Subgroups — #18077400

Order 4864.

578 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#64520	C₂	1	1	yes	maximal, characteristic, complemented
2	#14564555	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#10597289	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562086	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561537	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561471	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3100	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	—	2	1	no	—
9	#11926622	—	2	1	no	—
10	#11926616	—	2	2	no	—
11	D₄×C₁₉⋊C₈	—	2	1	no	—
12	#11926568	C₂²	1	1	yes	characteristic
13	C₂×#10597294	—	2	1	no	—
14	C₂×#10597294	—	2	1	no	—
15	C₂×#10597289	—	2	1	no	—
16	#11926508	—	2	1	no	—
17	C₄×#64520	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
19	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
20	#11926306	—	2	1	no	—
21	D₄⋊(C₁₉⋊C₈)	—	2	2	no	—
22	C₁₉×#532	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#480	—	2	1	no	—
25	C₁₉×#474	C₄	1	1	yes	characteristic, complemented
26	C₁₉×#474	C₄	1	1	yes	characteristic, complemented
27	C₁₉×#459	C₄	1	1	yes	characteristic, complemented
28	C₁₉×#459	C₄	1	1	yes	characteristic, complemented
29	C₁₉×#447	—	2	1	no	—
30	C₄×D₈×C₁₉	—	2	1	no	—
31	C₄×D₈×C₁₉	—	2	1	no	—
32	C₁₉×#431	C₂²	1	1	yes	characteristic
33	C₂×#41×C₁₉	—	2	1	no	—
34	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₉	—	2	1	no	—
36	C₂×D₈×C₁₉	—	2	1	no	—
37	C₂×D₈×C₁₉	—	2	1	no	—
38	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
39	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
40	C₁₉×#124	—	2	1	no	—
41	C₁₉×#121	—	2	1	no	—
42	C₁₉×#121	—	2	1	no	—
43	C₄×D₄×C₁₉	—	2	1	no	—
44	C₄×D₄×C₁₉	—	2	1	no	—
45	C₄×D₄×C₁₉	—	2	1	no	—
46	C₄×D₄×C₁₉	—	2	1	no	—
47	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
48	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
49	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
50	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
51	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
52	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
54	C₂×C₄⋊Dic₁₉	—	2	1	no	—
55	C₂×C₄×Dic₁₉	—	2	1	no	—
56	C₂×#64520	—	2	2	no	—
57	C₂×#64520	—	2	1	no	—
58	C₂×#64520	—	4	2	no	—
59	C₂×#64520	—	4	2	no	—
60	C₂×#64520	D₄	1	1	yes	characteristic
61	C₂×#64520	D₄	1	1	yes	characteristic
62	C₂²×C₁₉⋊C₈	—	2	2	no	—
63	C₂²×C₁₉⋊C₈	—	2	1	no	—
64	C₁₉×#107	—	2	1	no	—
65	C₁₉×#107	—	2	1	no	—
66	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
67	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
68	C₁₉×#102	—	2	1	no	—
69	C₁₉×#102	—	2	1	no	—
70	C₁₉×#102	—	2	1	no	—
71	C₁₉×#102	—	2	1	no	—
72	C₁₉×C₂²⋊C₈	—	2	1	no	—
73	C₄×C₈×C₁₉	—	2	1	no	—
74	#10597294	—	4	2	no	—
75	#10597294	—	4	2	no	—
76	#10597289	—	2	4	no	—
77	C₁₉⋊#95	—	2	1	no	—
78	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
79	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
80	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
81	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
82	#10597260	—	2	1	no	—
83	C₄×C₁₉⋊C₈	—	2	1	no	—
84	C₄×C₁₉⋊C₈	—	2	1	no	—
85	C₄×C₁₉⋊C₈	—	2	1	no	—
86	C₂⁴×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	C₂×Q₈×C₁₉	—	2	1	no	—
92	C₂×D₄×C₁₉	—	2	2	no	—
93	C₂×D₄×C₁₉	—	2	1	no	—
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	—	4	1	no	—
98	C₂×D₄×C₁₉	—	4	1	no	—
99	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
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	—	2	1	no	—
105	C₂²×C₄×C₁₉	—	2	1	no	—
106	C₂²×C₄×C₁₉	—	4	1	no	—
107	C₂²×C₄×C₁₉	—	4	1	no	—
108	C₂²×C₄×C₁₉	—	4	1	no	—
109	C₂²×C₄×C₁₉	—	4	1	no	—
110	C₂²×C₄×C₁₉	—	4	1	no	—
111	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
114	C₂²×Dic₁₉	—	4	1	no	—
115	D₈×C₁₉	—	4	2	no	—
116	D₈×C₁₉	—	4	2	no	—
117	C₂×C₈×C₁₉	—	2	1	no	—
118	C₂×C₈×C₁₉	—	2	1	no	—
119	C₄⋊C₄×C₁₉	—	2	1	no	—
120	C₄⋊C₄×C₁₉	—	2	1	no	—
121	C₄⋊C₄×C₁₉	—	2	1	no	—
122	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
123	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²⋊C₄×C₁₉	—	2	1	no	—
125	C₂²⋊C₄×C₁₉	—	2	1	no	—
126	C₂²⋊C₄×C₁₉	—	2	1	no	—
127	C₂²⋊C₄×C₁₉	—	2	1	no	—
128	C₂²⋊C₄×C₁₉	—	4	1	no	—
129	C₂²⋊C₄×C₁₉	—	4	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	—	2	1	no	—
139	#64520	—	2	1	no	—
140	#64520	—	2	1	no	—
141	#64520	—	4	4	no	—
142	#64520	—	4	1	no	—
143	#64520	—	4	1	no	—
144	#64520	D₈	1	2	yes	complemented
145	C₂×C₁₉⋊C₈	—	2	1	no	—
146	C₂×C₁₉⋊C₈	—	2	2	no	—
147	C₂×C₁₉⋊C₈	—	2	1	no	—
148	C₂×C₁₉⋊C₈	—	2	2	no	—
149	C₂×C₁₉⋊C₈	—	4	4	no	—
150	C₂×C₁₉⋊C₈	—	4	1	no	—
151	C₂×C₁₉⋊C₈	—	4	1	no	—
152	#8991	—	19	1	no	maximal, Sylow
153	C₂³×C₁₉	—	2	1	no	—
154	C₂³×C₁₉	—	2	1	no	—
155	C₂³×C₁₉	—	4	2	no	—
156	C₂³×C₁₉	—	4	1	no	—
157	C₂³×C₁₉	—	4	1	no	—
158	C₂³×C₁₉	—	4	1	no	—
159	C₂³×C₁₉	—	8	1	no	—
160	C₂³×C₁₉	#121	1	1	yes	characteristic
161	Q₈×C₁₉	—	4	1	no	—
162	Q₈×C₁₉	—	4	1	no	—
163	D₄×C₁₉	—	2	1	no	—
164	D₄×C₁₉	—	2	1	no	—
165	D₄×C₁₉	—	2	1	no	—
166	D₄×C₁₉	—	4	2	no	—
167	D₄×C₁₉	—	4	2	no	—
168	D₄×C₁₉	—	4	1	no	—
169	D₄×C₁₉	—	4	1	no	—
170	D₄×C₁₉	—	4	1	no	—
171	D₄×C₁₉	—	4	1	no	—
172	D₄×C₁₉	—	8	1	no	—
173	D₄×C₁₉	—	8	1	no	—
174	D₄×C₁₉	#104	1	2	yes	complemented
175	C₂×C₄×C₁₉	—	2	1	no	—
176	C₂×C₄×C₁₉	—	2	1	no	—
177	C₂×C₄×C₁₉	—	2	1	no	—
178	C₂×C₄×C₁₉	—	2	1	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	4	1	no	—
181	C₂×C₄×C₁₉	—	4	1	no	—
182	C₂×C₄×C₁₉	—	4	1	no	—
183	C₂×C₄×C₁₉	—	4	1	no	—
184	C₂×C₄×C₁₉	—	4	1	no	—
185	C₂×C₄×C₁₉	—	4	1	no	—
186	C₂×C₄×C₁₉	—	4	1	no	—
187	C₂×C₄×C₁₉	—	4	1	no	—
188	C₂×C₄×C₁₉	—	4	1	no	—
189	C₂×C₄×C₁₉	—	4	1	no	—
190	C₂×C₄×C₁₉	—	4	1	no	—
191	C₂×C₄×C₁₉	—	8	1	no	—
192	C₂×C₄×C₁₉	—	8	1	no	—
193	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
194	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
197	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
198	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
199	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
200	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
201	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
202	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
203	C₂×Dic₁₉	—	4	2	no	—
204	C₂×Dic₁₉	—	8	1	no	—
205	C₂×Dic₁₉	—	8	1	no	—
206	C₈×C₁₉	—	4	1	no	—
207	C₈×C₁₉	—	4	1	no	—
208	C₁₉⋊C₈	—	2	2	no	—
209	C₁₉⋊C₈	—	4	2	no	—
210	C₁₉⋊C₈	—	4	2	no	—
211	C₁₉⋊C₈	—	4	1	no	—
212	#3100	D₁₉	1	1	yes	characteristic
213	D₄×M₁₆	—	19	1	no	—
214	#1980	—	19	1	no	—
215	C₄×#102	—	19	1	no	—
216	#1492	—	19	1	no	—
217	#1303	—	19	1	no	—
218	#1278	—	19	1	no	—
219	C₂²×C₁₉	—	2	1	no	—
220	C₂²×C₁₉	—	2	1	no	—
221	C₂²×C₁₉	—	2	2	no	—
222	C₂²×C₁₉	—	4	1	no	—
223	C₂²×C₁₉	—	4	1	no	—
224	C₂²×C₁₉	—	4	1	no	—
225	C₂²×C₁₉	—	4	1	no	—
226	C₂²×C₁₉	—	4	1	no	—
227	C₂²×C₁₉	—	8	2	no	—
228	C₂²×C₁₉	—	8	2	no	—
229	C₂²×C₁₉	—	8	1	no	—
230	C₂²×C₁₉	—	8	1	no	—
231	C₂²×C₁₉	—	8	1	no	—
232	C₂²×C₁₉	#386	1	1	yes	characteristic
233	C₂²×C₁₉	#459	1	1	yes	characteristic
234	C₂²×C₁₉	#463	1	1	yes	characteristic
235	C₄×C₁₉	—	2	1	no	—
236	C₄×C₁₉	—	2	1	no	—
237	C₄×C₁₉	—	2	1	no	—
238	C₄×C₁₉	—	4	1	no	—
239	C₄×C₁₉	—	4	1	no	—
240	C₄×C₁₉	—	8	1	no	—
241	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
242	C₄×C₁₉	#421	1	1	yes	characteristic
243	C₄×C₁₉	C₄×D₈	1	1	yes	characteristic
244	C₄×C₁₉	#442	1	1	yes	characteristic
245	C₄×C₁₉	#447	1	1	yes	characteristic
246	C₄×C₁₉	#449	1	1	yes	characteristic
247	Dic₁₉	—	8	2	no	—
248	C₂²×M₁₆	—	38	1	no	—
249	#532	C₂×D₁₉	1	1	yes	characteristic
250	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
251	#480	—	2	1	no	—
252	#474	Dic₁₉	1	1	yes	characteristic, complemented
253	#474	Dic₁₉	1	1	yes	characteristic, complemented
254	#459	Dic₁₉	1	1	yes	characteristic, complemented
255	#459	Dic₁₉	1	1	yes	characteristic, complemented
256	#447	—	2	1	no	—
257	C₄×D₈	—	2	1	no	—
258	C₄×D₈	—	2	1	no	—
259	#436	—	38	1	no	—
260	#435	—	38	2	no	—
261	C₈×D₄	—	38	1	no	—
262	#431	C₂×D₁₉	1	1	yes	characteristic
263	#423	—	19	1	no	—
264	C₂×#104	—	38	1	no	—
265	C₂×#104	—	38	1	no	—
266	C₂×#102	—	38	1	no	—
267	#407	—	38	1	no	—
268	C₄×M₁₆	—	19	1	no	—
269	C₂×C₄×C₈	—	19	1	no	—
270	C₄×C₄⋊C₄	—	19	1	no	—
271	#340	—	38	1	no	—
272	D₄⋊C₈	—	38	2	no	—
273	C₂×C₁₉	—	2	1	no	—
274	C₂×C₁₉	—	2	1	no	—
275	C₂×C₁₉	—	4	2	no	—
276	C₂×C₁₉	—	8	1	no	—
277	C₂×C₁₉	—	16	1	no	—
278	C₂×C₁₉	#1871	1	1	yes	characteristic
279	C₂×C₁₉	#1879	1	1	yes	characteristic
280	C₂×C₁₉	#1881	1	1	yes	characteristic
281	C₂×#41	—	2	1	no	—
282	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
283	C₂³×C₄	—	2	1	no	—
284	C₂×D₈	—	2	1	no	—
285	C₂×D₈	—	2	1	no	—
286	C₂×M₁₆	—	19	1	no	—
287	C₂×M₁₆	—	19	1	no	—
288	C₂×M₁₆	—	38	2	no	—
289	C₂×M₁₆	—	38	1	no	—
290	C₂×M₁₆	—	76	2	no	—
291	C₂×M₁₆	—	76	2	no	—
292	C₂²×C₈	—	38	2	no	—
293	C₂²×C₈	—	38	1	no	—
294	C₄⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
295	#127	C₂×Dic₁₉	1	1	yes	characteristic
296	#124	—	2	1	no	—
297	#121	—	2	1	no	—
298	#121	—	2	1	no	—
299	C₄×D₄	—	2	1	no	—
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	—	2	1	no	—
302	C₄×D₄	—	2	1	no	—
303	C₄×D₄	C₂×Dic₁₉	1	1	yes	characteristic
304	C₄×D₄	C₂×Dic₁₉	1	1	yes	characteristic
305	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
306	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
307	C₂×C₄⋊C₄	—	38	1	no	—
308	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₄²	—	38	1	no	—
311	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
312	#107	—	2	1	no	—
313	#107	—	2	1	no	—
314	C₄⋊C₈	—	19	2	no	—
315	C₄⋊C₈	—	38	1	no	—
316	C₄⋊C₈	C₂×Dic₁₉	1	1	yes	characteristic
317	C₄⋊C₈	C₂×Dic₁₉	1	1	yes	characteristic
318	#104	—	76	2	no	—
319	#104	—	76	2	no	—
320	#102	—	2	1	no	—
321	#102	—	2	1	no	—
322	#102	—	2	1	no	—
323	#102	—	2	1	no	—
324	#102	—	38	4	no	—
325	C₂²⋊C₈	—	2	1	no	—
326	C₂²⋊C₈	—	38	2	no	—
327	C₂²⋊C₈	—	38	2	no	—
328	#97	—	38	1	no	—
329	C₄×C₈	—	2	1	no	—
330	C₄×C₈	—	38	1	no	—
331	C₄×C₈	—	38	1	no	—
332	C₄×C₈	—	38	1	no	—
333	#95	—	38	1	no	—
334	C₁₉	#8991	1	1	yes	characteristic, complemented, Sylow
335	C₂⁴	—	2	1	no	—
336	#41	—	4	1	no	—
337	#41	—	4	1	no	—
338	#41	—	4	1	no	—
339	#41	—	4	1	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	—	4	1	no	—
347	C₂×D₄	—	4	1	no	—
348	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
349	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	4	1	no	—
356	C₂²×C₄	—	4	1	no	—
357	C₂²×C₄	—	4	1	no	—
358	C₂²×C₄	—	4	1	no	—
359	C₂²×C₄	—	4	1	no	—
360	C₂²×C₄	—	76	1	no	—
361	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
362	C₂²×C₄	#64543	1	1	yes	characteristic
363	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
364	D₈	—	4	2	no	—
365	D₈	—	4	2	no	—
366	M₁₆	—	19	2	no	—
367	M₁₆	—	38	1	no	—
368	M₁₆	—	38	1	no	—
369	M₁₆	—	38	1	no	—
370	M₁₆	—	76	4	no	—
371	M₁₆	—	76	1	no	—
372	M₁₆	—	76	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	38	1	no	—
376	C₂×C₈	—	38	2	no	—
377	C₂×C₈	—	38	1	no	—
378	C₂×C₈	—	38	2	no	—
379	C₂×C₈	—	76	4	no	—
380	C₂×C₈	—	76	1	no	—
381	C₂×C₈	—	76	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	38	2	no	—
386	C₄⋊C₄	—	76	1	no	—
387	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
388	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
389	C₂²⋊C₄	—	2	1	no	—
390	C₂²⋊C₄	—	2	1	no	—
391	C₂²⋊C₄	—	2	1	no	—
392	C₂²⋊C₄	—	2	1	no	—
393	C₂²⋊C₄	—	4	1	no	—
394	C₂²⋊C₄	—	4	1	no	—
395	C₄²	—	76	1	no	—
396	C₄²	—	76	1	no	—
397	C₄²	D₄×D₁₉	1	1	yes	characteristic
398	C₄²	#64543	1	1	yes	characteristic
399	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
400	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
401	C₂³	—	2	1	no	—
402	C₂³	—	2	1	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	1	no	—
405	C₂³	—	4	1	no	—
406	C₂³	—	4	1	no	—
407	C₂³	—	8	1	no	—
408	C₂³	#10597385	1	1	yes	characteristic
409	Q₈	—	4	1	no	—
410	Q₈	—	4	1	no	—
411	D₄	—	2	1	no	—
412	D₄	—	2	1	no	—
413	D₄	—	2	1	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	1	no	—
417	D₄	—	4	1	no	—
418	D₄	—	4	1	no	—
419	D₄	—	4	1	no	—
420	D₄	—	8	1	no	—
421	D₄	—	8	1	no	—
422	D₄	#10597294	1	2	yes	complemented
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	8	1	no	—
440	C₂×C₄	—	8	1	no	—
441	C₂×C₄	—	76	2	no	—
442	C₂×C₄	—	152	1	no	—
443	C₂×C₄	—	152	1	no	—
444	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
445	C₂×C₄	#10597357	1	1	yes	characteristic
446	C₂×C₄	#10597357	1	1	yes	characteristic
447	C₂×C₄	#10597358	1	1	yes	characteristic
448	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
449	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
450	C₂×C₄	#10597381	1	1	yes	characteristic
451	C₂×C₄	#10597383	1	1	yes	characteristic
452	C₂×C₄	#10597385	1	1	yes	characteristic
453	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
454	C₈	—	4	1	no	—
455	C₈	—	4	1	no	—
456	C₈	—	38	2	no	—
457	C₈	—	76	2	no	—
458	C₈	—	76	2	no	—
459	C₈	—	76	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	—	4	1	no	—
466	C₂²	—	4	1	no	—
467	C₂²	—	4	1	no	—
468	C₂²	—	8	2	no	—
469	C₂²	—	8	2	no	—
470	C₂²	—	8	1	no	—
471	C₂²	—	8	1	no	—
472	C₂²	—	8	1	no	—
473	C₂²	#11926424	1	1	yes	characteristic
474	C₂²	#11926737	1	1	yes	characteristic
475	C₂²	#11926757	1	1	yes	characteristic
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	1	no	—
479	C₄	—	4	1	no	—
480	C₄	—	4	1	no	—
481	C₄	—	8	1	no	—
482	C₄	—	152	2	no	—
483	C₄	C₂×#10597294	1	1	yes	characteristic
484	C₄	#11926561	1	1	yes	characteristic
485	C₄	D₈×Dic₁₉	1	1	yes	characteristic
486	C₄	#11926656	1	1	yes	characteristic
487	C₄	#11926676	1	1	yes	characteristic
488	C₄	#11926686	1	1	yes	characteristic
489	C₂	—	2	1	no	—
490	C₂	—	2	1	no	—
491	C₂	—	4	2	no	—
492	C₂	—	8	1	no	—
493	C₂	—	16	1	no	—
494	C₂	#14563938	1	1	yes	characteristic
495	C₂	#14563985	1	1	yes	characteristic
496	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×#3100	C₂
socle	C₂²×C₁₉	#386
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3100	D₁₉
hypocenter	C₁₉	#8991
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3100

Complements

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

N	H ≅ G/N	type
1. D₄×#64520	C₂	semidirect
2. #14564555	C₂	semidirect
3. C₄×#10597289	C₂	semidirect
4. #14562086	C₂	semidirect
5. #14561537	C₂	semidirect
6. #14561471	C₂	semidirect
25. C₁₉×#474	C₄	semidirect
26. C₁₉×#474	C₄	semidirect
27. C₁₉×#459	C₄	semidirect
28. C₁₉×#459	C₄	semidirect
144. #64520	D₈	semidirect
174. D₄×C₁₉	#104	semidirect
252. #474	Dic₁₉	semidirect
253. #474	Dic₁₉	semidirect
254. #459	Dic₁₉	semidirect
255. #459	Dic₁₉	semidirect
334. C₁₉	#8991	semidirect
422. D₄	#10597294	semidirect

Maximal subgroups

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

subgroup	index
D₄×#64520	2
#14564555	2
C₄×#10597289	2
#14562086	2
#14561537	2
#14561471	2
C₁₉×#3100	2
#8991	19