Subgroups — C₁₉×#32952 #18038911

Order 4864.

1266 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3573	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#473	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3059	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3022	C₂	1	2	yes	maximal
5	C₁₉×#1915	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1902	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1814	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1813	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#585	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#137	C₂²	1	4	yes	—
11	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
12	C₁₉×#568	—	2	4	no	—
13	C₁₉×#568	—	2	2	no	—
14	C₁₉×#568	C₂²	1	2	yes	—
15	C₁₉×#568	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#131	—	2	4	no	—
17	C₂×C₁₉×#131	—	2	2	no	—
18	C₂×C₁₉×#131	C₂²	1	2	yes	—
19	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
20	C₁₉×#536	C₂²	1	2	yes	—
21	C₁₉×#473	—	2	4	no	—
22	C₁₉×#473	—	2	4	no	—
23	C₁₉×#470	—	2	2	no	—
24	C₁₉×#467	—	2	2	no	—
25	C₁₉×#456	—	2	4	no	—
26	C₁₉×#455	—	2	4	no	—
27	C₂×C₁₉×#108	C₂²	1	2	yes	complemented
28	C₁₉×#427	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#421	C₂²	1	4	yes	—
30	C₁₉×#419	C₂²	1	2	yes	complemented
31	C₁₉×#413	C₂²	1	2	yes	—
32	C₂×C₁₉×#101	C₂²	1	4	yes	complemented
33	C₁₉×#344	C₂²	1	4	yes	complemented
34	C₁₉×#338	C₂²	1	2	yes	complemented
35	C₁₉×2₋¹⁺⁴	—	2	2	no	—
36	C₁₉×2₋¹⁺⁴	D₄	1	2	yes	—
37	C₁₉×H(5,𝔽₂)	—	2	2	no	—
38	C₁₉×H(5,𝔽₂)	—	2	2	no	—
39	C₁₉×H(5,𝔽₂)	D₄	1	2	yes	—
40	C₂×#41×C₁₉	—	2	4	no	—
41	C₂×#41×C₁₉	—	2	2	no	—
42	C₂×#41×C₁₉	C₂³	1	2	yes	—
43	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
44	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
45	C₁₉×#137	—	2	8	no	—
46	C₁₉×#137	—	2	8	no	—
47	C₂×Q₁₆×C₁₉	—	2	4	no	—
48	C₂×Q₁₆×C₁₉	—	2	1	no	—
49	C₂×Q₁₆×C₁₉	—	2	1	no	—
50	C₂×Q₁₆×C₁₉	—	2	2	no	—
51	C₂×Q₁₆×C₁₉	—	2	2	no	—
52	C₂×SD₁₆×C₁₉	—	2	4	no	—
53	C₁₉×#131	—	2	4	no	—
54	C₁₉×#131	—	2	8	no	—
55	C₁₉×#131	—	2	4	no	—
56	C₁₉×#131	—	2	4	no	—
57	C₁₉×#131	—	2	4	no	—
58	C₁₉×#131	—	2	2	no	—
59	C₁₉×#131	—	2	2	no	—
60	C₁₉×#131	—	2	4	no	—
61	C₁₉×#131	—	2	2	no	—
62	C₁₉×#131	—	2	2	no	—
63	C₁₉×#131	D₄	1	4	yes	—
64	C₁₉×#131	D₄	1	4	yes	—
65	C₂×M₁₆×C₁₉	—	2	8	no	—
66	C₂×M₁₆×C₁₉	—	2	4	no	—
67	C₂×M₁₆×C₁₉	—	2	2	no	—
68	C₂×M₁₆×C₁₉	—	2	4	no	—
69	C₂×M₁₆×C₁₉	—	2	2	no	—
70	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
71	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
72	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
73	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₉	—	2	4	no	—
75	C₂²×C₈×C₁₉	—	2	2	no	—
76	C₂²×C₈×C₁₉	D₄	1	2	yes	—
77	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
78	C₁₉×C₄⋊Q₈	—	2	2	no	—
79	C₁₉×#124	—	2	2	no	—
80	C₁₉×#123	—	2	4	no	—
81	C₁₉×C₂²⋊Q₈	—	2	4	no	—
82	C₁₉×#117	C₂³	1	2	yes	—
83	C₁₉×#108	—	2	2	no	—
84	C₁₉×#108	—	2	2	no	—
85	C₁₉×#107	—	2	1	no	—
86	C₁₉×#106	—	2	1	no	—
87	C₁₉×#104	—	2	8	no	—
88	C₁₉×#103	—	2	4	no	—
89	C₁₉×#101	—	2	2	no	—
90	C₁₉×#101	—	2	8	no	—
91	C₁₉×#100	—	2	2	no	—
92	#41×C₁₉	—	2	4	no	—
93	#41×C₁₉	—	2	8	no	—
94	#41×C₁₉	—	2	4	no	—
95	#41×C₁₉	—	2	4	no	—
96	#41×C₁₉	—	2	4	no	—
97	#41×C₁₉	—	2	4	no	—
98	#41×C₁₉	—	2	2	no	—
99	#41×C₁₉	—	2	2	no	—
100	#41×C₁₉	—	2	2	no	—
101	#41×C₁₉	—	2	2	no	—
102	#41×C₁₉	C₂×D₄	1	4	yes	—
103	#41×C₁₉	C₂×D₄	1	4	yes	—
104	C₂×Q₈×C₁₉	—	2	2	no	—
105	C₂×Q₈×C₁₉	—	2	4	no	—
106	C₂×Q₈×C₁₉	—	2	2	no	—
107	C₂×Q₈×C₁₉	—	2	2	no	—
108	C₂×Q₈×C₁₉	—	2	4	no	—
109	C₂×Q₈×C₁₉	—	2	4	no	—
110	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₂×Q₈×C₁₉	#41	1	2	yes	—
112	C₂×D₄×C₁₉	—	2	8	no	—
113	C₂×D₄×C₁₉	—	2	2	no	—
114	C₂×D₄×C₁₉	—	2	4	no	—
115	C₂×D₄×C₁₉	—	2	2	no	—
116	C₂×D₄×C₁₉	—	2	4	no	—
117	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₂×D₄×C₁₉	#41	1	2	yes	—
119	C₂×D₄×C₁₉	#41	1	2	yes	—
120	C₂²×C₄×C₁₉	—	2	4	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
125	Q₁₆×C₁₉	—	4	8	no	—
126	Q₁₆×C₁₉	—	4	1	no	—
127	Q₁₆×C₁₉	—	4	1	no	—
128	Q₁₆×C₁₉	—	4	2	no	—
129	SD₁₆×C₁₉	—	4	8	no	—
130	M₁₆×C₁₉	—	2	4	no	—
131	M₁₆×C₁₉	—	2	8	no	—
132	M₁₆×C₁₉	—	2	2	no	—
133	M₁₆×C₁₉	—	2	2	no	—
134	M₁₆×C₁₉	—	2	4	no	—
135	M₁₆×C₁₉	—	2	4	no	—
136	M₁₆×C₁₉	—	2	4	no	—
137	M₁₆×C₁₉	—	2	4	no	—
138	M₁₆×C₁₉	—	2	4	no	—
139	M₁₆×C₁₉	C₂×D₄	1	4	yes	—
140	C₂×C₈×C₁₉	—	2	4	no	—
141	C₂×C₈×C₁₉	—	2	8	no	—
142	C₂×C₈×C₁₉	—	2	2	no	—
143	C₂×C₈×C₁₉	—	2	4	no	—
144	C₂×C₈×C₁₉	—	2	2	no	—
145	C₂×C₈×C₁₉	—	2	4	no	—
146	C₂×C₈×C₁₉	—	2	2	no	—
147	C₂×C₈×C₁₉	—	2	4	no	—
148	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
149	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
150	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
152	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₄⋊C₄×C₁₉	—	2	2	no	—
154	C₄⋊C₄×C₁₉	—	4	4	no	—
155	C₂²⋊C₄×C₁₉	—	2	2	no	—
156	C₂²⋊C₄×C₁₉	—	4	4	no	—
157	C₄²×C₁₉	—	2	2	no	—
158	#32952	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
159	C₂³×C₁₉	—	2	4	no	—
160	C₂³×C₁₉	—	2	2	no	—
161	C₂³×C₁₉	#121	1	2	yes	—
162	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
163	Q₈×C₁₉	—	2	4	no	—
164	Q₈×C₁₉	—	2	2	no	—
165	Q₈×C₁₉	—	2	2	no	—
166	Q₈×C₁₉	—	4	2	no	—
167	Q₈×C₁₉	—	4	4	no	—
168	Q₈×C₁₉	—	4	2	no	—
169	Q₈×C₁₉	#121	1	4	yes	—
170	D₄×C₁₉	—	2	8	no	—
171	D₄×C₁₉	—	2	4	no	—
172	D₄×C₁₉	—	2	4	no	—
173	D₄×C₁₉	—	2	4	no	—
174	D₄×C₁₉	—	2	4	no	—
175	D₄×C₁₉	—	2	2	no	—
176	D₄×C₁₉	—	2	2	no	—
177	D₄×C₁₉	#121	1	4	yes	—
178	C₂×C₄×C₁₉	—	2	4	no	—
179	C₂×C₄×C₁₉	—	2	8	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	2	4	no	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	2	4	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	4	no	—
188	C₂×C₄×C₁₉	#121	1	2	yes	—
189	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
190	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
193	C₈×C₁₉	—	2	4	no	—
194	C₈×C₁₉	—	2	2	no	—
195	C₈×C₁₉	—	4	4	no	—
196	C₈×C₁₉	#120	1	1	yes	characteristic
197	C₈×C₁₉	#120	1	2	yes	—
198	C₈×C₁₉	#120	1	1	yes	characteristic
199	#3573	C₂×C₁₉	1	1	yes	characteristic
200	C₂×#473	C₂×C₁₉	1	2	yes	complemented
201	#3059	C₂×C₁₉	1	1	yes	characteristic, complemented
202	#3022	C₂×C₁₉	1	2	yes	—
203	#1915	C₂×C₁₉	1	2	yes	complemented
204	#1902	C₂×C₁₉	1	4	yes	complemented
205	#1814	C₂×C₁₉	1	2	yes	complemented
206	#1813	C₂×C₁₉	1	1	yes	characteristic, complemented
207	C₂²×C₁₉	—	2	2	no	—
208	C₂²×C₁₉	—	2	4	no	—
209	C₂²×C₁₉	—	4	1	no	—
210	C₂²×C₁₉	—	4	2	no	—
211	C₂²×C₁₉	—	8	2	no	—
212	C₂²×C₁₉	—	8	4	no	—
213	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
214	C₂²×C₁₉	#525	1	2	yes	—
215	C₄×C₁₉	—	2	4	no	—
216	C₄×C₁₉	—	2	2	no	—
217	C₄×C₁₉	—	8	2	no	—
218	C₄×C₁₉	—	8	2	no	—
219	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
220	C₄×C₁₉	C₂×#121	1	2	yes	—
221	C₄×C₁₉	#525	1	1	yes	characteristic
222	#585	C₂²×C₁₉	1	1	yes	characteristic
223	C₂×#137	C₂²×C₁₉	1	4	yes	—
224	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
225	#568	—	2	4	no	—
226	#568	—	2	2	no	—
227	#568	C₂²×C₁₉	1	2	yes	—
228	#568	C₂²×C₁₉	1	1	yes	characteristic
229	C₂×#131	—	2	4	no	—
230	C₂×#131	—	2	2	no	—
231	C₂×#131	C₂²×C₁₉	1	2	yes	—
232	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
233	#536	C₂²×C₁₉	1	2	yes	—
234	#473	—	2	4	no	—
235	#473	—	2	4	no	—
236	#470	—	2	2	no	—
237	#467	—	2	2	no	—
238	#456	—	2	4	no	—
239	#455	—	2	4	no	—
240	C₂×#108	C₂²×C₁₉	1	2	yes	complemented
241	#427	C₂²×C₁₉	1	1	yes	characteristic, complemented
242	#421	C₂²×C₁₉	1	4	yes	—
243	#419	C₂²×C₁₉	1	2	yes	complemented
244	#413	C₂²×C₁₉	1	2	yes	—
245	C₂×#101	C₂²×C₁₉	1	4	yes	complemented
246	#344	C₂²×C₁₉	1	4	yes	complemented
247	#338	C₂²×C₁₉	1	2	yes	complemented
248	C₂×C₁₉	—	2	1	no	—
249	C₂×C₁₉	—	2	2	no	—
250	C₂×C₁₉	—	4	2	no	—
251	C₂×C₁₉	—	4	4	no	—
252	C₂×C₁₉	#2847	1	1	yes	characteristic
253	2₋¹⁺⁴	—	2	2	no	—
254	2₋¹⁺⁴	D₄×C₁₉	1	2	yes	—
255	H(5,𝔽₂)	—	2	2	no	—
256	H(5,𝔽₂)	—	2	2	no	—
257	H(5,𝔽₂)	D₄×C₁₉	1	2	yes	—
258	C₂×#41	—	2	4	no	—
259	C₂×#41	—	2	2	no	—
260	C₂×#41	C₂³×C₁₉	1	2	yes	—
261	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
262	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
263	#137	—	2	8	no	—
264	#137	—	2	8	no	—
265	C₂×Q₁₆	—	2	4	no	—
266	C₂×Q₁₆	—	2	1	no	—
267	C₂×Q₁₆	—	2	1	no	—
268	C₂×Q₁₆	—	2	2	no	—
269	C₂×Q₁₆	—	2	2	no	—
270	C₂×SD₁₆	—	2	4	no	—
271	#131	—	2	4	no	—
272	#131	—	2	8	no	—
273	#131	—	2	4	no	—
274	#131	—	2	4	no	—
275	#131	—	2	4	no	—
276	#131	—	2	2	no	—
277	#131	—	2	2	no	—
278	#131	—	2	4	no	—
279	#131	—	2	2	no	—
280	#131	—	2	2	no	—
281	#131	D₄×C₁₉	1	4	yes	—
282	#131	D₄×C₁₉	1	4	yes	—
283	C₂×M₁₆	—	2	8	no	—
284	C₂×M₁₆	—	2	4	no	—
285	C₂×M₁₆	—	2	2	no	—
286	C₂×M₁₆	—	2	4	no	—
287	C₂×M₁₆	—	2	2	no	—
288	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
289	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
290	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
291	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
292	C₂²×C₈	—	2	4	no	—
293	C₂²×C₈	—	2	2	no	—
294	C₂²×C₈	D₄×C₁₉	1	2	yes	—
295	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
296	C₄⋊Q₈	—	2	2	no	—
297	#124	—	2	2	no	—
298	#123	—	2	4	no	—
299	C₂²⋊Q₈	—	2	4	no	—
300	#117	C₂³×C₁₉	1	2	yes	—
301	#108	—	2	2	no	—
302	#108	—	2	2	no	—
303	#107	—	2	1	no	—
304	#106	—	2	1	no	—
305	#104	—	2	8	no	—
306	#103	—	2	4	no	—
307	#101	—	2	2	no	—
308	#101	—	2	8	no	—
309	#100	—	2	2	no	—
310	C₁₉	#32952	1	1	yes	characteristic, direct product factor, Sylow
311	#41	—	2	4	no	—
312	#41	—	2	8	no	—
313	#41	—	2	4	no	—
314	#41	—	2	4	no	—
315	#41	—	2	4	no	—
316	#41	—	2	4	no	—
317	#41	—	2	2	no	—
318	#41	—	2	2	no	—
319	#41	—	2	2	no	—
320	#41	—	2	2	no	—
321	#41	C₂×D₄×C₁₉	1	4	yes	—
322	#41	C₂×D₄×C₁₉	1	4	yes	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	4	no	—
325	C₂×Q₈	—	2	4	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	4	no	—
329	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
330	C₂×Q₈	#41×C₁₉	1	2	yes	—
331	C₂×D₄	—	2	8	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	4	no	—
336	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
337	C₂×D₄	#41×C₁₉	1	2	yes	—
338	C₂×D₄	#41×C₁₉	1	2	yes	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
343	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
344	Q₁₆	—	4	8	no	—
345	Q₁₆	—	4	1	no	—
346	Q₁₆	—	4	1	no	—
347	Q₁₆	—	4	2	no	—
348	SD₁₆	—	4	8	no	—
349	M₁₆	—	2	4	no	—
350	M₁₆	—	2	8	no	—
351	M₁₆	—	2	2	no	—
352	M₁₆	—	2	2	no	—
353	M₁₆	—	2	4	no	—
354	M₁₆	—	2	4	no	—
355	M₁₆	—	2	4	no	—
356	M₁₆	—	2	4	no	—
357	M₁₆	—	2	4	no	—
358	M₁₆	C₂×D₄×C₁₉	1	4	yes	—
359	C₂×C₈	—	2	4	no	—
360	C₂×C₈	—	2	8	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	4	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	4	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	4	no	—
367	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
368	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
369	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
370	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
371	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	4	4	no	—
374	C₂²⋊C₄	—	2	2	no	—
375	C₂²⋊C₄	—	4	4	no	—
376	C₄²	—	2	2	no	—
377	C₂³	—	2	4	no	—
378	C₂³	—	2	2	no	—
379	C₂³	C₁₉×#121	1	2	yes	—
380	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
381	Q₈	—	2	4	no	—
382	Q₈	—	2	2	no	—
383	Q₈	—	2	2	no	—
384	Q₈	—	4	2	no	—
385	Q₈	—	4	4	no	—
386	Q₈	—	4	2	no	—
387	Q₈	C₁₉×#121	1	4	yes	—
388	D₄	—	2	8	no	—
389	D₄	—	2	4	no	—
390	D₄	—	2	4	no	—
391	D₄	—	2	4	no	—
392	D₄	—	2	4	no	—
393	D₄	—	2	2	no	—
394	D₄	—	2	2	no	—
395	D₄	C₁₉×#121	1	4	yes	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	8	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	C₁₉×#121	1	2	yes	—
407	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
408	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
409	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
410	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
411	C₈	—	2	4	no	—
412	C₈	—	2	2	no	—
413	C₈	—	4	4	no	—
414	C₈	C₁₉×#120	1	1	yes	characteristic
415	C₈	C₁₉×#120	1	2	yes	—
416	C₈	C₁₉×#120	1	1	yes	characteristic
417	C₂²	—	2	2	no	—
418	C₂²	—	2	4	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	8	2	no	—
422	C₂²	—	8	4	no	—
423	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
424	C₂²	C₁₉×#525	1	2	yes	—
425	C₄	—	2	4	no	—
426	C₄	—	2	2	no	—
427	C₄	—	8	2	no	—
428	C₄	—	8	2	no	—
429	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
430	C₄	C₂×C₁₉×#121	1	2	yes	—
431	C₄	C₁₉×#525	1	1	yes	characteristic
432	C₂	—	2	1	no	—
433	C₂	—	2	2	no	—
434	C₂	—	4	2	no	—
435	C₂	—	4	4	no	—
436	C₂	C₁₉×#2847	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#2847
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#585	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#473	C₂	semidirect
3. C₁₉×#3059	C₂	semidirect
5. C₁₉×#1915	C₂	semidirect
6. C₁₉×#1902	C₂	semidirect
7. C₁₉×#1814	C₂	semidirect
8. C₁₉×#1813	C₂	semidirect
11. C₂²×Q₁₆×C₁₉	C₂²	semidirect
27. C₂×C₁₉×#108	C₂²	semidirect
28. C₁₉×#427	C₂²	semidirect
30. C₁₉×#419	C₂²	semidirect
32. C₂×C₁₉×#101	C₂²	semidirect
33. C₁₉×#344	C₂²	semidirect
34. C₁₉×#338	C₂²	semidirect
158. #32952	C₁₉	direct (N × H)
200. C₂×#473	C₂×C₁₉	semidirect
201. #3059	C₂×C₁₉	semidirect
203. #1915	C₂×C₁₉	semidirect
204. #1902	C₂×C₁₉	semidirect
205. #1814	C₂×C₁₉	semidirect
206. #1813	C₂×C₁₉	semidirect
224. C₂²×Q₁₆	C₂²×C₁₉	semidirect
240. C₂×#108	C₂²×C₁₉	semidirect
241. #427	C₂²×C₁₉	semidirect
243. #419	C₂²×C₁₉	semidirect
245. C₂×#101	C₂²×C₁₉	semidirect
246. #344	C₂²×C₁₉	semidirect
247. #338	C₂²×C₁₉	semidirect
310. C₁₉	#32952	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3573	2
C₂×C₁₉×#473	2
C₁₉×#3059	2
C₁₉×#3022	2
C₁₉×#1915	2
C₁₉×#1902	2
C₁₉×#1814	2
C₁₉×#1813	2
#32952	19

Subgroups — C19×#32952 #18038911

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32952 #18038911