Subgroups — #18077755

Order 4864.

488 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	#14572774	C₂	1	1	yes	maximal, characteristic, complemented
2	#14564434	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562223	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562078	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561535	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561484	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3105	C₂	1	1	yes	maximal, characteristic
8	#11926675	—	2	1	no	—
9	#11926616	—	2	1	no	—
10	#11926616	—	2	1	no	—
11	D₄×C₁₉⋊C₈	—	2	1	no	—
12	#11926605	—	2	1	no	—
13	#11926601	C₂²	1	1	yes	characteristic
14	#11926571	—	2	1	no	—
15	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
17	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
18	C₄×#64520	C₂²	1	1	yes	characteristic
19	C₂×#10597260	C₂²	1	1	yes	characteristic
20	#11926286	—	2	1	no	—
21	#11926284	—	2	1	no	—
22	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
23	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
24	C₁₉×#529	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#484	C₄	1	1	yes	characteristic
27	C₁₉×#481	C₄	1	1	yes	characteristic
28	C₁₉×#478	—	2	1	no	—
29	C₁₉×#463	—	2	1	no	—
30	C₁₉×#450	C₄	1	1	yes	characteristic
31	C₁₉×#447	C₄	1	1	yes	characteristic
32	C₄×SD₁₆×C₁₉	—	2	1	no	—
33	C₄×D₈×C₁₉	—	2	1	no	—
34	C₁₉×#431	C₂²	1	1	yes	characteristic
35	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₉	—	2	1	no	—
37	C₂×SD₁₆×C₁₉	—	2	1	no	—
38	C₂×D₈×C₁₉	—	2	1	no	—
39	C₁₉×#126	—	2	1	no	—
40	C₁₉×#125	D₄	1	1	yes	characteristic
41	C₁₉×#124	D₄	1	1	yes	characteristic
42	C₁₉×#123	—	2	1	no	—
43	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
44	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
45	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
46	C₄×D₄×C₁₉	—	2	1	no	—
47	C₄×D₄×C₁₉	—	2	1	no	—
48	C₄×D₄×C₁₉	—	2	1	no	—
49	C₄×D₄×C₁₉	—	2	1	no	—
50	C₄×D₄×C₁₉	—	2	1	no	—
51	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
52	C₁₉×#117	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
54	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
56	C₂×#64520	—	2	1	no	—
57	C₂×#64520	—	2	1	no	—
58	C₂²×C₁₉⋊C₈	—	2	1	no	—
59	C₂²×C₁₉⋊C₈	—	2	1	no	—
60	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
61	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
62	C₁₉×#107	—	2	1	no	—
63	C₁₉×#106	—	2	1	no	—
64	C₁₉×C₄⋊C₈	—	2	1	no	—
65	C₁₉×#103	—	2	1	no	—
66	C₁₉×#102	—	2	1	no	—
67	C₁₉×#102	—	2	1	no	—
68	C₁₉×#102	—	2	1	no	—
69	C₁₉×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
70	C₁₉×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
71	C₄×C₈×C₁₉	—	2	1	no	—
72	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
73	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
74	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
75	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
76	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
77	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
78	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
79	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
80	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
81	C₄⋊(C₁₉⋊C₈)	D₄	1	1	yes	characteristic
82	C₄⋊(C₁₉⋊C₈)	D₄	1	1	yes	characteristic
83	#10597260	—	2	1	no	—
84	#10597260	—	2	1	no	—
85	#10597260	—	2	1	no	—
86	#10597260	—	2	1	no	—
87	#10597260	—	2	1	no	—
88	C₄×C₁₉⋊C₈	—	2	1	no	—
89	C₄×C₁₉⋊C₈	—	2	1	no	—
90	C₂⁴×C₁₉	—	2	1	no	—
91	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×D₄×C₁₉	—	2	1	no	—
93	C₂×D₄×C₁₉	—	2	1	no	—
94	C₂×D₄×C₁₉	—	2	1	no	—
95	C₂×D₄×C₁₉	—	4	2	no	—
96	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	—	2	1	no	—
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	—	4	1	no	—
100	C₂²×C₄×C₁₉	—	4	1	no	—
101	C₂²×C₄×C₁₉	—	4	1	no	—
102	C₂²×C₄×C₁₉	—	4	1	no	—
103	C₂²×C₄×C₁₉	—	4	1	no	—
104	C₂²×C₄×C₁₉	—	4	1	no	—
105	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
108	SD₁₆×C₁₉	—	4	2	no	—
109	D₈×C₁₉	—	4	2	no	—
110	C₂×C₈×C₁₉	—	2	1	no	—
111	C₂×C₈×C₁₉	—	2	1	no	—
112	C₄⋊C₄×C₁₉	—	2	1	no	—
113	C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₄⋊C₄×C₁₉	—	2	1	no	—
116	C₄⋊C₄×C₁₉	—	2	1	no	—
117	C₄⋊C₄×C₁₉	—	2	1	no	—
118	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
119	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²⋊C₄×C₁₉	—	2	1	no	—
121	C₂²⋊C₄×C₁₉	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₁₉	#41	1	1	yes	characteristic
132	#64520	—	2	2	no	—
133	#64520	—	4	1	no	—
134	#64520	—	8	1	no	—
135	C₂×C₁₉⋊C₈	—	2	2	no	—
136	C₂×C₁₉⋊C₈	—	2	1	no	—
137	C₂×C₁₉⋊C₈	—	2	1	no	—
138	C₂×C₁₉⋊C₈	—	2	1	no	—
139	C₂×C₁₉⋊C₈	—	2	1	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	—	8	1	no	—
146	#9052	—	19	1	no	maximal, Sylow
147	C₂³×C₁₉	—	2	2	no	—
148	C₂³×C₁₉	—	2	1	no	—
149	C₂³×C₁₉	—	4	1	no	—
150	C₂³×C₁₉	—	4	1	no	—
151	C₂³×C₁₉	—	4	1	no	—
152	C₂³×C₁₉	—	4	1	no	—
153	C₂³×C₁₉	—	4	1	no	—
154	C₂³×C₁₉	—	4	1	no	—
155	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
156	Q₈×C₁₉	—	4	1	no	—
157	D₄×C₁₉	—	2	2	no	—
158	D₄×C₁₉	—	2	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	—	4	1	no	—
164	C₂×C₄×C₁₉	—	2	1	no	—
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	1	no	—
169	C₂×C₄×C₁₉	—	2	1	no	—
170	C₂×C₄×C₁₉	—	2	1	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	4	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	—	8	1	no	—
181	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	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	#123	1	1	yes	characteristic
187	C₈×C₁₉	—	4	1	no	—
188	C₈×C₁₉	—	4	1	no	—
189	C₁₉⋊C₈	—	4	2	no	—
190	C₁₉⋊C₈	—	4	2	no	—
191	C₁₉⋊C₈	—	4	1	no	—
192	C₁₉⋊C₈	—	4	1	no	—
193	C₁₉⋊C₈	—	4	1	no	—
194	C₁₉⋊C₈	—	4	1	no	—
195	#3105	D₁₉	1	1	yes	characteristic
196	#2992	—	19	1	no	—
197	#1955	—	19	1	no	—
198	#1524	—	19	1	no	—
199	#1490	—	19	1	no	—
200	#1302	—	19	1	no	—
201	#1283	—	19	1	no	—
202	C₂²×C₁₉	—	2	1	no	—
203	C₂²×C₁₉	—	2	1	no	—
204	C₂²×C₁₉	—	4	2	no	—
205	C₂²×C₁₉	—	4	2	no	—
206	C₂²×C₁₉	—	4	1	no	—
207	C₂²×C₁₉	—	4	1	no	—
208	C₂²×C₁₉	—	4	2	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	—	8	1	no	—
214	C₂²×C₁₉	#386	1	1	yes	characteristic
215	C₂²×C₁₉	#443	1	1	yes	characteristic
216	C₂²×C₁₉	#444	1	1	yes	characteristic
217	C₄×C₁₉	—	2	1	no	—
218	C₄×C₁₉	—	2	1	no	—
219	C₄×C₁₉	—	2	1	no	—
220	C₄×C₁₉	—	2	1	no	—
221	C₄×C₁₉	—	2	1	no	—
222	C₄×C₁₉	—	4	1	no	—
223	C₄×C₁₉	—	4	1	no	—
224	C₄×C₁₉	—	4	1	no	—
225	C₄×C₁₉	—	8	1	no	—
226	C₄×C₁₉	#453	1	1	yes	characteristic
227	C₄×C₁₉	#454	1	1	yes	characteristic
228	#529	C₂×D₁₉	1	1	yes	characteristic
229	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
230	#484	Dic₁₉	1	1	yes	characteristic
231	#481	Dic₁₉	1	1	yes	characteristic
232	#478	—	2	1	no	—
233	#463	—	2	1	no	—
234	#450	Dic₁₉	1	1	yes	characteristic
235	#447	Dic₁₉	1	1	yes	characteristic
236	#446	—	38	1	no	—
237	C₄×SD₁₆	—	2	1	no	—
238	C₄×D₈	—	2	1	no	—
239	#435	—	38	1	no	—
240	#435	—	38	1	no	—
241	C₈×D₄	—	38	1	no	—
242	#433	—	38	1	no	—
243	#432	—	19	1	no	—
244	#431	C₂×D₁₉	1	1	yes	characteristic
245	#424	—	38	1	no	—
246	C₂×C₄⋊C₈	—	19	1	no	—
247	C₂×C₂²⋊C₈	—	38	1	no	—
248	C₂×C₂²⋊C₈	—	38	1	no	—
249	C₄×M₁₆	—	19	1	no	—
250	C₂×#97	—	19	1	no	—
251	#330	—	38	1	no	—
252	#329	—	38	1	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	—	8	1	no	—
258	C₂×C₁₉	—	8	2	no	—
259	C₂×C₁₉	#1876	1	1	yes	characteristic
260	C₂×C₁₉	#1883	1	1	yes	characteristic
261	C₂×C₁₉	#1891	1	1	yes	characteristic
262	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
263	C₂³×C₄	—	2	1	no	—
264	C₂×SD₁₆	—	2	1	no	—
265	C₂×D₈	—	2	1	no	—
266	C₂×M₁₆	—	38	1	no	—
267	C₂×M₁₆	—	38	1	no	—
268	C₂²×C₈	—	19	1	no	—
269	C₂²×C₈	—	19	1	no	—
270	C₂²×C₈	—	38	1	no	—
271	C₂²×C₈	—	38	1	no	—
272	#126	—	2	1	no	—
273	#125	C₂²⋊D₁₉	1	1	yes	characteristic
274	#124	C₂²⋊D₁₉	1	1	yes	characteristic
275	#123	—	2	1	no	—
276	C₂²⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
277	#121	C₂×Dic₁₉	1	1	yes	characteristic
278	C₄×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
279	C₄×D₄	—	2	1	no	—
280	C₄×D₄	—	2	1	no	—
281	C₄×D₄	—	2	1	no	—
282	C₄×D₄	—	2	1	no	—
283	C₄×D₄	—	2	1	no	—
284	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
285	#117	—	2	1	no	—
286	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
287	C₂×C₂²⋊C₄	—	2	1	no	—
288	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
289	#107	—	2	1	no	—
290	#106	—	2	1	no	—
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	—	19	1	no	—
293	C₄⋊C₈	—	19	1	no	—
294	C₄⋊C₈	—	38	1	no	—
295	C₄⋊C₈	—	38	1	no	—
296	C₄⋊C₈	—	38	1	no	—
297	C₄⋊C₈	—	38	1	no	—
298	#103	—	2	1	no	—
299	#102	—	2	1	no	—
300	#102	—	2	1	no	—
301	#102	—	2	1	no	—
302	C₂²⋊C₈	—	38	1	no	—
303	C₂²⋊C₈	—	38	1	no	—
304	C₂²⋊C₈	—	38	1	no	—
305	C₂²⋊C₈	—	76	2	no	—
306	C₂²⋊C₈	—	76	2	no	—
307	C₂²⋊C₈	C₂×Dic₁₉	1	1	yes	characteristic
308	C₂²⋊C₈	C₂×Dic₁₉	1	1	yes	characteristic
309	#97	—	38	1	no	—
310	#97	—	38	1	no	—
311	#97	—	38	1	no	—
312	#97	—	38	1	no	—
313	#97	—	38	1	no	—
314	C₄×C₈	—	2	1	no	—
315	C₄×C₈	—	38	1	no	—
316	C₄×C₈	—	38	1	no	—
317	C₁₉	#9052	1	1	yes	characteristic, complemented, Sylow
318	C₂⁴	—	2	1	no	—
319	C₂×Q₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	4	2	no	—
324	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	—	4	1	no	—
332	C₂²×C₄	—	4	1	no	—
333	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
334	C₂²×C₄	#64543	1	1	yes	characteristic
335	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
336	SD₁₆	—	4	2	no	—
337	D₈	—	4	2	no	—
338	M₁₆	—	38	2	no	—
339	M₁₆	—	76	1	no	—
340	M₁₆	—	152	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	38	2	no	—
344	C₂×C₈	—	38	1	no	—
345	C₂×C₈	—	38	1	no	—
346	C₂×C₈	—	38	1	no	—
347	C₂×C₈	—	38	1	no	—
348	C₂×C₈	—	76	1	no	—
349	C₂×C₈	—	76	1	no	—
350	C₂×C₈	—	76	1	no	—
351	C₂×C₈	—	76	1	no	—
352	C₂×C₈	—	76	1	no	—
353	C₂×C₈	—	152	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	—	2	1	no	—
359	C₄⋊C₄	—	2	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	—	2	1	no	—
366	C₂²⋊C₄	—	2	1	no	—
367	C₂²⋊C₄	—	4	1	no	—
368	C₂²⋊C₄	—	4	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	D₄×D₁₉	1	1	yes	characteristic
371	C₄²	#64543	1	1	yes	characteristic
372	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
373	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
374	C₂³	—	2	2	no	—
375	C₂³	—	2	1	no	—
376	C₂³	—	4	1	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	1	no	—
381	C₂³	—	4	1	no	—
382	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
383	Q₈	—	4	1	no	—
384	D₄	—	2	2	no	—
385	D₄	—	2	2	no	—
386	D₄	—	4	1	no	—
387	D₄	—	4	1	no	—
388	D₄	—	4	1	no	—
389	D₄	—	4	1	no	—
390	D₄	—	4	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	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	—	8	1	no	—
408	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
409	C₂×C₄	#10597381	1	1	yes	characteristic
410	C₂×C₄	#10597383	1	1	yes	characteristic
411	C₂×C₄	#10597385	1	1	yes	characteristic
412	C₂×C₄	#10597385	1	1	yes	characteristic
413	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
414	C₈	—	4	1	no	—
415	C₈	—	4	1	no	—
416	C₈	—	76	2	no	—
417	C₈	—	76	2	no	—
418	C₈	—	76	1	no	—
419	C₈	—	76	1	no	—
420	C₈	—	76	1	no	—
421	C₈	—	76	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	1	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	4	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	—	8	1	no	—
432	C₂²	—	8	1	no	—
433	C₂²	—	8	1	no	—
434	C₂²	#11926424	1	1	yes	characteristic
435	C₂²	#11926661	1	1	yes	characteristic
436	C₂²	#11926666	1	1	yes	characteristic
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	4	1	no	—
443	C₄	—	4	1	no	—
444	C₄	—	4	1	no	—
445	C₄	—	8	1	no	—
446	C₄	#11926710	1	1	yes	characteristic
447	C₄	#11926715	1	1	yes	characteristic
448	C₂	—	2	1	no	—
449	C₂	—	2	1	no	—
450	C₂	—	8	2	no	—
451	C₂	—	8	1	no	—
452	C₂	#14563964	1	1	yes	characteristic
453	C₂	#14564013	1	1	yes	characteristic
454	C₂	#14564054	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597383
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#3105	C₂
socle	C₂²×C₁₉	#386
prime radical	C₁₉×#447	C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3105	D₁₉
hypocenter	C₁₉	#9052
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3105

Complements

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

N	H ≅ G/N	type
1. #14572774	C₂	semidirect
2. #14564434	C₂	semidirect
3. #14562223	C₂	semidirect
4. #14562078	C₂	semidirect
5. #14561535	C₂	semidirect
6. #14561484	C₂	semidirect
317. C₁₉	#9052	semidirect

Maximal subgroups

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

subgroup	index
#14572774	2
#14564434	2
#14562223	2
#14562078	2
#14561535	2
#14561484	2
C₁₉×#3105	2
#9052	19