Subgroups — #18074632

Order 4864.

1016 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×D₇₆	C₂	1	1	yes	maximal, characteristic
2	#14564595	C₂	1	1	yes	maximal, characteristic, complemented
3	#14563632	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926291	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₈⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11926271	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1803	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×Q₈×D₁₉	—	2	1	no	—
9	Q₈×D₇₆	—	2	2	no	—
10	Q₈×D₇₆	—	2	2	no	—
11	Q₈×D₇₆	—	2	2	no	—
12	Q₈×D₇₆	C₄	1	4	yes	complemented
13	C₂×#10597315	—	2	1	no	—
14	C₂×#10597315	C₂²	1	1	yes	characteristic
15	C₂×#10597343	—	2	2	no	—
16	C₂×#10597343	—	2	1	no	—
17	C₂×C₄×D₇₆	—	2	1	no	—
18	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×#10597266	—	2	1	no	—
21	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
22	#11926306	—	2	1	no	—
23	#11926306	—	2	2	no	—
24	#11926291	—	2	2	no	—
25	Q₈⋊(C₁₉⋊C₈)	—	2	2	no	—
26	#11926271	—	2	2	no	—
27	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#103	—	2	1	no	—
30	C₁₉×#384	C₂²	1	1	yes	characteristic
31	C₁₉×#340	—	2	1	no	—
32	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
33	C₂×Q₈×D₁₉	—	2	4	no	—
34	C₂×Q₈×D₁₉	—	2	4	no	—
35	C₂×Q₈×D₁₉	—	4	2	no	—
36	C₂×Q₈×D₁₉	—	4	2	no	—
37	C₂×Q₈×D₁₉	—	4	2	no	—
38	C₂×Q₈×D₁₉	—	4	2	no	—
39	C₂²×D₇₆	D₄	1	1	yes	characteristic
40	C₂²×C₄×D₁₉	—	2	2	no	—
41	C₂²×C₄×D₁₉	—	2	1	no	—
42	C₂²×Dic₃₈	—	2	2	no	—
43	C₂²×Dic₃₈	—	2	1	no	—
44	C₂²×C₈×C₁₉	—	2	1	no	—
45	C₄×Q₈×C₁₉	—	2	1	no	—
46	C₄×Q₈×C₁₉	—	2	1	no	—
47	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
48	C₄×Q₈×C₁₉	D₄	1	2	yes	—
49	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₁₉	—	2	1	no	—
55	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
56	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
57	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
58	C₂×C₄⋊Dic₁₉	—	2	2	no	—
59	C₂×C₄⋊Dic₁₉	—	2	1	no	—
60	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
61	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
62	C₂²×C₁₉⋊C₈	—	2	1	no	—
63	C₂²×C₁₉⋊C₈	—	2	1	no	—
64	#10597343	—	2	4	no	—
65	#10597343	—	2	8	no	—
66	#10597343	—	2	4	no	—
67	#10597343	—	2	8	no	—
68	C₄×D₇₆	—	2	4	no	—
69	C₄×D₇₆	—	2	4	no	—
70	C₄×D₇₆	—	2	1	no	—
71	C₄×D₇₆	—	2	1	no	—
72	C₄×D₇₆	C₂×C₄	1	2	yes	—
73	C₄×D₇₆	D₄	1	2	yes	—
74	#10597315	—	2	4	no	—
75	#10597315	—	2	1	no	—
76	#10597315	—	2	1	no	—
77	#10597315	—	2	4	no	—
78	#10597315	C₂×C₄	1	2	yes	—
79	#10597315	D₄	1	2	yes	—
80	C₁₉×C₄⋊C₈	—	2	1	no	—
81	C₁₉×C₄⋊C₈	—	2	1	no	—
82	C₁₉×#103	—	4	2	no	—
83	#10597266	—	4	2	no	—
84	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
85	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
86	C₄×C₁₉⋊C₈	—	2	1	no	—
87	C₄×C₁₉⋊C₈	—	2	1	no	—
88	C₂³×D₁₉	—	2	1	no	—
89	C₂×Q₈×C₁₉	—	2	1	no	—
90	C₂×Q₈×C₁₉	—	2	1	no	—
91	C₂×Q₈×C₁₉	—	2	1	no	—
92	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
93	C₂×Q₈×C₁₉	D₈	1	2	yes	—
94	C₂×Q₈×C₁₉	SD₁₆	1	2	yes	—
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	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×Dic₁₉	—	2	1	no	—
102	C₂²×Dic₁₉	—	2	2	no	—
103	Q₈×D₁₉	—	4	8	no	—
104	Q₈×D₁₉	—	4	8	no	—
105	Q₈×D₁₉	—	4	8	no	—
106	Q₈×D₁₉	—	4	8	no	—
107	C₂×D₇₆	—	2	1	no	—
108	C₂×D₇₆	—	2	1	no	—
109	C₂×D₇₆	—	2	1	no	—
110	C₂×D₇₆	C₂²⋊C₄	1	2	yes	—
111	C₂×D₇₆	SD₁₆	1	2	yes	—
112	C₂×D₇₆	Q₁₆	1	2	yes	—
113	C₂×C₄×D₁₉	—	2	8	no	—
114	C₂×C₄×D₁₉	—	2	2	no	—
115	C₂×C₄×D₁₉	—	2	2	no	—
116	C₂×C₄×D₁₉	—	4	4	no	—
117	C₂×C₄×D₁₉	—	4	4	no	—
118	C₂×C₄×D₁₉	—	4	1	no	—
119	C₂×C₄×D₁₉	—	4	1	no	—
120	C₂×C₄×D₁₉	—	4	1	no	—
121	C₂×C₄×D₁₉	—	4	1	no	—
122	C₂×Dic₃₈	—	2	8	no	—
123	C₂×Dic₃₈	—	2	2	no	—
124	C₂×Dic₃₈	—	2	2	no	—
125	C₂×Dic₃₈	—	4	4	no	—
126	C₂×Dic₃₈	—	4	4	no	—
127	C₂×Dic₃₈	—	4	1	no	—
128	C₂×Dic₃₈	—	4	1	no	—
129	C₂×Dic₃₈	—	4	1	no	—
130	C₂×Dic₃₈	—	4	1	no	—
131	C₂×C₈×C₁₉	—	4	1	no	—
132	C₂×C₈×C₁₉	—	4	1	no	—
133	C₂×C₈×C₁₉	—	4	1	no	—
134	C₄⋊C₄×C₁₉	—	2	2	no	—
135	C₄⋊C₄×C₁₉	—	2	2	no	—
136	C₄⋊C₄×C₁₉	—	2	1	no	—
137	C₄⋊C₄×C₁₉	—	4	2	no	—
138	C₄⋊C₄×C₁₉	—	4	1	no	—
139	C₄⋊C₄×C₁₉	—	4	1	no	—
140	C₄⋊C₄×C₁₉	—	4	1	no	—
141	C₄⋊C₄×C₁₉	—	4	1	no	—
142	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
143	C₄²×C₁₉	—	2	2	no	—
144	C₄²×C₁₉	—	2	2	no	—
145	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
146	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
149	(C₂×D₁₉)⋊C₄	—	2	8	no	—
150	(C₂×D₁₉)⋊C₄	—	2	2	no	—
151	(C₂×D₁₉)⋊C₄	—	2	2	no	—
152	C₄⋊Dic₁₉	—	2	8	no	—
153	C₄⋊Dic₁₉	—	2	2	no	—
154	C₄⋊Dic₁₉	—	2	1	no	—
155	C₄⋊Dic₁₉	—	2	2	no	—
156	C₄⋊Dic₁₉	—	2	2	no	—
157	C₄⋊Dic₁₉	C₂²⋊C₄	1	2	yes	—
158	C₄⋊Dic₁₉	C₂²⋊C₄	1	4	yes	—
159	C₂×C₁₉⋊C₈	—	2	2	no	—
160	C₂×C₁₉⋊C₈	—	4	1	no	—
161	C₂×C₁₉⋊C₈	—	4	1	no	—
162	C₂×C₁₉⋊C₈	—	4	1	no	—
163	C₂×C₁₉⋊C₈	—	4	1	no	—
164	C₂×C₁₉⋊C₈	—	4	1	no	—
165	#8447	—	19	1	no	maximal, Sylow
166	C₂³×C₁₉	#120	1	1	yes	characteristic
167	C₂²×D₁₉	—	2	2	no	—
168	C₂²×D₁₉	—	2	2	no	—
169	C₂²×D₁₉	—	2	2	no	—
170	C₂²×D₁₉	—	4	1	no	—
171	C₂²×D₁₉	—	4	1	no	—
172	C₂²×D₁₉	—	4	1	no	—
173	C₂²×D₁₉	—	4	1	no	—
174	Q₈×C₁₉	—	2	2	no	—
175	Q₈×C₁₉	—	2	2	no	—
176	Q₈×C₁₉	—	2	2	no	—
177	Q₈×C₁₉	#102	1	4	yes	complemented
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	2	1	no	—
182	C₂×C₄×C₁₉	—	2	1	no	—
183	C₂×C₄×C₁₉	—	2	2	no	—
184	C₂×C₄×C₁₉	—	4	1	no	—
185	C₂×C₄×C₁₉	—	4	1	no	—
186	C₂×C₄×C₁₉	—	8	1	no	—
187	C₂×C₄×C₁₉	—	8	1	no	—
188	C₂×C₄×C₁₉	—	8	1	no	—
189	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
192	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
193	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
194	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
198	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
199	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
200	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
201	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
202	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
203	C₂×Dic₁₉	—	2	2	no	—
204	C₂×Dic₁₉	—	2	4	no	—
205	C₂×Dic₁₉	—	4	1	no	—
206	C₂×Dic₁₉	—	4	2	no	—
207	C₂×Dic₁₉	—	4	1	no	—
208	C₂×Dic₁₉	—	4	2	no	—
209	D₇₆	—	2	2	no	—
210	D₇₆	—	2	2	no	—
211	D₇₆	—	2	2	no	—
212	D₇₆	#103	1	4	yes	complemented
213	C₄×D₁₉	—	4	16	no	—
214	C₄×D₁₉	—	4	2	no	—
215	C₄×D₁₉	—	4	2	no	—
216	C₄×D₁₉	—	4	2	no	—
217	C₄×D₁₉	—	4	2	no	—
218	Dic₃₈	—	4	16	no	—
219	Dic₃₈	—	4	2	no	—
220	Dic₃₈	—	4	2	no	—
221	Dic₃₈	—	4	2	no	—
222	Dic₃₈	—	4	2	no	—
223	C₈×C₁₉	—	8	1	no	—
224	C₁₉⋊C₈	—	4	2	no	—
225	C₁₉⋊C₈	—	8	1	no	—
226	C₂×D₄×Q₈	—	19	1	no	—
227	#1990	—	19	1	no	—
228	#1803	D₁₉	1	1	yes	characteristic, complemented
229	#1802	—	19	1	no	—
230	C₂×#332	—	19	1	no	—
231	C₂×Q₈⋊C₈	—	19	1	no	—
232	C₂×D₄⋊C₈	—	19	1	no	—
233	C₂²×C₁₉	#379	1	1	yes	characteristic
234	C₂²×C₁₉	#447	1	1	yes	characteristic
235	C₂²×C₁₉	#448	1	1	yes	characteristic
236	C₂²×C₁₉	#450	1	1	yes	characteristic
237	C₂²×C₁₉	#451	1	1	yes	characteristic
238	C₂²×C₁₉	#454	1	1	yes	characteristic
239	C₂²×C₁₉	#456	1	1	yes	characteristic
240	C₂×D₁₉	—	2	4	no	—
241	C₂×D₁₉	—	4	2	no	—
242	C₂×D₁₉	—	4	2	no	—
243	C₂×D₁₉	—	4	2	no	—
244	C₂×D₁₉	—	4	2	no	—
245	C₂×D₁₉	—	4	2	no	—
246	C₂×D₁₉	—	4	2	no	—
247	C₄×C₁₉	—	2	1	no	—
248	C₄×C₁₉	—	2	1	no	—
249	C₄×C₁₉	—	2	4	no	—
250	C₄×C₁₉	—	4	2	no	—
251	C₄×C₁₉	—	16	1	no	—
252	C₄×C₁₉	C₂×#102	1	1	yes	characteristic
253	C₄×C₁₉	C₂×#103	1	1	yes	characteristic
254	C₄×C₁₉	#418	1	1	yes	characteristic
255	C₄×C₁₉	#419	1	1	yes	characteristic
256	C₄×C₁₉	#447	1	1	yes	characteristic
257	C₄×C₁₉	#448	1	1	yes	characteristic
258	C₄×C₁₉	#450	1	1	yes	characteristic
259	C₄×C₁₉	#451	1	1	yes	characteristic
260	Dic₁₉	—	4	2	no	—
261	Dic₁₉	—	4	4	no	—
262	C₂³×Q₈	—	38	1	no	—
263	D₄×Q₈	—	19	4	no	—
264	D₄×Q₈	—	38	2	no	—
265	D₄×Q₈	—	38	2	no	—
266	D₄×Q₈	—	38	2	no	—
267	C₂×C₄⋊Q₈	—	19	1	no	—
268	C₂×C₄⋊Q₈	—	38	1	no	—
269	C₂×C₂²⋊Q₈	—	38	2	no	—
270	C₂×C₂²⋊Q₈	—	38	1	no	—
271	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
272	C₂×C₄×D₄	—	19	1	no	—
273	C₂×C₄×D₄	—	38	1	no	—
274	C₂×C₄⋊C₈	—	19	1	no	—
275	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
276	C₂×#103	—	2	1	no	—
277	C₂×#102	—	38	1	no	—
278	C₂×C₄×C₈	—	19	1	no	—
279	#384	C₂×D₁₉	1	1	yes	characteristic
280	#340	—	2	1	no	—
281	#340	—	38	1	no	—
282	#340	—	38	2	no	—
283	#332	—	38	2	no	—
284	Q₈⋊C₈	—	38	2	no	—
285	D₄⋊C₈	—	38	2	no	—
286	C₂×C₁₉	#1627	1	1	yes	characteristic
287	C₂×C₁₉	#1637	1	1	yes	characteristic
288	C₂×C₁₉	#1649	1	1	yes	characteristic
289	C₂×C₁₉	#1651	1	1	yes	characteristic
290	C₂×C₁₉	#1786	1	1	yes	characteristic
291	C₂×C₁₉	#1787	1	1	yes	characteristic
292	C₂×C₁₉	#1793	1	1	yes	characteristic
293	D₁₉	—	4	4	no	—
294	C₂²×Q₈	—	38	2	no	—
295	C₂²×Q₈	—	38	4	no	—
296	C₂²×Q₈	—	38	4	no	—
297	C₂²×Q₈	—	38	1	no	—
298	C₂²×Q₈	—	76	2	no	—
299	C₂²×Q₈	—	76	2	no	—
300	C₂²×Q₈	—	76	2	no	—
301	C₂²×Q₈	—	76	2	no	—
302	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
303	C₂²×D₄	—	19	1	no	—
304	C₂³×C₄	—	38	2	no	—
305	C₂³×C₄	—	38	1	no	—
306	C₂²×C₈	—	2	1	no	—
307	C₂²×C₈	—	38	1	no	—
308	C₂²×C₈	—	38	1	no	—
309	C₄⋊Q₈	—	19	2	no	—
310	C₄⋊Q₈	—	19	2	no	—
311	C₄⋊Q₈	—	38	4	no	—
312	C₄⋊Q₈	—	38	4	no	—
313	C₄⋊Q₈	—	38	1	no	—
314	C₄⋊Q₈	—	38	1	no	—
315	C₂²⋊Q₈	—	38	8	no	—
316	C₂²⋊Q₈	—	38	4	no	—
317	C₂²⋊Q₈	—	38	8	no	—
318	C₂²⋊Q₈	—	38	4	no	—
319	C₄×Q₈	—	2	1	no	—
320	C₄×Q₈	—	2	1	no	—
321	C₄×Q₈	C₄×D₁₉	1	2	yes	—
322	C₄×Q₈	D₇₆	1	2	yes	—
323	C₄×D₄	—	19	2	no	—
324	C₄×D₄	—	19	2	no	—
325	C₄×D₄	—	38	4	no	—
326	C₄×D₄	—	38	4	no	—
327	C₄×D₄	—	38	1	no	—
328	C₄×D₄	—	38	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	19	1	no	—
334	C₂×C₄⋊C₄	—	19	2	no	—
335	C₂×C₄⋊C₄	—	38	2	no	—
336	C₂×C₄⋊C₄	—	38	1	no	—
337	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
338	C₂×C₂²⋊C₄	—	38	2	no	—
339	C₂×C₂²⋊C₄	—	38	1	no	—
340	C₂×C₄²	—	2	1	no	—
341	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
342	C₄⋊C₈	—	2	1	no	—
343	C₄⋊C₈	—	2	1	no	—
344	C₄⋊C₈	—	38	1	no	—
345	C₄⋊C₈	—	38	1	no	—
346	#103	—	4	2	no	—
347	#102	—	76	2	no	—
348	C₄×C₈	—	38	1	no	—
349	C₄×C₈	—	38	1	no	—
350	C₁₉	#8447	1	1	yes	characteristic, complemented, Sylow
351	C₂⁴	—	38	1	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	38	8	no	—
356	C₂×Q₈	—	38	2	no	—
357	C₂×Q₈	—	38	2	no	—
358	C₂×Q₈	—	76	4	no	—
359	C₂×Q₈	—	76	4	no	—
360	C₂×Q₈	—	76	8	no	—
361	C₂×Q₈	—	76	8	no	—
362	C₂×Q₈	—	76	8	no	—
363	C₂×Q₈	—	76	8	no	—
364	C₂×Q₈	—	76	1	no	—
365	C₂×Q₈	—	76	1	no	—
366	C₂×Q₈	—	76	1	no	—
367	C₂×Q₈	—	76	1	no	—
368	C₂×Q₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
369	C₂×Q₈	#64525	1	2	yes	—
370	C₂×Q₈	#64527	1	2	yes	—
371	C₂×D₄	—	19	2	no	—
372	C₂×D₄	—	19	2	no	—
373	C₂×D₄	—	19	2	no	—
374	C₂×D₄	—	38	1	no	—
375	C₂×D₄	—	38	1	no	—
376	C₂×D₄	—	38	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	4	1	no	—
380	C₂²×C₄	—	38	8	no	—
381	C₂²×C₄	—	38	2	no	—
382	C₂²×C₄	—	38	1	no	—
383	C₂²×C₄	—	38	2	no	—
384	C₂²×C₄	—	38	2	no	—
385	C₂²×C₄	—	76	4	no	—
386	C₂²×C₄	—	76	4	no	—
387	C₂²×C₄	—	76	1	no	—
388	C₂²×C₄	—	76	1	no	—
389	C₂²×C₄	—	76	1	no	—
390	C₂²×C₄	—	76	1	no	—
391	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
392	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
393	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
394	C₂×C₈	—	4	1	no	—
395	C₂×C₈	—	4	1	no	—
396	C₂×C₈	—	4	1	no	—
397	C₂×C₈	—	38	2	no	—
398	C₂×C₈	—	76	1	no	—
399	C₂×C₈	—	76	1	no	—
400	C₂×C₈	—	76	1	no	—
401	C₂×C₈	—	76	1	no	—
402	C₂×C₈	—	76	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	4	2	no	—
407	C₄⋊C₄	—	4	1	no	—
408	C₄⋊C₄	—	4	1	no	—
409	C₄⋊C₄	—	4	1	no	—
410	C₄⋊C₄	—	4	1	no	—
411	C₄⋊C₄	—	19	2	no	—
412	C₄⋊C₄	—	19	4	no	—
413	C₄⋊C₄	—	38	8	no	—
414	C₄⋊C₄	—	38	2	no	—
415	C₄⋊C₄	—	38	1	no	—
416	C₄⋊C₄	—	38	2	no	—
417	C₄⋊C₄	—	38	2	no	—
418	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
419	C₂²⋊C₄	—	38	8	no	—
420	C₂²⋊C₄	—	38	2	no	—
421	C₂²⋊C₄	—	38	2	no	—
422	C₄²	—	2	2	no	—
423	C₄²	—	2	2	no	—
424	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
425	C₄²	C₂×D₇₆	1	1	yes	characteristic
426	C₄²	D₄×D₁₉	1	1	yes	characteristic
427	C₄²	D₄×D₁₉	1	1	yes	characteristic
428	C₂³	—	38	2	no	—
429	C₂³	—	38	2	no	—
430	C₂³	—	38	2	no	—
431	C₂³	—	76	1	no	—
432	C₂³	—	76	1	no	—
433	C₂³	—	76	1	no	—
434	C₂³	—	76	1	no	—
435	C₂³	#10597383	1	1	yes	characteristic
436	Q₈	—	2	2	no	—
437	Q₈	—	2	2	no	—
438	Q₈	—	2	2	no	—
439	Q₈	—	76	16	no	—
440	Q₈	—	76	2	no	—
441	Q₈	—	76	2	no	—
442	Q₈	—	76	2	no	—
443	Q₈	—	76	2	no	—
444	Q₈	#10597266	1	4	yes	complemented
445	D₄	—	19	4	no	—
446	D₄	—	38	2	no	—
447	D₄	—	38	2	no	—
448	D₄	—	38	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	8	1	no	—
458	C₂×C₄	—	8	1	no	—
459	C₂×C₄	—	8	1	no	—
460	C₂×C₄	—	38	4	no	—
461	C₂×C₄	—	38	2	no	—
462	C₂×C₄	—	76	16	no	—
463	C₂×C₄	—	76	2	no	—
464	C₂×C₄	—	76	1	no	—
465	C₂×C₄	—	76	2	no	—
466	C₂×C₄	—	76	1	no	—
467	C₂×C₄	—	76	2	no	—
468	C₂×C₄	—	76	2	no	—
469	C₂×C₄	—	76	2	no	—
470	C₂×C₄	—	76	2	no	—
471	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
472	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
473	C₂×C₄	#10597328	1	1	yes	characteristic
474	C₂×C₄	#10597328	1	1	yes	characteristic
475	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
476	C₂×C₄	#10597361	1	1	yes	characteristic
477	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
478	C₂×C₄	#10597364	1	1	yes	characteristic
479	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
480	C₂×C₄	C₂×#64525	1	1	yes	characteristic
481	C₂×C₄	#10597383	1	1	yes	characteristic
482	C₂×C₄	C₂×#64527	1	1	yes	characteristic
483	C₂×C₄	#10597395	1	1	yes	characteristic
484	C₂×C₄	#10597395	1	1	yes	characteristic
485	C₈	—	8	1	no	—
486	C₈	—	76	2	no	—
487	C₈	—	152	1	no	—
488	C₂²	—	38	4	no	—
489	C₂²	—	76	2	no	—
490	C₂²	—	76	2	no	—
491	C₂²	—	76	2	no	—
492	C₂²	—	76	2	no	—
493	C₂²	—	76	2	no	—
494	C₂²	—	76	2	no	—
495	C₂²	#11926399	1	1	yes	characteristic
496	C₂²	#11926677	1	1	yes	characteristic
497	C₂²	#11926681	1	1	yes	characteristic
498	C₂²	#11926694	1	1	yes	characteristic
499	C₂²	#11926698	1	1	yes	characteristic
500	C₂²	#11926715	1	1	yes	characteristic
501	C₂²	#11926725	1	1	yes	characteristic
502	C₄	—	2	1	no	—
503	C₄	—	2	1	no	—
504	C₄	—	2	4	no	—
505	C₄	—	4	2	no	—
506	C₄	—	16	1	no	—
507	C₄	—	76	4	no	—
508	C₄	—	76	2	no	—
509	C₄	C₂×#10597266	1	1	yes	characteristic
510	C₄	#103×D₁₉	1	1	yes	characteristic
511	C₄	#11926548	1	1	yes	characteristic
512	C₄	#11926551	1	1	yes	characteristic
513	C₄	#11926677	1	1	yes	characteristic
514	C₄	#11926684	1	1	yes	characteristic
515	C₄	#11926694	1	1	yes	characteristic
516	C₄	#11926701	1	1	yes	characteristic
517	C₂	—	76	4	no	—
518	C₂	#14562736	1	1	yes	characteristic
519	C₂	#14562798	1	1	yes	characteristic
520	C₂	#14562882	1	1	yes	characteristic
521	C₂	#14562897	1	1	yes	characteristic
522	C₂	#14563565	1	1	yes	characteristic
523	C₂	#14563568	1	1	yes	characteristic
524	C₂	#14563592	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597383
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1803	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂²×D₇₆	D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1803	D₁₉
hypocenter	C₁₉	#8447
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1803

Complements

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

N	H ≅ G/N	type
2. #14564595	C₂	semidirect
4. C₂×#11926291	C₂	semidirect
5. C₂×Q₈⋊(C₁₉⋊C₈)	C₂	semidirect
7. C₁₉×#1803	C₂	semidirect
12. Q₈×D₇₆	C₄	semidirect
177. Q₈×C₁₉	#102	semidirect
212. D₇₆	#103	semidirect
228. #1803	D₁₉	semidirect
350. C₁₉	#8447	semidirect
444. 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×Q₈×D₇₆	2
#14564595	2
#14563632	2
C₂×#11926291	2
C₂×Q₈⋊(C₁₉⋊C₈)	2
C₂×#11926271	2
C₁₉×#1803	2
#8447	19