Group #18025037 — subgroups

Subgroups — C₁₉×#19078 #18025037

Order 4864.

944 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 944 conjugacy classes of subgroups — too many to draw. Only its 230 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×#3550	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3165	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3152	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1660	C₂	1	8	yes	maximal, complemented
5	C₁₉×#1526	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1525	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#137	—	2	2	no	—
8	C₁₉×#563	C₂²	1	4	yes	—
9	C₁₉×#559	—	2	1	no	—
10	Q₈²×C₁₉	—	2	1	no	—
11	C₁₉×#556	—	2	2	no	—
12	D₄×Q₈×C₁₉	—	2	2	no	—
13	C₁₉×#542	—	2	4	no	—
14	C₁₉×#536	—	2	2	no	—
15	C₁₉×#533	C₂²	1	2	yes	—
16	C₁₉×#532	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₁₉×#501	C₂²	1	8	yes	—
19	C₁₉×#500	—	2	2	no	—
20	C₁₉×#498	—	2	2	no	—
21	C₁₉×#497	C₂²	1	4	yes	—
22	C₁₉×#494	—	2	1	no	—
23	C₁₉×#492	—	2	1	no	—
24	C₁₉×#428	—	2	4	no	—
25	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
26	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#330	C₂²	1	8	yes	—
28	C₁₉×#329	C₂²	1	4	yes	—
29	C₂×#41×C₁₉	D₄	1	2	yes	—
30	C₂²×Q₈×C₁₉	—	2	2	no	—
31	C₂²×Q₈×C₁₉	—	2	1	no	—
32	C₁₉×#137	—	4	8	no	—
33	C₂×Q₁₆×C₁₉	—	2	4	no	—
34	C₂×SD₁₆×C₁₉	—	2	4	no	—
35	C₂×M₁₆×C₁₉	—	2	2	no	—
36	C₂×M₁₆×C₁₉	—	2	1	no	—
37	C₁₉×C₄⋊Q₈	—	2	4	no	—
38	C₁₉×C₄⋊Q₈	—	2	4	no	—
39	C₁₉×C₄⋊Q₈	—	2	2	no	—
40	C₁₉×C₄⋊Q₈	—	2	1	no	—
41	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
42	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
43	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
44	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
45	C₁₉×#127	D₄	1	1	yes	characteristic
46	C₁₉×#126	—	2	8	no	—
47	C₁₉×#125	C₂³	1	4	yes	—
48	C₁₉×#124	—	2	4	no	—
49	C₁₉×#124	—	2	4	no	—
50	C₁₉×#124	C₂³	1	2	yes	—
51	C₁₉×#123	—	2	4	no	—
52	C₁₉×#123	—	2	4	no	—
53	C₁₉×C₂²⋊Q₈	—	2	4	no	—
54	C₁₉×C₂²⋊Q₈	—	2	2	no	—
55	C₁₉×C₂²⋊Q₈	—	2	2	no	—
56	C₁₉×C₂²⋊Q₈	—	2	8	no	—
57	C₁₉×#121	—	2	2	no	—
58	C₄×Q₈×C₁₉	—	2	4	no	—
59	C₄×Q₈×C₁₉	—	2	2	no	—
60	C₄×Q₈×C₁₉	—	2	2	no	—
61	C₄×D₄×C₁₉	—	2	4	no	—
62	C₄×D₄×C₁₉	—	2	2	no	—
63	C₁₉×#117	—	2	2	no	—
64	C₁₉×#117	D₄	1	4	yes	—
65	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
66	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
67	C₁₉×#107	—	2	8	no	—
68	C₁₉×#106	—	2	8	no	—
69	C₁₉×#97	C₂³	1	2	yes	—
70	C₁₉×#97	C₂³	1	4	yes	—
71	C₄×C₈×C₁₉	—	2	1	no	—
72	C₄×C₈×C₁₉	—	2	2	no	—
73	#41×C₁₉	—	4	4	no	—
74	C₂×Q₈×C₁₉	—	2	4	no	—
75	C₂×Q₈×C₁₉	—	2	2	no	—
76	C₂×Q₈×C₁₉	—	2	2	no	—
77	C₂×Q₈×C₁₉	—	2	2	no	—
78	C₂×Q₈×C₁₉	—	4	4	no	—
79	C₂×Q₈×C₁₉	—	4	1	no	—
80	C₂×Q₈×C₁₉	—	8	4	no	—
81	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
82	C₂×D₄×C₁₉	—	2	2	no	—
83	C₂×D₄×C₁₉	—	2	2	no	—
84	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₁₉	—	2	4	no	—
86	C₂²×C₄×C₁₉	—	2	2	no	—
87	C₂²×C₄×C₁₉	—	4	1	no	—
88	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
90	Q₁₆×C₁₉	—	4	8	no	—
91	SD₁₆×C₁₉	—	4	8	no	—
92	M₁₆×C₁₉	—	2	8	no	—
93	M₁₆×C₁₉	—	2	4	no	—
94	C₂×C₈×C₁₉	—	2	2	no	—
95	C₂×C₈×C₁₉	—	2	4	no	—
96	C₄⋊C₄×C₁₉	—	2	8	no	—
97	C₄⋊C₄×C₁₉	—	2	2	no	—
98	C₄⋊C₄×C₁₉	—	2	2	no	—
99	C₄⋊C₄×C₁₉	—	2	2	no	—
100	C₄⋊C₄×C₁₉	—	2	4	no	—
101	C₄⋊C₄×C₁₉	—	2	4	no	—
102	C₄⋊C₄×C₁₉	—	2	4	no	—
103	C₄⋊C₄×C₁₉	—	4	2	no	—
104	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
105	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
106	C₂²⋊C₄×C₁₉	—	2	4	no	—
107	C₂²⋊C₄×C₁₉	—	2	8	no	—
108	C₂²⋊C₄×C₁₉	—	2	4	no	—
109	C₂²⋊C₄×C₁₉	—	2	4	no	—
110	C₄²×C₁₉	—	2	4	no	—
111	C₄²×C₁₉	—	2	4	no	—
112	C₄²×C₁₉	C₂×D₄	1	2	yes	—
113	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
115	#19078	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂³×C₁₉	—	2	2	no	—
117	C₂³×C₁₉	#120	1	1	yes	characteristic
118	Q₈×C₁₉	—	4	2	no	—
119	Q₈×C₁₉	—	4	4	no	—
120	Q₈×C₁₉	—	4	4	no	—
121	Q₈×C₁₉	—	4	4	no	—
122	Q₈×C₁₉	—	8	4	no	—
123	Q₈×C₁₉	—	8	2	no	—
124	D₄×C₁₉	—	4	2	no	—
125	D₄×C₁₉	—	4	4	no	—
126	D₄×C₁₉	—	8	2	no	—
127	C₂×C₄×C₁₉	—	2	2	no	—
128	C₂×C₄×C₁₉	—	2	4	no	—
129	C₂×C₄×C₁₉	—	2	4	no	—
130	C₂×C₄×C₁₉	—	2	2	no	—
131	C₂×C₄×C₁₉	—	2	4	no	—
132	C₂×C₄×C₁₉	—	4	4	no	—
133	C₂×C₄×C₁₉	—	4	2	no	—
134	C₂×C₄×C₁₉	—	8	4	no	—
135	C₂×C₄×C₁₉	—	8	2	no	—
136	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
137	C₂×C₄×C₁₉	#120	1	2	yes	—
138	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
139	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
140	C₈×C₁₉	—	2	8	no	—
141	C₈×C₁₉	—	2	4	no	—
142	#3550	C₂×C₁₉	1	1	yes	characteristic
143	#3165	C₂×C₁₉	1	2	yes	complemented
144	#3152	C₂×C₁₉	1	1	yes	characteristic
145	#1660	C₂×C₁₉	1	8	yes	complemented
146	#1526	C₂×C₁₉	1	2	yes	complemented
147	#1525	C₂×C₁₉	1	1	yes	characteristic
148	C₂²×C₁₉	—	2	1	no	—
149	C₂²×C₁₉	—	2	2	no	—
150	C₂²×C₁₉	—	4	2	no	—
151	C₂²×C₁₉	—	4	4	no	—
152	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
153	C₄×C₁₉	—	2	1	no	—
154	C₄×C₁₉	—	2	2	no	—
155	C₄×C₁₉	—	4	2	no	—
156	C₄×C₁₉	—	4	4	no	—
157	C₄×C₁₉	—	4	4	no	—
158	C₄×C₁₉	—	8	2	no	—
159	C₄×C₁₉	#453	1	2	yes	—
160	C₄×C₁₉	#456	1	4	yes	—
161	C₂×#137	—	2	2	no	—
162	#563	C₂²×C₁₉	1	4	yes	—
163	#559	—	2	1	no	—
164	Q₈²	—	2	1	no	—
165	#556	—	2	2	no	—
166	D₄×Q₈	—	2	2	no	—
167	#542	—	2	4	no	—
168	#536	—	2	2	no	—
169	#533	C₂²×C₁₉	1	2	yes	—
170	#532	C₂²×C₁₉	1	1	yes	characteristic
171	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
172	#501	C₂²×C₁₉	1	8	yes	—
173	#500	—	2	2	no	—
174	#498	—	2	2	no	—
175	#497	C₂²×C₁₉	1	4	yes	—
176	#494	—	2	1	no	—
177	#492	—	2	1	no	—
178	#428	—	2	4	no	—
179	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
180	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
181	#330	C₂²×C₁₉	1	8	yes	—
182	#329	C₂²×C₁₉	1	4	yes	—
183	C₂×C₁₉	—	4	1	no	—
184	C₂×C₁₉	—	8	2	no	—
185	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
186	C₂×C₁₉	C₂×#456	1	2	yes	—
187	C₂×#41	D₄×C₁₉	1	2	yes	—
188	C₂²×Q₈	—	2	2	no	—
189	C₂²×Q₈	—	2	1	no	—
190	#137	—	4	8	no	—
191	C₂×Q₁₆	—	2	4	no	—
192	C₂×SD₁₆	—	2	4	no	—
193	C₂×M₁₆	—	2	1	no	—
194	C₂×M₁₆	—	2	2	no	—
195	C₄⋊Q₈	—	2	4	no	—
196	C₄⋊Q₈	—	2	4	no	—
197	C₄⋊Q₈	—	2	2	no	—
198	C₄⋊Q₈	—	2	1	no	—
199	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
200	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
201	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
202	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
203	#127	D₄×C₁₉	1	1	yes	characteristic
204	#126	—	2	8	no	—
205	#125	C₂³×C₁₉	1	4	yes	—
206	#124	—	2	4	no	—
207	#124	—	2	4	no	—
208	#124	C₂³×C₁₉	1	2	yes	—
209	#123	—	2	4	no	—
210	#123	—	2	4	no	—
211	C₂²⋊Q₈	—	2	4	no	—
212	C₂²⋊Q₈	—	2	2	no	—
213	C₂²⋊Q₈	—	2	2	no	—
214	C₂²⋊Q₈	—	2	8	no	—
215	#121	—	2	2	no	—
216	C₄×Q₈	—	2	4	no	—
217	C₄×Q₈	—	2	2	no	—
218	C₄×Q₈	—	2	2	no	—
219	C₄×D₄	—	2	4	no	—
220	C₄×D₄	—	2	2	no	—
221	#117	—	2	2	no	—
222	#117	D₄×C₁₉	1	4	yes	—
223	C₂×C₄⋊C₄	—	2	2	no	—
224	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
225	#107	—	2	8	no	—
226	#106	—	2	8	no	—
227	#97	C₂³×C₁₉	1	4	yes	—
228	#97	C₂³×C₁₉	1	2	yes	—
229	C₄×C₈	—	2	1	no	—
230	C₄×C₈	—	2	2	no	—
231	C₁₉	#19078	1	1	yes	characteristic, direct product factor, Sylow
232	#41	—	4	4	no	—
233	C₂×Q₈	—	2	4	no	—
234	C₂×Q₈	—	2	2	no	—
235	C₂×Q₈	—	2	2	no	—
236	C₂×Q₈	—	2	2	no	—
237	C₂×Q₈	—	4	4	no	—
238	C₂×Q₈	—	4	1	no	—
239	C₂×Q₈	—	8	4	no	—
240	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
241	C₂×D₄	—	2	2	no	—
242	C₂×D₄	—	2	2	no	—
243	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
244	C₂²×C₄	—	2	4	no	—
245	C₂²×C₄	—	2	2	no	—
246	C₂²×C₄	—	4	1	no	—
247	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
248	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
249	Q₁₆	—	4	8	no	—
250	SD₁₆	—	4	8	no	—
251	M₁₆	—	2	8	no	—
252	M₁₆	—	2	4	no	—
253	C₂×C₈	—	2	4	no	—
254	C₂×C₈	—	2	2	no	—
255	C₄⋊C₄	—	2	8	no	—
256	C₄⋊C₄	—	2	2	no	—
257	C₄⋊C₄	—	2	2	no	—
258	C₄⋊C₄	—	2	2	no	—
259	C₄⋊C₄	—	2	4	no	—
260	C₄⋊C₄	—	2	4	no	—
261	C₄⋊C₄	—	2	4	no	—
262	C₄⋊C₄	—	4	2	no	—
263	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
264	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
265	C₂²⋊C₄	—	2	4	no	—
266	C₂²⋊C₄	—	2	8	no	—
267	C₂²⋊C₄	—	2	4	no	—
268	C₂²⋊C₄	—	2	4	no	—
269	C₄²	—	2	4	no	—
270	C₄²	—	2	4	no	—
271	C₄²	C₂×D₄×C₁₉	1	2	yes	—
272	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
273	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
274	C₂³	—	2	2	no	—
275	C₂³	C₁₉×#120	1	1	yes	characteristic
276	Q₈	—	4	2	no	—
277	Q₈	—	4	4	no	—
278	Q₈	—	4	4	no	—
279	Q₈	—	4	4	no	—
280	Q₈	—	8	4	no	—
281	Q₈	—	8	2	no	—
282	D₄	—	4	2	no	—
283	D₄	—	4	4	no	—
284	D₄	—	8	2	no	—
285	C₂×C₄	—	2	2	no	—
286	C₂×C₄	—	2	4	no	—
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	4	no	—
290	C₂×C₄	—	4	4	no	—
291	C₂×C₄	—	4	2	no	—
292	C₂×C₄	—	8	4	no	—
293	C₂×C₄	—	8	2	no	—
294	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
295	C₂×C₄	C₁₉×#120	1	2	yes	—
296	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
297	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
298	C₈	—	2	4	no	—
299	C₈	—	2	8	no	—
300	C₂²	—	2	1	no	—
301	C₂²	—	2	2	no	—
302	C₂²	—	4	2	no	—
303	C₂²	—	4	4	no	—
304	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
305	C₄	—	2	1	no	—
306	C₄	—	2	2	no	—
307	C₄	—	4	2	no	—
308	C₄	—	4	4	no	—
309	C₄	—	4	4	no	—
310	C₄	—	8	2	no	—
311	C₄	C₁₉×#453	1	2	yes	—
312	C₄	C₁₉×#456	1	4	yes	—
313	C₂	—	4	1	no	—
314	C₂	—	8	2	no	—
315	C₂	C₂×C₁₉×#453	1	1	yes	characteristic
316	C₂	C₂×C₁₉×#456	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#3550

C₂

yes

maximal, characteristic

C₁₉×#3165

C₂

yes

maximal, complemented

C₁₉×#3152

C₂

yes

maximal, characteristic

C₁₉×#1660

C₂

yes

maximal, complemented

C₁₉×#1526

C₂

yes

maximal, complemented

C₁₉×#1525

C₂

yes

maximal, characteristic

C₂×C₁₉×#137

—

C₁₉×#563

C₂²

yes

—

C₁₉×#559

—

Q₈²×C₁₉

—

C₁₉×#556

—

D₄×Q₈×C₁₉

—

C₁₉×#542

—

C₁₉×#536

—

C₁₉×#533

C₂²

yes

—

C₁₉×#532

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#501

C₂²

yes

—

C₁₉×#500

—

C₁₉×#498

—

C₁₉×#497

C₂²

yes

—

C₁₉×#494

—

C₁₉×#492

—

C₁₉×#428

—

C₄×M₁₆×C₁₉

C₂²

yes

—

C₄×M₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#330

C₂²

yes

—

C₁₉×#329

C₂²

yes

—

C₂×#41×C₁₉

D₄

yes

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₁₉×#137

—

C₂×Q₁₆×C₁₉

—

C₂×SD₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

D₄

yes

characteristic

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×C₄⋊Q₈

C₂³

yes

—

C₁₉×#127

D₄

yes

characteristic

C₁₉×#126

—

C₁₉×#125

C₂³

yes

—

C₁₉×#124

—

C₁₉×#124

—

C₁₉×#124

C₂³

yes

—

C₁₉×#123

—

C₁₉×#123

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₁₉×#121

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₁₉×#117

—

C₁₉×#117

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×#107

—

C₁₉×#106

—

C₁₉×#97

C₂³

yes

—

C₁₉×#97

C₂³

yes

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

#41×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×D₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

Q₁₆×C₁₉

—

SD₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

100

C₄⋊C₄×C₁₉

—

101

C₄⋊C₄×C₁₉

—

102

C₄⋊C₄×C₁₉

—

103

C₄⋊C₄×C₁₉

—

104

C₄⋊C₄×C₁₉

C₂×D₄

yes

—

105

C₄⋊C₄×C₁₉

C₂×D₄

yes

—

106

C₂²⋊C₄×C₁₉

—

107

C₂²⋊C₄×C₁₉

—

108

C₂²⋊C₄×C₁₉

—

109

C₂²⋊C₄×C₁₉

—

110

C₄²×C₁₉

—

111

C₄²×C₁₉

—

112

C₄²×C₁₉

C₂×D₄

yes

—

113

C₄²×C₁₉

C₂×D₄

yes

characteristic

114

C₄²×C₁₉

C₂⁴

yes

characteristic

115

#19078

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

116

C₂³×C₁₉

—

117

C₂³×C₁₉

#120

yes

characteristic

118

Q₈×C₁₉

—

119

Q₈×C₁₉

—

120

Q₈×C₁₉

—

121

Q₈×C₁₉

—

122

Q₈×C₁₉

—

123

Q₈×C₁₉

—

124

D₄×C₁₉

—

125

D₄×C₁₉

—

126

D₄×C₁₉

—

127

C₂×C₄×C₁₉

—

128

C₂×C₄×C₁₉

—

129

C₂×C₄×C₁₉

—

130

C₂×C₄×C₁₉

—

131

C₂×C₄×C₁₉

—

132

C₂×C₄×C₁₉

—

133

C₂×C₄×C₁₉

—

134

C₂×C₄×C₁₉

—

135

C₂×C₄×C₁₉

—

136

C₂×C₄×C₁₉

#120

yes

characteristic

137

C₂×C₄×C₁₉

#120

yes

—

138

C₂×C₄×C₁₉

C₂²×D₄

yes

—

139

C₂×C₄×C₁₉

C₂²×D₄

yes

characteristic

140

C₈×C₁₉

—

141

C₈×C₁₉

—

142

#3550

C₂×C₁₉

yes

characteristic

143

#3165

C₂×C₁₉

yes

complemented

144

#3152

C₂×C₁₉

yes

characteristic

145

#1660

C₂×C₁₉

yes

complemented

146

#1526

C₂×C₁₉

yes

complemented

147

#1525

C₂×C₁₉

yes

characteristic

148

C₂²×C₁₉

—

149

C₂²×C₁₉

—

150

C₂²×C₁₉

—

151

C₂²×C₁₉

—

152

C₂²×C₁₉

C₂×#120

yes

characteristic

153

C₄×C₁₉

—

154

C₄×C₁₉

—

155

C₄×C₁₉

—

156

C₄×C₁₉

—

157

C₄×C₁₉

—

158

C₄×C₁₉

—

159

C₄×C₁₉

#453

yes

—

160

C₄×C₁₉

#456

yes

—

161

C₂×#137

—

162

#563

C₂²×C₁₉

yes

—

163

#559

—

164

Q₈²

—

165

#556

—

166

D₄×Q₈

—

167

#542

—

168

#536

—

169

#533

C₂²×C₁₉

yes

—

170

#532

C₂²×C₁₉

yes

characteristic

171

C₂×C₄⋊Q₈

C₂²×C₁₉

yes

characteristic

172

#501

C₂²×C₁₉

yes

—

173

#500

—

174

#498

—

175

#497

C₂²×C₁₉

yes

—

176

#494

—

177

#492

—

178

#428

—

179

C₄×M₁₆

C₂²×C₁₉

yes

characteristic

180

C₄×M₁₆

C₂²×C₁₉

yes

—

181

#330

C₂²×C₁₉

yes

—

182

#329

C₂²×C₁₉

yes

—

183

C₂×C₁₉

—

184

C₂×C₁₉

—

185

C₂×C₁₉

C₂×#453

yes

characteristic

186

C₂×C₁₉

C₂×#456

yes

—

187

C₂×#41

D₄×C₁₉

yes

—

188

C₂²×Q₈

—

189

C₂²×Q₈

—

190

#137

—

191

C₂×Q₁₆

—

192

C₂×SD₁₆

—

193

C₂×M₁₆

—

194

C₂×M₁₆

—

195

C₄⋊Q₈

—

196

C₄⋊Q₈

—

197

C₄⋊Q₈

—

198

C₄⋊Q₈

—

199

C₄⋊Q₈

D₄×C₁₉

yes

characteristic

200

C₄⋊Q₈

D₄×C₁₉

yes

—

201

C₄⋊Q₈

D₄×C₁₉

yes

—

202

C₄⋊Q₈

C₂³×C₁₉

yes

—

203

#127

D₄×C₁₉

yes

characteristic

204

#126

—

205

#125

C₂³×C₁₉

yes

—

206

#124

—

207

#124

—

208

#124

C₂³×C₁₉

yes

—

209

#123

—

210

#123

—

211

C₂²⋊Q₈

—

212

C₂²⋊Q₈

—

213

C₂²⋊Q₈

—

214

C₂²⋊Q₈

—

215

#121

—

216

C₄×Q₈

—

217

C₄×Q₈

—

218

C₄×Q₈

—

219

C₄×D₄

—

220

C₄×D₄

—

221

#117

—

222

#117

D₄×C₁₉

yes

—

223

C₂×C₄⋊C₄

—

224

C₂×C₄²

C₂³×C₁₉

yes

characteristic

225

#107

—

226

#106

—

227

#97

C₂³×C₁₉

yes

—

228

#97

C₂³×C₁₉

yes

—

229

C₄×C₈

—

230

C₄×C₈

—

231

C₁₉

#19078

yes

characteristic, direct product factor, Sylow

232

#41

—

233

C₂×Q₈

—

234

C₂×Q₈

—

235

C₂×Q₈

—

236

C₂×Q₈

—

237

C₂×Q₈

—

238

C₂×Q₈

—

239

C₂×Q₈

—

240

C₂×Q₈

C₂×D₄×C₁₉

yes

—

241

C₂×D₄

—

242

C₂×D₄

—

243

C₂×D₄

C₂×D₄×C₁₉

yes

—

244

C₂²×C₄

—

245

C₂²×C₄

—

246

C₂²×C₄

—

247

C₂²×C₄

C₂×D₄×C₁₉

yes

—

248

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

249

Q₁₆

—

250

SD₁₆

—

251

M₁₆

—

252

M₁₆

—

253

C₂×C₈

—

254

C₂×C₈

—

255

C₄⋊C₄

—

256

C₄⋊C₄

—

257

C₄⋊C₄

—

258

C₄⋊C₄

—

259

C₄⋊C₄

—

260

C₄⋊C₄

—

261

C₄⋊C₄

—

262

C₄⋊C₄

—

263

C₄⋊C₄

C₂×D₄×C₁₉

yes

—

264

C₄⋊C₄

C₂×D₄×C₁₉

yes

—

265

C₂²⋊C₄

—

266

C₂²⋊C₄

—

267

C₂²⋊C₄

—

268

C₂²⋊C₄

—

269

C₄²

—

270

C₄²

—

271

C₄²

C₂×D₄×C₁₉

yes

—

272

C₄²

C₂×D₄×C₁₉

yes

characteristic

273

C₄²

C₂⁴×C₁₉

yes

characteristic

274

C₂³

—

275

C₂³

C₁₉×#120

yes

characteristic

276

Q₈

—

277

Q₈

—

278

Q₈

—

279

Q₈

—

280

Q₈

—

281

Q₈

—

282

D₄

—

283

D₄

—

284

D₄

—

285

C₂×C₄

—

286

C₂×C₄

—

287

C₂×C₄

—

288

C₂×C₄

—

289

C₂×C₄

—

290

C₂×C₄

—

291

C₂×C₄

—

292

C₂×C₄

—

293

C₂×C₄

—

294

C₂×C₄

C₁₉×#120

yes

characteristic

295

C₂×C₄

C₁₉×#120

yes

—

296

C₂×C₄

C₂²×D₄×C₁₉

yes

—

297

C₂×C₄

C₂²×D₄×C₁₉

yes

characteristic

298

C₈

—

299

C₈

—

300

C₂²

—

301

C₂²

—

302

C₂²

—

303

C₂²

—

304

C₂²

C₂×C₁₉×#120

yes

characteristic

305

C₄

—

306

C₄

—

307

C₄

—

308

C₄

—

309

C₄

—

310

C₄

—

311

C₄

C₁₉×#453

yes

—

312

C₄

C₁₉×#456

yes

—

313

C₂

—

314

C₂

—

315

C₂

C₂×C₁₉×#453

yes

characteristic

316

C₂

C₂×C₁₉×#456

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

C₂×#120

commutator, Frattini, cosocle

C₄²

C₂⁴×C₁₉

prime radical

C₁₉×#532

C₂²

LCS

G ▷ C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
2. C₁₉×#3165	C₂	semidirect
4. C₁₉×#1660	C₂	semidirect
5. C₁₉×#1526	C₂	semidirect
115. #19078	C₁₉	direct (N × H)
143. #3165	C₂×C₁₉	semidirect
145. #1660	C₂×C₁₉	semidirect
146. #1526	C₂×C₁₉	semidirect
231. C₁₉	#19078	direct (N × H)

H ≅ G/N

type

2. C₁₉×#3165

C₂

semidirect

4. C₁₉×#1660

C₂

semidirect

5. C₁₉×#1526

C₂

semidirect

115. #19078

C₁₉

direct (N × H)

143. #3165

C₂×C₁₉

semidirect

145. #1660

C₂×C₁₉

semidirect

146. #1526

C₂×C₁₉

semidirect

231. C₁₉

#19078

direct (N × H)

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

subgroup	index
C₁₉×#3550	2
C₁₉×#3165	2
C₁₉×#3152	2
C₁₉×#1660	2
C₁₉×#1526	2
C₁₉×#1525	2
#19078	19

subgroup

index

C₁₉×#3550

C₁₉×#3165

C₁₉×#3152

C₁₉×#1660

C₁₉×#1526

C₁₉×#1525

#19078

Subgroups — C₁₉×#19078 #18025037

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#19078 #18025037

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19078 #18025037