—
243	C₂³	—	4	8	no	—
244	C₂³	—	4	32	no	—
245	C₂³	—	4	32	no	—
246	C₂³	—	4	32	no	—
247	C₂³	—	4	8	no	—
248	C₂³	—	4	8	no	—
249	C₂³	—	4	8	no	—
250	C₂³	—	4	32	no	—
251	C₂³	—	4	32	no	—
252	C₂³	—	4	32	no	—
253	C₂³	—	4	32	no	—
254	C₂³	—	4	8	no	—
255	C₂³	—	4	8	no	—
256	C₂³	—	4	8	no	—
257	C₂³	C₁₉×#99	1	8	yes	—
258	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
259	C₂³	C₁₉×#117	1	2	yes	—
260	C₂³	C₄×D₄×C₁₉	1	4	yes	—
261	C₂³	C₁₉×#120	1	2	yes	—
262	C₂³	C₁₉×#121	1	4	yes	—
263	C₂³	C₁₉×#121	1	4	yes	—
264	C₂³	C₁₉×#123	1	4	yes	—
265	C₂³	C₁₉×#123	1	2	yes	—
266	C₂³	C₁₉×#123	1	4	yes	—
267	C₂³	C₁₉×#124	1	4	yes	—
268	C₂³	C₁₉×#126	1	4	yes	—
269	C₂×C₄	—	4	16	no	—
270	C₂×C₄	—	4	4	no	—
271	C₂×C₄	—	4	8	no	—
272	C₂×C₄	—	4	8	no	—
273	C₂×C₄	—	8	8	no	—
274	C₂×C₄	—	8	8	no	—
275	C₂×C₄	—	8	8	no	—
276	C₂²	—	2	4	no	—
277	C₂²	—	2	8	no	—
278	C₂²	—	2	8	no	—
279	C₂²	—	2	4	no	—
280	C₂²	—	2	8	no	—
281	C₂²	—	2	4	no	—
282	C₂²	—	2	16	no	—
283	C₂²	—	2	8	no	—
284	C₂²	—	4	4	no	—
285	C₂²	—	4	4	no	—
286	C₂²	—	4	4	no	—
287	C₂²	—	4	4	no	—
288	C₂²	—	4	32	no	—
289	C₂²	—	4	32	no	—
290	C₂²	—	4	32	no	—
291	C₂²	—	4	8	no	—
292	C₂²	—	4	4	no	—
293	C₂²	—	4	4	no	—
294	C₂²	C₁₉×#381	1	1	yes	characteristic
295	C₂²	C₁₉×#386	1	2	yes	—
296	C₂²	C₁₉×#388	1	4	yes	—
297	C₂²	C₁₉×#394	1	4	yes	—
298	C₂²	C₁₉×#397	1	4	yes	—
299	C₂²	C₂×C₁₉×#99	1	4	yes	—
300	C₄	—	8	8	no	—
301	C₄	—	8	4	no	—
302	C₂	—	2	4	no	—
303	C₂	—	2	4	no	—
304	C₂	—	2	4	no	—
305	C₂	—	4	8	no	—
306	C₂	C₁₉×#1440	1	1	yes	characteristic
307	C₂	C₁₉×#1819	1	2	yes	—
308	C₂	C₁₉×#1898	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×#379

C₂

yes

maximal

C₂×C₁₉×#379

C₂

yes

maximal, characteristic

C₂×C₁₉×#342

C₂

yes

maximal, complemented

C₂⁶×C₁₉

C₂²

yes

characteristic

C₂²×C₂²⋊C₄×C₁₉

—

C₂²×C₂²⋊C₄×C₁₉

C₄

yes

complemented

C₂²×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂²×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₁₉×#379

—

C₁₉×#379

—

C₁₉×#342

—

C₂⁵×C₁₉

—

C₂⁵×C₁₉

—

C₂⁵×C₁₉

—

C₂⁵×C₁₉

—

C₂⁵×C₁₉

C₂×C₄

yes

—

C₂⁵×C₁₉

D₄

yes

—

C₂⁵×C₁₉

C₂³

yes

characteristic

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

D₄

yes

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

—

C₂⁴×C₁₉

C₂²×C₄

yes

characteristic

C₂⁴×C₁₉

C₂×D₄

yes

—

C₂⁴×C₁₉

C₂×D₄

yes

—

C₂⁴×C₁₉

#41

yes

—

C₂⁴×C₁₉

#41

yes

—

C₂²×C₄×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

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

#11196

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

100

C₂³×C₁₉

—

101

C₂³×C₁₉

—

102

C₂³×C₁₉

—

103

C₂³×C₁₉

#99

yes

—

104

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

105

C₂³×C₁₉

#117

yes

—

106

C₂³×C₁₉

C₄×D₄

yes

—

107

C₂³×C₁₉

#120

yes

—

108

C₂³×C₁₉

#121

yes

—

109

C₂³×C₁₉

#121

yes

—

110

C₂³×C₁₉

#123

yes

—

111

C₂³×C₁₉

#123

yes

—

112

C₂³×C₁₉

#123

yes

—

113

C₂³×C₁₉

#124

yes

—

114

C₂³×C₁₉

#126

yes

—

115

C₂×C₄×C₁₉

—

116

C₂×C₄×C₁₉

—

117

C₂×C₄×C₁₉

—

118

C₂×C₄×C₁₉

—

119

C₂×C₄×C₁₉

—

120

C₂×C₄×C₁₉

—

121

C₂×C₄×C₁₉

—

122

C₂×#379

C₂×C₁₉

yes

—

123

C₂×#379

C₂×C₁₉

yes

characteristic

124

C₂×#342

C₂×C₁₉

yes

complemented

125

C₂²×C₁₉

—

126

C₂²×C₁₉

—

127

C₂²×C₁₉

—

128

C₂²×C₁₉

—

129

C₂²×C₁₉

—

130

C₂²×C₁₉

—

131

C₂²×C₁₉

—

132

C₂²×C₁₉

—

133

C₂²×C₁₉

—

134

C₂²×C₁₉

—

135

C₂²×C₁₉

—

136

C₂²×C₁₉

—

137

C₂²×C₁₉

—

138

C₂²×C₁₉

—

139

C₂²×C₁₉

—

140

C₂²×C₁₉

—

141

C₂²×C₁₉

—

142

C₂²×C₁₉

—

143

C₂²×C₁₉

#381

yes

characteristic

144

C₂²×C₁₉

#386

yes

—

145

C₂²×C₁₉

#388

yes

—

146

C₂²×C₁₉

#394

yes

—

147

C₂²×C₁₉

#397

yes

—

148

C₂²×C₁₉

C₂×#99

yes

—

149

C₄×C₁₉

—

150

C₄×C₁₉

—

151

C₂⁶

C₂²×C₁₉

yes

characteristic

152

C₂²×C₂²⋊C₄

—

153

C₂²×C₂²⋊C₄

C₄×C₁₉

yes

complemented

154

C₂²×C₂²⋊C₄

C₂²×C₁₉

yes

—

155

C₂²×C₂²⋊C₄

C₂²×C₁₉

yes

—

156

#379

—

157

#379

—

158

#342

—

159

C₂×C₁₉

—

160

C₂×C₁₉

—

161

C₂×C₁₉

—

162

C₂×C₁₉

—

163

C₂×C₁₉

#1440

yes

characteristic

164

C₂×C₁₉

#1819

yes

—

165

C₂×C₁₉

#1898

yes

—

166

C₂⁵

—

167

C₂⁵

—

168

C₂⁵

—

169

C₂⁵

—

170

C₂⁵

C₂×C₄×C₁₉

yes

—

171

C₂⁵

D₄×C₁₉

yes

—

172

C₂⁵

C₂³×C₁₉

yes

characteristic

173

C₂³×C₄

—

174

C₂³×C₄

C₂×C₄×C₁₉

yes

—

175

C₂×C₂²⋊C₄

—

176

C₂×C₂²⋊C₄

—

177

C₂×C₂²⋊C₄

—

178

C₂×C₂²⋊C₄

—

179

C₂×C₂²⋊C₄

—

180

C₂×C₂²⋊C₄

—

181

C₂×C₂²⋊C₄

—

182

C₂×C₂²⋊C₄

—

183

C₂×C₂²⋊C₄

—

184

C₂×C₂²⋊C₄

—

185

C₂×C₂²⋊C₄

—

186

C₂×C₂²⋊C₄

—

187

C₂×C₂²⋊C₄

—

188

C₂×C₂²⋊C₄

—

189

C₂×C₂²⋊C₄

D₄×C₁₉

yes

—

190

C₁₉

#11196

yes

characteristic, direct product factor, Sylow

191

C₂⁴

—

192

C₂⁴

—

193

C₂⁴

—

194

C₂⁴

—

195

C₂⁴

—

196

C₂⁴

—

197

C₂⁴

—

198

C₂⁴

—

199

C₂⁴

—

200

C₂⁴

—

201

C₂⁴

—

202

C₂⁴

—

203

C₂⁴

—

204

C₂⁴

—

205

C₂⁴

—

206

C₂⁴

—

207

C₂⁴

—

208

C₂⁴

—

209

C₂⁴

C₂²⋊C₄×C₁₉

yes

—

210

C₂⁴

C₂²×C₄×C₁₉

yes

characteristic

211

C₂⁴

C₂×D₄×C₁₉

yes

—

212

C₂⁴

C₂×D₄×C₁₉

yes

—

213

C₂⁴

#41×C₁₉

yes

—

214

C₂⁴

#41×C₁₉

yes

—

215

C₂²×C₄

—

216

C₂²×C₄

—

217

C₂²×C₄

—

218

C₂²×C₄

—

219

C₂²×C₄

—

220

C₂²×C₄

—

221

C₂²×C₄

—

222

C₂²⋊C₄

—

223

C₂²⋊C₄

—

224

C₂²⋊C₄

—

225

C₂²⋊C₄

—

226

C₂²⋊C₄

—

227

C₂²⋊C₄

—

228

C₂²⋊C₄

—

229

C₂²⋊C₄

—

230

C₂²⋊C₄

—

231

C₂²⋊C₄

—

232

C₂³

—

233

C₂³

—

234

C₂³

—

235

C₂³

—

236

C₂³

—

237

C₂³

—

238

C₂³

—

239

C₂³

—

240

C₂³

—

241

C₂³

—

242

C₂³

—

243

C₂³

—

244

C₂³

—

245

C₂³

—

246

C₂³

—

247

C₂³

—

248

C₂³

—

249

C₂³

—

250

C₂³

—

251

C₂³

—

252

C₂³

—

253

C₂³

—

254

C₂³

—

255

C₂³

—

256

C₂³

—

257

C₂³

C₁₉×#99

yes

—

258

C₂³

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

259

C₂³

C₁₉×#117

yes

—

260

C₂³

C₄×D₄×C₁₉

yes

—

261

C₂³

C₁₉×#120

yes

—

262

C₂³

C₁₉×#121

yes

—

263

C₂³

C₁₉×#121

yes

—

264

C₂³

C₁₉×#123

yes

—

265

C₂³

C₁₉×#123

yes

—

266

C₂³

C₁₉×#123

yes

—

267

C₂³

C₁₉×#124

yes

—

268

C₂³

C₁₉×#126

yes

—

269

C₂×C₄

—

270

C₂×C₄

—

271

C₂×C₄

—

272

C₂×C₄

—

273

C₂×C₄

—

274

C₂×C₄

—

275

C₂×C₄

—

276

C₂²

—

277

C₂²

—

278

C₂²

—

279

C₂²

—

280

C₂²

—

281

C₂²

—

282

C₂²

—

283

C₂²

—

284

C₂²

—

285

C₂²

—

286

C₂²

—

287

C₂²

—

288

C₂²

—

289

C₂²

—

290

C₂²

—

291

C₂²

—

292

C₂²

—

293

C₂²

—

294

C₂²

C₁₉×#381

yes

characteristic

295

C₂²

C₁₉×#386

yes

—

296

C₂²

C₁₉×#388

yes

—

297

C₂²

C₁₉×#394

yes

—

298

C₂²

C₁₉×#397

yes

—

299

C₂²

C₂×C₁₉×#99

yes

—

300

C₄

—

301

C₄

—

302

C₂

—

303

C₂

—

304

C₂

—

305

C₂

—

306

C₂

C₁₉×#1440

yes

characteristic

307

C₂

C₁₉×#1819

yes

—

308

C₂

C₁₉×#1898

yes

—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×C₂²⋊C₄
commutator	C₂⁴	C₂²×C₄×C₁₉
Frattini, cosocle	C₂⁵	C₂³×C₁₉
prime radical	C₂⁶×C₁₉	C₂²
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁶×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂³×C₁₉

C₂×C₂²⋊C₄

commutator

C₂⁴

C₂²×C₄×C₁₉

Frattini, cosocle

C₂⁵

C₂³×C₁₉

prime radical

C₂⁶×C₁₉

C₂²

LCS

G ▷ C₂⁴ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₁₉ ◁ C₂⁶×C₁₉ ◁ G

N	H ≅ G/N	type
3. C₂×C₁₉×#342	C₂	semidirect
6. C₂²×C₂²⋊C₄×C₁₉	C₄	semidirect
77. #11196	C₁₉	direct (N × H)
124. C₂×#342	C₂×C₁₉	semidirect
153. C₂²×C₂²⋊C₄	C₄×C₁₉	semidirect
190. C₁₉	#11196	direct (N × H)

H ≅ G/N

type

3. C₂×C₁₉×#342

C₂

semidirect

6. C₂²×C₂²⋊C₄×C₁₉

C₄

semidirect

77. #11196

C₁₉

direct (N × H)

124. C₂×#342

C₂×C₁₉

semidirect

153. C₂²×C₂²⋊C₄

C₄×C₁₉

semidirect

190. C₁₉

#11196

direct (N × H)

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

subgroup	index
C₂×C₁₉×#379	2
C₂×C₁₉×#342	2
#11196	19

subgroup

index

C₂×C₁₉×#379

C₂×C₁₉×#342

#11196

Subgroups — C₁₉×#11196 #18017155

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#11196 #18017155

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11196 #18017155