Subgroups — #18074643

Order 4864.

788 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	C₂×#11927267	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×#11926289	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	#11927267	—	2	2	no	—
9	#11927267	—	2	2	no	—
10	#11927267	—	2	2	no	—
11	#11927267	C₄	1	4	yes	complemented
12	C₂×#10597315	C₂²	1	1	yes	characteristic
13	C₂×#10597344	—	2	2	no	—
14	C₂×#10597321	—	2	1	no	—
15	C₂×#10597392	—	2	1	no	—
16	C₂×C₄×Dic₃₈	—	2	1	no	—
17	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
18	C₂×#10597338	—	2	1	no	—
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	#11926289	—	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	C₂²×D₇₆	D₄	1	1	yes	characteristic
34	C₂²×C₄×D₁₉	—	2	1	no	—
35	C₂²×Dic₃₈	—	2	1	no	—
36	C₂²×C₈×C₁₉	—	2	1	no	—
37	C₄×Q₈×C₁₉	—	2	1	no	—
38	C₄×Q₈×C₁₉	—	2	1	no	—
39	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
40	C₄×Q₈×C₁₉	D₄	1	2	yes	—
41	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
43	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
44	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
45	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₉	—	2	1	no	—
47	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
48	#10597392	—	2	4	no	—
49	#10597392	—	2	4	no	—
50	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
51	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
52	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
53	C₂×C₄⋊Dic₁₉	—	2	1	no	—
54	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
55	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
56	C₂×Dic₁₉⋊C₄	—	2	2	no	—
57	C₂×C₄×Dic₁₉	—	2	2	no	—
58	C₂²×C₁₉⋊C₈	—	2	1	no	—
59	C₂²×C₁₉⋊C₈	—	2	1	no	—
60	#10597344	—	2	8	no	—
61	#10597344	—	2	8	no	—
62	#10597338	—	2	4	no	—
63	#10597338	—	2	4	no	—
64	#10597321	—	2	4	no	—
65	#10597321	—	2	4	no	—
66	C₄×D₇₆	—	2	1	no	—
67	C₄×D₇₆	—	2	1	no	—
68	C₄×D₇₆	C₂×C₄	1	2	yes	—
69	C₄×D₇₆	D₄	1	2	yes	—
70	#10597315	—	2	1	no	—
71	#10597315	—	2	1	no	—
72	#10597315	C₂×C₄	1	2	yes	—
73	#10597315	D₄	1	2	yes	—
74	C₄×Dic₃₈	—	2	4	no	—
75	C₄×Dic₃₈	—	2	4	no	—
76	C₁₉×C₄⋊C₈	—	2	1	no	—
77	C₁₉×C₄⋊C₈	—	2	1	no	—
78	C₁₉×#103	—	4	2	no	—
79	#10597266	—	4	2	no	—
80	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
81	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
82	C₄×C₁₉⋊C₈	—	2	1	no	—
83	C₄×C₁₉⋊C₈	—	2	1	no	—
84	C₂³×D₁₉	—	2	1	no	—
85	C₂×Q₈×C₁₉	—	2	1	no	—
86	C₂×Q₈×C₁₉	—	2	1	no	—
87	C₂×Q₈×C₁₉	—	2	1	no	—
88	C₂×Q₈×C₁₉	—	2	1	no	—
89	C₂×Q₈×C₁₉	—	2	1	no	—
90	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
91	C₂²×C₄×C₁₉	—	2	1	no	—
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	4	1	no	—
94	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×Dic₁₉	—	2	2	no	—
98	C₂²×Dic₁₉	—	2	1	no	—
99	C₂×D₇₆	—	2	1	no	—
100	C₂×D₇₆	—	2	1	no	—
101	C₂×D₇₆	—	2	1	no	—
102	C₂×D₇₆	—	2	1	no	—
103	C₂×D₇₆	—	2	1	no	—
104	C₂×D₇₆	C₂²⋊C₄	1	2	yes	—
105	C₂×C₄×D₁₉	—	2	2	no	—
106	C₂×C₄×D₁₉	—	2	2	no	—
107	C₂×C₄×D₁₉	—	4	1	no	—
108	C₂×C₄×D₁₉	—	4	1	no	—
109	C₂×C₄×D₁₉	—	4	1	no	—
110	C₂×C₄×D₁₉	—	4	1	no	—
111	C₂×Dic₃₈	—	2	2	no	—
112	C₂×Dic₃₈	—	2	2	no	—
113	C₂×Dic₃₈	—	4	1	no	—
114	C₂×Dic₃₈	—	4	1	no	—
115	C₂×Dic₃₈	—	4	1	no	—
116	C₂×Dic₃₈	—	4	1	no	—
117	C₂×C₈×C₁₉	—	4	1	no	—
118	C₂×C₈×C₁₉	—	4	1	no	—
119	C₂×C₈×C₁₉	—	4	1	no	—
120	C₄⋊C₄×C₁₉	—	2	2	no	—
121	C₄⋊C₄×C₁₉	—	2	2	no	—
122	C₄⋊C₄×C₁₉	—	2	1	no	—
123	C₄⋊C₄×C₁₉	—	4	2	no	—
124	C₄⋊C₄×C₁₉	—	4	1	no	—
125	C₄⋊C₄×C₁₉	—	4	1	no	—
126	C₄⋊C₄×C₁₉	—	4	1	no	—
127	C₄⋊C₄×C₁₉	—	4	1	no	—
128	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
129	C₄²×C₁₉	—	2	2	no	—
130	C₄²×C₁₉	—	2	2	no	—
131	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
135	(C₂×D₁₉)⋊C₄	—	2	8	no	—
136	(C₂×D₁₉)⋊C₄	—	2	8	no	—
137	(C₂×D₁₉)⋊C₄	—	2	2	no	—
138	(C₂×D₁₉)⋊C₄	—	2	2	no	—
139	C₄⋊Dic₁₉	—	2	2	no	—
140	C₄⋊Dic₁₉	—	2	2	no	—
141	C₄⋊Dic₁₉	—	2	1	no	—
142	C₄⋊Dic₁₉	—	2	2	no	—
143	C₄⋊Dic₁₉	C₂²⋊C₄	1	2	yes	—
144	C₄⋊Dic₁₉	C₂²⋊C₄	1	4	yes	—
145	Dic₁₉⋊C₄	—	2	8	no	—
146	C₄×Dic₁₉	—	2	8	no	—
147	C₂×C₁₉⋊C₈	—	2	2	no	—
148	C₂×C₁₉⋊C₈	—	4	1	no	—
149	C₂×C₁₉⋊C₈	—	4	1	no	—
150	C₂×C₁₉⋊C₈	—	4	1	no	—
151	C₂×C₁₉⋊C₈	—	4	1	no	—
152	C₂×C₁₉⋊C₈	—	4	1	no	—
153	#8449	—	19	1	no	maximal, Sylow
154	C₂³×C₁₉	#120	1	1	yes	characteristic
155	C₂²×D₁₉	—	2	2	no	—
156	C₂²×D₁₉	—	4	1	no	—
157	C₂²×D₁₉	—	4	1	no	—
158	C₂²×D₁₉	—	4	1	no	—
159	C₂²×D₁₉	—	4	1	no	—
160	C₂²×D₁₉	—	4	1	no	—
161	C₂²×D₁₉	—	4	1	no	—
162	Q₈×C₁₉	—	2	2	no	—
163	Q₈×C₁₉	—	2	2	no	—
164	Q₈×C₁₉	—	4	1	no	—
165	Q₈×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	2	1	no	—
167	C₂×C₄×C₁₉	—	2	1	no	—
168	C₂×C₄×C₁₉	—	2	2	no	—
169	C₂×C₄×C₁₉	—	2	2	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	—	8	1	no	—
175	C₂×C₄×C₁₉	—	8	1	no	—
176	C₂×C₄×C₁₉	—	8	1	no	—
177	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
182	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
185	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
187	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
188	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
190	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
191	C₂×Dic₁₉	—	2	2	no	—
192	C₂×Dic₁₉	—	2	4	no	—
193	C₂×Dic₁₉	—	4	2	no	—
194	C₂×Dic₁₉	—	4	1	no	—
195	C₂×Dic₁₉	—	4	2	no	—
196	C₂×Dic₁₉	—	4	1	no	—
197	D₇₆	—	2	2	no	—
198	D₇₆	—	2	2	no	—
199	D₇₆	—	4	1	no	—
200	D₇₆	—	4	1	no	—
201	C₄×D₁₉	—	4	2	no	—
202	C₄×D₁₉	—	4	2	no	—
203	C₄×D₁₉	—	4	2	no	—
204	C₄×D₁₉	—	4	2	no	—
205	Dic₃₈	—	4	2	no	—
206	Dic₃₈	—	4	2	no	—
207	Dic₃₈	—	4	2	no	—
208	Dic₃₈	—	4	2	no	—
209	C₈×C₁₉	—	8	1	no	—
210	C₁₉⋊C₈	—	4	2	no	—
211	C₁₉⋊C₈	—	8	1	no	—
212	C₂×#556	—	19	1	no	—
213	#1990	—	19	1	no	—
214	#1803	D₁₉	1	1	yes	characteristic, complemented
215	#1802	—	19	1	no	—
216	C₂×#332	—	19	1	no	—
217	C₂×Q₈⋊C₈	—	19	1	no	—
218	C₂×D₄⋊C₈	—	19	1	no	—
219	C₂²×C₁₉	#379	1	1	yes	characteristic
220	C₂²×C₁₉	#449	1	1	yes	characteristic
221	C₂²×C₁₉	#449	1	1	yes	characteristic
222	C₂²×C₁₉	#452	1	1	yes	characteristic
223	C₂²×C₁₉	#452	1	1	yes	characteristic
224	C₂²×C₁₉	#454	1	1	yes	characteristic
225	C₂²×C₁₉	#456	1	1	yes	characteristic
226	C₂×D₁₉	—	4	2	no	—
227	C₂×D₁₉	—	4	2	no	—
228	C₂×D₁₉	—	4	2	no	—
229	C₂×D₁₉	—	8	1	no	—
230	C₂×D₁₉	—	8	1	no	—
231	C₂×D₁₉	—	8	1	no	—
232	C₂×D₁₉	—	8	1	no	—
233	C₄×C₁₉	—	2	1	no	—
234	C₄×C₁₉	—	2	1	no	—
235	C₄×C₁₉	—	4	2	no	—
236	C₄×C₁₉	—	4	2	no	—
237	C₄×C₁₉	—	16	1	no	—
238	C₄×C₁₉	#416	1	1	yes	characteristic
239	C₄×C₁₉	#416	1	1	yes	characteristic
240	C₄×C₁₉	#417	1	1	yes	characteristic
241	C₄×C₁₉	#417	1	1	yes	characteristic
242	C₄×C₁₉	#449	1	1	yes	characteristic
243	C₄×C₁₉	#449	1	1	yes	characteristic
244	C₄×C₁₉	#452	1	1	yes	characteristic
245	C₄×C₁₉	#452	1	1	yes	characteristic
246	Dic₁₉	—	4	4	no	—
247	Dic₁₉	—	4	2	no	—
248	#556	—	19	4	no	—
249	#556	—	38	2	no	—
250	#556	—	38	2	no	—
251	#556	—	38	2	no	—
252	C₂×C₄⋊Q₈	—	19	1	no	—
253	C₂×#126	—	38	2	no	—
254	C₂×#124	—	38	1	no	—
255	C₂×C₂²⋊Q₈	—	38	1	no	—
256	C₂×C₄×Q₈	—	38	1	no	—
257	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
258	C₂×C₄×D₄	—	19	1	no	—
259	C₂×#117	—	38	1	no	—
260	C₂×C₄⋊C₈	—	19	1	no	—
261	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
262	C₂×#103	—	2	1	no	—
263	C₂×#102	—	38	1	no	—
264	C₂×C₄×C₈	—	19	1	no	—
265	#384	C₂×D₁₉	1	1	yes	characteristic
266	#340	—	2	1	no	—
267	#340	—	38	1	no	—
268	#340	—	38	2	no	—
269	#332	—	38	2	no	—
270	Q₈⋊C₈	—	38	2	no	—
271	D₄⋊C₈	—	38	2	no	—
272	C₂×C₁₉	#1628	1	1	yes	characteristic
273	C₂×C₁₉	#1638	1	1	yes	characteristic
274	C₂×C₁₉	#1650	1	1	yes	characteristic
275	C₂×C₁₉	#1652	1	1	yes	characteristic
276	C₂×C₁₉	#1788	1	1	yes	characteristic
277	C₂×C₁₉	#1788	1	1	yes	characteristic
278	C₂×C₁₉	#1793	1	1	yes	characteristic
279	D₁₉	—	8	2	no	—
280	C₂²×Q₈	—	38	1	no	—
281	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
282	C₂²×D₄	—	19	1	no	—
283	C₂³×C₄	—	38	1	no	—
284	C₂²×C₈	—	2	1	no	—
285	C₂²×C₈	—	38	1	no	—
286	C₂²×C₈	—	38	1	no	—
287	C₄⋊Q₈	—	19	2	no	—
288	C₄⋊Q₈	—	19	2	no	—
289	C₄⋊Q₈	—	38	1	no	—
290	C₄⋊Q₈	—	38	1	no	—
291	#126	—	38	8	no	—
292	#126	—	38	8	no	—
293	#124	—	38	4	no	—
294	#124	—	38	4	no	—
295	C₂²⋊Q₈	—	38	4	no	—
296	C₂²⋊Q₈	—	38	4	no	—
297	C₄×Q₈	—	2	1	no	—
298	C₄×Q₈	—	2	1	no	—
299	C₄×Q₈	—	38	4	no	—
300	C₄×Q₈	—	38	4	no	—
301	C₄×Q₈	C₄×D₁₉	1	2	yes	—
302	C₄×Q₈	D₇₆	1	2	yes	—
303	C₄×D₄	—	19	2	no	—
304	C₄×D₄	—	19	2	no	—
305	C₄×D₄	—	38	1	no	—
306	C₄×D₄	—	38	1	no	—
307	#117	—	38	4	no	—
308	#117	—	38	4	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	19	1	no	—
314	C₂×C₄⋊C₄	—	19	2	no	—
315	C₂×C₄⋊C₄	—	38	2	no	—
316	C₂×C₄⋊C₄	—	38	1	no	—
317	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
318	C₂×C₂²⋊C₄	—	38	2	no	—
319	C₂×C₂²⋊C₄	—	38	2	no	—
320	C₂×C₂²⋊C₄	—	38	1	no	—
321	C₂×C₄²	—	2	1	no	—
322	C₂×C₄²	—	38	2	no	—
323	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
324	C₄⋊C₈	—	2	1	no	—
325	C₄⋊C₈	—	2	1	no	—
326	C₄⋊C₈	—	38	1	no	—
327	C₄⋊C₈	—	38	1	no	—
328	#103	—	4	2	no	—
329	#102	—	76	2	no	—
330	C₄×C₈	—	38	1	no	—
331	C₄×C₈	—	38	1	no	—
332	C₁₉	#8449	1	1	yes	characteristic, complemented, Sylow
333	C₂⁴	—	38	1	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	38	2	no	—
340	C₂×Q₈	—	38	2	no	—
341	C₂×Q₈	—	76	1	no	—
342	C₂×Q₈	—	76	1	no	—
343	C₂×Q₈	—	76	1	no	—
344	C₂×Q₈	—	76	1	no	—
345	C₂×Q₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
346	C₂×D₄	—	19	2	no	—
347	C₂×D₄	—	38	1	no	—
348	C₂×D₄	—	38	1	no	—
349	C₂×D₄	—	38	1	no	—
350	C₂×D₄	—	38	1	no	—
351	C₂×D₄	—	38	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	4	1	no	—
355	C₂²×C₄	—	38	1	no	—
356	C₂²×C₄	—	38	2	no	—
357	C₂²×C₄	—	38	2	no	—
358	C₂²×C₄	—	38	2	no	—
359	C₂²×C₄	—	76	1	no	—
360	C₂²×C₄	—	76	1	no	—
361	C₂²×C₄	—	76	1	no	—
362	C₂²×C₄	—	76	1	no	—
363	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
364	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
365	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
366	C₂×C₈	—	4	1	no	—
367	C₂×C₈	—	4	1	no	—
368	C₂×C₈	—	4	1	no	—
369	C₂×C₈	—	38	2	no	—
370	C₂×C₈	—	76	1	no	—
371	C₂×C₈	—	76	1	no	—
372	C₂×C₈	—	76	1	no	—
373	C₂×C₈	—	76	1	no	—
374	C₂×C₈	—	76	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	4	2	no	—
379	C₄⋊C₄	—	4	1	no	—
380	C₄⋊C₄	—	4	1	no	—
381	C₄⋊C₄	—	4	1	no	—
382	C₄⋊C₄	—	4	1	no	—
383	C₄⋊C₄	—	19	2	no	—
384	C₄⋊C₄	—	19	4	no	—
385	C₄⋊C₄	—	38	8	no	—
386	C₄⋊C₄	—	38	2	no	—
387	C₄⋊C₄	—	38	1	no	—
388	C₄⋊C₄	—	38	2	no	—
389	C₄⋊C₄	—	38	2	no	—
390	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
391	C₂²⋊C₄	—	38	8	no	—
392	C₂²⋊C₄	—	38	8	no	—
393	C₂²⋊C₄	—	38	2	no	—
394	C₂²⋊C₄	—	38	2	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	38	8	no	—
398	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
399	C₄²	C₂×D₇₆	1	1	yes	characteristic
400	C₄²	D₄×D₁₉	1	1	yes	characteristic
401	C₄²	D₄×D₁₉	1	1	yes	characteristic
402	C₂³	—	38	2	no	—
403	C₂³	—	76	1	no	—
404	C₂³	—	76	1	no	—
405	C₂³	—	76	1	no	—
406	C₂³	—	76	1	no	—
407	C₂³	—	76	1	no	—
408	C₂³	—	76	1	no	—
409	C₂³	#10597383	1	1	yes	characteristic
410	Q₈	—	2	2	no	—
411	Q₈	—	2	2	no	—
412	Q₈	—	4	1	no	—
413	Q₈	—	4	1	no	—
414	Q₈	—	76	2	no	—
415	Q₈	—	76	2	no	—
416	Q₈	—	76	2	no	—
417	Q₈	—	76	2	no	—
418	D₄	—	38	2	no	—
419	D₄	—	38	2	no	—
420	D₄	—	76	1	no	—
421	D₄	—	76	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	8	1	no	—
431	C₂×C₄	—	8	1	no	—
432	C₂×C₄	—	8	1	no	—
433	C₂×C₄	—	38	2	no	—
434	C₂×C₄	—	38	4	no	—
435	C₂×C₄	—	76	1	no	—
436	C₂×C₄	—	76	2	no	—
437	C₂×C₄	—	76	1	no	—
438	C₂×C₄	—	76	2	no	—
439	C₂×C₄	—	76	2	no	—
440	C₂×C₄	—	76	2	no	—
441	C₂×C₄	—	76	2	no	—
442	C₂×C₄	—	76	2	no	—
443	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
444	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
445	C₂×C₄	#10597328	1	1	yes	characteristic
446	C₂×C₄	#10597328	1	1	yes	characteristic
447	C₂×C₄	#10597360	1	1	yes	characteristic
448	C₂×C₄	#10597362	1	1	yes	characteristic
449	C₂×C₄	#10597364	1	1	yes	characteristic
450	C₂×C₄	#10597365	1	1	yes	characteristic
451	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
452	C₂×C₄	#10597378	1	1	yes	characteristic
453	C₂×C₄	#10597383	1	1	yes	characteristic
454	C₂×C₄	#10597388	1	1	yes	characteristic
455	C₂×C₄	#10597396	1	1	yes	characteristic
456	C₂×C₄	#10597396	1	1	yes	characteristic
457	C₈	—	8	1	no	—
458	C₈	—	76	2	no	—
459	C₈	—	152	1	no	—
460	C₂²	—	76	2	no	—
461	C₂²	—	76	2	no	—
462	C₂²	—	76	2	no	—
463	C₂²	—	152	1	no	—
464	C₂²	—	152	1	no	—
465	C₂²	—	152	1	no	—
466	C₂²	—	152	1	no	—
467	C₂²	#11926399	1	1	yes	characteristic
468	C₂²	#11926687	1	1	yes	characteristic
469	C₂²	#11926688	1	1	yes	characteristic
470	C₂²	#11926704	1	1	yes	characteristic
471	C₂²	#11926705	1	1	yes	characteristic
472	C₂²	#11926715	1	1	yes	characteristic
473	C₂²	#11926725	1	1	yes	characteristic
474	C₄	—	2	1	no	—
475	C₄	—	2	1	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	2	no	—
478	C₄	—	16	1	no	—
479	C₄	—	76	2	no	—
480	C₄	—	76	4	no	—
481	C₄	#11926538	1	1	yes	characteristic
482	C₄	#11926539	1	1	yes	characteristic
483	C₄	#11926543	1	1	yes	characteristic
484	C₄	#11926544	1	1	yes	characteristic
485	C₄	#11926687	1	1	yes	characteristic
486	C₄	#11926692	1	1	yes	characteristic
487	C₄	#11926704	1	1	yes	characteristic
488	C₄	#11926709	1	1	yes	characteristic
489	C₂	—	152	2	no	—
490	C₂	#14562744	1	1	yes	characteristic
491	C₂	#14562806	1	1	yes	characteristic
492	C₂	#14562890	1	1	yes	characteristic
493	C₂	#14562903	1	1	yes	characteristic
494	C₂	#14563573	1	1	yes	characteristic
495	C₂	#14563574	1	1	yes	characteristic
496	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	#8449
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×#11926289	C₂	semidirect
5. C₂×Q₈⋊(C₁₉⋊C₈)	C₂	semidirect
7. C₁₉×#1803	C₂	semidirect
11. #11927267	C₄	semidirect
214. #1803	D₁₉	semidirect
332. C₁₉	#8449	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11927267	2
#14564595	2
#14563632	2
C₂×#11926289	2
C₂×Q₈⋊(C₁₉⋊C₈)	2
C₂×#11926271	2
C₁₉×#1803	2
#8449	19