Subgroups — #18077428

Order 4864.

530 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14572203	C₂	1	1	yes	maximal, characteristic, complemented
2	#14562086	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562034	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562017	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561532	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561469	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3035	C₂	1	1	yes	maximal, characteristic
8	C₂×#10597394	—	2	1	no	—
9	#11926597	C₂²	1	1	yes	characteristic
10	#11926571	—	2	2	no	—
11	#11926571	—	2	1	no	—
12	#11926568	—	2	1	no	—
13	#11926568	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
15	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
17	Q₈⋊(C₁₉⋊C₈)	—	2	1	no	—
18	D₄⋊(C₁₉⋊C₈)	—	2	2	no	—
19	D₄⋊(C₁₉⋊C₈)	—	2	1	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
28	C₁₉×#461	C₄	1	1	yes	characteristic
29	C₁₉×#460	C₄	1	1	yes	characteristic
30	C₁₉×#459	C₄	1	1	yes	characteristic
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	#10597394	—	4	2	no	—
60	#10597394	—	4	2	no	—
61	C₂×#64520	—	2	2	no	—
62	C₂×#64520	—	2	1	no	—
63	C₂²×C₁₉⋊C₈	—	2	2	no	—
64	C₂²×C₁₉⋊C₈	—	2	1	no	—
65	C₂²×C₁₉⋊C₈	—	2	1	no	—
66	C₁₉×C₄⋊C₈	—	2	1	no	—
67	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
68	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
69	C₁₉×#103	—	2	1	no	—
70	C₁₉×#103	—	2	1	no	—
71	C₁₉×#102	—	2	1	no	—
72	C₁₉×#102	—	2	1	no	—
73	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
74	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
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)	D₄	1	1	yes	characteristic
80	C₄⋊(C₁₉⋊C₈)	D₄	1	1	yes	characteristic
81	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
82	C₄×C₁₉⋊C₈	—	2	1	no	—
83	C₄×C₁₉⋊C₈	—	2	1	no	—
84	C₄×C₁₉⋊C₈	—	2	1	no	—
85	#41×C₁₉	—	2	1	no	—
86	#41×C₁₉	—	2	1	no	—
87	#41×C₁₉	—	4	1	no	—
88	#41×C₁₉	—	4	1	no	—
89	#41×C₁₉	—	4	1	no	—
90	#41×C₁₉	—	4	1	no	—
91	#41×C₁₉	D₈	1	2	yes	—
92	#41×C₁₉	SD₁₆	1	2	yes	—
93	C₂×Q₈×C₁₉	—	2	1	no	—
94	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
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	—	2	1	no	—
99	C₂×D₄×C₁₉	—	4	1	no	—
100	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	—	2	1	no	—
102	C₂²×C₄×C₁₉	—	2	1	no	—
103	C₂²×C₄×C₁₉	—	2	1	no	—
104	C₂²×C₄×C₁₉	—	4	1	no	—
105	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
134	#64520	—	4	4	no	—
135	#64520	—	4	1	no	—
136	#64520	—	4	1	no	—
137	C₂×C₁₉⋊C₈	—	2	2	no	—
138	C₂×C₁₉⋊C₈	—	2	1	no	—
139	C₂×C₁₉⋊C₈	—	2	2	no	—
140	C₂×C₁₉⋊C₈	—	2	1	no	—
141	C₂×C₁₉⋊C₈	—	4	4	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	C₂×C₁₉⋊C₈	—	4	1	no	—
147	#8995	—	19	1	no	maximal, Sylow
148	C₂³×C₁₉	—	2	1	no	—
149	C₂³×C₁₉	—	4	1	no	—
150	C₂³×C₁₉	#123	1	1	yes	characteristic
151	Q₈×C₁₉	—	2	1	no	—
152	Q₈×C₁₉	—	4	1	no	—
153	Q₈×C₁₉	—	4	1	no	—
154	Q₈×C₁₉	#102	1	2	yes	—
155	D₄×C₁₉	—	2	2	no	—
156	D₄×C₁₉	—	2	2	no	—
157	D₄×C₁₉	—	2	1	no	—
158	D₄×C₁₉	—	4	2	no	—
159	D₄×C₁₉	—	4	1	no	—
160	D₄×C₁₉	—	4	1	no	—
161	D₄×C₁₉	—	4	1	no	—
162	D₄×C₁₉	—	4	1	no	—
163	D₄×C₁₉	—	8	1	no	—
164	D₄×C₁₉	—	8	1	no	—
165	D₄×C₁₉	#102	1	2	yes	—
166	C₂×C₄×C₁₉	—	2	1	no	—
167	C₂×C₄×C₁₉	—	2	1	no	—
168	C₂×C₄×C₁₉	—	2	1	no	—
169	C₂×C₄×C₁₉	—	2	2	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	1	no	—
172	C₂×C₄×C₁₉	—	2	1	no	—
173	C₂×C₄×C₁₉	—	4	1	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	—	8	1	no	—
180	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
185	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
186	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
188	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
190	C₈×C₁₉	—	4	1	no	—
191	C₈×C₁₉	—	4	1	no	—
192	C₁₉⋊C₈	—	4	2	no	—
193	C₁₉⋊C₈	—	4	1	no	—
194	C₁₉⋊C₈	—	4	2	no	—
195	C₁₉⋊C₈	—	4	1	no	—
196	C₁₉⋊C₈	—	8	1	no	—
197	#3035	D₁₉	1	1	yes	characteristic
198	#2906	—	19	1	no	—
199	#1492	—	19	1	no	—
200	#1480	—	19	1	no	—
201	#1476	—	19	1	no	—
202	#1301	—	19	1	no	—
203	#1277	—	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	1	no	—
208	C₂²×C₁₉	—	4	1	no	—
209	C₂²×C₁₉	—	8	1	no	—
210	C₂²×C₁₉	—	8	1	no	—
211	C₂²×C₁₉	—	8	1	no	—
212	C₂²×C₁₉	#386	1	1	yes	characteristic
213	C₂²×C₁₉	#480	1	1	yes	characteristic
214	C₂²×C₁₉	#481	1	1	yes	characteristic
215	C₄×C₁₉	—	2	2	no	—
216	C₄×C₁₉	—	2	1	no	—
217	C₄×C₁₉	—	2	1	no	—
218	C₄×C₁₉	—	2	1	no	—
219	C₄×C₁₉	—	4	1	no	—
220	C₄×C₁₉	—	4	1	no	—
221	C₄×C₁₉	—	8	1	no	—
222	C₄×C₁₉	C₂×#102	1	1	yes	characteristic
223	C₄×C₁₉	#417	1	1	yes	characteristic
224	C₄×C₁₉	#443	1	1	yes	characteristic
225	C₄×C₁₉	#444	1	1	yes	characteristic
226	C₄×C₁₉	#447	1	1	yes	characteristic
227	C₄×C₁₉	#448	1	1	yes	characteristic
228	C₂×#135	—	2	1	no	—
229	C₂×#131	—	38	1	no	—
230	#532	C₂×D₁₉	1	1	yes	characteristic
231	C₄×#41	C₂×D₁₉	1	1	yes	characteristic
232	#464	—	2	1	no	—
233	#463	—	2	1	no	—
234	#462	Dic₁₉	1	1	yes	characteristic
235	#461	Dic₁₉	1	1	yes	characteristic
236	#460	Dic₁₉	1	1	yes	characteristic
237	#459	Dic₁₉	1	1	yes	characteristic
238	#431	—	19	1	no	—
239	#424	—	38	2	no	—
240	#424	—	38	1	no	—
241	#423	—	19	1	no	—
242	#423	—	38	1	no	—
243	C₂×C₄⋊C₈	—	19	1	no	—
244	C₂×C₄⋊C₈	—	38	1	no	—
245	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
246	#416	—	2	1	no	—
247	C₂×C₄×C₈	—	19	1	no	—
248	Q₈⋊C₈	—	38	1	no	—
249	D₄⋊C₈	—	38	1	no	—
250	D₄⋊C₈	—	38	1	no	—
251	D₄⋊C₈	—	38	2	no	—
252	D₄⋊C₈	—	38	1	no	—
253	C₂×C₁₉	—	2	1	no	—
254	C₂×C₁₉	—	2	1	no	—
255	C₂×C₁₉	—	4	2	no	—
256	C₂×C₁₉	—	16	1	no	—
257	C₂×C₁₉	#1874	1	1	yes	characteristic
258	C₂×C₁₉	#1876	1	1	yes	characteristic
259	C₂×C₁₉	#1881	1	1	yes	characteristic
260	C₂×#41	—	2	1	no	—
261	C₂×#41	C₂²⋊D₁₉	1	1	yes	characteristic
262	#135	—	4	2	no	—
263	#135	—	4	2	no	—
264	C₂×Q₁₆	—	2	1	no	—
265	C₂×SD₁₆	—	2	1	no	—
266	C₂×SD₁₆	—	2	1	no	—
267	C₂×D₈	—	2	1	no	—
268	#131	—	76	2	no	—
269	#131	—	76	2	no	—
270	C₂×M₁₆	—	38	2	no	—
271	C₂×M₁₆	—	38	1	no	—
272	C₂²×C₈	—	2	1	no	—
273	C₂²×C₈	—	38	2	no	—
274	C₂²×C₈	—	38	1	no	—
275	C₂²×C₈	—	38	1	no	—
276	C₄⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
277	#127	C₂×Dic₁₉	1	1	yes	characteristic
278	#124	—	2	1	no	—
279	#121	—	2	1	no	—
280	#121	—	2	1	no	—
281	C₄×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
282	C₄×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
283	C₄×D₄	—	2	1	no	—
284	C₄×D₄	—	2	1	no	—
285	C₄×D₄	—	2	1	no	—
286	C₄×D₄	—	2	1	no	—
287	C₄×D₄	C₂×Dic₁₉	1	1	yes	characteristic
288	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
289	#117	—	2	1	no	—
290	#117	C₂²⋊D₁₉	1	1	yes	characteristic
291	C₂×C₄²	—	2	1	no	—
292	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
293	C₄⋊C₈	—	2	1	no	—
294	C₄⋊C₈	—	19	1	no	—
295	C₄⋊C₈	—	19	1	no	—
296	C₄⋊C₈	—	19	2	no	—
297	C₄⋊C₈	—	38	2	no	—
298	C₄⋊C₈	—	38	2	no	—
299	C₄⋊C₈	—	38	1	no	—
300	C₄⋊C₈	—	38	1	no	—
301	C₄⋊C₈	—	38	1	no	—
302	C₄⋊C₈	C₂×Dic₁₉	1	1	yes	characteristic
303	C₄⋊C₈	C₂×Dic₁₉	1	1	yes	characteristic
304	#103	—	2	1	no	—
305	#103	—	2	1	no	—
306	#102	—	2	1	no	—
307	#102	—	2	1	no	—
308	C₂²⋊C₈	—	38	1	no	—
309	C₄×C₈	—	38	1	no	—
310	C₄×C₈	—	38	1	no	—
311	C₄×C₈	—	38	1	no	—
312	C₁₉	#8995	1	1	yes	characteristic, complemented, Sylow
313	#41	—	2	1	no	—
314	#41	—	2	1	no	—
315	#41	—	4	1	no	—
316	#41	—	4	1	no	—
317	#41	—	4	1	no	—
318	#41	—	4	1	no	—
319	#41	#64525	1	2	yes	—
320	#41	#64526	1	2	yes	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
323	C₂×D₄	—	2	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	C₂²⋊Dic₁₉	1	1	yes	characteristic
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	4	1	no	—
333	C₂²×C₄	#64543	1	1	yes	characteristic
334	C₂²×C₄	#64543	1	1	yes	characteristic
335	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
336	Q₁₆	—	4	2	no	—
337	SD₁₆	—	4	2	no	—
338	SD₁₆	—	4	2	no	—
339	D₈	—	4	2	no	—
340	M₁₆	—	76	4	no	—
341	M₁₆	—	76	1	no	—
342	M₁₆	—	76	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	4	1	no	—
346	C₂×C₈	—	4	1	no	—
347	C₂×C₈	—	38	2	no	—
348	C₂×C₈	—	38	1	no	—
349	C₂×C₈	—	38	1	no	—
350	C₂×C₈	—	38	2	no	—
351	C₂×C₈	—	76	1	no	—
352	C₂×C₈	—	76	4	no	—
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	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
362	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
363	C₂²⋊C₄	—	2	1	no	—
364	C₂²⋊C₄	—	2	1	no	—
365	C₂²⋊C₄	—	2	1	no	—
366	C₂²⋊C₄	—	4	1	no	—
367	C₂²⋊C₄	—	4	1	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	—	2	1	no	—
371	C₄²	D₄×D₁₉	1	1	yes	characteristic
372	C₄²	D₄×D₁₉	1	1	yes	characteristic
373	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
374	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
375	C₂³	—	2	1	no	—
376	C₂³	—	4	1	no	—
377	C₂³	#10597381	1	1	yes	characteristic
378	Q₈	—	2	1	no	—
379	Q₈	—	4	1	no	—
380	Q₈	—	4	1	no	—
381	Q₈	#10597289	1	2	yes	—
382	D₄	—	2	2	no	—
383	D₄	—	2	2	no	—
384	D₄	—	2	1	no	—
385	D₄	—	4	2	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	#10597289	1	2	yes	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	8	1	no	—
405	C₂×C₄	—	8	1	no	—
406	C₂×C₄	—	8	1	no	—
407	C₂×C₄	C₂×#64525	1	1	yes	characteristic
408	C₂×C₄	C₂×#64526	1	1	yes	characteristic
409	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
410	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
411	C₂×C₄	#10597383	1	1	yes	characteristic
412	C₂×C₄	#10597385	1	1	yes	characteristic
413	C₂×C₄	#10597385	1	1	yes	characteristic
414	C₂×C₄	#10597395	1	1	yes	characteristic
415	C₂×C₄	#10597397	1	1	yes	characteristic
416	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
417	C₈	—	4	1	no	—
418	C₈	—	4	1	no	—
419	C₈	—	76	2	no	—
420	C₈	—	76	1	no	—
421	C₈	—	76	2	no	—
422	C₈	—	76	1	no	—
423	C₈	—	152	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	4	1	no	—
429	C₂²	—	8	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	—	8	1	no	—
432	C₂²	#11926424	1	1	yes	characteristic
433	C₂²	#11926855	1	1	yes	characteristic
434	C₂²	#11926860	1	1	yes	characteristic
435	C₄	—	2	2	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	1	no	—
441	C₄	—	8	1	no	—
442	C₄	C₂×#10597289	1	1	yes	characteristic
443	C₄	#11926545	1	1	yes	characteristic
444	C₄	#11926661	1	1	yes	characteristic
445	C₄	#11926666	1	1	yes	characteristic
446	C₄	#11926677	1	1	yes	characteristic
447	C₄	#11926682	1	1	yes	characteristic
448	C₂	—	2	1	no	—
449	C₂	—	2	1	no	—
450	C₂	—	4	2	no	—
451	C₂	—	16	1	no	—
452	C₂	#14563953	1	1	yes	characteristic
453	C₂	#14563964	1	1	yes	characteristic
454	C₂	#14563999	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597383
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	#8995
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. #14572203	C₂	semidirect
2. #14562086	C₂	semidirect
3. #14562034	C₂	semidirect
4. #14562017	C₂	semidirect
5. #14561532	C₂	semidirect
6. #14561469	C₂	semidirect
312. C₁₉	#8995	semidirect

Maximal subgroups

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

subgroup	index
#14572203	2
#14562086	2
#14562034	2
#14562017	2
#14561532	2
#14561469	2
C₁₉×#3035	2
#8995	19