Subgroups — C₁₉×#32990 #18038949

Order 4864.

1574 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#518	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3094	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2433	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1887	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1856	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1826	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1783	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×#127	C₂²	1	2	yes	—
10	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#120	—	2	2	no	—
12	C₁₉×#518	—	2	2	no	—
13	C₁₉×#518	—	2	4	no	—
14	C₁₉×#518	C₂²	1	4	yes	—
15	C₂×C₄×D₄×C₁₉	—	2	2	no	—
16	C₂×C₄×D₄×C₁₉	—	2	2	no	—
17	C₂×C₁₉×#117	C₂²	1	2	yes	—
18	C₂²×C₂²⋊C₄×C₁₉	—	2	2	no	—
19	C₁₉×#482	—	2	4	no	—
20	C₁₉×#481	—	2	2	no	—
21	C₁₉×#480	—	2	2	no	—
22	C₁₉×#428	C₂²	1	4	yes	complemented
23	C₁₉×#418	C₂²	1	4	yes	complemented
24	C₂×C₁₉×#100	C₂²	1	4	yes	—
25	C₁₉×#407	C₂²	1	2	yes	—
26	C₁₉×#392	—	2	2	no	—
27	C₁₉×#390	C₂²	1	2	yes	—
28	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₁₉×#339	C₂²	1	8	yes	complemented
30	C₂⁵×C₁₉	D₄	1	2	yes	—
31	C₂²×D₄×C₁₉	—	2	8	no	—
32	C₂²×D₄×C₁₉	—	2	1	no	—
33	C₂²×D₄×C₁₉	—	2	4	no	—
34	C₂²×D₄×C₁₉	—	2	2	no	—
35	C₂²×D₄×C₁₉	—	2	2	no	—
36	C₂²×D₄×C₁₉	D₄	1	2	yes	—
37	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
38	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₉	—	2	2	no	—
40	C₂³×C₄×C₁₉	—	2	2	no	—
41	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
42	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
43	C₁₉×#127	—	2	8	no	—
44	C₁₉×#121	—	2	2	no	—
45	C₁₉×#121	—	2	2	no	—
46	C₁₉×#120	—	4	8	no	—
47	C₄×D₄×C₁₉	—	2	8	no	—
48	C₄×D₄×C₁₉	—	2	8	no	—
49	C₄×D₄×C₁₉	—	2	8	no	—
50	C₄×D₄×C₁₉	—	2	8	no	—
51	C₁₉×#117	—	2	2	no	—
52	C₁₉×#117	—	2	2	no	—
53	C₁₉×#117	D₄	1	4	yes	complemented
54	C₁₉×#117	C₂³	1	4	yes	—
55	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	complemented
56	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	complemented
57	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
60	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₄²×C₁₉	—	2	2	no	—
66	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
67	C₁₉×#107	—	2	4	no	—
68	C₁₉×#106	—	2	4	no	—
69	C₁₉×#102	—	2	4	no	—
70	C₁₉×#102	—	2	4	no	—
71	C₁₉×#100	—	2	8	no	—
72	C₁₉×C₂²⋊C₈	—	2	2	no	—
73	C₁₉×C₂²⋊C₈	—	2	2	no	—
74	C₁₉×#95	—	2	1	no	—
75	C₂⁴×C₁₉	—	2	2	no	—
76	C₂⁴×C₁₉	—	2	2	no	—
77	C₂⁴×C₁₉	—	2	8	no	—
78	C₂⁴×C₁₉	—	2	1	no	—
79	C₂⁴×C₁₉	—	4	4	no	—
80	C₂⁴×C₁₉	—	8	2	no	—
81	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
83	C₂×D₄×C₁₉	—	2	16	no	—
84	C₂×D₄×C₁₉	—	2	16	no	—
85	C₂×D₄×C₁₉	—	2	8	no	—
86	C₂×D₄×C₁₉	—	2	4	no	—
87	C₂×D₄×C₁₉	—	2	4	no	—
88	C₂×D₄×C₁₉	—	2	2	no	—
89	C₂×D₄×C₁₉	—	2	4	no	—
90	C₂×D₄×C₁₉	—	2	4	no	—
91	C₂×D₄×C₁₉	—	4	8	no	—
92	C₂×D₄×C₁₉	—	4	4	no	—
93	C₂×D₄×C₁₉	—	4	1	no	—
94	C₂×D₄×C₁₉	—	4	1	no	—
95	C₂×D₄×C₁₉	—	4	8	no	—
96	C₂×D₄×C₁₉	—	8	4	no	—
97	C₂×D₄×C₁₉	#41	1	8	yes	—
98	C₂²×C₄×C₁₉	—	2	4	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	8	no	—
103	C₂²×C₄×C₁₉	—	2	8	no	—
104	C₂²×C₄×C₁₉	—	2	1	no	—
105	C₂²×C₄×C₁₉	—	8	4	no	—
106	C₂²×C₄×C₁₉	—	8	4	no	—
107	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
111	M₁₆×C₁₉	—	2	8	no	—
112	C₂×C₈×C₁₉	—	2	4	no	—
113	C₄⋊C₄×C₁₉	—	2	2	no	—
114	C₄⋊C₄×C₁₉	—	2	2	no	—
115	C₄⋊C₄×C₁₉	—	2	2	no	—
116	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
117	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
118	C₂²⋊C₄×C₁₉	—	2	16	no	—
119	C₂²⋊C₄×C₁₉	—	2	4	no	—
120	C₂²⋊C₄×C₁₉	—	2	4	no	—
121	C₂²⋊C₄×C₁₉	—	2	4	no	—
122	C₂²⋊C₄×C₁₉	—	4	8	no	—
123	C₂²⋊C₄×C₁₉	—	4	2	no	—
124	C₄²×C₁₉	—	2	4	no	—
125	C₄²×C₁₉	—	2	4	no	—
126	C₄²×C₁₉	—	2	4	no	—
127	#32990	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
128	C₂³×C₁₉	—	2	8	no	—
129	C₂³×C₁₉	—	2	8	no	—
130	C₂³×C₁₉	—	2	4	no	—
131	C₂³×C₁₉	—	2	2	no	—
132	C₂³×C₁₉	—	2	2	no	—
133	C₂³×C₁₉	—	2	4	no	—
134	C₂³×C₁₉	—	4	1	no	—
135	C₂³×C₁₉	—	4	4	no	—
136	C₂³×C₁₉	—	4	4	no	—
137	C₂³×C₁₉	—	4	4	no	—
138	C₂³×C₁₉	—	4	2	no	—
139	C₂³×C₁₉	—	4	2	no	—
140	C₂³×C₁₉	—	4	4	no	—
141	C₂³×C₁₉	—	4	1	no	—
142	C₂³×C₁₉	—	4	2	no	—
143	C₂³×C₁₉	—	8	2	no	—
144	C₂³×C₁₉	—	8	2	no	—
145	C₂³×C₁₉	—	8	16	no	—
146	C₂³×C₁₉	#120	1	1	yes	characteristic
147	C₂³×C₁₉	#120	1	1	yes	characteristic
148	C₂³×C₁₉	#123	1	8	yes	—
149	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
150	D₄×C₁₉	—	2	16	no	—
151	D₄×C₁₉	—	2	16	no	—
152	D₄×C₁₉	—	4	4	no	—
153	D₄×C₁₉	—	8	16	no	—
154	D₄×C₁₉	—	8	2	no	—
155	D₄×C₁₉	—	8	2	no	—
156	C₂×C₄×C₁₉	—	2	2	no	—
157	C₂×C₄×C₁₉	—	2	4	no	—
158	C₂×C₄×C₁₉	—	2	4	no	—
159	C₂×C₄×C₁₉	—	2	4	no	—
160	C₂×C₄×C₁₉	—	2	4	no	—
161	C₂×C₄×C₁₉	—	2	4	no	—
162	C₂×C₄×C₁₉	—	4	4	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	4	4	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	8	8	no	—
169	C₂×C₄×C₁₉	—	8	8	no	—
170	C₂×C₄×C₁₉	#120	1	2	yes	—
171	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
172	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
173	C₈×C₁₉	—	4	4	no	—
174	C₂×#518	C₂×C₁₉	1	1	yes	characteristic, complemented
175	#3094	C₂×C₁₉	1	2	yes	complemented
176	#2433	C₂×C₁₉	1	1	yes	characteristic
177	#1887	C₂×C₁₉	1	4	yes	complemented
178	#1856	C₂×C₁₉	1	4	yes	complemented
179	#1826	C₂×C₁₉	1	2	yes	complemented
180	#1783	C₂×C₁₉	1	1	yes	characteristic, complemented
181	C₂²×C₁₉	—	2	1	no	—
182	C₂²×C₁₉	—	2	1	no	—
183	C₂²×C₁₉	—	2	1	no	—
184	C₂²×C₁₉	—	2	1	no	—
185	C₂²×C₁₉	—	2	1	no	—
186	C₂²×C₁₉	—	2	8	no	—
187	C₂²×C₁₉	—	2	1	no	—
188	C₂²×C₁₉	—	2	1	no	—
189	C₂²×C₁₉	—	4	4	no	—
190	C₂²×C₁₉	—	4	8	no	—
191	C₂²×C₁₉	—	4	16	no	—
192	C₂²×C₁₉	—	4	4	no	—
193	C₂²×C₁₉	—	4	4	no	—
194	C₂²×C₁₉	—	8	4	no	—
195	C₂²×C₁₉	—	8	4	no	—
196	C₂²×C₁₉	—	8	8	no	—
197	C₂²×C₁₉	—	8	1	no	—
198	C₂²×C₁₉	—	8	1	no	—
199	C₂²×C₁₉	—	8	1	no	—
200	C₂²×C₁₉	#453	1	2	yes	—
201	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
202	C₂²×C₁₉	C₂×#123	1	2	yes	—
203	C₄×C₁₉	—	2	2	no	—
204	C₄×C₁₉	—	4	4	no	—
205	C₄×C₁₉	—	4	4	no	—
206	C₄×C₁₉	—	4	4	no	—
207	C₄×C₁₉	—	8	1	no	—
208	C₄×C₁₉	#525	1	4	yes	—
209	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
210	C₂×#127	C₂²×C₁₉	1	2	yes	—
211	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
212	C₂×#120	—	2	2	no	—
213	#518	—	2	2	no	—
214	#518	—	2	4	no	—
215	#518	C₂²×C₁₉	1	4	yes	—
216	C₂×C₄×D₄	—	2	2	no	—
217	C₂×C₄×D₄	—	2	2	no	—
218	C₂×#117	C₂²×C₁₉	1	2	yes	—
219	C₂²×C₂²⋊C₄	—	2	2	no	—
220	#482	—	2	4	no	—
221	#481	—	2	2	no	—
222	#480	—	2	2	no	—
223	#428	C₂²×C₁₉	1	4	yes	complemented
224	#418	C₂²×C₁₉	1	4	yes	complemented
225	C₂×#100	C₂²×C₁₉	1	4	yes	—
226	#407	C₂²×C₁₉	1	2	yes	—
227	#392	—	2	2	no	—
228	#390	C₂²×C₁₉	1	2	yes	—
229	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
230	#339	C₂²×C₁₉	1	8	yes	complemented
231	C₂×C₁₉	—	2	2	no	—
232	C₂×C₁₉	—	2	2	no	—
233	C₂×C₁₉	—	4	1	no	—
234	C₂×C₁₉	—	4	8	no	—
235	C₂×C₁₉	—	16	1	no	—
236	C₂×C₁₉	#2849	1	1	yes	characteristic
237	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
238	C₂×C₁₉	#3019	1	1	yes	characteristic
239	C₂⁵	D₄×C₁₉	1	2	yes	—
240	C₂²×D₄	—	2	8	no	—
241	C₂²×D₄	—	2	1	no	—
242	C₂²×D₄	—	2	4	no	—
243	C₂²×D₄	—	2	2	no	—
244	C₂²×D₄	—	2	2	no	—
245	C₂²×D₄	D₄×C₁₉	1	2	yes	—
246	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
247	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
248	C₂³×C₄	—	2	2	no	—
249	C₂³×C₄	—	2	2	no	—
250	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
251	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
252	#127	—	2	8	no	—
253	#121	—	2	2	no	—
254	#121	—	2	2	no	—
255	#120	—	4	8	no	—
256	C₄×D₄	—	2	8	no	—
257	C₄×D₄	—	2	8	no	—
258	C₄×D₄	—	2	8	no	—
259	C₄×D₄	—	2	8	no	—
260	#117	—	2	2	no	—
261	#117	—	2	2	no	—
262	#117	D₄×C₁₉	1	4	yes	complemented
263	#117	C₂³×C₁₉	1	4	yes	—
264	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	complemented
265	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	complemented
266	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
267	C₂×C₂²⋊C₄	—	2	4	no	—
268	C₂×C₂²⋊C₄	—	2	8	no	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₂²⋊C₄	—	2	8	no	—
271	C₂×C₂²⋊C₄	—	2	1	no	—
272	C₂×C₂²⋊C₄	—	2	4	no	—
273	C₂×C₂²⋊C₄	—	2	1	no	—
274	C₂×C₄²	—	2	2	no	—
275	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
276	#107	—	2	4	no	—
277	#106	—	2	4	no	—
278	#102	—	2	4	no	—
279	#102	—	2	4	no	—
280	#100	—	2	8	no	—
281	C₂²⋊C₈	—	2	2	no	—
282	C₂²⋊C₈	—	2	2	no	—
283	#95	—	2	1	no	—
284	C₁₉	#32990	1	1	yes	characteristic, direct product factor, Sylow
285	C₂⁴	—	2	2	no	—
286	C₂⁴	—	2	2	no	—
287	C₂⁴	—	2	8	no	—
288	C₂⁴	—	2	1	no	—
289	C₂⁴	—	4	4	no	—
290	C₂⁴	—	8	2	no	—
291	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
292	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
293	C₂×D₄	—	2	16	no	—
294	C₂×D₄	—	2	16	no	—
295	C₂×D₄	—	2	8	no	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	4	no	—
300	C₂×D₄	—	2	4	no	—
301	C₂×D₄	—	4	8	no	—
302	C₂×D₄	—	4	4	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	4	8	no	—
306	C₂×D₄	—	8	4	no	—
307	C₂×D₄	#41×C₁₉	1	8	yes	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	8	no	—
313	C₂²×C₄	—	2	8	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	8	4	no	—
316	C₂²×C₄	—	8	4	no	—
317	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
319	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
320	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
321	M₁₆	—	2	8	no	—
322	C₂×C₈	—	2	4	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
327	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
328	C₂²⋊C₄	—	2	16	no	—
329	C₂²⋊C₄	—	2	4	no	—
330	C₂²⋊C₄	—	2	4	no	—
331	C₂²⋊C₄	—	2	4	no	—
332	C₂²⋊C₄	—	4	8	no	—
333	C₂²⋊C₄	—	4	2	no	—
334	C₄²	—	2	4	no	—
335	C₄²	—	2	4	no	—
336	C₄²	—	2	4	no	—
337	C₂³	—	2	8	no	—
338	C₂³	—	2	8	no	—
339	C₂³	—	2	2	no	—
340	C₂³	—	2	4	no	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	4	no	—
343	C₂³	—	4	1	no	—
344	C₂³	—	4	4	no	—
345	C₂³	—	4	4	no	—
346	C₂³	—	4	4	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	4	no	—
350	C₂³	—	4	1	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	8	2	no	—
353	C₂³	—	8	2	no	—
354	C₂³	—	8	16	no	—
355	C₂³	C₁₉×#120	1	1	yes	characteristic
356	C₂³	C₁₉×#120	1	1	yes	characteristic
357	C₂³	C₁₉×#123	1	8	yes	—
358	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
359	D₄	—	2	16	no	—
360	D₄	—	2	16	no	—
361	D₄	—	4	4	no	—
362	D₄	—	8	16	no	—
363	D₄	—	8	2	no	—
364	D₄	—	8	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	8	8	no	—
378	C₂×C₄	—	8	8	no	—
379	C₂×C₄	C₁₉×#120	1	2	yes	—
380	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
381	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
382	C₈	—	4	4	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	8	no	—
391	C₂²	—	4	4	no	—
392	C₂²	—	4	8	no	—
393	C₂²	—	4	16	no	—
394	C₂²	—	4	4	no	—
395	C₂²	—	4	4	no	—
396	C₂²	—	8	4	no	—
397	C₂²	—	8	4	no	—
398	C₂²	—	8	8	no	—
399	C₂²	—	8	1	no	—
400	C₂²	—	8	1	no	—
401	C₂²	—	8	1	no	—
402	C₂²	C₁₉×#453	1	2	yes	—
403	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
404	C₂²	C₂×C₁₉×#123	1	2	yes	—
405	C₄	—	2	2	no	—
406	C₄	—	4	4	no	—
407	C₄	—	4	4	no	—
408	C₄	—	4	4	no	—
409	C₄	—	8	1	no	—
410	C₄	C₁₉×#525	1	4	yes	—
411	C₂	—	2	2	no	—
412	C₂	—	2	2	no	—
413	C₂	—	4	1	no	—
414	C₂	—	4	8	no	—
415	C₂	—	16	1	no	—
416	C₂	C₁₉×#2849	1	1	yes	characteristic
417	C₂	C₂×C₁₉×#453	1	1	yes	characteristic
418	C₂	C₁₉×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#2433	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₁₉×#518	C₂	semidirect
2. C₁₉×#3094	C₂	semidirect
4. C₁₉×#1887	C₂	semidirect
5. C₁₉×#1856	C₂	semidirect
6. C₁₉×#1826	C₂	semidirect
7. C₁₉×#1783	C₂	semidirect
22. C₁₉×#428	C₂²	semidirect
23. C₁₉×#418	C₂²	semidirect
29. C₁₉×#339	C₂²	semidirect
53. C₁₉×#117	D₄	semidirect
55. C₂×C₄⋊C₄×C₁₉	D₄	semidirect
56. C₂×C₄⋊C₄×C₁₉	D₄	semidirect
127. #32990	C₁₉	direct (N × H)
174. C₂×#518	C₂×C₁₉	semidirect
175. #3094	C₂×C₁₉	semidirect
177. #1887	C₂×C₁₉	semidirect
178. #1856	C₂×C₁₉	semidirect
179. #1826	C₂×C₁₉	semidirect
180. #1783	C₂×C₁₉	semidirect
223. #428	C₂²×C₁₉	semidirect
224. #418	C₂²×C₁₉	semidirect
230. #339	C₂²×C₁₉	semidirect
262. #117	D₄×C₁₉	semidirect
264. C₂×C₄⋊C₄	D₄×C₁₉	semidirect
265. C₂×C₄⋊C₄	D₄×C₁₉	semidirect
284. C₁₉	#32990	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#518	2
C₁₉×#3094	2
C₁₉×#2433	2
C₁₉×#1887	2
C₁₉×#1856	2
C₁₉×#1826	2
C₁₉×#1783	2
#32990	19

Subgroups — C19×#32990 #18038949

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32990 #18038949