Subgroups — #18077314

Order 4864.

660 conjugacy classes of subgroups.

The subgroup lattice has 464 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	Q₈×C₄⋊C₄×C₁₉	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	—	2	1	no	—
21	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#389	—	2	2	no	—
23	C₁₉×#389	—	2	1	no	—
24	C₁₉×#384	—	2	1	no	—
25	C₁₉×#384	C₂²	1	1	yes	characteristic
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	—	4	2	no	—
35	C₄×Q₈×C₁₉	—	4	2	no	—
36	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
37	C₄×Q₈×C₁₉	D₄	1	2	yes	—
38	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
40	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
41	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
43	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
46	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
47	C₂×C₄²×C₁₉	—	2	1	no	—
48	C₂×C₄²×C₁₉	—	2	2	no	—
49	C₂×C₄²×C₁₉	—	2	1	no	—
50	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
51	C₂×#64527	—	2	4	no	—
52	C₂×#64527	—	4	2	no	—
53	C₂×#64527	—	4	2	no	—
54	C₂²×C₁₉⋊C₈	—	2	1	no	—
55	C₂²×C₁₉⋊C₈	—	2	1	no	—
56	C₂²×C₁₉⋊C₈	—	2	1	no	—
57	#10597320	—	2	1	no	—
58	#10597320	—	2	1	no	—
59	#10597320	—	2	1	no	—
60	#10597320	C₂×C₄	1	2	yes	—
61	C₁₉×#95	—	2	2	no	—
62	C₁₉×#95	—	2	1	no	—
63	#10597266	—	2	4	no	—
64	#10597266	—	4	4	no	—
65	#10597266	—	4	2	no	—
66	#10597266	—	4	2	no	—
67	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
68	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
69	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
70	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
71	C₄×C₁₉⋊C₈	—	2	1	no	—
72	C₄×C₁₉⋊C₈	—	2	1	no	—
73	C₂³×D₁₉	—	4	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	C₂×Q₈×C₁₉	D₈	1	2	yes	—
79	C₂×Q₈×C₁₉	SD₁₆	1	2	yes	—
80	C₂²×C₄×C₁₉	—	2	1	no	—
81	C₂²×C₄×C₁₉	—	2	1	no	—
82	C₂²×C₄×C₁₉	—	2	1	no	—
83	C₂²×C₄×C₁₉	—	2	1	no	—
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
88	C₂×D₇₆	—	2	2	no	—
89	C₂×D₇₆	—	2	2	no	—
90	C₂×D₇₆	—	2	2	no	—
91	C₂×D₇₆	—	4	2	no	—
92	C₂×D₇₆	—	4	2	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	C₂×D₇₆	—	4	1	no	—
103	C₂×D₇₆	—	4	1	no	—
104	C₄⋊C₄×C₁₉	—	2	2	no	—
105	C₄⋊C₄×C₁₉	—	2	2	no	—
106	C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₄⋊C₄×C₁₉	—	2	1	no	—
109	C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₄⋊C₄×C₁₉	—	4	2	no	—
111	C₄⋊C₄×C₁₉	—	4	4	no	—
112	C₄⋊C₄×C₁₉	—	4	1	no	—
113	C₄⋊C₄×C₁₉	—	4	1	no	—
114	C₄⋊C₄×C₁₉	—	4	1	no	—
115	C₄⋊C₄×C₁₉	—	4	1	no	—
116	C₄⋊C₄×C₁₉	—	8	2	no	—
117	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
118	C₄⋊C₄×C₁₉	SD₁₆	1	2	yes	complemented
119	C₄²×C₁₉	—	2	2	no	—
120	C₄²×C₁₉	—	2	2	no	—
121	C₄²×C₁₉	—	4	4	no	—
122	C₄²×C₁₉	—	4	1	no	—
123	C₄²×C₁₉	—	4	1	no	—
124	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₁₉	#41	1	1	yes	characteristic
127	C₄²×C₁₉	#41	1	1	yes	characteristic
128	#64527	—	4	8	no	—
129	C₂×C₁₉⋊C₈	—	2	2	no	—
130	C₂×C₁₉⋊C₈	—	2	2	no	—
131	C₂×C₁₉⋊C₈	—	4	1	no	—
132	C₂×C₁₉⋊C₈	—	4	1	no	—
133	C₂×C₁₉⋊C₈	—	4	1	no	—
134	C₂×C₁₉⋊C₈	—	4	1	no	—
135	C₂×C₁₉⋊C₈	—	4	1	no	—
136	C₂×C₁₉⋊C₈	—	4	1	no	—
137	C₂×C₁₉⋊C₈	—	4	1	no	—
138	#8979	—	19	1	no	maximal, Sylow
139	C₂³×C₁₉	#120	1	1	yes	characteristic
140	C₂²×D₁₉	—	4	2	no	—
141	C₂²×D₁₉	—	8	1	no	—
142	C₂²×D₁₉	—	8	1	no	—
143	C₂²×D₁₉	—	8	1	no	—
144	C₂²×D₁₉	—	8	1	no	—
145	C₂²×D₁₉	—	8	1	no	—
146	C₂²×D₁₉	—	8	1	no	—
147	Q₈×C₁₉	—	2	2	no	—
148	Q₈×C₁₉	—	2	2	no	—
149	Q₈×C₁₉	—	2	2	no	—
150	Q₈×C₁₉	#102	1	4	yes	complemented
151	C₂×C₄×C₁₉	—	2	2	no	—
152	C₂×C₄×C₁₉	—	2	2	no	—
153	C₂×C₄×C₁₉	—	2	2	no	—
154	C₂×C₄×C₁₉	—	2	1	no	—
155	C₂×C₄×C₁₉	—	2	1	no	—
156	C₂×C₄×C₁₉	—	2	2	no	—
157	C₂×C₄×C₁₉	—	2	2	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
178	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
179	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
182	D₇₆	—	4	4	no	—
183	D₇₆	—	4	2	no	—
184	D₇₆	—	4	2	no	—
185	D₇₆	—	4	2	no	—
186	D₇₆	—	4	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	C₁₉⋊C₈	—	4	2	no	—
193	C₁₉⋊C₈	—	4	2	no	—
194	C₁₉⋊C₈	—	8	1	no	—
195	C₂×#460	—	19	1	no	—
196	Q₈×C₄⋊C₄	D₁₉	1	1	yes	characteristic, complemented
197	#1982	—	19	1	no	—
198	#1957	—	19	1	no	—
199	C₂×Q₈⋊C₈	—	19	1	no	—
200	#1296	—	19	1	no	—
201	#1279	—	19	1	no	—
202	C₂²×C₁₉	#386	1	1	yes	characteristic
203	C₂²×C₁₉	#447	1	1	yes	characteristic
204	C₂²×C₁₉	#448	1	1	yes	characteristic
205	C₂²×C₁₉	#448	1	1	yes	characteristic
206	C₂²×C₁₉	#449	1	1	yes	characteristic
207	C₂²×C₁₉	#453	1	1	yes	characteristic
208	C₂²×C₁₉	#454	1	1	yes	characteristic
209	C₂×D₁₉	—	8	2	no	—
210	C₂×D₁₉	—	8	2	no	—
211	C₂×D₁₉	—	8	2	no	—
212	C₂×D₁₉	—	16	1	no	—
213	C₂×D₁₉	—	16	1	no	—
214	C₂×D₁₉	—	16	1	no	—
215	C₂×D₁₉	—	16	1	no	—
216	C₄×C₁₉	—	2	4	no	—
217	C₄×C₁₉	—	2	1	no	—
218	C₄×C₁₉	—	2	1	no	—
219	C₄×C₁₉	—	4	2	no	—
220	C₄×C₁₉	—	4	2	no	—
221	C₄×C₁₉	—	8	1	no	—
222	C₄×C₁₉	—	8	2	no	—
223	C₄×C₁₉	C₂×#102	1	1	yes	characteristic
224	C₄×C₁₉	#417	1	1	yes	characteristic
225	C₄×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
226	C₄×C₁₉	#440	1	1	yes	characteristic
227	C₄×C₁₉	#460	1	1	yes	characteristic
228	C₄×C₁₉	#464	1	1	yes	characteristic
229	C₄×C₁₉	#480	1	1	yes	characteristic
230	C₄×C₁₉	#481	1	1	yes	characteristic
231	C₂²×SD₁₆	—	38	1	no	—
232	C₂×#127	—	19	1	no	—
233	C₂×C₄×Q₈	—	2	1	no	—
234	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
235	#460	—	19	4	no	—
236	#460	—	38	2	no	—
237	C₂×C₄⋊C₈	—	19	1	no	—
238	C₂×C₄⋊C₈	—	19	1	no	—
239	C₂×#102	—	38	1	no	—
240	C₂×#102	—	38	2	no	—
241	C₂×#102	—	38	1	no	—
242	C₂×#102	—	38	1	no	—
243	C₂×C₄×C₈	—	19	1	no	—
244	#389	—	2	1	no	—
245	#389	—	2	2	no	—
246	#384	—	2	1	no	—
247	#384	C₂×D₁₉	1	1	yes	characteristic
248	C₄×C₄⋊C₄	—	2	1	no	—
249	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
250	Q₈⋊C₈	—	38	2	no	—
251	C₂×C₁₉	#1621	1	1	yes	characteristic
252	C₂×C₁₉	#1623	1	1	yes	characteristic
253	C₂×C₁₉	#1626	1	1	yes	characteristic
254	C₂×C₁₉	#1627	1	1	yes	characteristic
255	C₂×C₁₉	#1874	1	1	yes	characteristic
256	C₂×C₁₉	#1880	1	1	yes	characteristic
257	C₂×C₁₉	#1883	1	1	yes	characteristic
258	D₁₉	—	16	2	no	—
259	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
260	C₂²×D₄	—	38	1	no	—
261	C₂²×D₄	—	38	1	no	—
262	C₂²×D₄	—	38	1	no	—
263	C₂×SD₁₆	—	38	4	no	—
264	C₂×SD₁₆	—	76	2	no	—
265	C₂×SD₁₆	—	76	2	no	—
266	C₂²×C₈	—	38	1	no	—
267	C₂²×C₈	—	38	1	no	—
268	C₂²×C₈	—	38	1	no	—
269	#127	—	19	2	no	—
270	#127	—	38	1	no	—
271	#127	—	38	1	no	—
272	#127	—	38	1	no	—
273	C₄×Q₈	—	2	1	no	—
274	C₄×Q₈	—	2	1	no	—
275	C₄×Q₈	—	4	2	no	—
276	C₄×Q₈	—	4	2	no	—
277	C₄×Q₈	C₄×D₁₉	1	2	yes	—
278	C₄×Q₈	D₇₆	1	2	yes	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
288	C₂×C₄²	—	2	1	no	—
289	C₂×C₄²	—	2	2	no	—
290	C₂×C₄²	—	2	1	no	—
291	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
292	C₄⋊C₈	—	19	2	no	—
293	C₄⋊C₈	—	38	1	no	—
294	C₄⋊C₈	—	38	1	no	—
295	C₄⋊C₈	—	38	1	no	—
296	#102	—	38	4	no	—
297	#102	—	76	2	no	—
298	#102	—	76	4	no	—
299	#102	—	76	2	no	—
300	C₄×C₈	—	38	1	no	—
301	C₄×C₈	—	38	1	no	—
302	#95	—	2	2	no	—
303	#95	—	2	1	no	—
304	C₁₉	#8979	1	1	yes	characteristic, complemented, Sylow
305	C₂⁴	—	76	1	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
310	C₂×Q₈	#64525	1	2	yes	—
311	C₂×Q₈	#64527	1	2	yes	—
312	C₂×D₄	—	38	2	no	—
313	C₂×D₄	—	38	2	no	—
314	C₂×D₄	—	38	2	no	—
315	C₂×D₄	—	76	2	no	—
316	C₂×D₄	—	76	2	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	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	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
334	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
335	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
336	SD₁₆	—	76	8	no	—
337	C₂×C₈	—	38	2	no	—
338	C₂×C₈	—	38	2	no	—
339	C₂×C₈	—	76	1	no	—
340	C₂×C₈	—	76	1	no	—
341	C₂×C₈	—	76	1	no	—
342	C₂×C₈	—	76	1	no	—
343	C₂×C₈	—	76	1	no	—
344	C₂×C₈	—	76	1	no	—
345	C₂×C₈	—	76	1	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	4	4	no	—
354	C₄⋊C₄	—	4	1	no	—
355	C₄⋊C₄	—	4	1	no	—
356	C₄⋊C₄	—	4	1	no	—
357	C₄⋊C₄	—	4	1	no	—
358	C₄⋊C₄	—	8	2	no	—
359	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
360	C₄⋊C₄	#64527	1	2	yes	complemented
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	4	4	no	—
364	C₄²	—	4	1	no	—
365	C₄²	—	4	1	no	—
366	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
367	C₄²	C₂×D₇₆	1	1	yes	characteristic
368	C₄²	#64541	1	1	yes	characteristic
369	C₄²	#64541	1	1	yes	characteristic
370	C₂³	—	76	2	no	—
371	C₂³	—	152	1	no	—
372	C₂³	—	152	1	no	—
373	C₂³	—	152	1	no	—
374	C₂³	—	152	1	no	—
375	C₂³	—	152	1	no	—
376	C₂³	—	152	1	no	—
377	C₂³	#10597399	1	1	yes	characteristic
378	Q₈	—	2	2	no	—
379	Q₈	—	2	2	no	—
380	Q₈	—	2	2	no	—
381	Q₈	#10597266	1	4	yes	complemented
382	D₄	—	76	4	no	—
383	D₄	—	76	2	no	—
384	D₄	—	76	2	no	—
385	D₄	—	76	2	no	—
386	D₄	—	76	2	no	—
387	D₄	—	152	2	no	—
388	D₄	—	152	1	no	—
389	D₄	—	152	1	no	—
390	D₄	—	152	1	no	—
391	D₄	—	152	1	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	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	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
410	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
411	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
412	C₂×C₄	#10597375	1	1	yes	characteristic
413	C₂×C₄	#10597376	1	1	yes	characteristic
414	C₂×C₄	#10597376	1	1	yes	characteristic
415	C₂×C₄	C₂×#64525	1	1	yes	characteristic
416	C₂×C₄	#10597378	1	1	yes	characteristic
417	C₂×C₄	C₂×#64527	1	1	yes	characteristic
418	C₂×C₄	C₂×#64527	1	1	yes	characteristic
419	C₂×C₄	#10597388	1	1	yes	characteristic
420	C₂×C₄	#10597388	1	1	yes	characteristic
421	C₂×C₄	#10597395	1	1	yes	characteristic
422	C₂×C₄	#10597396	1	1	yes	characteristic
423	C₈	—	76	2	no	—
424	C₈	—	76	2	no	—
425	C₈	—	152	1	no	—
426	C₂²	—	304	1	no	—
427	C₂²	—	304	1	no	—
428	C₂²	—	304	1	no	—
429	C₂²	—	304	1	no	—
430	C₂²	—	152	2	no	—
431	C₂²	—	152	2	no	—
432	C₂²	—	152	2	no	—
433	C₂²	#11926423	1	1	yes	characteristic
434	C₂²	#11926678	1	1	yes	characteristic
435	C₂²	#11926683	1	1	yes	characteristic
436	C₂²	#11926683	1	1	yes	characteristic
437	C₂²	#11926689	1	1	yes	characteristic
438	C₂²	#11926712	1	1	yes	characteristic
439	C₂²	#11926717	1	1	yes	characteristic
440	C₄	—	2	4	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	4	2	no	—
444	C₄	—	4	2	no	—
445	C₄	—	8	1	no	—
446	C₄	—	8	2	no	—
447	C₄	C₂×#10597266	1	1	yes	characteristic
448	C₄	#11926543	1	1	yes	characteristic
449	C₄	C₄×#64527	1	1	yes	characteristic
450	C₄	#11926642	1	1	yes	characteristic
451	C₄	#11926744	1	1	yes	characteristic
452	C₄	#11926766	1	1	yes	characteristic
453	C₄	#11926857	1	1	yes	characteristic
454	C₄	#11926862	1	1	yes	characteristic
455	C₂	—	304	2	no	—
456	C₂	#14562700	1	1	yes	characteristic
457	C₂	#14562713	1	1	yes	characteristic
458	C₂	#14562731	1	1	yes	characteristic
459	C₂	#14562738	1	1	yes	characteristic
460	C₂	#14563952	1	1	yes	characteristic
461	C₂	#14563990	1	1	yes	characteristic
462	C₂	#14564011	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597399
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	Q₈×C₄⋊C₄×C₁₉	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂×#10597320	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	Q₈×C₄⋊C₄	D₁₉
hypocenter	C₁₉	#8979
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ Q₈×C₄⋊C₄

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. Q₈×C₄⋊C₄×C₁₉	C₂	semidirect
11. #11926744	C₄	semidirect
118. C₄⋊C₄×C₁₉	SD₁₆	semidirect
150. Q₈×C₁₉	#102	semidirect
196. Q₈×C₄⋊C₄	D₁₉	semidirect
304. C₁₉	#8979	semidirect
360. C₄⋊C₄	#64527	semidirect
381. Q₈	#10597266	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
Q₈×C₄⋊C₄×C₁₉	2
#8979	19