Subgroups — #18074115

Order 4864.

794 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14564430	C₂	1	1	yes	maximal, characteristic, complemented
2	#14563627	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562325	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562312	C₂	1	1	yes	maximal, characteristic, complemented
5	#14562090	C₂	1	1	yes	maximal, characteristic, complemented
6	#14562086	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3506	C₂	1	1	yes	maximal, characteristic
8	#11926568	C₂²	1	1	yes	characteristic
9	#11926568	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×#10597290	—	2	1	no	—
12	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
13	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	#11926313	—	2	1	no	—
15	#11926293	—	2	1	no	—
16	#11926290	—	2	1	no	—
17	#11926290	—	2	1	no	—
18	#11926288	—	2	1	no	—
19	Q₈⋊(C₁₉⋊C₈)	—	2	2	no	—
20	D₄⋊(C₁₉⋊C₈)	—	2	2	no	—
21	C₁₉×#559	—	2	2	no	—
22	C₁₉×#556	—	2	1	no	—
23	C₁₉×#555	—	2	1	no	—
24	C₁₉×#553	—	2	2	no	—
25	C₁₉×#550	—	2	1	no	—
26	C₁₉×#547	—	2	1	no	—
27	C₁₉×#538	C₄	1	4	yes	—
28	C₁₉×#535	—	2	1	no	—
29	C₁₉×#533	C₂²	1	1	yes	characteristic
30	C₁₉×#532	C₂²	1	1	yes	characteristic
31	C₁₉×#525	—	2	2	no	—
32	C₁₉×#520	—	2	1	no	—
33	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
34	C₂×#41×C₁₉	—	2	2	no	—
35	C₂×#41×C₁₉	—	2	1	no	—
36	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₉	D₄	1	2	yes	—
38	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
39	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
40	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
41	C₁₉×#127	—	2	2	no	—
42	C₁₉×#127	D₄	1	1	yes	characteristic
43	C₁₉×#126	—	2	4	no	—
44	C₁₉×#125	—	2	1	no	—
45	C₁₉×#124	—	2	2	no	—
46	C₁₉×#124	—	2	4	no	—
47	C₁₉×#124	—	2	1	no	—
48	C₁₉×#123	—	2	4	no	—
49	C₁₉×#123	—	2	4	no	—
50	C₁₉×C₂²⋊Q₈	—	2	2	no	—
51	C₁₉×C₂²⋊Q₈	—	2	1	no	—
52	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
53	C₁₉×#121	—	2	2	no	—
54	C₁₉×#121	—	2	2	no	—
55	C₁₉×#121	—	2	2	no	—
56	C₁₉×#121	—	2	4	no	—
57	C₁₉×#121	—	2	1	no	—
58	C₁₉×#121	C₂×C₄	1	2	yes	—
59	C₁₉×#120	—	2	4	no	—
60	C₄×Q₈×C₁₉	—	2	2	no	—
61	C₄×Q₈×C₁₉	—	2	1	no	—
62	C₄×Q₈×C₁₉	D₄	1	2	yes	—
63	C₄×D₄×C₁₉	—	2	2	no	—
64	C₄×D₄×C₁₉	—	2	4	no	—
65	C₄×D₄×C₁₉	—	2	4	no	—
66	C₄×D₄×C₁₉	—	2	1	no	—
67	C₄×D₄×C₁₉	—	2	1	no	—
68	C₄×D₄×C₁₉	—	2	1	no	—
69	C₄×D₄×C₁₉	—	2	1	no	—
70	C₄×D₄×C₁₉	—	2	1	no	—
71	C₄×D₄×C₁₉	D₄	1	2	yes	—
72	C₁₉×#117	—	2	2	no	—
73	C₁₉×#117	—	2	2	no	—
74	C₁₉×#117	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
77	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
78	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
79	C₂×#64520	—	2	1	no	—
80	C₂×#64520	—	2	1	no	—
81	C₂²×C₁₉⋊C₈	—	2	1	no	—
82	C₂²×C₁₉⋊C₈	—	2	1	no	—
83	#10597290	—	4	2	no	—
84	C₂²⋊(C₁₉⋊C₈)	—	4	4	no	—
85	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
86	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
87	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
88	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
89	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
90	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
91	C₄×C₁₉⋊C₈	—	2	1	no	—
92	C₄×C₁₉⋊C₈	—	2	1	no	—
93	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
94	#41×C₁₉	—	4	1	no	—
95	#41×C₁₉	—	4	1	no	—
96	#41×C₁₉	—	4	1	no	—
97	#41×C₁₉	—	4	1	no	—
98	#41×C₁₉	—	8	2	no	—
99	#41×C₁₉	—	8	2	no	—
100	C₂×Q₈×C₁₉	—	2	1	no	—
101	C₂×Q₈×C₁₉	—	2	1	no	—
102	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
103	C₂×D₄×C₁₉	—	2	2	no	—
104	C₂×D₄×C₁₉	—	2	4	no	—
105	C₂×D₄×C₁₉	—	2	4	no	—
106	C₂×D₄×C₁₉	—	2	1	no	—
107	C₂×D₄×C₁₉	—	2	1	no	—
108	C₂×D₄×C₁₉	—	2	1	no	—
109	C₂×D₄×C₁₉	—	2	1	no	—
110	C₂×D₄×C₁₉	—	2	1	no	—
111	C₂×D₄×C₁₉	—	2	1	no	—
112	C₂×D₄×C₁₉	—	2	1	no	—
113	C₂×D₄×C₁₉	—	2	1	no	—
114	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
115	C₂²×C₄×C₁₉	—	2	4	no	—
116	C₂²×C₄×C₁₉	—	2	2	no	—
117	C₂²×C₄×C₁₉	—	2	2	no	—
118	C₂²×C₄×C₁₉	—	2	2	no	—
119	C₂²×C₄×C₁₉	—	4	2	no	—
120	C₂²×C₄×C₁₉	—	4	2	no	—
121	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
122	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₄⋊C₄×C₁₉	—	2	4	no	—
126	C₄⋊C₄×C₁₉	—	2	2	no	—
127	C₄⋊C₄×C₁₉	—	2	1	no	—
128	C₄⋊C₄×C₁₉	—	2	1	no	—
129	C₄⋊C₄×C₁₉	—	2	1	no	—
130	C₄⋊C₄×C₁₉	—	2	1	no	—
131	C₄⋊C₄×C₁₉	—	2	1	no	—
132	C₄⋊C₄×C₁₉	—	2	1	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
135	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
136	C₂²⋊C₄×C₁₉	—	2	4	no	—
137	C₂²⋊C₄×C₁₉	—	2	4	no	—
138	C₂²⋊C₄×C₁₉	—	2	4	no	—
139	C₂²⋊C₄×C₁₉	—	2	2	no	—
140	C₂²⋊C₄×C₁₉	—	2	2	no	—
141	C₂²⋊C₄×C₁₉	—	2	2	no	—
142	C₂²⋊C₄×C₁₉	—	2	2	no	—
143	C₂²⋊C₄×C₁₉	—	2	2	no	—
144	C₄²×C₁₉	—	2	4	no	—
145	C₄²×C₁₉	—	2	2	no	—
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	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
150	#64520	—	4	1	no	—
151	#64520	—	4	1	no	—
152	#64520	—	4	1	no	—
153	#64520	—	4	1	no	—
154	C₂×C₁₉⋊C₈	—	2	2	no	—
155	C₂×C₁₉⋊C₈	—	4	1	no	—
156	C₂×C₁₉⋊C₈	—	4	1	no	—
157	C₂×C₁₉⋊C₈	—	4	2	no	—
158	C₂×C₁₉⋊C₈	—	4	1	no	—
159	C₂×C₁₉⋊C₈	—	4	1	no	—
160	C₂×C₁₉⋊C₈	—	4	1	no	—
161	#8358	—	19	1	no	maximal, Sylow
162	C₂³×C₁₉	—	2	2	no	—
163	C₂³×C₁₉	—	2	2	no	—
164	C₂³×C₁₉	—	2	2	no	—
165	C₂³×C₁₉	—	2	2	no	—
166	C₂³×C₁₉	—	4	2	no	—
167	C₂³×C₁₉	—	4	2	no	—
168	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	Q₈×C₁₉	—	4	2	no	—
170	Q₈×C₁₉	—	4	1	no	—
171	Q₈×C₁₉	—	4	1	no	—
172	Q₈×C₁₉	—	4	1	no	—
173	Q₈×C₁₉	—	4	1	no	—
174	D₄×C₁₉	—	4	2	no	—
175	D₄×C₁₉	—	4	2	no	—
176	D₄×C₁₉	—	4	2	no	—
177	D₄×C₁₉	—	4	1	no	—
178	D₄×C₁₉	—	4	1	no	—
179	D₄×C₁₉	—	4	1	no	—
180	D₄×C₁₉	—	4	1	no	—
181	D₄×C₁₉	—	4	1	no	—
182	D₄×C₁₉	—	4	1	no	—
183	D₄×C₁₉	—	4	1	no	—
184	D₄×C₁₉	—	4	1	no	—
185	D₄×C₁₉	—	8	4	no	—
186	D₄×C₁₉	—	8	4	no	—
187	C₂×C₄×C₁₉	—	2	1	no	—
188	C₂×C₄×C₁₉	—	2	1	no	—
189	C₂×C₄×C₁₉	—	2	2	no	—
190	C₂×C₄×C₁₉	—	2	2	no	—
191	C₂×C₄×C₁₉	—	2	2	no	—
192	C₂×C₄×C₁₉	—	2	2	no	—
193	C₂×C₄×C₁₉	—	4	1	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	4	2	no	—
196	C₂×C₄×C₁₉	—	4	2	no	—
197	C₂×C₄×C₁₉	—	4	2	no	—
198	C₂×C₄×C₁₉	—	4	2	no	—
199	C₂×C₄×C₁₉	—	8	2	no	—
200	C₂×C₄×C₁₉	—	8	4	no	—
201	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
202	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
204	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
205	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
206	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
207	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
208	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
209	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
210	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
211	C₁₉⋊C₈	—	4	2	no	—
212	C₁₉⋊C₈	—	8	1	no	—
213	C₁₉⋊C₈	—	8	1	no	—
214	C₁₉⋊C₈	—	8	1	no	—
215	#3506	D₁₉	1	1	yes	characteristic
216	#1954	—	19	1	no	—
217	#1800	—	19	1	no	—
218	#1550	—	19	1	no	—
219	#1547	—	19	1	no	—
220	#1493	—	19	1	no	—
221	#1492	—	19	1	no	—
222	C₂²×C₁₉	—	2	1	no	—
223	C₂²×C₁₉	—	2	1	no	—
224	C₂²×C₁₉	—	4	4	no	—
225	C₂²×C₁₉	—	4	2	no	—
226	C₂²×C₁₉	—	4	2	no	—
227	C₂²×C₁₉	—	4	2	no	—
228	C₂²×C₁₉	—	4	2	no	—
229	C₂²×C₁₉	—	4	2	no	—
230	C₂²×C₁₉	—	4	2	no	—
231	C₂²×C₁₉	—	8	2	no	—
232	C₂²×C₁₉	#379	1	1	yes	characteristic
233	C₂²×C₁₉	#416	1	1	yes	characteristic
234	C₂²×C₁₉	#417	1	1	yes	characteristic
235	C₄×C₁₉	—	2	1	no	—
236	C₄×C₁₉	—	2	1	no	—
237	C₄×C₁₉	—	2	1	no	—
238	C₄×C₁₉	—	4	2	no	—
239	C₄×C₁₉	—	4	2	no	—
240	C₄×C₁₉	—	4	2	no	—
241	C₄×C₁₉	—	4	2	no	—
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	C₄×C₁₉	#453	1	1	yes	characteristic
247	C₄×C₁₉	#455	1	1	yes	characteristic
248	#559	—	2	2	no	—
249	#556	—	2	1	no	—
250	#555	—	2	1	no	—
251	#553	—	2	2	no	—
252	#550	—	2	1	no	—
253	#547	—	2	1	no	—
254	#538	Dic₁₉	1	4	yes	—
255	#535	—	2	1	no	—
256	#533	C₂×D₁₉	1	1	yes	characteristic
257	#532	C₂×D₁₉	1	1	yes	characteristic
258	#525	—	2	2	no	—
259	#520	—	2	1	no	—
260	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
261	#423	—	19	1	no	—
262	#423	—	19	1	no	—
263	C₂×C₄⋊C₈	—	19	1	no	—
264	C₂×#100	—	38	1	no	—
265	C₂×C₂²⋊C₈	—	38	2	no	—
266	C₂×C₄×C₈	—	19	1	no	—
267	#343	—	38	1	no	—
268	#333	—	38	1	no	—
269	#332	—	38	1	no	—
270	#332	—	38	1	no	—
271	#331	—	38	1	no	—
272	Q₈⋊C₈	—	38	2	no	—
273	D₄⋊C₈	—	38	2	no	—
274	C₂×C₁₉	—	2	1	no	—
275	C₂×C₁₉	—	2	1	no	—
276	C₂×C₁₉	—	8	2	no	—
277	C₂×C₁₉	—	8	2	no	—
278	C₂×C₁₉	#1788	1	1	yes	characteristic
279	C₂×C₁₉	#1791	1	1	yes	characteristic
280	C₂×C₁₉	#1792	1	1	yes	characteristic
281	C₂×#41	—	2	2	no	—
282	C₂×#41	—	2	1	no	—
283	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
284	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
285	C₂×M₁₆	—	38	1	no	—
286	C₂×M₁₆	—	38	1	no	—
287	C₂²×C₈	—	38	1	no	—
288	C₂²×C₈	—	38	1	no	—
289	C₄⋊Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
290	C₄⋊Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
291	C₄⋊Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
292	#127	—	2	2	no	—
293	#127	C₂²⋊D₁₉	1	1	yes	characteristic
294	#126	—	2	4	no	—
295	#125	—	2	1	no	—
296	#124	—	2	2	no	—
297	#124	—	2	4	no	—
298	#124	—	2	1	no	—
299	#123	—	2	4	no	—
300	#123	—	2	4	no	—
301	C₂²⋊Q₈	—	2	2	no	—
302	C₂²⋊Q₈	—	2	1	no	—
303	C₂²⋊Q₈	C₂×Dic₁₉	1	2	yes	—
304	#121	—	2	2	no	—
305	#121	—	2	2	no	—
306	#121	—	2	2	no	—
307	#121	—	2	4	no	—
308	#121	—	2	1	no	—
309	#121	C₂×Dic₁₉	1	2	yes	—
310	#120	—	2	4	no	—
311	C₄×Q₈	—	2	2	no	—
312	C₄×Q₈	—	2	1	no	—
313	C₄×Q₈	C₂²⋊D₁₉	1	2	yes	—
314	C₄×D₄	—	2	2	no	—
315	C₄×D₄	—	2	4	no	—
316	C₄×D₄	—	2	4	no	—
317	C₄×D₄	—	2	1	no	—
318	C₄×D₄	—	2	1	no	—
319	C₄×D₄	—	2	1	no	—
320	C₄×D₄	—	2	1	no	—
321	C₄×D₄	—	2	1	no	—
322	C₄×D₄	C₂²⋊D₁₉	1	2	yes	—
323	#117	—	2	2	no	—
324	#117	—	2	2	no	—
325	#117	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
328	C₂×C₂²⋊C₄	C₂×Dic₁₉	1	2	yes	—
329	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
330	C₄⋊C₈	—	38	1	no	—
331	C₄⋊C₈	—	38	1	no	—
332	C₄⋊C₈	—	38	1	no	—
333	C₄⋊C₈	—	38	1	no	—
334	C₄⋊C₈	—	38	1	no	—
335	C₄⋊C₈	—	38	1	no	—
336	#100	—	76	2	no	—
337	C₂²⋊C₈	—	76	4	no	—
338	C₄×C₈	—	38	1	no	—
339	C₄×C₈	—	38	1	no	—
340	C₁₉	#8358	1	1	yes	characteristic, complemented, Sylow
341	C₂⁴	C₂²⋊Dic₁₉	1	2	yes	—
342	#41	—	4	1	no	—
343	#41	—	4	1	no	—
344	#41	—	4	1	no	—
345	#41	—	4	1	no	—
346	#41	—	8	2	no	—
347	#41	—	8	2	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	2	4	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	4	2	no	—
368	C₂²×C₄	—	4	2	no	—
369	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
370	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
371	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
372	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
373	M₁₆	—	76	1	no	—
374	M₁₆	—	76	1	no	—
375	M₁₆	—	76	1	no	—
376	M₁₆	—	76	1	no	—
377	C₂×C₈	—	38	2	no	—
378	C₂×C₈	—	76	1	no	—
379	C₂×C₈	—	76	1	no	—
380	C₂×C₈	—	76	2	no	—
381	C₂×C₈	—	76	1	no	—
382	C₂×C₈	—	76	1	no	—
383	C₂×C₈	—	76	1	no	—
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
394	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
395	C₂²⋊C₄	—	2	4	no	—
396	C₂²⋊C₄	—	2	4	no	—
397	C₂²⋊C₄	—	2	4	no	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₂²⋊C₄	—	2	2	no	—
400	C₂²⋊C₄	—	2	2	no	—
401	C₂²⋊C₄	—	2	2	no	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₄²	—	2	4	no	—
404	C₄²	—	2	2	no	—
405	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
406	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
407	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
408	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
409	C₂³	—	2	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
416	Q₈	—	4	2	no	—
417	Q₈	—	4	1	no	—
418	Q₈	—	4	1	no	—
419	Q₈	—	4	1	no	—
420	Q₈	—	4	1	no	—
421	D₄	—	4	2	no	—
422	D₄	—	4	2	no	—
423	D₄	—	4	2	no	—
424	D₄	—	4	1	no	—
425	D₄	—	4	1	no	—
426	D₄	—	4	1	no	—
427	D₄	—	4	1	no	—
428	D₄	—	4	1	no	—
429	D₄	—	4	1	no	—
430	D₄	—	4	1	no	—
431	D₄	—	4	1	no	—
432	D₄	—	8	4	no	—
433	D₄	—	8	4	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	8	2	no	—
447	C₂×C₄	—	8	4	no	—
448	C₂×C₄	#10597395	1	1	yes	characteristic
449	C₂×C₄	#10597396	1	1	yes	characteristic
450	C₂×C₄	#10597396	1	1	yes	characteristic
451	C₂×C₄	#10597397	1	1	yes	characteristic
452	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
453	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
454	C₂×C₄	#10597399	1	1	yes	characteristic
455	C₂×C₄	#10597399	1	1	yes	characteristic
456	C₂×C₄	#10597399	1	1	yes	characteristic
457	C₂×C₄	#10597399	1	1	yes	characteristic
458	C₈	—	76	2	no	—
459	C₈	—	152	1	no	—
460	C₈	—	152	1	no	—
461	C₈	—	152	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	4	4	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	8	2	no	—
472	C₂²	#11926400	1	1	yes	characteristic
473	C₂²	#11926540	1	1	yes	characteristic
474	C₂²	#11926545	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	4	2	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	2	no	—
481	C₄	—	4	2	no	—
482	C₄	#11926689	1	1	yes	characteristic
483	C₄	#11926689	1	1	yes	characteristic
484	C₄	#11926706	1	1	yes	characteristic
485	C₄	#11926706	1	1	yes	characteristic
486	C₄	#11926712	1	1	yes	characteristic
487	C₄	#11926722	1	1	yes	characteristic
488	C₂	—	2	1	no	—
489	C₂	—	2	1	no	—
490	C₂	—	8	2	no	—
491	C₂	—	8	2	no	—
492	C₂	#14563575	1	1	yes	characteristic
493	C₂	#14563586	1	1	yes	characteristic
494	C₂	#14563589	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926400
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#3506	C₂
socle	C₂²×C₁₉	#379
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3506	D₁₉
hypocenter	C₁₉	#8358
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3506

Complements

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

N	H ≅ G/N	type
1. #14564430	C₂	semidirect
2. #14563627	C₂	semidirect
3. #14562325	C₂	semidirect
4. #14562312	C₂	semidirect
5. #14562090	C₂	semidirect
6. #14562086	C₂	semidirect
340. C₁₉	#8358	semidirect

Maximal subgroups

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

subgroup	index
#14564430	2
#14563627	2
#14562325	2
#14562312	2
#14562090	2
#14562086	2
C₁₉×#3506	2
#8358	19