Subgroups — #18077307

Order 4864.

616 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	C₂×#11926744	C₂	1	1	yes	maximal, characteristic
2	#14564562	C₂	1	1	yes	maximal, characteristic
3	#14564440	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561518	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2355	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64527	—	2	1	no	—
9	C₂×#10597320	C₂²	1	1	yes	characteristic
10	#11926744	—	2	2	no	—
11	#11926744	C₄	1	4	yes	complemented
12	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×#10597266	—	2	1	no	—
15	C₂×#10597266	—	2	2	no	—
16	C₂×#10597266	—	2	1	no	—
17	C₂×#10597266	—	2	1	no	—
18	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
19	Q₈⋊(C₁₉⋊C₈)	—	2	2	no	—
20	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#391	—	2	1	no	—
22	C₁₉×#387	—	2	2	no	—
23	C₁₉×#384	C₂²	1	1	yes	characteristic
24	C₁₉×#382	—	2	1	no	—
25	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
26	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
27	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
28	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
29	C₂²×D₇₆	—	2	1	no	—
30	C₂²×D₇₆	—	2	1	no	—
31	C₂²×D₇₆	—	2	1	no	—
32	C₄×Q₈×C₁₉	—	2	1	no	—
33	C₄×Q₈×C₁₉	—	2	1	no	—
34	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
35	C₄×Q₈×C₁₉	D₄	1	2	yes	—
36	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
41	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
42	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
43	C₂×C₄²×C₁₉	—	2	1	no	—
44	C₂×C₄²×C₁₉	—	2	1	no	—
45	C₂×C₄²×C₁₉	—	2	2	no	—
46	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
47	C₂×#64527	—	2	4	no	—
48	C₂×#64527	—	4	2	no	—
49	C₂×#64527	—	4	2	no	—
50	C₂²×C₁₉⋊C₈	—	2	1	no	—
51	C₂²×C₁₉⋊C₈	—	2	1	no	—
52	C₂²×C₁₉⋊C₈	—	2	1	no	—
53	#10597320	—	2	1	no	—
54	#10597320	—	2	1	no	—
55	#10597320	—	2	1	no	—
56	#10597320	C₂×C₄	1	2	yes	—
57	C₁₉×#95	—	2	2	no	—
58	C₁₉×#95	—	2	2	no	—
59	C₁₉×#95	—	2	2	no	—
60	C₁₉×#95	—	2	1	no	—
61	#10597266	—	2	4	no	—
62	#10597266	—	4	4	no	—
63	#10597266	—	4	2	no	—
64	#10597266	—	4	2	no	—
65	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
66	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
67	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
68	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
69	C₄×C₁₉⋊C₈	—	2	1	no	—
70	C₄×C₁₉⋊C₈	—	2	1	no	—
71	C₂³×D₁₉	—	4	1	no	—
72	C₂×Q₈×C₁₉	—	2	1	no	—
73	C₂×Q₈×C₁₉	—	2	1	no	—
74	C₂×Q₈×C₁₉	—	2	1	no	—
75	C₂×Q₈×C₁₉	—	2	1	no	—
76	C₂×Q₈×C₁₉	—	2	1	no	—
77	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
78	C₂²×C₄×C₁₉	—	2	1	no	—
79	C₂²×C₄×C₁₉	—	2	1	no	—
80	C₂²×C₄×C₁₉	—	2	1	no	—
81	C₂²×C₄×C₁₉	—	2	2	no	—
82	C₂²×C₄×C₁₉	—	2	1	no	—
83	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
86	C₂×D₇₆	—	2	2	no	—
87	C₂×D₇₆	—	2	2	no	—
88	C₂×D₇₆	—	2	2	no	—
89	C₂×D₇₆	—	4	2	no	—
90	C₂×D₇₆	—	4	2	no	—
91	C₂×D₇₆	—	4	1	no	—
92	C₂×D₇₆	—	4	1	no	—
93	C₂×D₇₆	—	4	1	no	—
94	C₂×D₇₆	—	4	1	no	—
95	C₂×D₇₆	—	4	1	no	—
96	C₂×D₇₆	—	4	1	no	—
97	C₂×D₇₆	—	4	1	no	—
98	C₂×D₇₆	—	4	1	no	—
99	C₂×D₇₆	—	4	1	no	—
100	C₂×D₇₆	—	4	1	no	—
101	C₂×D₇₆	—	4	1	no	—
102	C₄⋊C₄×C₁₉	—	2	2	no	—
103	C₄⋊C₄×C₁₉	—	2	2	no	—
104	C₄⋊C₄×C₁₉	—	2	1	no	—
105	C₄⋊C₄×C₁₉	—	2	1	no	—
106	C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₄⋊C₄×C₁₉	—	4	2	no	—
109	C₄⋊C₄×C₁₉	—	4	1	no	—
110	C₄⋊C₄×C₁₉	—	4	1	no	—
111	C₄⋊C₄×C₁₉	—	4	1	no	—
112	C₄⋊C₄×C₁₉	—	4	1	no	—
113	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
114	C₄⋊C₄×C₁₉	SD₁₆	1	2	yes	complemented
115	C₄²×C₁₉	—	2	2	no	—
116	C₄²×C₁₉	—	2	2	no	—
117	C₄²×C₁₉	—	4	1	no	—
118	C₄²×C₁₉	—	4	1	no	—
119	C₄²×C₁₉	—	8	2	no	—
120	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₁₉	#41	1	1	yes	characteristic
123	C₄²×C₁₉	#41	1	1	yes	characteristic
124	#64527	—	4	8	no	—
125	C₂×C₁₉⋊C₈	—	2	2	no	—
126	C₂×C₁₉⋊C₈	—	2	2	no	—
127	C₂×C₁₉⋊C₈	—	4	1	no	—
128	C₂×C₁₉⋊C₈	—	4	1	no	—
129	C₂×C₁₉⋊C₈	—	4	1	no	—
130	C₂×C₁₉⋊C₈	—	4	1	no	—
131	C₂×C₁₉⋊C₈	—	4	1	no	—
132	C₂×C₁₉⋊C₈	—	4	1	no	—
133	C₂×C₁₉⋊C₈	—	4	1	no	—
134	#8978	—	19	1	no	maximal, Sylow
135	C₂³×C₁₉	#120	1	1	yes	characteristic
136	C₂²×D₁₉	—	4	2	no	—
137	C₂²×D₁₉	—	8	1	no	—
138	C₂²×D₁₉	—	8	1	no	—
139	C₂²×D₁₉	—	8	1	no	—
140	C₂²×D₁₉	—	8	1	no	—
141	C₂²×D₁₉	—	8	1	no	—
142	C₂²×D₁₉	—	8	1	no	—
143	Q₈×C₁₉	—	2	2	no	—
144	Q₈×C₁₉	—	2	2	no	—
145	Q₈×C₁₉	—	4	1	no	—
146	Q₈×C₁₉	—	4	1	no	—
147	C₂×C₄×C₁₉	—	2	1	no	—
148	C₂×C₄×C₁₉	—	2	1	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	2	no	—
151	C₂×C₄×C₁₉	—	2	2	no	—
152	C₂×C₄×C₁₉	—	4	1	no	—
153	C₂×C₄×C₁₉	—	4	1	no	—
154	C₂×C₄×C₁₉	—	4	1	no	—
155	C₂×C₄×C₁₉	—	4	1	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
168	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
169	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
171	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
174	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
175	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
176	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
178	D₇₆	—	4	4	no	—
179	D₇₆	—	4	2	no	—
180	D₇₆	—	4	2	no	—
181	D₇₆	—	4	2	no	—
182	D₇₆	—	4	2	no	—
183	D₇₆	—	8	2	no	—
184	D₇₆	—	8	1	no	—
185	D₇₆	—	8	1	no	—
186	D₇₆	—	8	1	no	—
187	D₇₆	—	8	1	no	—
188	C₁₉⋊C₈	—	4	2	no	—
189	C₁₉⋊C₈	—	4	2	no	—
190	C₁₉⋊C₈	—	8	1	no	—
191	C₂×#460	—	19	1	no	—
192	#2355	D₁₉	1	1	yes	characteristic, complemented
193	#1982	—	19	1	no	—
194	#1957	—	19	1	no	—
195	C₂×Q₈⋊C₈	—	19	1	no	—
196	#1296	—	19	1	no	—
197	#1279	—	19	1	no	—
198	C₂²×C₁₉	#386	1	1	yes	characteristic
199	C₂²×C₁₉	#448	1	1	yes	characteristic
200	C₂²×C₁₉	#449	1	1	yes	characteristic
201	C₂²×C₁₉	#449	1	1	yes	characteristic
202	C₂²×C₁₉	#449	1	1	yes	characteristic
203	C₂²×C₁₉	#453	1	1	yes	characteristic
204	C₂²×C₁₉	#454	1	1	yes	characteristic
205	C₂×D₁₉	—	8	2	no	—
206	C₂×D₁₉	—	8	2	no	—
207	C₂×D₁₉	—	8	2	no	—
208	C₂×D₁₉	—	16	1	no	—
209	C₂×D₁₉	—	16	1	no	—
210	C₂×D₁₉	—	16	1	no	—
211	C₂×D₁₉	—	16	1	no	—
212	C₄×C₁₉	—	2	1	no	—
213	C₄×C₁₉	—	2	1	no	—
214	C₄×C₁₉	—	4	2	no	—
215	C₄×C₁₉	—	4	2	no	—
216	C₄×C₁₉	—	4	2	no	—
217	C₄×C₁₉	—	8	2	no	—
218	C₄×C₁₉	—	8	1	no	—
219	C₄×C₁₉	#416	1	1	yes	characteristic
220	C₄×C₁₉	#418	1	1	yes	characteristic
221	C₄×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
222	C₄×C₁₉	#440	1	1	yes	characteristic
223	C₄×C₁₉	#460	1	1	yes	characteristic
224	C₄×C₁₉	#464	1	1	yes	characteristic
225	C₄×C₁₉	#482	1	1	yes	characteristic
226	C₄×C₁₉	#482	1	1	yes	characteristic
227	C₂²×SD₁₆	—	38	1	no	—
228	C₂×#127	—	19	1	no	—
229	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
230	#460	—	19	4	no	—
231	#460	—	38	2	no	—
232	C₂×C₄⋊C₈	—	19	1	no	—
233	C₂×C₄⋊C₈	—	19	1	no	—
234	C₂×#102	—	38	1	no	—
235	C₂×#102	—	38	2	no	—
236	C₂×#102	—	38	1	no	—
237	C₂×#102	—	38	1	no	—
238	C₂×C₄×C₈	—	19	1	no	—
239	#391	—	2	1	no	—
240	#387	—	2	2	no	—
241	#384	C₂×D₁₉	1	1	yes	characteristic
242	#382	—	2	1	no	—
243	C₄×C₄⋊C₄	—	2	1	no	—
244	C₄×C₄⋊C₄	—	2	1	no	—
245	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
246	Q₈⋊C₈	—	38	2	no	—
247	C₂×C₁₉	#1620	1	1	yes	characteristic
248	C₂×C₁₉	#1622	1	1	yes	characteristic
249	C₂×C₁₉	#1626	1	1	yes	characteristic
250	C₂×C₁₉	#1628	1	1	yes	characteristic
251	C₂×C₁₉	#1875	1	1	yes	characteristic
252	C₂×C₁₉	#1880	1	1	yes	characteristic
253	C₂×C₁₉	#1883	1	1	yes	characteristic
254	D₁₉	—	16	2	no	—
255	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
256	C₂²×D₄	—	38	1	no	—
257	C₂²×D₄	—	38	1	no	—
258	C₂²×D₄	—	38	1	no	—
259	C₂×SD₁₆	—	38	4	no	—
260	C₂×SD₁₆	—	76	2	no	—
261	C₂×SD₁₆	—	76	2	no	—
262	C₂²×C₈	—	38	1	no	—
263	C₂²×C₈	—	38	1	no	—
264	C₂²×C₈	—	38	1	no	—
265	#127	—	19	2	no	—
266	#127	—	38	1	no	—
267	#127	—	38	1	no	—
268	#127	—	38	1	no	—
269	C₄×Q₈	—	2	1	no	—
270	C₄×Q₈	—	2	1	no	—
271	C₄×Q₈	C₄×D₁₉	1	2	yes	—
272	C₄×Q₈	D₇₆	1	2	yes	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
280	C₂×C₄²	—	2	1	no	—
281	C₂×C₄²	—	2	1	no	—
282	C₂×C₄²	—	2	2	no	—
283	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
284	C₄⋊C₈	—	19	2	no	—
285	C₄⋊C₈	—	38	1	no	—
286	C₄⋊C₈	—	38	1	no	—
287	C₄⋊C₈	—	38	1	no	—
288	#102	—	38	4	no	—
289	#102	—	76	2	no	—
290	#102	—	76	4	no	—
291	#102	—	76	2	no	—
292	C₄×C₈	—	38	1	no	—
293	C₄×C₈	—	38	1	no	—
294	#95	—	2	2	no	—
295	#95	—	2	2	no	—
296	#95	—	2	2	no	—
297	#95	—	2	1	no	—
298	C₁₉	#8978	1	1	yes	characteristic, complemented, Sylow
299	C₂⁴	—	76	1	no	—
300	C₂×Q₈	—	2	1	no	—
301	C₂×Q₈	—	2	1	no	—
302	C₂×Q₈	—	2	1	no	—
303	C₂×Q₈	—	2	1	no	—
304	C₂×Q₈	—	2	1	no	—
305	C₂×Q₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
306	C₂×D₄	—	38	2	no	—
307	C₂×D₄	—	38	2	no	—
308	C₂×D₄	—	38	2	no	—
309	C₂×D₄	—	76	2	no	—
310	C₂×D₄	—	76	2	no	—
311	C₂×D₄	—	76	1	no	—
312	C₂×D₄	—	76	1	no	—
313	C₂×D₄	—	76	1	no	—
314	C₂×D₄	—	76	1	no	—
315	C₂×D₄	—	76	1	no	—
316	C₂×D₄	—	76	1	no	—
317	C₂×D₄	—	76	1	no	—
318	C₂×D₄	—	76	1	no	—
319	C₂×D₄	—	76	1	no	—
320	C₂×D₄	—	76	1	no	—
321	C₂×D₄	—	76	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
328	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
329	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
330	SD₁₆	—	76	8	no	—
331	C₂×C₈	—	38	2	no	—
332	C₂×C₈	—	38	2	no	—
333	C₂×C₈	—	76	1	no	—
334	C₂×C₈	—	76	1	no	—
335	C₂×C₈	—	76	1	no	—
336	C₂×C₈	—	76	1	no	—
337	C₂×C₈	—	76	1	no	—
338	C₂×C₈	—	76	1	no	—
339	C₂×C₈	—	76	1	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	4	2	no	—
347	C₄⋊C₄	—	4	1	no	—
348	C₄⋊C₄	—	4	1	no	—
349	C₄⋊C₄	—	4	1	no	—
350	C₄⋊C₄	—	4	1	no	—
351	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
352	C₄⋊C₄	#64527	1	2	yes	complemented
353	C₄²	—	2	2	no	—
354	C₄²	—	2	2	no	—
355	C₄²	—	4	1	no	—
356	C₄²	—	4	1	no	—
357	C₄²	—	8	2	no	—
358	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
359	C₄²	C₂×D₇₆	1	1	yes	characteristic
360	C₄²	#64541	1	1	yes	characteristic
361	C₄²	#64541	1	1	yes	characteristic
362	C₂³	—	76	2	no	—
363	C₂³	—	152	1	no	—
364	C₂³	—	152	1	no	—
365	C₂³	—	152	1	no	—
366	C₂³	—	152	1	no	—
367	C₂³	—	152	1	no	—
368	C₂³	—	152	1	no	—
369	C₂³	#10597399	1	1	yes	characteristic
370	Q₈	—	2	2	no	—
371	Q₈	—	2	2	no	—
372	Q₈	—	4	1	no	—
373	Q₈	—	4	1	no	—
374	D₄	—	76	4	no	—
375	D₄	—	76	2	no	—
376	D₄	—	76	2	no	—
377	D₄	—	76	2	no	—
378	D₄	—	76	2	no	—
379	D₄	—	152	2	no	—
380	D₄	—	152	1	no	—
381	D₄	—	152	1	no	—
382	D₄	—	152	1	no	—
383	D₄	—	152	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
402	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
403	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
404	C₂×C₄	#10597375	1	1	yes	characteristic
405	C₂×C₄	#10597376	1	1	yes	characteristic
406	C₂×C₄	#10597376	1	1	yes	characteristic
407	C₂×C₄	C₂×#64527	1	1	yes	characteristic
408	C₂×C₄	#10597388	1	1	yes	characteristic
409	C₂×C₄	#10597395	1	1	yes	characteristic
410	C₂×C₄	#10597395	1	1	yes	characteristic
411	C₂×C₄	#10597395	1	1	yes	characteristic
412	C₂×C₄	#10597396	1	1	yes	characteristic
413	C₂×C₄	#10597396	1	1	yes	characteristic
414	C₂×C₄	#10597396	1	1	yes	characteristic
415	C₈	—	76	2	no	—
416	C₈	—	76	2	no	—
417	C₈	—	152	1	no	—
418	C₂²	—	304	1	no	—
419	C₂²	—	304	1	no	—
420	C₂²	—	304	1	no	—
421	C₂²	—	304	1	no	—
422	C₂²	—	152	2	no	—
423	C₂²	—	152	2	no	—
424	C₂²	—	152	2	no	—
425	C₂²	#11926423	1	1	yes	characteristic
426	C₂²	#11926683	1	1	yes	characteristic
427	C₂²	#11926689	1	1	yes	characteristic
428	C₂²	#11926689	1	1	yes	characteristic
429	C₂²	#11926689	1	1	yes	characteristic
430	C₂²	#11926712	1	1	yes	characteristic
431	C₂²	#11926717	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	4	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	8	2	no	—
438	C₄	—	8	1	no	—
439	C₄	#11926538	1	1	yes	characteristic
440	C₄	#11926548	1	1	yes	characteristic
441	C₄	C₄×#64527	1	1	yes	characteristic
442	C₄	#11926642	1	1	yes	characteristic
443	C₄	#11926744	1	1	yes	characteristic
444	C₄	#11926766	1	1	yes	characteristic
445	C₄	#11926868	1	1	yes	characteristic
446	C₄	#11926868	1	1	yes	characteristic
447	C₂	—	304	2	no	—
448	C₂	#14562694	1	1	yes	characteristic
449	C₂	#14562707	1	1	yes	characteristic
450	C₂	#14562731	1	1	yes	characteristic
451	C₂	#14562745	1	1	yes	characteristic
452	C₂	#14563957	1	1	yes	characteristic
453	C₂	#14563990	1	1	yes	characteristic
454	C₂	#14564011	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597399
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2355	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂×#10597320	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2355	D₁₉
hypocenter	C₁₉	#8978
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2355

Complements

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

N	H ≅ G/N	type
4. C₂×Q₈⋊(C₁₉⋊C₈)	C₂	semidirect
5. #14561518	C₂	semidirect
6. #14561476	C₂	semidirect
7. C₁₉×#2355	C₂	semidirect
11. #11926744	C₄	semidirect
114. C₄⋊C₄×C₁₉	SD₁₆	semidirect
192. #2355	D₁₉	semidirect
298. C₁₉	#8978	semidirect
352. C₄⋊C₄	#64527	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926744	2
#14564562	2
#14564440	2
C₂×Q₈⋊(C₁₉⋊C₈)	2
#14561518	2
#14561476	2
C₁₉×#2355	2
#8978	19