Subgroups — #18078944

Order 4864.

612 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926739	C₂	1	1	yes	maximal, characteristic
2	#14564475	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562304	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562060	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561509	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561486	C₂	1	1	yes	maximal, characteristic, complemented
7	D₄×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64525	C₄	1	2	yes	—
9	C₂×#10597320	C₂²	1	1	yes	characteristic
10	#11926739	—	2	1	no	—
11	#11926739	—	2	1	no	—
12	#11926739	—	2	1	no	—
13	#11926739	—	2	1	no	—
14	#11926597	C₂²	1	1	yes	characteristic
15	#11926568	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×#10597266	C₄	1	2	yes	—
18	C₂×#10597280	—	2	1	no	—
19	C₂×#10597280	—	2	1	no	—
20	#11926287	—	2	2	no	—
21	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
22	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
23	C₂²×M₁₆×C₁₉	—	2	1	no	—
24	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#436	—	2	1	no	—
26	C₁₉×#435	—	2	2	no	—
27	C₈×D₄×C₁₉	—	2	1	no	—
28	C₁₉×#423	C₂²	1	1	yes	characteristic
29	C₁₉×#407	—	2	1	no	—
30	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
31	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₉	—	2	1	no	—
33	C₂²×D₇₆	—	2	1	no	—
34	C₂²×D₇₆	—	2	1	no	—
35	C₂²×D₇₆	C₂×C₄	1	2	yes	—
36	C₂×M₁₆×C₁₉	—	2	2	no	—
37	C₂×M₁₆×C₁₉	—	2	1	no	—
38	C₂×M₁₆×C₁₉	—	4	2	no	—
39	C₂×M₁₆×C₁₉	—	4	2	no	—
40	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
41	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₁₉	—	2	2	no	—
43	C₄×D₄×C₁₉	—	2	1	no	—
44	C₄×D₄×C₁₉	—	2	1	no	—
45	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
46	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
47	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
48	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
52	C₂×#64525	—	2	2	no	—
53	C₂×#64525	—	2	2	no	—
54	C₂×#64525	—	4	4	no	—
55	C₂×#64520	—	2	1	no	—
56	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
57	#10597320	—	2	1	no	—
58	#10597320	—	2	1	no	—
59	#10597320	—	2	1	no	—
60	#10597320	—	2	1	no	—
61	C₁₉×C₄⋊C₈	—	2	1	no	—
62	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
63	C₁₉×C₂²⋊C₈	—	2	2	no	—
64	C₁₉×C₂²⋊C₈	—	2	2	no	—
65	C₁₉×#97	—	2	1	no	—
66	C₄×C₈×C₁₉	—	2	1	no	—
67	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
68	#10597280	—	4	2	no	—
69	#10597280	—	4	2	no	—
70	#10597266	—	2	2	no	—
71	#10597266	—	2	2	no	—
72	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
73	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
74	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
75	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
76	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
77	C₄×C₁₉⋊C₈	—	2	1	no	—
78	C₂⁴×C₁₉	—	2	1	no	—
79	C₂³×D₁₉	—	2	2	no	—
80	C₂×D₄×C₁₉	—	2	2	no	—
81	C₂×D₄×C₁₉	—	2	1	no	—
82	C₂×D₄×C₁₉	—	4	1	no	—
83	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
84	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	—	2	1	no	—
86	C₂²×C₄×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	—	2	1	no	—
88	C₂²×C₄×C₁₉	—	2	1	no	—
89	C₂²×C₄×C₁₉	—	2	1	no	—
90	C₂²×C₄×C₁₉	—	4	1	no	—
91	C₂²×C₄×C₁₉	—	4	1	no	—
92	C₂²×C₄×C₁₉	—	4	1	no	—
93	C₂²×C₄×C₁₉	—	4	1	no	—
94	C₂²×C₄×C₁₉	C₂²×C₄	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×D₇₆	—	2	2	no	—
98	C₂×D₇₆	—	2	2	no	—
99	C₂×D₇₆	—	4	2	no	—
100	C₂×D₇₆	—	4	2	no	—
101	C₂×D₇₆	—	4	1	no	—
102	C₂×D₇₆	—	4	1	no	—
103	C₂×D₇₆	—	4	1	no	—
104	C₂×D₇₆	—	4	1	no	—
105	C₂×D₇₆	—	4	1	no	—
106	C₂×D₇₆	—	4	1	no	—
107	C₂×D₇₆	—	4	1	no	—
108	C₂×D₇₆	—	4	1	no	—
109	C₂×D₇₆	—	8	2	no	—
110	M₁₆×C₁₉	—	2	1	no	—
111	M₁₆×C₁₉	—	2	1	no	—
112	M₁₆×C₁₉	—	2	1	no	—
113	M₁₆×C₁₉	—	4	4	no	—
114	M₁₆×C₁₉	—	4	1	no	—
115	M₁₆×C₁₉	—	4	1	no	—
116	M₁₆×C₁₉	D₈	1	2	yes	complemented
117	C₂×C₈×C₁₉	—	2	1	no	—
118	C₂×C₈×C₁₉	—	2	2	no	—
119	C₂×C₈×C₁₉	—	2	1	no	—
120	C₂×C₈×C₁₉	—	4	4	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	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	#64525	—	4	4	no	—
133	#64525	—	4	4	no	—
134	#64520	—	4	1	no	—
135	#64520	—	4	1	no	—
136	C₂×C₁₉⋊C₈	—	2	2	no	—
137	C₂×C₁₉⋊C₈	—	4	2	no	—
138	C₂×C₁₉⋊C₈	—	4	1	no	—
139	C₂×C₁₉⋊C₈	—	4	1	no	—
140	#9253	—	19	1	no	maximal, Sylow
141	C₂³×C₁₉	—	2	1	no	—
142	C₂³×C₁₉	—	2	1	no	—
143	C₂³×C₁₉	—	4	2	no	—
144	C₂³×C₁₉	—	4	1	no	—
145	C₂³×C₁₉	—	4	1	no	—
146	C₂³×C₁₉	—	8	1	no	—
147	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
148	C₂²×D₁₉	—	4	2	no	—
149	C₂²×D₁₉	—	4	2	no	—
150	C₂²×D₁₉	—	4	2	no	—
151	C₂²×D₁₉	—	8	2	no	—
152	C₂²×D₁₉	—	8	2	no	—
153	D₄×C₁₉	—	2	1	no	—
154	D₄×C₁₉	—	2	1	no	—
155	D₄×C₁₉	—	2	1	no	—
156	D₄×C₁₉	—	4	2	no	—
157	D₄×C₁₉	#100	1	2	yes	complemented
158	C₂×C₄×C₁₉	—	2	1	no	—
159	C₂×C₄×C₁₉	—	2	1	no	—
160	C₂×C₄×C₁₉	—	2	1	no	—
161	C₂×C₄×C₁₉	—	2	1	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	4	1	no	—
173	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
181	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
182	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
183	D₇₆	—	4	2	no	—
184	D₇₆	—	4	2	no	—
185	D₇₆	—	8	2	no	—
186	D₇₆	—	8	2	no	—
187	D₇₆	—	8	2	no	—
188	D₇₆	—	8	1	no	—
189	D₇₆	—	8	1	no	—
190	D₇₆	—	8	1	no	—
191	D₇₆	—	8	1	no	—
192	C₈×C₁₉	—	2	2	no	—
193	C₈×C₁₉	—	4	2	no	—
194	C₈×C₁₉	—	4	1	no	—
195	C₁₉⋊C₈	—	4	2	no	—
196	C₁₉⋊C₈	—	8	1	no	—
197	C₁₉⋊C₈	—	8	1	no	—
198	C₂×#459	—	19	1	no	—
199	D₄×M₁₆	D₁₉	1	1	yes	characteristic, complemented
200	#1965	—	19	1	no	—
201	#1545	—	19	1	no	—
202	#1486	—	19	1	no	—
203	#1292	—	19	1	no	—
204	#1283	—	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	—	4	1	no	—
211	C₂²×C₁₉	—	4	1	no	—
212	C₂²×C₁₉	—	4	1	no	—
213	C₂²×C₁₉	—	8	2	no	—
214	C₂²×C₁₉	—	8	2	no	—
215	C₂²×C₁₉	#386	1	1	yes	characteristic
216	C₂²×C₁₉	C₄×D₈	1	1	yes	characteristic
217	C₂²×C₁₉	#442	1	1	yes	characteristic
218	C₂×D₁₉	—	8	2	no	—
219	C₂×D₁₉	—	8	2	no	—
220	C₂×D₁₉	—	8	2	no	—
221	C₂×D₁₉	—	16	2	no	—
222	C₂×D₁₉	—	16	2	no	—
223	C₄×C₁₉	—	2	1	no	—
224	C₄×C₁₉	—	2	1	no	—
225	C₄×C₁₉	—	2	1	no	—
226	C₄×C₁₉	—	4	1	no	—
227	C₄×C₁₉	—	4	1	no	—
228	C₄×C₁₉	C₂×#100	1	1	yes	characteristic
229	C₄×C₁₉	#413	1	1	yes	characteristic
230	C₄×C₁₉	#447	1	1	yes	characteristic
231	C₄×C₁₉	#449	1	1	yes	characteristic
232	C₄×C₁₉	#459	1	1	yes	characteristic
233	C₄×C₁₉	#463	1	1	yes	characteristic
234	C₂²×D₈	—	19	2	no	—
235	C₂²×M₁₆	—	2	1	no	—
236	C₂×#127	—	19	1	no	—
237	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
238	#459	—	38	1	no	—
239	#459	—	38	1	no	—
240	#459	—	38	1	no	—
241	#459	—	38	1	no	—
242	#436	—	2	1	no	—
243	#435	—	2	2	no	—
244	C₈×D₄	—	2	1	no	—
245	#431	—	19	1	no	—
246	#423	—	19	1	no	—
247	#423	C₂×D₁₉	1	1	yes	characteristic
248	C₂×C₄⋊C₈	—	19	1	no	—
249	C₂×#102	—	19	2	no	—
250	C₂×#100	—	38	1	no	—
251	C₂×#100	—	38	1	no	—
252	#407	—	2	1	no	—
253	C₄×M₁₆	C₂×D₁₉	1	1	yes	characteristic
254	#331	—	38	2	no	—
255	D₄⋊C₈	—	38	1	no	—
256	D₄⋊C₈	—	38	1	no	—
257	C₂×C₁₉	—	2	1	no	—
258	C₂×C₁₉	—	2	1	no	—
259	C₂×C₁₉	—	4	2	no	—
260	C₂×C₁₉	—	8	1	no	—
261	C₂×C₁₉	#1879	1	1	yes	characteristic
262	C₂×C₁₉	#1900	1	1	yes	characteristic
263	C₂×C₁₉	#1903	1	1	yes	characteristic
264	D₁₉	—	16	2	no	—
265	C₂²×D₄	—	19	2	no	—
266	C₂²×D₄	—	38	1	no	—
267	C₂²×D₄	—	38	1	no	—
268	C₂²×D₄	C₄×D₁₉	1	1	yes	characteristic
269	C₂³×C₄	—	2	1	no	—
270	C₂×D₈	—	38	2	no	—
271	C₂×D₈	—	38	2	no	—
272	C₂×D₈	—	76	4	no	—
273	C₂×M₁₆	—	2	2	no	—
274	C₂×M₁₆	—	2	1	no	—
275	C₂×M₁₆	—	4	2	no	—
276	C₂×M₁₆	—	4	2	no	—
277	C₂×M₁₆	—	38	1	no	—
278	C₂×M₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
279	C₂×M₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	—	19	2	no	—
282	#127	—	38	1	no	—
283	#127	—	38	1	no	—
284	#127	—	38	1	no	—
285	#127	—	38	1	no	—
286	C₄×D₄	—	2	1	no	—
287	C₄×D₄	—	2	1	no	—
288	C₄×D₄	D₇₆	1	1	yes	characteristic
289	C₄×D₄	D₇₆	1	1	yes	characteristic
290	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
291	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
295	C₄⋊C₈	—	2	1	no	—
296	C₄⋊C₈	—	38	1	no	—
297	C₄⋊C₈	—	38	1	no	—
298	C₄⋊C₈	—	38	1	no	—
299	C₄⋊C₈	—	38	1	no	—
300	C₄⋊C₈	—	38	1	no	—
301	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
302	#102	—	38	2	no	—
303	#102	—	38	2	no	—
304	#100	—	76	2	no	—
305	#100	—	76	2	no	—
306	C₂²⋊C₈	—	2	2	no	—
307	C₂²⋊C₈	—	2	2	no	—
308	C₂²⋊C₈	—	38	1	no	—
309	#97	—	2	1	no	—
310	C₄×C₈	—	2	1	no	—
311	C₄×C₈	—	38	1	no	—
312	C₁₉	#9253	1	1	yes	characteristic, complemented, Sylow
313	C₂⁴	—	2	1	no	—
314	C₂⁴	—	38	2	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	38	2	no	—
319	C₂×D₄	—	38	2	no	—
320	C₂×D₄	—	76	2	no	—
321	C₂×D₄	—	76	2	no	—
322	C₂×D₄	—	76	1	no	—
323	C₂×D₄	—	76	1	no	—
324	C₂×D₄	—	76	1	no	—
325	C₂×D₄	—	76	1	no	—
326	C₂×D₄	—	76	1	no	—
327	C₂×D₄	—	76	1	no	—
328	C₂×D₄	—	76	1	no	—
329	C₂×D₄	—	76	1	no	—
330	C₂×D₄	—	152	2	no	—
331	C₂×D₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
332	C₂×D₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	—	4	1	no	—
340	C₂²×C₄	—	4	1	no	—
341	C₂²×C₄	—	4	1	no	—
342	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
343	C₂²×C₄	#64541	1	1	yes	characteristic
344	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
345	D₈	—	76	4	no	—
346	D₈	—	76	4	no	—
347	M₁₆	—	2	1	no	—
348	M₁₆	—	2	1	no	—
349	M₁₆	—	2	1	no	—
350	M₁₆	—	4	4	no	—
351	M₁₆	—	4	1	no	—
352	M₁₆	—	4	1	no	—
353	M₁₆	—	76	1	no	—
354	M₁₆	—	76	1	no	—
355	M₁₆	#64525	1	2	yes	complemented
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	4	4	no	—
360	C₂×C₈	—	38	2	no	—
361	C₂×C₈	—	76	2	no	—
362	C₂×C₈	—	76	1	no	—
363	C₂×C₈	—	76	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
366	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
367	C₂²⋊C₄	—	2	1	no	—
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	1	no	—
371	C₄²	C₂×D₇₆	1	1	yes	characteristic
372	C₄²	#64541	1	1	yes	characteristic
373	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
374	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
375	C₂³	—	2	1	no	—
376	C₂³	—	2	1	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	8	1	no	—
381	C₂³	—	76	2	no	—
382	C₂³	—	76	2	no	—
383	C₂³	—	76	2	no	—
384	C₂³	—	152	2	no	—
385	C₂³	—	152	2	no	—
386	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
387	D₄	—	2	1	no	—
388	D₄	—	2	1	no	—
389	D₄	—	2	1	no	—
390	D₄	—	4	2	no	—
391	D₄	—	76	2	no	—
392	D₄	—	76	2	no	—
393	D₄	—	152	2	no	—
394	D₄	—	152	2	no	—
395	D₄	—	152	2	no	—
396	D₄	—	152	1	no	—
397	D₄	—	152	1	no	—
398	D₄	—	152	1	no	—
399	D₄	—	152	1	no	—
400	D₄	#10597280	1	2	yes	complemented
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
417	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
418	C₂×C₄	#10597375	1	1	yes	characteristic
419	C₂×C₄	#10597376	1	1	yes	characteristic
420	C₂×C₄	#10597376	1	1	yes	characteristic
421	C₂×C₄	C₂×#64525	1	1	yes	characteristic
422	C₂×C₄	#10597378	1	1	yes	characteristic
423	C₂×C₄	#10597395	1	1	yes	characteristic
424	C₂×C₄	#10597396	1	1	yes	characteristic
425	C₂×C₄	#10597399	1	1	yes	characteristic
426	C₈	—	2	2	no	—
427	C₈	—	4	2	no	—
428	C₈	—	4	1	no	—
429	C₈	—	76	2	no	—
430	C₈	—	152	1	no	—
431	C₈	—	152	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	8	2	no	—
441	C₂²	—	8	2	no	—
442	C₂²	—	304	2	no	—
443	C₂²	—	304	2	no	—
444	C₂²	—	152	2	no	—
445	C₂²	—	152	2	no	—
446	C₂²	—	152	2	no	—
447	C₂²	#11926423	1	1	yes	characteristic
448	C₂²	C₄×#64525	1	1	yes	characteristic
449	C₂²	#11926654	1	1	yes	characteristic
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	4	1	no	—
454	C₄	—	4	1	no	—
455	C₄	C₂×#10597280	1	1	yes	characteristic
456	C₄	#11926526	1	1	yes	characteristic
457	C₄	#11926678	1	1	yes	characteristic
458	C₄	#11926689	1	1	yes	characteristic
459	C₄	#11926739	1	1	yes	characteristic
460	C₄	#11926759	1	1	yes	characteristic
461	C₂	—	2	1	no	—
462	C₂	—	2	1	no	—
463	C₂	—	4	2	no	—
464	C₂	—	8	1	no	—
465	C₂	—	304	2	no	—
466	C₂	#14563983	1	1	yes	characteristic
467	C₂	#14564098	1	1	yes	characteristic
468	C₂	#14564115	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926423
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	D₄×M₁₆×C₁₉	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂×#11926739	C₂
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	D₄×M₁₆	D₁₉
hypocenter	C₁₉	#9253
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ D₄×M₁₆

Complements

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

N	H ≅ G/N	type
2. #14564475	C₂	semidirect
3. #14562304	C₂	semidirect
4. #14562060	C₂	semidirect
5. #14561509	C₂	semidirect
6. #14561486	C₂	semidirect
7. D₄×M₁₆×C₁₉	C₂	semidirect
116. M₁₆×C₁₉	D₈	semidirect
157. D₄×C₁₉	#100	semidirect
199. D₄×M₁₆	D₁₉	semidirect
312. C₁₉	#9253	semidirect
355. M₁₆	#64525	semidirect
400. D₄	#10597280	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926739	2
#14564475	2
#14562304	2
#14562060	2
#14561509	2
#14561486	2
D₄×M₁₆×C₁₉	2
#9253	19