Subgroups — #18078631

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	#41×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#14563655	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562130	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562086	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561532	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561474	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3035	C₂	1	1	yes	maximal, characteristic
8	Q₈×C₁₉⋊C₈	—	2	1	no	—
9	D₄×C₁₉⋊C₈	—	2	2	no	—
10	D₄×C₁₉⋊C₈	—	2	1	no	—
11	#11926597	—	2	1	no	—
12	#11926597	C₂²	1	1	yes	characteristic
13	#11926568	C₂²	1	1	yes	characteristic
14	C₂×#10597294	—	2	1	no	—
15	C₂×C₄×C₁₉⋊C₈	—	2	1	no	—
16	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
17	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
18	#11926303	—	2	1	no	—
19	#11926278	—	2	2	no	—
20	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
21	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
22	C₂×C₁₉×#135	—	2	1	no	—
23	C₁₉×#532	C₂²	1	1	yes	characteristic
24	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#464	—	2	1	no	—
26	C₁₉×#463	—	2	1	no	—
27	C₁₉×#462	C₄	1	1	yes	characteristic, complemented
28	C₁₉×#461	C₄	1	1	yes	characteristic, complemented
29	C₁₉×#460	C₄	1	1	yes	characteristic, complemented
30	C₁₉×#459	C₄	1	1	yes	characteristic, complemented
31	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₁₉×#416	—	2	1	no	—
33	C₂×#41×C₁₉	—	2	1	no	—
34	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
35	C₁₉×#135	—	4	2	no	—
36	C₁₉×#135	—	4	2	no	—
37	C₂×Q₁₆×C₁₉	—	2	1	no	—
38	C₂×SD₁₆×C₁₉	—	2	1	no	—
39	C₂×SD₁₆×C₁₉	—	2	1	no	—
40	C₂×D₈×C₁₉	—	2	1	no	—
41	C₂²×C₈×C₁₉	—	2	1	no	—
42	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
43	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
44	C₁₉×#124	—	2	1	no	—
45	C₁₉×#121	—	2	1	no	—
46	C₁₉×#121	—	2	1	no	—
47	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
48	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
49	C₄×D₄×C₁₉	—	2	1	no	—
50	C₄×D₄×C₁₉	—	2	1	no	—
51	C₄×D₄×C₁₉	—	2	1	no	—
52	C₄×D₄×C₁₉	—	2	1	no	—
53	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
54	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
55	C₁₉×#117	—	2	1	no	—
56	C₁₉×#117	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₁₉	—	2	1	no	—
58	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊Dic₁₉	—	2	1	no	—
60	C₂×C₄×Dic₁₉	—	2	1	no	—
61	C₂×#64520	—	2	1	no	—
62	C₂²×C₁₉⋊C₈	—	2	2	no	—
63	C₂²×C₁₉⋊C₈	—	2	1	no	—
64	C₁₉×C₄⋊C₈	—	2	1	no	—
65	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
66	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
67	C₁₉×#103	—	2	1	no	—
68	C₁₉×#103	—	2	1	no	—
69	C₁₉×#102	—	2	1	no	—
70	C₁₉×#102	—	2	1	no	—
71	#10597294	—	4	2	no	—
72	C₁₉⋊#95	—	2	1	no	—
73	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
74	C₂²⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
75	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
76	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
77	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
78	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
79	C₄×C₁₉⋊C₈	—	2	2	no	—
80	C₄×C₁₉⋊C₈	—	2	1	no	—
81	C₄×C₁₉⋊C₈	—	2	1	no	—
82	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
83	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
84	#41×C₁₉	—	2	1	no	—
85	#41×C₁₉	—	2	1	no	—
86	#41×C₁₉	—	4	1	no	—
87	#41×C₁₉	—	4	1	no	—
88	#41×C₁₉	—	4	1	no	—
89	#41×C₁₉	—	4	1	no	—
90	#41×C₁₉	D₈	1	2	yes	—
91	#41×C₁₉	SD₁₆	1	2	yes	—
92	C₂×Q₈×C₁₉	—	2	1	no	—
93	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×D₄×C₁₉	—	2	1	no	—
95	C₂×D₄×C₁₉	—	2	1	no	—
96	C₂×D₄×C₁₉	—	2	1	no	—
97	C₂×D₄×C₁₉	—	2	1	no	—
98	C₂×D₄×C₁₉	—	4	1	no	—
99	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	—	2	1	no	—
101	C₂²×C₄×C₁₉	—	2	1	no	—
102	C₂²×C₄×C₁₉	—	2	1	no	—
103	C₂²×C₄×C₁₉	—	4	1	no	—
104	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
107	C₂²×Dic₁₉	—	4	1	no	—
108	Q₁₆×C₁₉	—	4	2	no	—
109	SD₁₆×C₁₉	—	4	2	no	—
110	SD₁₆×C₁₉	—	4	2	no	—
111	D₈×C₁₉	—	4	2	no	—
112	C₂×C₈×C₁₉	—	2	1	no	—
113	C₂×C₈×C₁₉	—	2	1	no	—
114	C₂×C₈×C₁₉	—	4	1	no	—
115	C₂×C₈×C₁₉	—	4	1	no	—
116	C₄⋊C₄×C₁₉	—	2	1	no	—
117	C₄⋊C₄×C₁₉	—	2	1	no	—
118	C₄⋊C₄×C₁₉	—	2	1	no	—
119	C₄⋊C₄×C₁₉	—	2	1	no	—
120	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
121	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
122	C₂²⋊C₄×C₁₉	—	2	1	no	—
123	C₂²⋊C₄×C₁₉	—	2	1	no	—
124	C₂²⋊C₄×C₁₉	—	2	1	no	—
125	C₂²⋊C₄×C₁₉	—	4	1	no	—
126	C₂²⋊C₄×C₁₉	—	4	1	no	—
127	C₄²×C₁₉	—	2	1	no	—
128	C₄²×C₁₉	—	2	1	no	—
129	C₄²×C₁₉	—	2	1	no	—
130	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₁₉	#41	1	1	yes	characteristic
134	C₄⋊Dic₁₉	—	2	2	no	—
135	C₄⋊Dic₁₉	—	4	1	no	—
136	C₄×Dic₁₉	—	4	1	no	—
137	C₄×Dic₁₉	—	4	1	no	—
138	#64520	—	4	1	no	—
139	#64520	—	4	1	no	—
140	C₂×C₁₉⋊C₈	—	2	1	no	—
141	C₂×C₁₉⋊C₈	—	2	2	no	—
142	C₂×C₁₉⋊C₈	—	2	1	no	—
143	C₂×C₁₉⋊C₈	—	4	2	no	—
144	C₂×C₁₉⋊C₈	—	4	4	no	—
145	C₂×C₁₉⋊C₈	—	4	1	no	—
146	#9208	—	19	1	no	maximal, Sylow
147	C₂³×C₁₉	—	2	1	no	—
148	C₂³×C₁₉	—	4	1	no	—
149	C₂³×C₁₉	#121	1	1	yes	characteristic
150	Q₈×C₁₉	—	2	1	no	—
151	Q₈×C₁₉	—	4	1	no	—
152	Q₈×C₁₉	—	4	1	no	—
153	Q₈×C₁₉	#102	1	2	yes	—
154	D₄×C₁₉	—	2	2	no	—
155	D₄×C₁₉	—	2	2	no	—
156	D₄×C₁₉	—	2	1	no	—
157	D₄×C₁₉	—	4	1	no	—
158	D₄×C₁₉	—	4	1	no	—
159	D₄×C₁₉	—	4	1	no	—
160	D₄×C₁₉	—	4	1	no	—
161	D₄×C₁₉	—	8	1	no	—
162	D₄×C₁₉	—	8	1	no	—
163	D₄×C₁₉	—	8	1	no	—
164	D₄×C₁₉	#102	1	2	yes	—
165	C₂×C₄×C₁₉	—	2	1	no	—
166	C₂×C₄×C₁₉	—	2	1	no	—
167	C₂×C₄×C₁₉	—	2	1	no	—
168	C₂×C₄×C₁₉	—	2	2	no	—
169	C₂×C₄×C₁₉	—	2	2	no	—
170	C₂×C₄×C₁₉	—	2	1	no	—
171	C₂×C₄×C₁₉	—	2	1	no	—
172	C₂×C₄×C₁₉	—	4	1	no	—
173	C₂×C₄×C₁₉	—	4	2	no	—
174	C₂×C₄×C₁₉	—	4	1	no	—
175	C₂×C₄×C₁₉	—	4	1	no	—
176	C₂×C₄×C₁₉	—	4	1	no	—
177	C₂×C₄×C₁₉	—	8	1	no	—
178	C₂×C₄×C₁₉	—	8	1	no	—
179	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
185	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
186	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
187	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
188	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
189	C₂×Dic₁₉	—	4	2	no	—
190	C₂×Dic₁₉	—	8	1	no	—
191	C₂×Dic₁₉	—	8	1	no	—
192	C₈×C₁₉	—	4	1	no	—
193	C₈×C₁₉	—	4	1	no	—
194	C₁₉⋊C₈	—	2	2	no	—
195	C₁₉⋊C₈	—	4	2	no	—
196	C₁₉⋊C₈	—	4	1	no	—
197	C₁₉⋊C₈	—	8	1	no	—
198	#3035	D₁₉	1	1	yes	characteristic
199	C₈×#41	—	19	1	no	—
200	#1806	—	19	1	no	—
201	#1502	—	19	1	no	—
202	#1492	—	19	1	no	—
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	—	2	2	no	—
208	C₂²×C₁₉	—	4	1	no	—
209	C₂²×C₁₉	—	4	1	no	—
210	C₂²×C₁₉	—	8	1	no	—
211	C₂²×C₁₉	—	8	1	no	—
212	C₂²×C₁₉	—	8	1	no	—
213	C₂²×C₁₉	#386	1	1	yes	characteristic
214	C₂²×C₁₉	#465	1	1	yes	characteristic
215	C₂²×C₁₉	#466	1	1	yes	characteristic
216	C₄×C₁₉	—	2	1	no	—
217	C₄×C₁₉	—	2	2	no	—
218	C₄×C₁₉	—	2	1	no	—
219	C₄×C₁₉	—	2	1	no	—
220	C₄×C₁₉	—	4	1	no	—
221	C₄×C₁₉	—	4	1	no	—
222	C₄×C₁₉	—	8	1	no	—
223	C₄×C₁₉	C₂×#102	1	1	yes	characteristic
224	C₄×C₁₉	#416	1	1	yes	characteristic
225	C₄×C₁₉	#443	1	1	yes	characteristic
226	C₄×C₁₉	#444	1	1	yes	characteristic
227	C₄×C₁₉	#465	1	1	yes	characteristic
228	C₄×C₁₉	#466	1	1	yes	characteristic
229	Dic₁₉	—	8	2	no	—
230	C₂×#135	—	2	1	no	—
231	#532	C₂×D₁₉	1	1	yes	characteristic
232	C₄×#41	C₂×D₁₉	1	1	yes	characteristic
233	#464	—	2	1	no	—
234	#463	—	2	1	no	—
235	#462	Dic₁₉	1	1	yes	characteristic, complemented
236	#461	Dic₁₉	1	1	yes	characteristic, complemented
237	#460	Dic₁₉	1	1	yes	characteristic, complemented
238	#459	Dic₁₉	1	1	yes	characteristic, complemented
239	C₈×Q₈	—	38	1	no	—
240	C₈×D₄	—	38	2	no	—
241	C₈×D₄	—	38	1	no	—
242	#431	—	19	1	no	—
243	#431	—	38	1	no	—
244	#423	—	19	1	no	—
245	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
246	C₂×#104	—	38	1	no	—
247	#416	—	2	1	no	—
248	C₂×C₄×C₈	—	19	1	no	—
249	C₂×C₄×C₈	—	38	1	no	—
250	C₄×C₄⋊C₄	—	19	1	no	—
251	#339	—	38	1	no	—
252	#327	—	38	2	no	—
253	D₄⋊C₈	—	38	1	no	—
254	D₄⋊C₈	—	38	1	no	—
255	C₂×C₁₉	—	2	1	no	—
256	C₂×C₁₉	—	2	1	no	—
257	C₂×C₁₉	—	4	2	no	—
258	C₂×C₁₉	—	16	1	no	—
259	C₂×C₁₉	#1876	1	1	yes	characteristic
260	C₂×C₁₉	#1893	1	1	yes	characteristic
261	C₂×C₁₉	#1906	1	1	yes	characteristic
262	C₂×#41	—	2	1	no	—
263	C₂×#41	C₂²⋊D₁₉	1	1	yes	characteristic
264	#135	—	4	2	no	—
265	#135	—	4	2	no	—
266	C₂×Q₁₆	—	2	1	no	—
267	C₂×SD₁₆	—	2	1	no	—
268	C₂×SD₁₆	—	2	1	no	—
269	C₂×D₈	—	2	1	no	—
270	C₂×M₁₆	—	38	1	no	—
271	C₂²×C₈	—	2	1	no	—
272	C₂²×C₈	—	38	2	no	—
273	C₂²×C₈	—	38	1	no	—
274	C₄⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
275	#127	C₂×Dic₁₉	1	1	yes	characteristic
276	#124	—	2	1	no	—
277	#121	—	2	1	no	—
278	#121	—	2	1	no	—
279	C₄×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
280	C₄×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
281	C₄×D₄	—	2	1	no	—
282	C₄×D₄	—	2	1	no	—
283	C₄×D₄	—	2	1	no	—
284	C₄×D₄	—	2	1	no	—
285	C₄×D₄	C₂×Dic₁₉	1	1	yes	characteristic
286	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
287	#117	—	2	1	no	—
288	#117	C₂²⋊D₁₉	1	1	yes	characteristic
289	C₂×C₄⋊C₄	—	38	1	no	—
290	C₂×C₄²	—	2	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	—	38	2	no	—
295	C₄⋊C₈	—	38	1	no	—
296	C₄⋊C₈	—	38	1	no	—
297	C₄⋊C₈	—	38	1	no	—
298	C₄⋊C₈	C₂×Dic₁₉	1	1	yes	characteristic
299	C₄⋊C₈	C₂×Dic₁₉	1	1	yes	characteristic
300	#104	—	76	2	no	—
301	#103	—	2	1	no	—
302	#103	—	2	1	no	—
303	#102	—	2	1	no	—
304	#102	—	2	1	no	—
305	C₂²⋊C₈	—	19	2	no	—
306	C₂²⋊C₈	—	38	2	no	—
307	C₄×C₈	—	19	1	no	—
308	C₄×C₈	—	19	1	no	—
309	C₄×C₈	—	38	2	no	—
310	C₄×C₈	—	38	1	no	—
311	C₄×C₈	—	38	1	no	—
312	#95	—	38	1	no	—
313	C₁₉	#9208	1	1	yes	characteristic, complemented, Sylow
314	#41	—	2	1	no	—
315	#41	—	2	1	no	—
316	#41	—	4	1	no	—
317	#41	—	4	1	no	—
318	#41	—	4	1	no	—
319	#41	—	4	1	no	—
320	#41	#64525	1	2	yes	—
321	#41	#64526	1	2	yes	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	4	1	no	—
329	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	4	1	no	—
334	C₂²×C₄	—	76	1	no	—
335	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
336	C₂²×C₄	#64543	1	1	yes	characteristic
337	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
338	Q₁₆	—	4	2	no	—
339	SD₁₆	—	4	2	no	—
340	SD₁₆	—	4	2	no	—
341	D₈	—	4	2	no	—
342	M₁₆	—	76	1	no	—
343	M₁₆	—	76	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	4	1	no	—
347	C₂×C₈	—	4	1	no	—
348	C₂×C₈	—	38	1	no	—
349	C₂×C₈	—	38	1	no	—
350	C₂×C₈	—	38	2	no	—
351	C₂×C₈	—	76	2	no	—
352	C₂×C₈	—	76	4	no	—
353	C₂×C₈	—	76	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	38	2	no	—
359	C₄⋊C₄	—	76	1	no	—
360	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
361	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
362	C₂²⋊C₄	—	2	1	no	—
363	C₂²⋊C₄	—	2	1	no	—
364	C₂²⋊C₄	—	2	1	no	—
365	C₂²⋊C₄	—	4	1	no	—
366	C₂²⋊C₄	—	4	1	no	—
367	C₄²	—	2	1	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	—	76	1	no	—
371	C₄²	—	76	1	no	—
372	C₄²	D₄×D₁₉	1	1	yes	characteristic
373	C₄²	#64543	1	1	yes	characteristic
374	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
375	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
376	C₂³	—	2	1	no	—
377	C₂³	—	4	1	no	—
378	C₂³	#10597385	1	1	yes	characteristic
379	Q₈	—	2	1	no	—
380	Q₈	—	4	1	no	—
381	Q₈	—	4	1	no	—
382	Q₈	#10597289	1	2	yes	—
383	D₄	—	2	2	no	—
384	D₄	—	2	2	no	—
385	D₄	—	2	1	no	—
386	D₄	—	4	1	no	—
387	D₄	—	4	1	no	—
388	D₄	—	4	1	no	—
389	D₄	—	4	1	no	—
390	D₄	—	8	1	no	—
391	D₄	—	8	1	no	—
392	D₄	—	8	1	no	—
393	D₄	#10597289	1	2	yes	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	8	1	no	—
407	C₂×C₄	—	8	1	no	—
408	C₂×C₄	—	76	2	no	—
409	C₂×C₄	—	152	1	no	—
410	C₂×C₄	—	152	1	no	—
411	C₂×C₄	C₂×#64525	1	1	yes	characteristic
412	C₂×C₄	C₂×#64526	1	1	yes	characteristic
413	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
414	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
415	C₂×C₄	#10597381	1	1	yes	characteristic
416	C₂×C₄	#10597383	1	1	yes	characteristic
417	C₂×C₄	#10597385	1	1	yes	characteristic
418	C₂×C₄	#10597396	1	1	yes	characteristic
419	C₂×C₄	#10597396	1	1	yes	characteristic
420	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
421	C₈	—	4	1	no	—
422	C₈	—	4	1	no	—
423	C₈	—	38	2	no	—
424	C₈	—	76	1	no	—
425	C₈	—	76	2	no	—
426	C₈	—	152	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	4	1	no	—
432	C₂²	—	8	1	no	—
433	C₂²	—	8	1	no	—
434	C₂²	—	8	1	no	—
435	C₂²	#11926424	1	1	yes	characteristic
436	C₂²	#11926771	1	1	yes	characteristic
437	C₂²	#11926778	1	1	yes	characteristic
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	2	no	—
442	C₄	—	4	1	no	—
443	C₄	—	4	1	no	—
444	C₄	—	8	1	no	—
445	C₄	—	152	2	no	—
446	C₄	C₂×#10597289	1	1	yes	characteristic
447	C₄	#11926540	1	1	yes	characteristic
448	C₄	#11926661	1	1	yes	characteristic
449	C₄	#11926666	1	1	yes	characteristic
450	C₄	#11926771	1	1	yes	characteristic
451	C₄	#11926778	1	1	yes	characteristic
452	C₂	—	2	1	no	—
453	C₂	—	2	1	no	—
454	C₂	—	4	2	no	—
455	C₂	—	16	1	no	—
456	C₂	#14563964	1	1	yes	characteristic
457	C₂	#14564064	1	1	yes	characteristic
458	C₂	#14564138	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597385
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#3035	C₂
socle	C₂²×C₁₉	#386
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3035	D₁₉
hypocenter	C₁₉	#9208
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3035

Complements

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

N	H ≅ G/N	type
1. #41×C₁₉⋊C₈	C₂	semidirect
2. #14563655	C₂	semidirect
3. #14562130	C₂	semidirect
4. #14562086	C₂	semidirect
5. #14561532	C₂	semidirect
6. #14561474	C₂	semidirect
27. C₁₉×#462	C₄	semidirect
28. C₁₉×#461	C₄	semidirect
29. C₁₉×#460	C₄	semidirect
30. C₁₉×#459	C₄	semidirect
235. #462	Dic₁₉	semidirect
236. #461	Dic₁₉	semidirect
237. #460	Dic₁₉	semidirect
238. #459	Dic₁₉	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
#41×C₁₉⋊C₈	2
#14563655	2
#14562130	2
#14562086	2
#14561532	2
#14561474	2
C₁₉×#3035	2
#9208	19