Subgroups — #18078632

Order 4864.

532 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	#14573084	C₂	1	1	yes	maximal, characteristic
2	C₈×#64541	C₂	1	1	yes	maximal, characteristic, complemented
3	#14563652	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562130	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561530	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561475	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1492	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10597396	—	2	1	no	—
9	C₄×#64541	C₂²	1	1	yes	characteristic
10	#11926763	—	2	1	no	—
11	#11926756	—	2	1	no	—
12	#11926751	C₄	1	1	yes	characteristic, complemented
13	#11926746	C₄	1	1	yes	characteristic, complemented
14	#11926741	C₄	1	1	yes	characteristic, complemented
15	#11926736	C₄	1	1	yes	characteristic, complemented
16	C₈×Dic₃₈	—	2	1	no	—
17	C₈×D₇₆	—	2	1	no	—
18	C₈×C₂²⋊D₁₉	—	2	2	no	—
19	#11926597	C₂²	1	1	yes	characteristic
20	#11926595	—	2	1	no	—
21	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×#10597282	—	2	1	no	—
23	#11926540	—	2	1	no	—
24	C₄×C₈×D₁₉	—	2	1	no	—
25	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
26	#11926305	—	2	1	no	—
27	#11926278	—	2	2	no	—
28	C₁₉×#532	C₂²	1	1	yes	characteristic
29	C₁₉×#423	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
31	C₁₉×D₄⋊C₈	—	2	1	no	—
32	C₁₉×D₄⋊C₈	—	2	1	no	—
33	C₂×#41×C₁₉	—	2	1	no	—
34	C₂×#64541	D₄	1	1	yes	characteristic
35	C₂×M₁₆×C₁₉	—	2	1	no	—
36	C₂²×C₈×C₁₉	—	2	1	no	—
37	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
38	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
39	C₁₉×#124	—	2	1	no	—
40	C₁₉×#121	—	2	1	no	—
41	C₁₉×#121	—	2	1	no	—
42	C₄×D₄×C₁₉	—	2	1	no	—
43	C₄×D₄×C₁₉	—	2	1	no	—
44	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
45	#10597396	—	4	2	no	—
46	#10597396	—	4	2	no	—
47	C₂×#64528	—	2	1	no	—
48	C₂×#64527	—	2	1	no	—
49	C₂×#64526	—	2	1	no	—
50	C₂×#64525	—	2	1	no	—
51	C₄×C₂²⋊D₁₉	—	2	1	no	—
52	C₄×C₂²⋊D₁₉	—	2	1	no	—
53	#10597372	D₄	1	1	yes	characteristic
54	C₂×C₄⋊Dic₁₉	—	2	1	no	—
55	C₂×C₄×Dic₁₉	—	2	1	no	—
56	C₂²×C₁₉⋊C₈	—	2	1	no	—
57	C₂×C₈×D₁₉	—	2	2	no	—
58	C₄×D₇₆	C₂×C₄	1	1	yes	characteristic
59	C₄×D₇₆	D₄	1	1	yes	characteristic
60	#10597318	—	2	1	no	—
61	C₄²×D₁₉	—	2	1	no	—
62	C₄×Dic₃₈	C₂×C₄	1	1	yes	characteristic
63	C₄×Dic₃₈	D₄	1	1	yes	characteristic
64	C₁₉×C₄⋊C₈	—	2	1	no	—
65	C₁₉×C₄⋊C₈	—	2	1	no	—
66	C₄×C₈×C₁₉	—	2	1	no	—
67	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
68	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
69	#10597292	—	2	1	no	—
70	#10597292	—	2	1	no	—
71	#10597289	—	2	1	no	—
72	#10597289	—	2	1	no	—
73	C₁₉⋊#95	—	2	1	no	—
74	C₂²⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
75	#10597282	—	4	2	no	—
76	(C₂×D₁₉)⋊C₈	—	2	2	no	—
77	Dic₁₉⋊C₈	—	2	2	no	—
78	C₈×Dic₁₉	—	2	2	no	—
79	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
80	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
81	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
82	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
83	C₄×C₁₉⋊C₈	—	2	1	no	—
84	#41×C₁₉	—	4	1	no	—
85	#41×C₁₉	—	4	1	no	—
86	#41×C₁₉	—	4	1	no	—
87	#41×C₁₉	—	4	1	no	—
88	C₂×Q₈×C₁₉	—	2	1	no	—
89	C₂×D₄×C₁₉	—	2	1	no	—
90	C₂×D₄×C₁₉	—	2	1	no	—
91	C₂×D₄×C₁₉	—	2	1	no	—
92	C₂×D₄×C₁₉	—	4	1	no	—
93	C₂²×C₄×C₁₉	—	4	1	no	—
94	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
97	C₂×C₂²⋊D₁₉	—	2	1	no	—
98	C₂²×Dic₁₉	—	4	1	no	—
99	#64541	—	2	1	no	—
100	#64541	—	2	1	no	—
101	#64541	D₈	1	2	yes	—
102	#64541	SD₁₆	1	2	yes	—
103	C₂×D₇₆	C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₄×D₁₉	—	2	1	no	—
105	C₂×C₄×D₁₉	—	2	1	no	—
106	C₂×C₄×D₁₉	—	2	1	no	—
107	C₂×Dic₃₈	C₂²⋊C₄	1	1	yes	characteristic
108	M₁₆×C₁₉	—	4	1	no	—
109	M₁₆×C₁₉	—	4	1	no	—
110	C₂×C₈×C₁₉	—	2	1	no	—
111	C₂×C₈×C₁₉	—	2	1	no	—
112	C₂×C₈×C₁₉	—	4	2	no	—
113	C₂×C₈×C₁₉	—	4	1	no	—
114	C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₄⋊C₄×C₁₉	—	2	1	no	—
116	C₂²⋊C₄×C₁₉	—	4	1	no	—
117	C₂²⋊C₄×C₁₉	—	4	1	no	—
118	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₁₉	#41	1	1	yes	characteristic
122	C₂²⋊Dic₁₉	—	2	1	no	—
123	#64528	—	4	2	no	—
124	#64527	—	4	2	no	—
125	#64526	—	4	2	no	—
126	#64525	—	4	2	no	—
127	(C₂×D₁₉)⋊C₄	—	2	1	no	—
128	(C₂×D₁₉)⋊C₄	—	2	1	no	—
129	C₄⋊Dic₁₉	—	2	2	no	—
130	C₄⋊Dic₁₉	—	4	1	no	—
131	C₄⋊Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
132	C₄⋊Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
133	Dic₁₉⋊C₄	—	2	1	no	—
134	Dic₁₉⋊C₄	—	2	1	no	—
135	C₄×Dic₁₉	—	2	1	no	—
136	C₄×Dic₁₉	—	2	1	no	—
137	C₄×Dic₁₉	—	2	1	no	—
138	C₄×Dic₁₉	—	4	1	no	—
139	C₄×Dic₁₉	—	4	1	no	—
140	C₂×C₁₉⋊C₈	—	2	1	no	—
141	C₂×C₁₉⋊C₈	—	2	1	no	—
142	C₂×C₁₉⋊C₈	—	2	2	no	—
143	C₂×C₁₉⋊C₈	—	4	1	no	—
144	C₂×C₁₉⋊C₈	—	4	1	no	—
145	C₈×D₁₉	—	4	4	no	—
146	#9208	—	19	1	no	maximal, Sylow
147	C₂³×C₁₉	—	4	1	no	—
148	C₂³×C₁₉	#121	1	1	yes	characteristic
149	C₂²×D₁₉	—	2	1	no	—
150	Q₈×C₁₉	—	4	1	no	—
151	Q₈×C₁₉	—	4	1	no	—
152	D₄×C₁₉	—	4	1	no	—
153	D₄×C₁₉	—	4	1	no	—
154	D₄×C₁₉	—	4	1	no	—
155	D₄×C₁₉	—	4	1	no	—
156	D₄×C₁₉	—	8	1	no	—
157	D₄×C₁₉	—	8	1	no	—
158	D₄×C₁₉	—	8	1	no	—
159	C₂×C₄×C₁₉	—	2	1	no	—
160	C₂×C₄×C₁₉	—	2	1	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	8	1	no	—
164	C₂×C₄×C₁₉	—	8	1	no	—
165	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
169	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
175	C₂²⋊D₁₉	—	2	2	no	—
176	C₂²⋊D₁₉	—	2	2	no	—
177	C₂×Dic₁₉	—	2	1	no	—
178	C₂×Dic₁₉	—	2	1	no	—
179	C₂×Dic₁₉	—	2	1	no	—
180	C₂×Dic₁₉	—	4	2	no	—
181	C₂×Dic₁₉	—	8	1	no	—
182	C₂×Dic₁₉	—	8	1	no	—
183	D₇₆	—	2	1	no	—
184	D₇₆	#102	1	2	yes	—
185	C₄×D₁₉	—	2	2	no	—
186	C₄×D₁₉	—	2	2	no	—
187	C₄×D₁₉	—	4	2	no	—
188	C₄×D₁₉	—	4	1	no	—
189	C₄×D₁₉	—	4	1	no	—
190	Dic₃₈	—	2	1	no	—
191	Dic₃₈	#102	1	2	yes	—
192	C₈×C₁₉	—	2	2	no	—
193	C₈×C₁₉	—	4	1	no	—
194	C₈×C₁₉	—	8	1	no	—
195	C₁₉⋊C₈	—	4	2	no	—
196	C₁₉⋊C₈	—	4	1	no	—
197	C₁₉⋊C₈	—	4	1	no	—
198	#3035	—	19	1	no	—
199	C₈×#41	—	19	1	no	—
200	#1806	—	19	1	no	—
201	#1502	—	19	1	no	—
202	#1492	D₁₉	1	1	yes	characteristic, complemented
203	#1301	—	19	1	no	—
204	#1279	—	19	1	no	—
205	C₂²×C₁₉	—	2	1	no	—
206	C₂²×C₁₉	—	2	1	no	—
207	C₂²×C₁₉	—	8	1	no	—
208	C₂²×C₁₉	—	8	1	no	—
209	C₂²×C₁₉	—	8	1	no	—
210	C₂²×C₁₉	#386	1	1	yes	characteristic
211	C₂²×C₁₉	#465	1	1	yes	characteristic
212	C₂²×C₁₉	#466	1	1	yes	characteristic
213	C₂×D₁₉	—	2	2	no	—
214	C₂×D₁₉	—	4	1	no	—
215	C₂×D₁₉	—	4	1	no	—
216	C₄×C₁₉	—	2	1	no	—
217	C₄×C₁₉	—	2	1	no	—
218	C₄×C₁₉	—	2	1	no	—
219	C₄×C₁₉	—	8	1	no	—
220	C₄×C₁₉	C₂×#102	1	1	yes	characteristic
221	C₄×C₁₉	#416	1	1	yes	characteristic
222	C₄×C₁₉	#443	1	1	yes	characteristic
223	C₄×C₁₉	#444	1	1	yes	characteristic
224	C₄×C₁₉	#465	1	1	yes	characteristic
225	C₄×C₁₉	#466	1	1	yes	characteristic
226	Dic₁₉	—	2	2	no	—
227	Dic₁₉	—	4	1	no	—
228	Dic₁₉	—	4	1	no	—
229	Dic₁₉	—	8	2	no	—
230	C₂×#135	—	38	1	no	—
231	#532	C₂×D₁₉	1	1	yes	characteristic
232	C₄×#41	—	19	1	no	—
233	#464	—	38	1	no	—
234	#463	—	38	1	no	—
235	#462	—	19	1	no	—
236	#461	—	19	1	no	—
237	#460	—	19	1	no	—
238	#459	—	19	1	no	—
239	C₈×Q₈	—	38	1	no	—
240	C₈×D₄	—	38	1	no	—
241	C₈×D₄	—	38	2	no	—
242	#431	—	19	1	no	—
243	#431	—	38	1	no	—
244	#423	C₂×D₁₉	1	1	yes	characteristic
245	C₂×C₄⋊C₈	—	19	1	no	—
246	C₂×#104	—	38	1	no	—
247	#416	—	38	1	no	—
248	C₂×C₄×C₈	—	38	1	no	—
249	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
250	C₄×C₄⋊C₄	—	19	1	no	—
251	#339	—	38	1	no	—
252	#327	—	38	2	no	—
253	D₄⋊C₈	—	2	1	no	—
254	D₄⋊C₈	—	2	1	no	—
255	C₂×C₁₉	—	2	1	no	—
256	C₂×C₁₉	—	2	1	no	—
257	C₂×C₁₉	—	16	1	no	—
258	C₂×C₁₉	#1876	1	1	yes	characteristic
259	C₂×C₁₉	#1893	1	1	yes	characteristic
260	C₂×C₁₉	#1906	1	1	yes	characteristic
261	D₁₉	—	4	2	no	—
262	C₂×#41	—	2	1	no	—
263	C₂×#41	—	19	1	no	—
264	#135	—	76	2	no	—
265	#135	—	76	2	no	—
266	C₂×Q₁₆	—	38	1	no	—
267	C₂×SD₁₆	—	38	1	no	—
268	C₂×SD₁₆	—	38	1	no	—
269	C₂×D₈	—	38	1	no	—
270	C₂×M₁₆	—	2	1	no	—
271	C₂²×C₈	—	2	1	no	—
272	C₂²×C₈	—	38	2	no	—
273	C₂²×C₈	—	38	1	no	—
274	C₄⋊Q₈	C₄×D₁₉	1	1	yes	characteristic
275	#127	C₄×D₁₉	1	1	yes	characteristic
276	#124	—	2	1	no	—
277	#121	—	2	1	no	—
278	#121	—	2	1	no	—
279	C₄×Q₈	—	19	1	no	—
280	C₄×Q₈	—	19	1	no	—
281	C₄×D₄	—	2	1	no	—
282	C₄×D₄	—	2	1	no	—
283	C₄×D₄	—	19	1	no	—
284	C₄×D₄	—	19	1	no	—
285	C₄×D₄	—	38	1	no	—
286	C₄×D₄	—	38	1	no	—
287	#117	—	19	1	no	—
288	#117	—	38	1	no	—
289	C₂×C₄⋊C₄	—	38	1	no	—
290	C₂×C₄²	—	38	1	no	—
291	C₂×C₄²	—	38	1	no	—
292	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
293	C₄⋊C₈	—	2	1	no	—
294	C₄⋊C₈	—	2	1	no	—
295	C₄⋊C₈	—	19	1	no	—
296	C₄⋊C₈	—	19	1	no	—
297	C₄⋊C₈	—	38	2	no	—
298	C₄⋊C₈	—	38	1	no	—
299	C₄⋊C₈	—	38	1	no	—
300	#104	—	76	2	no	—
301	#103	—	38	1	no	—
302	#103	—	38	1	no	—
303	#102	—	38	1	no	—
304	#102	—	38	1	no	—
305	C₂²⋊C₈	—	19	2	no	—
306	C₂²⋊C₈	—	38	2	no	—
307	C₄×C₈	—	2	1	no	—
308	C₄×C₈	—	38	2	no	—
309	C₄×C₈	—	38	1	no	—
310	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
311	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
312	#95	—	38	1	no	—
313	C₁₉	#9208	1	1	yes	characteristic, complemented, Sylow
314	#41	—	4	1	no	—
315	#41	—	4	1	no	—
316	#41	—	4	1	no	—
317	#41	—	4	1	no	—
318	#41	—	19	2	no	—
319	#41	—	19	2	no	—
320	#41	—	38	1	no	—
321	#41	—	38	1	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	19	1	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	4	1	no	—
328	C₂×D₄	—	19	1	no	—
329	C₂×D₄	—	38	1	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	—	38	1	no	—
332	C₂²×C₄	—	38	1	no	—
333	C₂²×C₄	—	38	1	no	—
334	C₂²×C₄	—	76	1	no	—
335	C₂²×C₄	#64541	1	1	yes	characteristic
336	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
337	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
338	Q₁₆	—	76	2	no	—
339	SD₁₆	—	76	2	no	—
340	SD₁₆	—	76	2	no	—
341	D₈	—	76	2	no	—
342	M₁₆	—	4	1	no	—
343	M₁₆	—	4	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	4	2	no	—
347	C₂×C₈	—	4	1	no	—
348	C₂×C₈	—	38	2	no	—
349	C₂×C₈	—	38	1	no	—
350	C₂×C₈	—	38	1	no	—
351	C₂×C₈	—	76	4	no	—
352	C₂×C₈	—	76	1	no	—
353	C₂×C₈	—	76	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	19	1	no	—
357	C₄⋊C₄	—	19	1	no	—
358	C₄⋊C₄	—	38	2	no	—
359	C₄⋊C₄	—	38	1	no	—
360	C₄⋊C₄	—	38	1	no	—
361	C₄⋊C₄	—	76	1	no	—
362	C₂²⋊C₄	—	4	1	no	—
363	C₂²⋊C₄	—	4	1	no	—
364	C₂²⋊C₄	—	38	1	no	—
365	C₂²⋊C₄	—	38	1	no	—
366	C₂²⋊C₄	—	38	1	no	—
367	C₄²	—	38	1	no	—
368	C₄²	—	38	1	no	—
369	C₄²	—	38	1	no	—
370	C₄²	—	76	1	no	—
371	C₄²	—	76	1	no	—
372	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
373	C₄²	D₄×D₁₉	1	1	yes	characteristic
374	C₄²	#64543	1	1	yes	characteristic
375	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
376	C₂³	—	4	1	no	—
377	C₂³	—	38	1	no	—
378	C₂³	#10597330	1	1	yes	characteristic
379	Q₈	—	4	1	no	—
380	Q₈	—	4	1	no	—
381	Q₈	—	19	2	no	—
382	Q₈	—	38	1	no	—
383	D₄	—	4	1	no	—
384	D₄	—	4	1	no	—
385	D₄	—	4	1	no	—
386	D₄	—	4	1	no	—
387	D₄	—	8	1	no	—
388	D₄	—	8	1	no	—
389	D₄	—	8	1	no	—
390	D₄	—	19	2	no	—
391	D₄	—	38	2	no	—
392	D₄	—	38	2	no	—
393	D₄	—	38	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	8	1	no	—
399	C₂×C₄	—	8	1	no	—
400	C₂×C₄	—	38	1	no	—
401	C₂×C₄	—	38	2	no	—
402	C₂×C₄	—	38	2	no	—
403	C₂×C₄	—	38	1	no	—
404	C₂×C₄	—	38	1	no	—
405	C₂×C₄	—	76	2	no	—
406	C₂×C₄	—	76	1	no	—
407	C₂×C₄	—	76	1	no	—
408	C₂×C₄	—	76	2	no	—
409	C₂×C₄	—	152	1	no	—
410	C₂×C₄	—	152	1	no	—
411	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
412	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
413	C₂×C₄	#10597329	1	1	yes	characteristic
414	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
415	C₂×C₄	#10597358	1	1	yes	characteristic
416	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
417	C₂×C₄	#10597362	1	1	yes	characteristic
418	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
419	C₂×C₄	#10597383	1	1	yes	characteristic
420	C₂×C₄	#10597384	1	1	yes	characteristic
421	C₈	—	2	2	no	—
422	C₈	—	4	1	no	—
423	C₈	—	8	1	no	—
424	C₈	—	76	2	no	—
425	C₈	—	76	1	no	—
426	C₈	—	76	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	8	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	—	8	1	no	—
432	C₂²	—	38	2	no	—
433	C₂²	—	76	1	no	—
434	C₂²	—	76	1	no	—
435	C₂²	#11926420	1	1	yes	characteristic
436	C₂²	#11926772	1	1	yes	characteristic
437	C₂²	#11926779	1	1	yes	characteristic
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	8	1	no	—
442	C₄	—	38	2	no	—
443	C₄	—	76	1	no	—
444	C₄	—	76	1	no	—
445	C₄	—	152	2	no	—
446	C₄	#102×D₁₉	1	1	yes	characteristic
447	C₄	#11926537	1	1	yes	characteristic
448	C₄	#11926659	1	1	yes	characteristic
449	C₄	#11926664	1	1	yes	characteristic
450	C₄	#11926770	1	1	yes	characteristic
451	C₄	#11926777	1	1	yes	characteristic
452	C₂	—	2	1	no	—
453	C₂	—	2	1	no	—
454	C₂	—	16	1	no	—
455	C₂	—	76	2	no	—
456	C₂	#14563965	1	1	yes	characteristic
457	C₂	#14564060	1	1	yes	characteristic
458	C₂	#14564139	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597384
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1492	C₂
socle	C₂²×C₁₉	#386
prime radical	#14573084	C₂
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1492	D₁₉
hypocenter	C₁₉	#9208
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1492

Complements

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

N	H ≅ G/N	type
2. C₈×#64541	C₂	semidirect
3. #14563652	C₂	semidirect
4. #14562130	C₂	semidirect
5. #14561530	C₂	semidirect
6. #14561475	C₂	semidirect
7. C₁₉×#1492	C₂	semidirect
12. #11926751	C₄	semidirect
13. #11926746	C₄	semidirect
14. #11926741	C₄	semidirect
15. #11926736	C₄	semidirect
202. #1492	D₁₉	semidirect
313. C₁₉	#9208	semidirect

Maximal subgroups

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

subgroup	index
#14573084	2
C₈×#64541	2
#14563652	2
#14562130	2
#14561530	2
#14561475	2
C₁₉×#1492	2
#9208	19