Subgroups — C₁₉×#32972 #18038931

Order 4864.

1210 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₉×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3079	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2567	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1859	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1857	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1806	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1801	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1793	C₂	1	2	yes	maximal
9	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₁₉×#520	—	2	2	no	—
12	C₁₉×#520	—	2	2	no	—
13	C₁₉×#520	C₂²	1	2	yes	—
14	C₁₉×#519	—	2	2	no	—
15	C₁₉×#519	C₂²	1	1	yes	characteristic
16	C₄×#41×C₁₉	—	2	2	no	—
17	C₄×#41×C₁₉	—	2	2	no	—
18	C₄×#41×C₁₉	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₁₉	—	2	2	no	—
20	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#477	—	2	2	no	—
22	C₁₉×#476	—	2	2	no	—
23	C₁₉×#475	—	2	2	no	—
24	C₁₉×#474	—	2	2	no	—
25	C₁₉×#428	C₂²	1	4	yes	—
26	C₁₉×#423	C₂²	1	2	yes	—
27	C₂×C₁₉×#104	C₂²	1	4	yes	—
28	C₁₉×#417	C₂²	1	4	yes	—
29	C₂×C₁₉×#101	C₂²	1	2	yes	—
30	C₁₉×#395	—	2	2	no	—
31	C₁₉×#391	C₂²	1	2	yes	—
32	C₁₉×#389	—	2	2	no	—
33	C₁₉×#384	C₂²	1	2	yes	—
34	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
35	C₁₉×#343	C₂²	1	2	yes	—
36	C₁₉×#339	C₂²	1	4	yes	—
37	C₁₉×2₋¹⁺⁴	—	2	4	no	—
38	C₁₉×2₋¹⁺⁴	—	2	2	no	—
39	C₁₉×2₋¹⁺⁴	Q₈	1	4	yes	complemented
40	C₂×#41×C₁₉	—	2	2	no	—
41	C₂×#41×C₁₉	—	2	2	no	—
42	C₂×#41×C₁₉	C₂³	1	2	yes	—
43	C₂²×Q₈×C₁₉	—	2	2	no	—
44	C₂²×Q₈×C₁₉	—	2	1	no	—
45	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
47	C₁₉×C₄⋊Q₈	—	2	2	no	—
48	C₁₉×C₄⋊Q₈	—	2	2	no	—
49	C₄×Q₈×C₁₉	—	2	2	no	—
50	C₄×Q₈×C₁₉	—	2	4	no	—
51	C₄×Q₈×C₁₉	—	2	2	no	—
52	C₄×Q₈×C₁₉	—	2	2	no	—
53	C₄×Q₈×C₁₉	—	2	2	no	—
54	C₄×Q₈×C₁₉	—	2	2	no	—
55	C₄×Q₈×C₁₉	—	2	2	no	—
56	C₄×Q₈×C₁₉	—	2	2	no	—
57	C₄×Q₈×C₁₉	D₄	1	2	yes	—
58	C₄×Q₈×C₁₉	D₄	1	2	yes	—
59	C₄×D₄×C₁₉	—	2	2	no	—
60	C₄×D₄×C₁₉	—	2	4	no	—
61	C₄×D₄×C₁₉	—	2	2	no	—
62	C₄×D₄×C₁₉	—	2	2	no	—
63	C₄×D₄×C₁₉	—	2	2	no	—
64	C₄×D₄×C₁₉	—	2	4	no	—
65	C₄×D₄×C₁₉	—	2	2	no	—
66	C₄×D₄×C₁₉	D₄	1	2	yes	—
67	C₄×D₄×C₁₉	D₄	1	2	yes	—
68	C₁₉×#117	—	2	4	no	—
69	C₁₉×#117	—	2	4	no	—
70	C₁₉×#117	—	2	2	no	—
71	C₁₉×#117	—	2	2	no	—
72	C₁₉×#117	—	2	2	no	—
73	C₁₉×#117	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
79	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₁₉	—	2	4	no	—
83	C₂×C₄²×C₁₉	—	2	2	no	—
84	C₂×C₄²×C₁₉	D₄	1	2	yes	—
85	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
86	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
87	C₁₉×#107	—	2	4	no	—
88	C₁₉×#106	—	2	4	no	—
89	C₁₉×C₄⋊C₈	—	2	2	no	—
90	C₁₉×C₄⋊C₈	—	2	2	no	—
91	C₁₉×#104	—	2	8	no	—
92	C₁₉×#103	—	2	4	no	—
93	C₁₉×#102	—	2	4	no	—
94	C₁₉×#101	—	2	4	no	—
95	C₁₉×#95	—	2	1	no	—
96	C₁₉×#95	—	2	4	no	—
97	#41×C₁₉	—	2	8	no	—
98	#41×C₁₉	—	2	8	no	—
99	#41×C₁₉	—	2	8	no	—
100	#41×C₁₉	—	2	8	no	—
101	#41×C₁₉	—	2	2	no	—
102	#41×C₁₉	—	2	2	no	—
103	#41×C₁₉	C₂×Q₈	1	4	yes	—
104	#41×C₁₉	#41	1	4	yes	—
105	C₂×Q₈×C₁₉	—	2	2	no	—
106	C₂×Q₈×C₁₉	—	2	8	no	—
107	C₂×Q₈×C₁₉	—	2	8	no	—
108	C₂×Q₈×C₁₉	—	2	2	no	—
109	C₂×Q₈×C₁₉	—	2	2	no	—
110	C₂×Q₈×C₁₉	—	4	2	no	—
111	C₂×Q₈×C₁₉	—	8	2	no	—
112	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
113	C₂×Q₈×C₁₉	C₂×Q₈	1	2	yes	—
114	C₂×Q₈×C₁₉	#41	1	2	yes	—
115	C₂×D₄×C₁₉	—	2	2	no	—
116	C₂×D₄×C₁₉	—	2	2	no	—
117	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₉	—	2	4	no	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	4	no	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	2	2	no	—
125	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
130	M₁₆×C₁₉	—	2	4	no	—
131	M₁₆×C₁₉	—	2	4	no	—
132	C₂×C₈×C₁₉	—	2	4	no	—
133	C₄⋊C₄×C₁₉	—	2	4	no	—
134	C₄⋊C₄×C₁₉	—	2	4	no	—
135	C₄⋊C₄×C₁₉	—	2	2	no	—
136	C₄⋊C₄×C₁₉	—	2	2	no	—
137	C₄⋊C₄×C₁₉	—	2	2	no	—
138	C₄⋊C₄×C₁₉	—	2	4	no	—
139	C₄⋊C₄×C₁₉	—	2	2	no	—
140	C₄⋊C₄×C₁₉	—	2	2	no	—
141	C₄⋊C₄×C₁₉	—	2	4	no	—
142	C₄⋊C₄×C₁₉	—	4	1	no	—
143	C₄⋊C₄×C₁₉	—	4	1	no	—
144	C₄⋊C₄×C₁₉	—	8	4	no	—
145	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
146	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
147	C₂²⋊C₄×C₁₉	—	2	4	no	—
148	C₂²⋊C₄×C₁₉	—	2	2	no	—
149	C₂²⋊C₄×C₁₉	—	2	2	no	—
150	C₂²⋊C₄×C₁₉	—	2	2	no	—
151	C₄²×C₁₉	—	2	4	no	—
152	C₄²×C₁₉	—	2	4	no	—
153	C₄²×C₁₉	—	2	2	no	—
154	C₄²×C₁₉	—	2	2	no	—
155	C₄²×C₁₉	—	2	2	no	—
156	C₄²×C₁₉	—	2	2	no	—
157	C₄²×C₁₉	—	2	2	no	—
158	C₄²×C₁₉	—	2	4	no	—
159	C₄²×C₁₉	C₂×D₄	1	2	yes	—
160	C₄²×C₁₉	C₂×D₄	1	2	yes	—
161	#32972	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
162	C₂³×C₁₉	—	2	2	no	—
163	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
164	Q₈×C₁₉	—	2	8	no	—
165	Q₈×C₁₉	—	2	4	no	—
166	Q₈×C₁₉	—	2	2	no	—
167	Q₈×C₁₉	—	2	4	no	—
168	Q₈×C₁₉	—	8	4	no	—
169	Q₈×C₁₉	C₂²⋊Q₈	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	2	no	—
174	D₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
175	C₂×C₄×C₁₉	—	2	16	no	—
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	2	4	no	—
180	C₂×C₄×C₁₉	—	2	4	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	2	4	no	—
183	C₂×C₄×C₁₉	—	2	2	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	2	2	no	—
186	C₂×C₄×C₁₉	—	4	1	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	4	no	—
190	C₂×C₄×C₁₉	—	4	2	no	—
191	C₂×C₄×C₁₉	—	4	4	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	8	2	no	—
194	C₂×C₄×C₁₉	—	8	4	no	—
195	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
196	C₂×C₄×C₁₉	#120	1	2	yes	—
197	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
198	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
199	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
200	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
201	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
202	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
203	C₈×C₁₉	—	4	4	no	—
204	C₄×2₋¹⁺⁴	C₂×C₁₉	1	1	yes	characteristic
205	#3079	C₂×C₁₉	1	2	yes	complemented
206	#2567	C₂×C₁₉	1	1	yes	characteristic, complemented
207	#1859	C₂×C₁₉	1	4	yes	complemented
208	#1857	C₂×C₁₉	1	2	yes	complemented
209	#1806	C₂×C₁₉	1	2	yes	complemented
210	#1801	C₂×C₁₉	1	1	yes	characteristic, complemented
211	#1793	C₂×C₁₉	1	2	yes	—
212	C₂²×C₁₉	—	2	1	no	—
213	C₂²×C₁₉	—	2	1	no	—
214	C₂²×C₁₉	—	2	4	no	—
215	C₂²×C₁₉	—	4	2	no	—
216	C₂²×C₁₉	—	4	2	no	—
217	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
218	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
219	C₂²×C₁₉	#525	1	1	yes	characteristic
220	C₄×C₁₉	—	2	4	no	—
221	C₄×C₁₉	—	2	4	no	—
222	C₄×C₁₉	—	2	1	no	—
223	C₄×C₁₉	—	2	2	no	—
224	C₄×C₁₉	—	4	4	no	—
225	C₄×C₁₉	—	4	2	no	—
226	C₄×C₁₉	—	4	2	no	—
227	C₄×C₁₉	—	4	2	no	—
228	C₄×C₁₉	—	8	2	no	—
229	C₄×C₁₉	#456	1	2	yes	—
230	C₄×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
231	C₄×C₁₉	#525	1	2	yes	—
232	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	1	yes	characteristic
233	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
234	#520	—	2	2	no	—
235	#520	—	2	2	no	—
236	#520	C₂²×C₁₉	1	2	yes	—
237	#519	—	2	2	no	—
238	#519	C₂²×C₁₉	1	1	yes	characteristic
239	C₄×#41	—	2	2	no	—
240	C₄×#41	—	2	2	no	—
241	C₄×#41	C₂²×C₁₉	1	2	yes	—
242	C₂×C₄×Q₈	—	2	2	no	—
243	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
244	#477	—	2	2	no	—
245	#476	—	2	2	no	—
246	#475	—	2	2	no	—
247	#474	—	2	2	no	—
248	#428	C₂²×C₁₉	1	4	yes	—
249	#423	C₂²×C₁₉	1	2	yes	—
250	C₂×#104	C₂²×C₁₉	1	4	yes	—
251	#417	C₂²×C₁₉	1	4	yes	—
252	C₂×#101	C₂²×C₁₉	1	2	yes	—
253	#395	—	2	2	no	—
254	#391	C₂²×C₁₉	1	2	yes	—
255	#389	—	2	2	no	—
256	#384	C₂²×C₁₉	1	2	yes	—
257	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
258	#343	C₂²×C₁₉	1	2	yes	—
259	#339	C₂²×C₁₉	1	4	yes	—
260	C₂×C₁₉	—	2	1	no	—
261	C₂×C₁₉	—	2	1	no	—
262	C₂×C₁₉	—	4	4	no	—
263	C₂×C₁₉	#2848	1	1	yes	characteristic
264	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
265	C₂×C₁₉	#3021	1	1	yes	characteristic
266	2₋¹⁺⁴	—	2	4	no	—
267	2₋¹⁺⁴	—	2	2	no	—
268	2₋¹⁺⁴	Q₈×C₁₉	1	4	yes	complemented
269	C₂×#41	—	2	2	no	—
270	C₂×#41	—	2	2	no	—
271	C₂×#41	C₂³×C₁₉	1	2	yes	—
272	C₂²×Q₈	—	2	2	no	—
273	C₂²×Q₈	—	2	1	no	—
274	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
275	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
276	C₄⋊Q₈	—	2	2	no	—
277	C₄⋊Q₈	—	2	2	no	—
278	C₄×Q₈	—	2	2	no	—
279	C₄×Q₈	—	2	4	no	—
280	C₄×Q₈	—	2	2	no	—
281	C₄×Q₈	—	2	2	no	—
282	C₄×Q₈	—	2	2	no	—
283	C₄×Q₈	—	2	2	no	—
284	C₄×Q₈	—	2	2	no	—
285	C₄×Q₈	—	2	2	no	—
286	C₄×Q₈	D₄×C₁₉	1	2	yes	—
287	C₄×Q₈	D₄×C₁₉	1	2	yes	—
288	C₄×D₄	—	2	2	no	—
289	C₄×D₄	—	2	4	no	—
290	C₄×D₄	—	2	2	no	—
291	C₄×D₄	—	2	2	no	—
292	C₄×D₄	—	2	2	no	—
293	C₄×D₄	—	2	4	no	—
294	C₄×D₄	—	2	2	no	—
295	C₄×D₄	D₄×C₁₉	1	2	yes	—
296	C₄×D₄	D₄×C₁₉	1	2	yes	—
297	#117	—	2	4	no	—
298	#117	—	2	4	no	—
299	#117	—	2	2	no	—
300	#117	—	2	2	no	—
301	#117	—	2	2	no	—
302	#117	C₂³×C₁₉	1	2	yes	—
303	C₂×C₄⋊C₄	—	2	4	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	4	no	—
308	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
309	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
310	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
311	C₂×C₄²	—	2	4	no	—
312	C₂×C₄²	—	2	2	no	—
313	C₂×C₄²	D₄×C₁₉	1	2	yes	—
314	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
315	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
316	#107	—	2	4	no	—
317	#106	—	2	4	no	—
318	C₄⋊C₈	—	2	2	no	—
319	C₄⋊C₈	—	2	2	no	—
320	#104	—	2	8	no	—
321	#103	—	2	4	no	—
322	#102	—	2	4	no	—
323	#101	—	2	4	no	—
324	#95	—	2	1	no	—
325	#95	—	2	4	no	—
326	C₁₉	#32972	1	1	yes	characteristic, direct product factor, Sylow
327	#41	—	2	8	no	—
328	#41	—	2	8	no	—
329	#41	—	2	8	no	—
330	#41	—	2	8	no	—
331	#41	—	2	2	no	—
332	#41	—	2	2	no	—
333	#41	C₂×Q₈×C₁₉	1	4	yes	—
334	#41	#41×C₁₉	1	4	yes	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	8	no	—
337	C₂×Q₈	—	2	8	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	4	2	no	—
341	C₂×Q₈	—	8	2	no	—
342	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
343	C₂×Q₈	C₂×Q₈×C₁₉	1	2	yes	—
344	C₂×Q₈	#41×C₁₉	1	2	yes	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
357	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
358	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
359	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
360	M₁₆	—	2	4	no	—
361	M₁₆	—	2	4	no	—
362	C₂×C₈	—	2	4	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	4	1	no	—
373	C₄⋊C₄	—	4	1	no	—
374	C₄⋊C₄	—	8	4	no	—
375	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
376	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
377	C₂²⋊C₄	—	2	4	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	—	2	2	no	—
381	C₄²	—	2	4	no	—
382	C₄²	—	2	4	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	2	4	no	—
389	C₄²	C₂×D₄×C₁₉	1	2	yes	—
390	C₄²	C₂×D₄×C₁₉	1	2	yes	—
391	C₂³	—	2	2	no	—
392	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
393	Q₈	—	2	8	no	—
394	Q₈	—	2	4	no	—
395	Q₈	—	2	2	no	—
396	Q₈	—	2	4	no	—
397	Q₈	—	8	4	no	—
398	Q₈	C₁₉×C₂²⋊Q₈	1	4	yes	—
399	D₄	—	2	8	no	—
400	D₄	—	2	4	no	—
401	D₄	—	2	4	no	—
402	D₄	—	2	2	no	—
403	D₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
404	C₂×C₄	—	2	16	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	8	2	no	—
423	C₂×C₄	—	8	4	no	—
424	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
425	C₂×C₄	C₁₉×#120	1	2	yes	—
426	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
427	C₂×C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
428	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
429	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
430	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
431	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
432	C₈	—	4	4	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	4	no	—
436	C₂²	—	4	2	no	—
437	C₂²	—	4	2	no	—
438	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
439	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
440	C₂²	C₁₉×#525	1	1	yes	characteristic
441	C₄	—	2	1	no	—
442	C₄	—	2	2	no	—
443	C₄	—	2	4	no	—
444	C₄	—	2	4	no	—
445	C₄	—	4	4	no	—
446	C₄	—	4	2	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	2	no	—
449	C₄	—	8	2	no	—
450	C₄	C₁₉×#456	1	2	yes	—
451	C₄	C₂×C₁₉×C₂²⋊Q₈	1	2	yes	—
452	C₄	C₁₉×#525	1	2	yes	—
453	C₂	—	2	1	no	—
454	C₂	—	2	1	no	—
455	C₂	—	4	4	no	—
456	C₂	C₁₉×#2848	1	1	yes	characteristic
457	C₂	C₂×C₁₉×#456	1	1	yes	characteristic
458	C₂	C₁₉×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×2₋¹⁺⁴	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3079	C₂	semidirect
3. C₁₉×#2567	C₂	semidirect
4. C₁₉×#1859	C₂	semidirect
5. C₁₉×#1857	C₂	semidirect
6. C₁₉×#1806	C₂	semidirect
7. C₁₉×#1801	C₂	semidirect
39. C₁₉×2₋¹⁺⁴	Q₈	semidirect
161. #32972	C₁₉	direct (N × H)
205. #3079	C₂×C₁₉	semidirect
206. #2567	C₂×C₁₉	semidirect
207. #1859	C₂×C₁₉	semidirect
208. #1857	C₂×C₁₉	semidirect
209. #1806	C₂×C₁₉	semidirect
210. #1801	C₂×C₁₉	semidirect
268. 2₋¹⁺⁴	Q₈×C₁₉	semidirect
326. C₁₉	#32972	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₉×2₋¹⁺⁴	2
C₁₉×#3079	2
C₁₉×#2567	2
C₁₉×#1859	2
C₁₉×#1857	2
C₁₉×#1806	2
C₁₉×#1801	2
C₁₉×#1793	2
#32972	19

Subgroups — C19×#32972 #18038931

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32972 #18038931