Subgroups — #18074547

Order 4864.

760 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563645	C₂	1	1	yes	maximal, characteristic, complemented
2	#14562292	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562199	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562195	C₂	1	1	yes	maximal, characteristic, complemented
5	#14562034	C₂	1	1	yes	maximal, characteristic, complemented
6	#14562026	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3506	C₂	1	1	yes	maximal, characteristic
8	#11926597	C₂²	1	1	yes	characteristic
9	#11926597	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×#10597289	—	2	1	no	—
12	#11926410	C₂²	1	1	yes	characteristic
13	#11926306	—	2	1	no	—
14	#11926293	—	2	1	no	—
15	#11926290	—	2	1	no	—
16	#11926281	—	2	2	no	—
17	#11926278	—	2	2	no	—
18	D₄⋊(C₁₉⋊C₈)	—	2	2	no	—
19	D₄⋊(C₁₉⋊C₈)	—	2	2	no	—
20	C₁₉×#559	—	2	2	no	—
21	C₁₉×#556	C₄	1	2	yes	complemented
22	C₁₉×#555	—	2	1	no	—
23	C₁₉×#553	—	2	2	no	—
24	C₁₉×#550	C₄	1	2	yes	complemented
25	C₁₉×#547	—	2	1	no	—
26	C₁₉×#538	—	2	2	no	—
27	C₁₉×#535	—	2	1	no	—
28	C₁₉×#533	C₂²	1	1	yes	characteristic
29	C₁₉×#532	C₂²	1	1	yes	characteristic
30	C₁₉×#525	—	2	2	no	—
31	C₁₉×#520	—	2	1	no	—
32	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
33	C₂×#41×C₁₉	—	2	2	no	—
34	C₂×#41×C₁₉	—	2	1	no	—
35	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₉	—	2	1	no	—
37	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
38	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
39	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
40	C₁₉×#127	—	2	2	no	—
41	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
42	C₁₉×#126	—	2	4	no	—
43	C₁₉×#125	—	2	1	no	—
44	C₁₉×#124	—	2	4	no	—
45	C₁₉×#124	—	2	2	no	—
46	C₁₉×#124	—	2	1	no	—
47	C₁₉×#123	—	2	4	no	—
48	C₁₉×#123	—	2	4	no	—
49	C₁₉×C₂²⋊Q₈	—	2	2	no	—
50	C₁₉×C₂²⋊Q₈	—	2	1	no	—
51	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
52	C₁₉×#121	—	2	2	no	—
53	C₁₉×#121	—	2	2	no	—
54	C₁₉×#121	—	2	4	no	—
55	C₁₉×#121	—	2	1	no	—
56	C₁₉×#121	—	2	2	no	—
57	C₁₉×#121	D₄	1	2	yes	—
58	C₁₉×#120	—	2	4	no	—
59	C₄×Q₈×C₁₉	—	2	2	no	—
60	C₄×Q₈×C₁₉	—	2	1	no	—
61	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
62	C₄×D₄×C₁₉	—	2	4	no	—
63	C₄×D₄×C₁₉	—	2	4	no	—
64	C₄×D₄×C₁₉	—	2	2	no	—
65	C₄×D₄×C₁₉	—	2	1	no	—
66	C₄×D₄×C₁₉	—	2	1	no	—
67	C₄×D₄×C₁₉	—	2	1	no	—
68	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
69	C₄×D₄×C₁₉	D₄	1	2	yes	—
70	C₄×D₄×C₁₉	D₄	1	2	yes	—
71	C₁₉×#117	—	2	2	no	—
72	C₁₉×#117	—	2	1	no	—
73	C₁₉×#117	—	2	2	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
75	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
76	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊Dic₁₉	—	2	1	no	—
79	C₂²×C₁₉⋊C₈	—	2	1	no	—
80	#10597289	—	4	2	no	—
81	C₁₉⋊#95	—	2	1	no	—
82	C₁₉⋊#95	—	2	1	no	—
83	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
84	C₂²⋊(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	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
89	C₄×C₁₉⋊C₈	—	2	1	no	—
90	C₄×C₁₉⋊C₈	—	2	1	no	—
91	C₂⁴×C₁₉	—	2	1	no	—
92	#41×C₁₉	—	4	1	no	—
93	#41×C₁₉	—	4	1	no	—
94	#41×C₁₉	—	4	1	no	—
95	#41×C₁₉	—	4	1	no	—
96	#41×C₁₉	—	8	4	no	—
97	C₂×Q₈×C₁₉	—	2	1	no	—
98	C₂×Q₈×C₁₉	—	2	1	no	—
99	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
100	C₂×D₄×C₁₉	—	2	2	no	—
101	C₂×D₄×C₁₉	—	2	4	no	—
102	C₂×D₄×C₁₉	—	2	4	no	—
103	C₂×D₄×C₁₉	—	2	1	no	—
104	C₂×D₄×C₁₉	—	2	1	no	—
105	C₂×D₄×C₁₉	—	2	1	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	C₂²⋊C₄	1	2	yes	—
111	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
112	C₂²×C₄×C₁₉	—	2	4	no	—
113	C₂²×C₄×C₁₉	—	2	1	no	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	2	2	no	—
117	C₂²×C₄×C₁₉	—	8	2	no	—
118	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×Dic₁₉	—	4	1	no	—
122	C₄⋊C₄×C₁₉	—	2	4	no	—
123	C₄⋊C₄×C₁₉	—	2	1	no	—
124	C₄⋊C₄×C₁₉	—	2	2	no	—
125	C₄⋊C₄×C₁₉	—	2	1	no	—
126	C₄⋊C₄×C₁₉	—	2	1	no	—
127	C₄⋊C₄×C₁₉	—	2	1	no	—
128	C₄⋊C₄×C₁₉	—	2	2	no	—
129	C₄⋊C₄×C₁₉	—	2	1	no	—
130	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
131	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
132	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
133	C₂²⋊C₄×C₁₉	—	2	4	no	—
134	C₂²⋊C₄×C₁₉	—	2	4	no	—
135	C₂²⋊C₄×C₁₉	—	2	4	no	—
136	C₂²⋊C₄×C₁₉	—	2	2	no	—
137	C₂²⋊C₄×C₁₉	—	2	2	no	—
138	C₂²⋊C₄×C₁₉	—	2	2	no	—
139	C₂²⋊C₄×C₁₉	—	2	2	no	—
140	C₂²⋊C₄×C₁₉	—	2	2	no	—
141	C₄²×C₁₉	—	2	4	no	—
142	C₄²×C₁₉	—	2	2	no	—
143	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
144	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₄⋊Dic₁₉	—	4	1	no	—
148	C₄⋊Dic₁₉	—	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	C₂×C₁₉⋊C₈	—	4	1	no	—
154	#8434	—	19	1	no	maximal, Sylow
155	C₂³×C₁₉	—	2	2	no	—
156	C₂³×C₁₉	—	2	2	no	—
157	C₂³×C₁₉	—	4	1	no	—
158	C₂³×C₁₉	—	4	1	no	—
159	C₂³×C₁₉	—	8	1	no	—
160	C₂³×C₁₉	—	8	1	no	—
161	C₂³×C₁₉	#120	1	1	yes	characteristic
162	Q₈×C₁₉	—	4	2	no	—
163	Q₈×C₁₉	—	4	1	no	—
164	Q₈×C₁₉	—	4	1	no	—
165	Q₈×C₁₉	—	8	1	no	—
166	D₄×C₁₉	—	2	2	no	—
167	D₄×C₁₉	—	2	2	no	—
168	D₄×C₁₉	—	4	2	no	—
169	D₄×C₁₉	—	4	2	no	—
170	D₄×C₁₉	—	4	2	no	—
171	D₄×C₁₉	—	4	2	no	—
172	D₄×C₁₉	—	4	1	no	—
173	D₄×C₁₉	—	4	1	no	—
174	D₄×C₁₉	—	4	1	no	—
175	D₄×C₁₉	—	4	1	no	—
176	D₄×C₁₉	—	8	4	no	—
177	D₄×C₁₉	—	8	4	no	—
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	2	no	—
182	C₂×C₄×C₁₉	—	4	1	no	—
183	C₂×C₄×C₁₉	—	4	1	no	—
184	C₂×C₄×C₁₉	—	4	4	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	8	2	no	—
188	C₂×C₄×C₁₉	—	8	1	no	—
189	C₂×C₄×C₁₉	—	8	4	no	—
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	C₂×C₂²⋊C₄	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	#120	1	1	yes	characteristic
196	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
197	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
198	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
199	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
200	C₂×Dic₁₉	—	8	1	no	—
201	C₂×Dic₁₉	—	8	1	no	—
202	C₂×Dic₁₉	—	8	1	no	—
203	C₁₉⋊C₈	—	8	1	no	—
204	C₁₉⋊C₈	—	8	1	no	—
205	C₁₉⋊C₈	—	8	1	no	—
206	#3506	D₁₉	1	1	yes	characteristic
207	#1804	—	19	1	no	—
208	#1542	—	19	1	no	—
209	#1518	—	19	1	no	—
210	#1517	—	19	1	no	—
211	#1480	—	19	1	no	—
212	#1478	—	19	1	no	—
213	C₂²×C₁₉	—	2	1	no	—
214	C₂²×C₁₉	—	2	1	no	—
215	C₂²×C₁₉	—	4	2	no	—
216	C₂²×C₁₉	—	4	2	no	—
217	C₂²×C₁₉	—	4	2	no	—
218	C₂²×C₁₉	—	4	2	no	—
219	C₂²×C₁₉	—	4	2	no	—
220	C₂²×C₁₉	—	4	2	no	—
221	C₂²×C₁₉	—	8	2	no	—
222	C₂²×C₁₉	—	8	2	no	—
223	C₂²×C₁₉	#379	1	1	yes	characteristic
224	C₂²×C₁₉	#449	1	1	yes	characteristic
225	C₂²×C₁₉	#452	1	1	yes	characteristic
226	C₄×C₁₉	—	2	1	no	—
227	C₄×C₁₉	—	2	1	no	—
228	C₄×C₁₉	—	2	1	no	—
229	C₄×C₁₉	—	2	1	no	—
230	C₄×C₁₉	—	4	2	no	—
231	C₄×C₁₉	—	4	2	no	—
232	C₄×C₁₉	—	4	2	no	—
233	C₄×C₁₉	—	4	2	no	—
234	C₄×C₁₉	#416	1	1	yes	characteristic
235	C₄×C₁₉	#417	1	1	yes	characteristic
236	C₄×C₁₉	#449	1	1	yes	characteristic
237	C₄×C₁₉	#452	1	1	yes	characteristic
238	Dic₁₉	—	16	1	no	—
239	#559	—	2	2	no	—
240	#556	Dic₁₉	1	2	yes	complemented
241	#555	—	2	1	no	—
242	#553	—	2	2	no	—
243	#550	Dic₁₉	1	2	yes	complemented
244	#547	—	2	1	no	—
245	#538	—	2	2	no	—
246	#535	—	2	1	no	—
247	#533	C₂×D₁₉	1	1	yes	characteristic
248	#532	C₂×D₁₉	1	1	yes	characteristic
249	#525	—	2	2	no	—
250	#520	—	2	1	no	—
251	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
252	#431	—	19	1	no	—
253	#431	—	19	1	no	—
254	C₂×C₄⋊C₈	—	19	1	no	—
255	C₂×#102	—	38	1	no	—
256	#382	—	19	1	no	—
257	#340	—	38	1	no	—
258	#333	—	38	1	no	—
259	#332	—	38	1	no	—
260	#328	—	38	2	no	—
261	#327	—	38	2	no	—
262	D₄⋊C₈	—	38	2	no	—
263	D₄⋊C₈	—	38	2	no	—
264	C₂×C₁₉	—	2	1	no	—
265	C₂×C₁₉	—	2	1	no	—
266	C₂×C₁₉	—	8	2	no	—
267	C₂×C₁₉	—	8	2	no	—
268	C₂×C₁₉	#1788	1	1	yes	characteristic
269	C₂×C₁₉	#1794	1	1	yes	characteristic
270	C₂×C₁₉	#1795	1	1	yes	characteristic
271	C₂×#41	—	2	2	no	—
272	C₂×#41	—	2	1	no	—
273	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
274	C₂³×C₄	—	2	1	no	—
275	C₂²×C₈	—	38	1	no	—
276	C₄⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
277	C₄⋊Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
278	C₄⋊Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
279	#127	—	2	2	no	—
280	#127	C₂×Dic₁₉	1	1	yes	characteristic
281	#126	—	2	4	no	—
282	#125	—	2	1	no	—
283	#124	—	2	4	no	—
284	#124	—	2	2	no	—
285	#124	—	2	1	no	—
286	#123	—	2	4	no	—
287	#123	—	2	4	no	—
288	C₂²⋊Q₈	—	2	2	no	—
289	C₂²⋊Q₈	—	2	1	no	—
290	C₂²⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
291	#121	—	2	2	no	—
292	#121	—	2	2	no	—
293	#121	—	2	4	no	—
294	#121	—	2	1	no	—
295	#121	—	2	2	no	—
296	#121	C₂²⋊D₁₉	1	2	yes	—
297	#120	—	2	4	no	—
298	C₄×Q₈	—	2	2	no	—
299	C₄×Q₈	—	2	1	no	—
300	C₄×Q₈	C₂×Dic₁₉	1	2	yes	—
301	C₄×D₄	—	2	4	no	—
302	C₄×D₄	—	2	4	no	—
303	C₄×D₄	—	2	2	no	—
304	C₄×D₄	—	2	1	no	—
305	C₄×D₄	—	2	1	no	—
306	C₄×D₄	—	2	1	no	—
307	C₄×D₄	C₂×Dic₁₉	1	2	yes	—
308	C₄×D₄	C₂²⋊D₁₉	1	2	yes	—
309	C₄×D₄	C₂²⋊D₁₉	1	2	yes	—
310	#117	—	2	2	no	—
311	#117	—	2	1	no	—
312	#117	—	2	2	no	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	—	38	1	no	—
315	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	—	2	1	no	—
317	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
318	C₄⋊C₈	—	38	1	no	—
319	C₄⋊C₈	—	38	1	no	—
320	C₄⋊C₈	—	38	1	no	—
321	C₄⋊C₈	—	38	1	no	—
322	#102	—	76	2	no	—
323	C₂²⋊C₈	—	38	1	no	—
324	C₂²⋊C₈	—	38	1	no	—
325	C₄×C₈	—	38	1	no	—
326	C₄×C₈	—	38	1	no	—
327	#95	—	38	1	no	—
328	#95	—	38	1	no	—
329	C₁₉	#8434	1	1	yes	characteristic, complemented, Sylow
330	C₂⁴	—	2	1	no	—
331	#41	—	4	1	no	—
332	#41	—	4	1	no	—
333	#41	—	4	1	no	—
334	#41	—	4	1	no	—
335	#41	—	8	4	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	4	no	—
341	C₂×D₄	—	2	4	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
350	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	8	2	no	—
357	C₂²×C₄	—	76	1	no	—
358	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
359	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
360	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
361	C₂×C₈	—	76	1	no	—
362	C₂×C₈	—	76	1	no	—
363	C₂×C₈	—	76	1	no	—
364	C₂×C₈	—	76	1	no	—
365	C₂×C₈	—	76	1	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	76	1	no	—
375	C₄⋊C₄	—	76	1	no	—
376	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
377	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
378	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
379	C₂²⋊C₄	—	2	4	no	—
380	C₂²⋊C₄	—	2	4	no	—
381	C₂²⋊C₄	—	2	4	no	—
382	C₂²⋊C₄	—	2	2	no	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₂²⋊C₄	—	2	2	no	—
385	C₂²⋊C₄	—	2	2	no	—
386	C₂²⋊C₄	—	2	2	no	—
387	C₄²	—	2	4	no	—
388	C₄²	—	2	2	no	—
389	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
390	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
391	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
392	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
393	C₂³	—	2	2	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	4	1	no	—
396	C₂³	—	4	1	no	—
397	C₂³	—	8	1	no	—
398	C₂³	—	8	1	no	—
399	C₂³	#10597399	1	1	yes	characteristic
400	Q₈	—	4	2	no	—
401	Q₈	—	4	1	no	—
402	Q₈	—	4	1	no	—
403	Q₈	—	8	1	no	—
404	D₄	—	2	2	no	—
405	D₄	—	2	2	no	—
406	D₄	—	4	2	no	—
407	D₄	—	4	2	no	—
408	D₄	—	4	2	no	—
409	D₄	—	4	2	no	—
410	D₄	—	4	1	no	—
411	D₄	—	4	1	no	—
412	D₄	—	4	1	no	—
413	D₄	—	4	1	no	—
414	D₄	—	8	4	no	—
415	D₄	—	8	4	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	8	2	no	—
426	C₂×C₄	—	8	1	no	—
427	C₂×C₄	—	8	4	no	—
428	C₂×C₄	—	152	1	no	—
429	C₂×C₄	—	152	1	no	—
430	C₂×C₄	—	152	1	no	—
431	C₂×C₄	#10597395	1	1	yes	characteristic
432	C₂×C₄	#10597396	1	1	yes	characteristic
433	C₂×C₄	#10597396	1	1	yes	characteristic
434	C₂×C₄	#10597397	1	1	yes	characteristic
435	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
436	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
437	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
438	C₂×C₄	#10597399	1	1	yes	characteristic
439	C₂×C₄	#10597399	1	1	yes	characteristic
440	C₂×C₄	#10597399	1	1	yes	characteristic
441	C₈	—	152	1	no	—
442	C₈	—	152	1	no	—
443	C₈	—	152	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	8	2	no	—
453	C₂²	—	8	2	no	—
454	C₂²	#11926400	1	1	yes	characteristic
455	C₂²	#11926689	1	1	yes	characteristic
456	C₂²	#11926706	1	1	yes	characteristic
457	C₄	—	2	1	no	—
458	C₄	—	2	1	no	—
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	4	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	2	no	—
465	C₄	—	304	1	no	—
466	C₄	#11926540	1	1	yes	characteristic
467	C₄	#11926545	1	1	yes	characteristic
468	C₄	#11926689	1	1	yes	characteristic
469	C₄	#11926706	1	1	yes	characteristic
470	C₂	—	2	1	no	—
471	C₂	—	2	1	no	—
472	C₂	—	8	2	no	—
473	C₂	—	8	2	no	—
474	C₂	#14563575	1	1	yes	characteristic
475	C₂	#14563599	1	1	yes	characteristic
476	C₂	#14563605	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926400
commutator	C₄²×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	#8434
LCS	G ▷ C₄²×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. #14563645	C₂	semidirect
2. #14562292	C₂	semidirect
3. #14562199	C₂	semidirect
4. #14562195	C₂	semidirect
5. #14562034	C₂	semidirect
6. #14562026	C₂	semidirect
21. C₁₉×#556	C₄	semidirect
24. C₁₉×#550	C₄	semidirect
240. #556	Dic₁₉	semidirect
243. #550	Dic₁₉	semidirect
329. C₁₉	#8434	semidirect

Maximal subgroups

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

subgroup	index
#14563645	2
#14562292	2
#14562199	2
#14562195	2
#14562034	2
#14562026	2
C₁₉×#3506	2
#8434	19