Subgroups — #18077398

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	#14573635	C₂	1	1	yes	maximal, characteristic
2	#14564554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#10597289	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562085	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561536	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561473	C₂	1	1	yes	maximal, characteristic, complemented
7	D₄×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927094	C₂²	1	1	yes	characteristic
9	#11926857	—	2	1	no	—
10	#11926824	C₄	1	1	yes	characteristic, complemented
11	#11926824	C₄	1	1	yes	characteristic, complemented
12	#11926739	C₄	1	1	yes	characteristic, complemented
13	#11926739	C₄	1	1	yes	characteristic, complemented
14	#11926678	—	2	1	no	—
15	C₄×#64525	—	2	1	no	—
16	C₄×#64525	—	2	1	no	—
17	#11926597	C₂²	1	1	yes	characteristic
18	C₂×#10597282	—	2	1	no	—
19	C₂×#10597282	—	2	1	no	—
20	C₂×#10597289	—	2	1	no	—
21	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
22	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
23	#11926306	—	2	1	no	—
24	#11926271	—	2	2	no	—
25	C₂²×M₁₆×C₁₉	—	2	1	no	—
26	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#436	—	2	1	no	—
28	C₁₉×#435	—	2	2	no	—
29	C₈×D₄×C₁₉	—	2	1	no	—
30	C₁₉×#423	C₂²	1	1	yes	characteristic
31	C₁₉×#407	—	2	1	no	—
32	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
33	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₉	—	2	1	no	—
35	C₂×#64541	—	2	1	no	—
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	C₂×C₄	1	1	yes	characteristic
46	C₄×D₄×C₁₉	C₂×C₄	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	D₄	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	1	no	—
53	C₂×#64525	—	2	1	no	—
54	#10597376	—	2	1	no	—
55	#10597376	—	2	1	no	—
56	C₂×C₄⋊Dic₁₉	—	2	1	no	—
57	C₂×C₄×Dic₁₉	—	2	1	no	—
58	C₂²×C₁₉⋊C₈	—	2	1	no	—
59	#10597321	—	2	1	no	—
60	#10597320	C₂×C₄	1	1	yes	characteristic
61	C₄×D₇₆	—	2	1	no	—
62	C₄×D₇₆	—	2	1	no	—
63	#10597315	C₂×C₄	1	1	yes	characteristic
64	C₁₉×C₄⋊C₈	—	2	1	no	—
65	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
66	C₁₉×C₂²⋊C₈	—	2	2	no	—
67	C₁₉×C₂²⋊C₈	—	2	2	no	—
68	C₁₉×#97	—	2	1	no	—
69	C₄×C₈×C₁₉	—	2	1	no	—
70	#10597289	—	2	4	no	—
71	#10597289	—	2	1	no	—
72	#10597289	—	2	1	no	—
73	C₁₉⋊#95	—	2	1	no	—
74	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
75	#10597282	—	4	2	no	—
76	#10597282	—	4	2	no	—
77	#10597266	—	2	1	no	—
78	#10597266	—	2	1	no	—
79	#10597264	—	2	1	no	—
80	#10597264	—	2	1	no	—
81	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
82	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
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	C₂×D₄×C₁₉	—	2	2	no	—
88	C₂×D₄×C₁₉	—	2	1	no	—
89	C₂×D₄×C₁₉	—	4	1	no	—
90	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
91	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	2	1	no	—
95	C₂²×C₄×C₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	—	2	1	no	—
97	C₂²×C₄×C₁₉	—	4	1	no	—
98	C₂²×C₄×C₁₉	—	4	1	no	—
99	C₂²×C₄×C₁₉	—	4	1	no	—
100	C₂²×C₄×C₁₉	—	4	1	no	—
101	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
104	C₂×C₂²⋊D₁₉	—	4	1	no	—
105	C₂²×Dic₁₉	—	4	1	no	—
106	#64541	—	4	1	no	—
107	#64541	—	4	1	no	—
108	#64541	—	4	1	no	—
109	#64541	—	4	1	no	—
110	C₂×D₇₆	—	2	1	no	—
111	C₂×D₇₆	—	2	1	no	—
112	C₂×D₇₆	—	2	1	no	—
113	C₂×C₄×D₁₉	—	4	1	no	—
114	C₂×Dic₃₈	—	2	1	no	—
115	M₁₆×C₁₉	—	2	1	no	—
116	M₁₆×C₁₉	—	2	1	no	—
117	M₁₆×C₁₉	—	2	1	no	—
118	M₁₆×C₁₉	—	4	4	no	—
119	M₁₆×C₁₉	—	4	1	no	—
120	M₁₆×C₁₉	—	4	1	no	—
121	M₁₆×C₁₉	D₈	1	2	yes	complemented
122	C₂×C₈×C₁₉	—	2	1	no	—
123	C₂×C₈×C₁₉	—	2	2	no	—
124	C₂×C₈×C₁₉	—	2	1	no	—
125	C₂×C₈×C₁₉	—	4	4	no	—
126	C₄⋊C₄×C₁₉	—	2	1	no	—
127	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
128	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
129	C₂²⋊C₄×C₁₉	—	2	1	no	—
130	C₂²⋊C₄×C₁₉	—	2	1	no	—
131	C₂²⋊C₄×C₁₉	—	2	1	no	—
132	C₂²⋊C₄×C₁₉	—	2	1	no	—
133	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
134	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₁₉	#41	1	1	yes	characteristic
137	#64525	—	4	2	no	—
138	#64525	—	4	2	no	—
139	(C₂×D₁₉)⋊C₄	—	4	1	no	—
140	(C₂×D₁₉)⋊C₄	—	4	1	no	—
141	C₄⋊Dic₁₉	—	2	2	no	—
142	C₄⋊Dic₁₉	—	2	1	no	—
143	C₄⋊Dic₁₉	—	2	1	no	—
144	C₄⋊Dic₁₉	—	4	1	no	—
145	C₄×Dic₁₉	—	4	1	no	—
146	C₄×Dic₁₉	—	4	1	no	—
147	C₂×C₁₉⋊C₈	—	2	2	no	—
148	C₂×C₁₉⋊C₈	—	2	1	no	—
149	C₂×C₁₉⋊C₈	—	2	1	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	—	8	1	no	—
159	C₂³×C₁₉	#121	1	1	yes	characteristic
160	C₂²×D₁₉	—	4	1	no	—
161	D₄×C₁₉	—	2	1	no	—
162	D₄×C₁₉	—	2	1	no	—
163	D₄×C₁₉	—	2	1	no	—
164	D₄×C₁₉	—	4	2	no	—
165	D₄×C₁₉	#104	1	2	yes	complemented
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	—	4	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	—	4	1	no	—
178	C₂×C₄×C₁₉	—	4	1	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	4	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	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
185	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
188	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
189	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
190	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
191	C₂²⋊D₁₉	—	8	1	no	—
192	C₂²⋊D₁₉	—	8	1	no	—
193	C₂×Dic₁₉	—	4	2	no	—
194	C₂×Dic₁₉	—	4	1	no	—
195	C₂×Dic₁₉	—	8	1	no	—
196	C₂×Dic₁₉	—	8	1	no	—
197	D₇₆	—	4	2	no	—
198	D₇₆	—	4	1	no	—
199	D₇₆	—	4	1	no	—
200	D₇₆	—	4	1	no	—
201	D₇₆	—	4	1	no	—
202	C₄×D₁₉	—	8	1	no	—
203	C₄×D₁₉	—	8	1	no	—
204	Dic₃₈	—	4	1	no	—
205	Dic₃₈	—	4	1	no	—
206	C₈×C₁₉	—	2	2	no	—
207	C₈×C₁₉	—	4	2	no	—
208	C₈×C₁₉	—	4	1	no	—
209	C₁₉⋊C₈	—	4	2	no	—
210	C₁₉⋊C₈	—	4	1	no	—
211	C₁₉⋊C₈	—	4	1	no	—
212	#3100	—	19	1	no	—
213	D₄×M₁₆	D₁₉	1	1	yes	characteristic, complemented
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	#386	1	1	yes	characteristic
230	C₂²×C₁₉	#459	1	1	yes	characteristic
231	C₂²×C₁₉	#463	1	1	yes	characteristic
232	C₂×D₁₉	—	8	1	no	—
233	C₂×D₁₉	—	8	1	no	—
234	C₂×D₁₉	—	8	1	no	—
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	C₂×#104	1	1	yes	characteristic
241	C₄×C₁₉	#421	1	1	yes	characteristic
242	C₄×C₁₉	C₄×D₈	1	1	yes	characteristic
243	C₄×C₁₉	#442	1	1	yes	characteristic
244	C₄×C₁₉	#447	1	1	yes	characteristic
245	C₄×C₁₉	#449	1	1	yes	characteristic
246	Dic₁₉	—	8	2	no	—
247	Dic₁₉	—	8	1	no	—
248	C₂²×M₁₆	—	2	1	no	—
249	#532	—	19	1	no	—
250	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
251	#480	—	38	1	no	—
252	#474	—	19	1	no	—
253	#474	—	19	1	no	—
254	#459	—	19	1	no	—
255	#459	—	19	1	no	—
256	#447	—	38	1	no	—
257	C₄×D₈	—	38	1	no	—
258	C₄×D₈	—	38	1	no	—
259	#436	—	2	1	no	—
260	#435	—	2	2	no	—
261	C₈×D₄	—	2	1	no	—
262	#431	—	19	1	no	—
263	#423	C₂×D₁₉	1	1	yes	characteristic
264	C₂×#104	—	38	1	no	—
265	C₂×#104	—	38	1	no	—
266	C₂×#102	—	38	1	no	—
267	#407	—	2	1	no	—
268	C₄×M₁₆	C₂×D₁₉	1	1	yes	characteristic
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	#1871	1	1	yes	characteristic
278	C₂×C₁₉	#1879	1	1	yes	characteristic
279	C₂×C₁₉	#1881	1	1	yes	characteristic
280	D₁₉	—	16	1	no	—
281	C₂×#41	—	38	1	no	—
282	C₂²×D₄	D₇₆	1	1	yes	characteristic
283	C₂³×C₄	—	2	1	no	—
284	C₂×D₈	—	38	1	no	—
285	C₂×D₈	—	38	1	no	—
286	C₂×M₁₆	—	2	2	no	—
287	C₂×M₁₆	—	2	1	no	—
288	C₂×M₁₆	—	4	2	no	—
289	C₂×M₁₆	—	4	2	no	—
290	C₂×M₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
291	C₂×M₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
292	C₂²×C₈	—	2	2	no	—
293	C₂²×C₈	—	38	1	no	—
294	C₄⋊Q₈	—	19	1	no	—
295	#127	—	19	1	no	—
296	#124	—	38	1	no	—
297	#121	—	38	1	no	—
298	#121	—	38	1	no	—
299	C₄×D₄	—	2	1	no	—
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	—	38	1	no	—
302	C₄×D₄	—	38	1	no	—
303	C₄×D₄	C₄×D₁₉	1	1	yes	characteristic
304	C₄×D₄	C₄×D₁₉	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	D₇₆	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	—	38	1	no	—
313	#107	—	38	1	no	—
314	C₄⋊C₈	—	2	1	no	—
315	C₄⋊C₈	—	19	1	no	—
316	C₄⋊C₈	—	19	1	no	—
317	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
318	#104	—	76	2	no	—
319	#104	—	76	2	no	—
320	#102	—	38	4	no	—
321	#102	—	38	1	no	—
322	#102	—	38	1	no	—
323	#102	—	38	1	no	—
324	#102	—	38	1	no	—
325	C₂²⋊C₈	—	2	2	no	—
326	C₂²⋊C₈	—	2	2	no	—
327	C₂²⋊C₈	—	38	1	no	—
328	#97	—	2	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	—	76	1	no	—
337	#41	—	76	1	no	—
338	#41	—	76	1	no	—
339	#41	—	76	1	no	—
340	C₂×Q₈	—	38	1	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	4	1	no	—
344	C₂×D₄	—	38	1	no	—
345	C₂×D₄	—	38	1	no	—
346	C₂×D₄	—	38	1	no	—
347	C₂×D₄	—	76	1	no	—
348	C₂×D₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
349	C₂×D₄	(C₂×D₁₉)⋊C₄	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	—	76	1	no	—
360	C₂²×C₄	—	76	1	no	—
361	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
362	C₂²×C₄	#64541	1	1	yes	characteristic
363	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
364	D₈	—	76	2	no	—
365	D₈	—	76	2	no	—
366	M₁₆	—	2	1	no	—
367	M₁₆	—	2	1	no	—
368	M₁₆	—	2	1	no	—
369	M₁₆	—	4	4	no	—
370	M₁₆	—	4	1	no	—
371	M₁₆	—	4	1	no	—
372	M₁₆	#64525	1	2	yes	complemented
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	4	4	no	—
377	C₂×C₈	—	38	2	no	—
378	C₂×C₈	—	38	1	no	—
379	C₂×C₈	—	38	1	no	—
380	C₂×C₈	—	76	1	no	—
381	C₂×C₈	—	76	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	38	2	no	—
384	C₄⋊C₄	—	38	1	no	—
385	C₄⋊C₄	—	38	1	no	—
386	C₄⋊C₄	—	76	1	no	—
387	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
388	C₄⋊C₄	(C₂×D₁₉)⋊C₄	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	—	76	1	no	—
394	C₂²⋊C₄	—	76	1	no	—
395	C₄²	—	76	1	no	—
396	C₄²	—	76	1	no	—
397	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
398	C₄²	#64541	1	1	yes	characteristic
399	C₄²	C₂×C₂²⋊D₁₉	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	—	8	1	no	—
407	C₂³	—	76	1	no	—
408	C₂³	#10597376	1	1	yes	characteristic
409	Q₈	—	76	1	no	—
410	Q₈	—	76	1	no	—
411	D₄	—	2	1	no	—
412	D₄	—	2	1	no	—
413	D₄	—	2	1	no	—
414	D₄	—	4	2	no	—
415	D₄	—	76	2	no	—
416	D₄	—	76	1	no	—
417	D₄	—	76	1	no	—
418	D₄	—	76	1	no	—
419	D₄	—	76	1	no	—
420	D₄	—	152	1	no	—
421	D₄	—	152	1	no	—
422	D₄	#10597282	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	—	76	2	no	—
439	C₂×C₄	—	76	1	no	—
440	C₂×C₄	—	152	1	no	—
441	C₂×C₄	—	152	1	no	—
442	C₂×C₄	—	152	1	no	—
443	C₂×C₄	—	152	1	no	—
444	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
445	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
446	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
447	C₂×C₄	#10597375	1	1	yes	characteristic
448	C₂×C₄	#10597376	1	1	yes	characteristic
449	C₂×C₄	C₂×#64525	1	1	yes	characteristic
450	C₂×C₄	#10597378	1	1	yes	characteristic
451	C₂×C₄	#10597395	1	1	yes	characteristic
452	C₂×C₄	#10597396	1	1	yes	characteristic
453	C₂×C₄	#10597399	1	1	yes	characteristic
454	C₈	—	2	2	no	—
455	C₈	—	4	2	no	—
456	C₈	—	4	1	no	—
457	C₈	—	76	2	no	—
458	C₈	—	76	1	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	—	152	1	no	—
471	C₂²	—	152	1	no	—
472	C₂²	—	152	1	no	—
473	C₂²	#11926423	1	1	yes	characteristic
474	C₂²	#11926739	1	1	yes	characteristic
475	C₂²	#11926759	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	—	152	2	no	—
482	C₄	—	152	1	no	—
483	C₄	C₂×#10597282	1	1	yes	characteristic
484	C₄	#11926560	1	1	yes	characteristic
485	C₄	C₄×#64525	1	1	yes	characteristic
486	C₄	#11926654	1	1	yes	characteristic
487	C₄	#11926678	1	1	yes	characteristic
488	C₄	#11926689	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	—	304	1	no	—
494	C₂	#14563937	1	1	yes	characteristic
495	C₂	#14563983	1	1	yes	characteristic
496	C₂	#14563997	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597399
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	D₄×M₁₆×C₁₉	C₂
socle	C₂²×C₁₉	#386
prime radical	#14573635	C₂
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	D₄×M₁₆	D₁₉
hypocenter	C₁₉	#8991
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ D₄×M₁₆

Complements

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

N	H ≅ G/N	type
2. #14564554	C₂	semidirect
3. C₄×#10597289	C₂	semidirect
4. #14562085	C₂	semidirect
5. #14561536	C₂	semidirect
6. #14561473	C₂	semidirect
7. D₄×M₁₆×C₁₉	C₂	semidirect
10. #11926824	C₄	semidirect
11. #11926824	C₄	semidirect
12. #11926739	C₄	semidirect
13. #11926739	C₄	semidirect
121. M₁₆×C₁₉	D₈	semidirect
165. D₄×C₁₉	#104	semidirect
213. D₄×M₁₆	D₁₉	semidirect
334. C₁₉	#8991	semidirect
372. M₁₆	#64525	semidirect
422. D₄	#10597282	semidirect

Maximal subgroups

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

subgroup	index
#14573635	2
#14564554	2
C₄×#10597289	2
#14562085	2
#14561536	2
#14561473	2
D₄×M₁₆×C₁₉	2
#8991	19