Subgroups — #18074376

Order 4864.

972 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	#14563619	C₂	1	1	yes	maximal, characteristic, complemented
2	#14562284	C₂	1	2	yes	maximal, complemented
3	#14562034	C₂	1	2	yes	maximal, complemented
4	#14561949	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3449	C₂	1	1	yes	maximal, characteristic
6	#11926597	C₂²	1	2	yes	complemented
7	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
8	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
9	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
10	#11926299	—	2	1	no	—
11	#11926290	—	2	2	no	—
12	#11926288	—	2	2	no	—
13	D₄⋊(C₁₉⋊C₈)	—	2	4	no	—
14	#11926270	—	2	1	no	—
15	#11926268	—	2	1	no	—
16	C₂²×#41×C₁₉	—	2	1	no	—
17	C₁₉×#537	—	2	1	no	—
18	C₁₉×#537	C₄	1	2	yes	—
19	C₁₉×#536	—	2	2	no	—
20	C₁₉×#535	—	2	2	no	—
21	C₁₉×#534	—	2	1	no	—
22	C₁₉×#534	C₄	1	2	yes	—
23	C₁₉×#532	—	2	1	no	—
24	C₁₉×#532	C₂²	1	2	yes	—
25	C₁₉×#525	—	2	4	no	—
26	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
27	C₂×#41×C₁₉	—	2	2	no	—
28	C₂×#41×C₁₉	—	2	2	no	—
29	C₂×#41×C₁₉	—	2	2	no	—
30	C₂×#41×C₁₉	—	2	2	no	—
31	C₂×#41×C₁₉	—	4	2	no	—
32	C₂×#41×C₁₉	—	4	2	no	—
33	C₂×#41×C₁₉	—	4	2	no	—
34	C₂×#41×C₁₉	—	4	2	no	—
35	C₂²×Q₈×C₁₉	—	2	1	no	—
36	C₂²×D₄×C₁₉	—	2	1	no	—
37	C₂²×D₄×C₁₉	—	2	2	no	—
38	C₂³×C₄×C₁₉	—	2	2	no	—
39	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
40	C₁₉×C₄⋊Q₈	—	2	1	no	—
41	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
42	C₁₉×#127	—	2	1	no	—
43	C₁₉×#127	D₄	1	2	yes	—
44	C₁₉×#124	—	2	2	no	—
45	C₁₉×#124	—	2	2	no	—
46	C₁₉×#123	—	2	4	no	—
47	C₁₉×#123	—	2	4	no	—
48	C₁₉×C₂²⋊Q₈	—	2	4	no	—
49	C₁₉×C₂²⋊Q₈	—	2	4	no	—
50	C₁₉×#121	—	2	4	no	—
51	C₁₉×#121	—	2	4	no	—
52	C₁₉×#121	—	2	2	no	—
53	C₁₉×#121	—	2	2	no	—
54	C₁₉×#121	—	2	2	no	—
55	C₁₉×#121	C₂×C₄	1	4	yes	—
56	C₁₉×#120	—	2	4	no	—
57	C₁₉×#120	—	2	4	no	—
58	C₄×D₄×C₁₉	—	2	2	no	—
59	C₄×D₄×C₁₉	—	2	2	no	—
60	C₄×D₄×C₁₉	—	2	2	no	—
61	C₄×D₄×C₁₉	D₄	1	4	yes	—
62	C₁₉×#117	—	2	2	no	—
63	C₁₉×#117	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
70	C₂²×C₁₉⋊C₈	—	2	1	no	—
71	C₂²×C₁₉⋊C₈	—	2	1	no	—
72	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
73	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
74	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
75	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
76	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
77	C₄×C₁₉⋊C₈	—	2	2	no	—
78	C₂⁴×C₁₉	—	2	2	no	—
79	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
80	#41×C₁₉	—	4	4	no	—
81	#41×C₁₉	—	4	4	no	—
82	#41×C₁₉	—	4	4	no	—
83	#41×C₁₉	—	4	4	no	—
84	#41×C₁₉	—	4	4	no	—
85	#41×C₁₉	—	4	4	no	—
86	#41×C₁₉	—	4	2	no	—
87	#41×C₁₉	—	4	2	no	—
88	#41×C₁₉	—	4	2	no	—
89	#41×C₁₉	—	4	2	no	—
90	C₂×Q₈×C₁₉	—	2	2	no	—
91	C₂×Q₈×C₁₉	—	2	2	no	—
92	C₂×Q₈×C₁₉	—	4	2	no	—
93	C₂×Q₈×C₁₉	—	4	2	no	—
94	C₂×D₄×C₁₉	—	2	4	no	—
95	C₂×D₄×C₁₉	—	2	2	no	—
96	C₂×D₄×C₁₉	—	2	4	no	—
97	C₂×D₄×C₁₉	—	2	2	no	—
98	C₂×D₄×C₁₉	—	2	2	no	—
99	C₂×D₄×C₁₉	—	2	2	no	—
100	C₂×D₄×C₁₉	—	2	2	no	—
101	C₂×D₄×C₁₉	—	4	2	no	—
102	C₂×D₄×C₁₉	—	4	2	no	—
103	C₂×D₄×C₁₉	—	4	4	no	—
104	C₂×D₄×C₁₉	—	4	4	no	—
105	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
106	C₂²×C₄×C₁₉	—	2	1	no	—
107	C₂²×C₄×C₁₉	—	2	1	no	—
108	C₂²×C₄×C₁₉	—	2	1	no	—
109	C₂²×C₄×C₁₉	—	2	1	no	—
110	C₂²×C₄×C₁₉	—	2	4	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	4	no	—
113	C₂²×C₄×C₁₉	—	4	4	no	—
114	C₂²×C₄×C₁₉	—	4	4	no	—
115	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	D₈	1	2	yes	—
119	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
120	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₄⋊C₄×C₁₉	—	2	2	no	—
124	C₄⋊C₄×C₁₉	—	2	2	no	—
125	C₄⋊C₄×C₁₉	—	2	2	no	—
126	C₄⋊C₄×C₁₉	—	2	2	no	—
127	C₄⋊C₄×C₁₉	—	2	2	no	—
128	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
129	C₂²⋊C₄×C₁₉	—	2	4	no	—
130	C₂²⋊C₄×C₁₉	—	2	4	no	—
131	C₂²⋊C₄×C₁₉	—	2	2	no	—
132	C₂²⋊C₄×C₁₉	—	2	4	no	—
133	C₂²⋊C₄×C₁₉	—	2	2	no	—
134	C₂²⋊C₄×C₁₉	—	2	4	no	—
135	C₄²×C₁₉	—	2	1	no	—
136	C₄²×C₁₉	—	2	1	no	—
137	C₄²×C₁₉	C₂×D₄	1	2	yes	—
138	C₄²×C₁₉	C₂×D₄	1	2	yes	—
139	C₂×C₁₉⋊C₈	—	4	2	no	—
140	C₂×C₁₉⋊C₈	—	4	1	no	—
141	C₂×C₁₉⋊C₈	—	4	1	no	—
142	C₂×C₁₉⋊C₈	—	4	1	no	—
143	C₂×C₁₉⋊C₈	—	4	1	no	—
144	C₂×C₁₉⋊C₈	—	4	1	no	—
145	C₂×C₁₉⋊C₈	—	4	1	no	—
146	#8409	—	19	1	no	maximal, Sylow
147	C₂³×C₁₉	—	2	1	no	—
148	C₂³×C₁₉	—	2	1	no	—
149	C₂³×C₁₉	—	2	4	no	—
150	C₂³×C₁₉	—	4	1	no	—
151	C₂³×C₁₉	—	4	1	no	—
152	C₂³×C₁₉	—	4	4	no	—
153	C₂³×C₁₉	—	8	2	no	—
154	C₂³×C₁₉	—	8	2	no	—
155	C₂³×C₁₉	#102	1	2	yes	—
156	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	Q₈×C₁₉	—	4	4	no	—
158	Q₈×C₁₉	—	4	2	no	—
159	Q₈×C₁₉	—	4	2	no	—
160	D₄×C₁₉	—	4	4	no	—
161	D₄×C₁₉	—	4	4	no	—
162	D₄×C₁₉	—	4	8	no	—
163	D₄×C₁₉	—	4	4	no	—
164	D₄×C₁₉	—	4	4	no	—
165	D₄×C₁₉	—	4	2	no	—
166	D₄×C₁₉	—	4	2	no	—
167	D₄×C₁₉	—	8	2	no	—
168	D₄×C₁₉	—	8	2	no	—
169	D₄×C₁₉	—	8	2	no	—
170	C₂×C₄×C₁₉	—	2	1	no	—
171	C₂×C₄×C₁₉	—	2	1	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	2	1	no	—
177	C₂×C₄×C₁₉	—	2	1	no	—
178	C₂×C₄×C₁₉	—	2	4	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	4	1	no	—
181	C₂×C₄×C₁₉	—	4	8	no	—
182	C₂×C₄×C₁₉	—	4	4	no	—
183	C₂×C₄×C₁₉	—	4	4	no	—
184	C₂×C₄×C₁₉	—	4	4	no	—
185	C₂×C₄×C₁₉	—	4	1	no	—
186	C₂×C₄×C₁₉	—	4	1	no	—
187	C₂×C₄×C₁₉	#102	1	2	yes	—
188	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
189	C₂×C₄×C₁₉	#120	1	2	yes	—
190	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
191	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
193	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
194	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
195	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
196	C₁₉⋊C₈	—	8	2	no	—
197	C₁₉⋊C₈	—	8	1	no	—
198	C₁₉⋊C₈	—	8	1	no	—
199	#3449	D₁₉	1	1	yes	characteristic
200	#1798	—	19	1	no	—
201	#1540	—	19	2	no	—
202	#1480	—	19	2	no	—
203	#1458	—	19	1	no	—
204	C₂²×C₁₉	—	2	1	no	—
205	C₂²×C₁₉	—	2	1	no	—
206	C₂²×C₁₉	—	2	2	no	—
207	C₂²×C₁₉	—	4	2	no	—
208	C₂²×C₁₉	—	4	1	no	—
209	C₂²×C₁₉	—	4	1	no	—
210	C₂²×C₁₉	—	4	4	no	—
211	C₂²×C₁₉	—	4	4	no	—
212	C₂²×C₁₉	—	4	4	no	—
213	C₂²×C₁₉	—	8	1	no	—
214	C₂²×C₁₉	—	8	8	no	—
215	C₂²×C₁₉	#379	1	1	yes	characteristic
216	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
217	C₂²×C₁₉	#418	1	1	yes	characteristic
218	C₄×C₁₉	—	2	2	no	—
219	C₄×C₁₉	—	2	2	no	—
220	C₄×C₁₉	—	2	2	no	—
221	C₄×C₁₉	—	4	1	no	—
222	C₄×C₁₉	—	4	4	no	—
223	C₄×C₁₉	—	4	1	no	—
224	C₄×C₁₉	#447	1	1	yes	characteristic
225	C₄×C₁₉	#447	1	1	yes	characteristic
226	C₄×C₁₉	#450	1	1	yes	characteristic
227	C₄×C₁₉	#450	1	1	yes	characteristic
228	C₂²×#41	—	2	1	no	—
229	#537	—	2	1	no	—
230	#537	Dic₁₉	1	2	yes	—
231	#536	—	2	2	no	—
232	#535	—	2	2	no	—
233	#534	—	2	1	no	—
234	#534	Dic₁₉	1	2	yes	—
235	#532	—	2	1	no	—
236	#532	C₂×D₁₉	1	2	yes	—
237	#525	—	2	4	no	—
238	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
239	#431	—	19	2	no	—
240	C₂×C₄⋊C₈	—	19	1	no	—
241	C₂×C₄⋊C₈	—	19	1	no	—
242	C₂×C₂²⋊C₈	—	38	1	no	—
243	#336	—	38	1	no	—
244	#332	—	38	2	no	—
245	#331	—	38	2	no	—
246	D₄⋊C₈	—	38	4	no	—
247	#324	—	38	1	no	—
248	#323	—	38	1	no	—
249	C₂×C₁₉	—	2	1	no	—
250	C₂×C₁₉	—	2	1	no	—
251	C₂×C₁₉	—	4	2	no	—
252	C₂×C₁₉	—	8	4	no	—
253	C₂×C₁₉	#1786	1	1	yes	characteristic
254	C₂×C₁₉	#1791	1	1	yes	characteristic
255	C₂×C₁₉	#1794	1	1	yes	characteristic
256	C₂×#41	—	2	2	no	—
257	C₂×#41	—	2	2	no	—
258	C₂×#41	—	2	2	no	—
259	C₂×#41	—	2	2	no	—
260	C₂×#41	—	4	2	no	—
261	C₂×#41	—	4	2	no	—
262	C₂×#41	—	4	2	no	—
263	C₂×#41	—	4	2	no	—
264	C₂²×Q₈	—	2	1	no	—
265	C₂²×D₄	—	2	1	no	—
266	C₂²×D₄	—	2	2	no	—
267	C₂³×C₄	—	2	2	no	—
268	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
269	C₂²×C₈	—	38	1	no	—
270	C₂²×C₈	—	38	1	no	—
271	C₄⋊Q₈	—	2	1	no	—
272	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
273	#127	—	2	1	no	—
274	#127	C₂²⋊D₁₉	1	2	yes	—
275	#124	—	2	2	no	—
276	#124	—	2	2	no	—
277	#123	—	2	4	no	—
278	#123	—	2	4	no	—
279	C₂²⋊Q₈	—	2	4	no	—
280	C₂²⋊Q₈	—	2	4	no	—
281	#121	—	2	4	no	—
282	#121	—	2	4	no	—
283	#121	—	2	2	no	—
284	#121	—	2	2	no	—
285	#121	—	2	2	no	—
286	#121	C₂×Dic₁₉	1	4	yes	—
287	#120	—	2	4	no	—
288	#120	—	2	4	no	—
289	C₄×D₄	—	2	2	no	—
290	C₄×D₄	—	2	2	no	—
291	C₄×D₄	—	2	2	no	—
292	C₄×D₄	C₂²⋊D₁₉	1	4	yes	—
293	#117	—	2	2	no	—
294	#117	—	2	2	no	—
295	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
297	C₂×C₂²⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
298	C₂×C₂²⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
299	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
300	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
301	C₄⋊C₈	—	38	2	no	—
302	C₄⋊C₈	—	38	2	no	—
303	C₄⋊C₈	—	38	2	no	—
304	C₂²⋊C₈	—	38	2	no	—
305	C₂²⋊C₈	—	76	2	no	—
306	C₄×C₈	—	38	2	no	—
307	C₁₉	#8409	1	1	yes	characteristic, complemented, Sylow
308	C₂⁴	—	2	2	no	—
309	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
310	#41	—	4	4	no	—
311	#41	—	4	4	no	—
312	#41	—	4	4	no	—
313	#41	—	4	4	no	—
314	#41	—	4	4	no	—
315	#41	—	4	2	no	—
316	#41	—	4	2	no	—
317	#41	—	4	2	no	—
318	#41	—	4	2	no	—
319	#41	—	4	4	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	4	2	no	—
323	C₂×Q₈	—	4	2	no	—
324	C₂×D₄	—	2	4	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	4	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	4	2	no	—
332	C₂×D₄	—	4	2	no	—
333	C₂×D₄	—	4	4	no	—
334	C₂×D₄	—	4	4	no	—
335	C₂×D₄	C₂²⋊Dic₁₉	1	4	yes	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	4	4	no	—
344	C₂²×C₄	—	4	4	no	—
345	C₂²×C₄	#64525	1	2	yes	—
346	C₂²×C₄	#64526	1	2	yes	—
347	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
348	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
349	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
350	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
353	C₂×C₈	—	76	1	no	—
354	C₂×C₈	—	76	1	no	—
355	C₂×C₈	—	76	1	no	—
356	C₂×C₈	—	76	1	no	—
357	C₂×C₈	—	76	2	no	—
358	C₂×C₈	—	76	1	no	—
359	C₂×C₈	—	76	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	C₂²⋊Dic₁₉	1	4	yes	—
366	C₂²⋊C₄	—	2	4	no	—
367	C₂²⋊C₄	—	2	4	no	—
368	C₂²⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	—	2	4	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	2	4	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	2	1	no	—
374	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
375	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
376	C₂³	—	2	1	no	—
377	C₂³	—	2	1	no	—
378	C₂³	—	2	4	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	1	no	—
381	C₂³	—	4	4	no	—
382	C₂³	—	8	2	no	—
383	C₂³	—	8	2	no	—
384	C₂³	#10597289	1	2	yes	—
385	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
386	Q₈	—	4	4	no	—
387	Q₈	—	4	2	no	—
388	Q₈	—	4	2	no	—
389	D₄	—	4	4	no	—
390	D₄	—	4	4	no	—
391	D₄	—	4	8	no	—
392	D₄	—	4	4	no	—
393	D₄	—	4	4	no	—
394	D₄	—	4	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	8	2	no	—
397	D₄	—	8	2	no	—
398	D₄	—	8	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	8	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	#10597289	1	2	yes	—
417	C₂×C₄	C₂×#64525	1	1	yes	characteristic
418	C₂×C₄	#10597378	1	1	yes	characteristic
419	C₂×C₄	#10597378	1	1	yes	characteristic
420	C₂×C₄	C₂×#64526	1	1	yes	characteristic
421	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	2	yes	—
422	C₂×C₄	#10597399	1	2	yes	—
423	C₂×C₄	#10597399	1	1	yes	characteristic
424	C₂×C₄	#10597399	1	1	yes	characteristic
425	C₈	—	152	2	no	—
426	C₈	—	152	1	no	—
427	C₈	—	152	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	4	no	—
435	C₂²	—	4	4	no	—
436	C₂²	—	4	4	no	—
437	C₂²	—	8	1	no	—
438	C₂²	—	8	8	no	—
439	C₂²	#11926400	1	1	yes	characteristic
440	C₂²	C₂×#10597289	1	1	yes	characteristic
441	C₂²	#11926549	1	1	yes	characteristic
442	C₄	—	2	2	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	4	1	no	—
446	C₄	—	4	1	no	—
447	C₄	—	4	4	no	—
448	C₄	#11926678	1	1	yes	characteristic
449	C₄	#11926678	1	1	yes	characteristic
450	C₄	#11926695	1	1	yes	characteristic
451	C₄	#11926695	1	1	yes	characteristic
452	C₂	—	2	1	no	—
453	C₂	—	2	1	no	—
454	C₂	—	4	2	no	—
455	C₂	—	8	4	no	—
456	C₂	#14563566	1	1	yes	characteristic
457	C₂	#14563586	1	1	yes	characteristic
458	C₂	#14563599	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597399
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#3449	C₂
socle	C₂²×C₁₉	#379
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3449	D₁₉
hypocenter	C₁₉	#8409
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3449

Complements

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

N	H ≅ G/N	type
1. #14563619	C₂	semidirect
2. #14562284	C₂	semidirect
3. #14562034	C₂	semidirect
4. #14561949	C₂	semidirect
6. #11926597	C₂²	semidirect
7. C₂×C₄⋊(C₁₉⋊C₈)	C₂²	semidirect
8. C₂×C₄⋊(C₁₉⋊C₈)	C₂²	semidirect
307. C₁₉	#8409	semidirect

Maximal subgroups

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

subgroup	index
#14563619	2
#14562284	2
#14562034	2
#14561949	2
C₁₉×#3449	2
#8409	19