Subgroups — #18074456

Order 4864.

942 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14564588	C₂	1	1	yes	maximal, characteristic, complemented
2	#14563655	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562312	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562307	C₂	1	1	yes	maximal, characteristic, complemented
5	#14562130	C₂	1	1	yes	maximal, characteristic, complemented
6	#14562022	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3499	C₂	1	1	yes	maximal, characteristic
8	#11926597	C₂²	1	1	yes	characteristic
9	#11926568	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×#10597294	—	2	1	no	—
12	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
13	#11926306	—	2	2	no	—
14	#11926303	—	2	1	no	—
15	#11926290	—	2	2	no	—
16	#11926290	—	2	1	no	—
17	#11926288	—	2	1	no	—
18	#11926278	—	2	2	no	—
19	Q₈⋊(C₁₉⋊C₈)	—	2	1	no	—
20	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
21	C₂×C₁₉×2₋¹⁺⁴	—	2	1	no	—
22	D₄×Q₈×C₁₉	—	2	1	no	—
23	D₄×Q₈×C₁₉	C₄	1	2	yes	complemented
24	C₁₉×#547	—	2	2	no	—
25	C₁₉×#547	—	2	1	no	—
26	C₁₉×#547	—	2	2	no	—
27	C₁₉×#547	C₄	1	2	yes	complemented
28	C₁₉×#536	—	2	2	no	—
29	C₁₉×#536	—	2	1	no	—
30	C₁₉×#532	—	2	1	no	—
31	C₁₉×#532	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
33	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
34	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
35	C₁₉×2₋¹⁺⁴	—	4	2	no	—
36	C₁₉×2₋¹⁺⁴	—	4	2	no	—
37	C₁₉×2₋¹⁺⁴	—	4	2	no	—
38	C₁₉×2₋¹⁺⁴	—	4	2	no	—
39	C₂×#41×C₁₉	—	2	2	no	—
40	C₂×#41×C₁₉	—	2	4	no	—
41	C₂×#41×C₁₉	—	2	2	no	—
42	C₂×#41×C₁₉	—	2	1	no	—
43	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
44	C₂²×Q₈×C₁₉	—	2	2	no	—
45	C₂²×Q₈×C₁₉	—	2	2	no	—
46	C₂²×Q₈×C₁₉	—	2	1	no	—
47	C₁₉×C₄⋊Q₈	—	2	2	no	—
48	C₁₉×C₄⋊Q₈	—	2	2	no	—
49	C₁₉×C₄⋊Q₈	—	2	2	no	—
50	C₁₉×C₄⋊Q₈	—	2	1	no	—
51	C₁₉×C₄⋊Q₈	—	2	1	no	—
52	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
53	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
54	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
55	C₁₉×#127	D₄	1	1	yes	characteristic
56	C₁₉×#124	—	2	2	no	—
57	C₁₉×#124	—	2	1	no	—
58	C₁₉×#123	—	2	4	no	—
59	C₁₉×#123	—	2	4	no	—
60	C₁₉×#123	—	2	4	no	—
61	C₁₉×C₂²⋊Q₈	—	2	4	no	—
62	C₁₉×C₂²⋊Q₈	—	2	2	no	—
63	C₁₉×C₂²⋊Q₈	—	2	4	no	—
64	C₁₉×C₂²⋊Q₈	—	2	2	no	—
65	C₁₉×#121	—	2	2	no	—
66	C₁₉×#121	—	2	2	no	—
67	C₁₉×#121	—	2	1	no	—
68	C₁₉×#121	D₄	1	2	yes	—
69	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
70	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
71	C₄×D₄×C₁₉	—	2	2	no	—
72	C₄×D₄×C₁₉	—	2	2	no	—
73	C₄×D₄×C₁₉	—	2	1	no	—
74	C₄×D₄×C₁₉	—	2	1	no	—
75	C₄×D₄×C₁₉	—	2	1	no	—
76	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
77	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
78	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
79	C₁₉×#117	—	2	1	no	—
80	C₁₉×#117	D₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
84	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
85	C₂×C₄²×C₁₉	—	2	1	no	—
86	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊Dic₁₉	—	2	1	no	—
88	C₂×C₄×Dic₁₉	—	2	1	no	—
89	C₂×#64520	—	2	1	no	—
90	C₂²×C₁₉⋊C₈	—	2	1	no	—
91	#10597294	—	4	2	no	—
92	C₁₉⋊#95	—	2	1	no	—
93	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
94	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
95	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
96	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
97	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
98	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
99	C₄×C₁₉⋊C₈	—	2	1	no	—
100	#41×C₁₉	—	2	1	no	—
101	#41×C₁₉	—	2	1	no	—
102	#41×C₁₉	—	4	4	no	—
103	#41×C₁₉	—	4	4	no	—
104	#41×C₁₉	—	4	8	no	—
105	#41×C₁₉	—	4	8	no	—
106	#41×C₁₉	—	4	4	no	—
107	#41×C₁₉	—	4	4	no	—
108	#41×C₁₉	—	4	1	no	—
109	#41×C₁₉	—	4	1	no	—
110	#41×C₁₉	—	4	1	no	—
111	#41×C₁₉	—	4	1	no	—
112	#41×C₁₉	D₈	1	2	yes	—
113	#41×C₁₉	SD₁₆	1	2	yes	—
114	C₂×Q₈×C₁₉	—	2	4	no	—
115	C₂×Q₈×C₁₉	—	2	2	no	—
116	C₂×Q₈×C₁₉	—	2	2	no	—
117	C₂×Q₈×C₁₉	—	2	1	no	—
118	C₂×Q₈×C₁₉	—	4	4	no	—
119	C₂×Q₈×C₁₉	—	4	4	no	—
120	C₂×Q₈×C₁₉	—	4	4	no	—
121	C₂×Q₈×C₁₉	—	4	4	no	—
122	C₂×Q₈×C₁₉	—	4	1	no	—
123	C₂×Q₈×C₁₉	—	4	1	no	—
124	C₂×Q₈×C₁₉	—	4	1	no	—
125	C₂×Q₈×C₁₉	—	4	1	no	—
126	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
127	C₂×D₄×C₁₉	—	2	1	no	—
128	C₂×D₄×C₁₉	—	2	4	no	—
129	C₂×D₄×C₁₉	—	2	2	no	—
130	C₂×D₄×C₁₉	—	2	1	no	—
131	C₂×D₄×C₁₉	—	2	1	no	—
132	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
133	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
134	C₂²×C₄×C₁₉	—	2	1	no	—
135	C₂²×C₄×C₁₉	—	2	4	no	—
136	C₂²×C₄×C₁₉	—	2	4	no	—
137	C₂²×C₄×C₁₉	—	2	2	no	—
138	C₂²×C₄×C₁₉	—	2	1	no	—
139	C₂²×C₄×C₁₉	—	2	2	no	—
140	C₂²×C₄×C₁₉	—	2	1	no	—
141	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×Dic₁₉	—	4	1	no	—
145	C₄⋊C₄×C₁₉	—	2	4	no	—
146	C₄⋊C₄×C₁₉	—	2	4	no	—
147	C₄⋊C₄×C₁₉	—	2	2	no	—
148	C₄⋊C₄×C₁₉	—	2	1	no	—
149	C₄⋊C₄×C₁₉	—	2	1	no	—
150	C₄⋊C₄×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	2	2	no	—
152	C₄⋊C₄×C₁₉	—	2	1	no	—
153	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
154	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
155	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
156	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
157	C₂²⋊C₄×C₁₉	—	2	4	no	—
158	C₂²⋊C₄×C₁₉	—	2	4	no	—
159	C₂²⋊C₄×C₁₉	—	2	1	no	—
160	C₂²⋊C₄×C₁₉	—	2	1	no	—
161	C₂²⋊C₄×C₁₉	—	2	2	no	—
162	C₂²⋊C₄×C₁₉	—	2	1	no	—
163	C₂²⋊C₄×C₁₉	—	2	2	no	—
164	C₄²×C₁₉	—	2	1	no	—
165	C₄²×C₁₉	—	2	1	no	—
166	C₄²×C₁₉	—	2	1	no	—
167	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
168	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₄⋊Dic₁₉	—	2	2	no	—
172	C₄⋊Dic₁₉	—	4	1	no	—
173	C₄×Dic₁₉	—	4	1	no	—
174	C₄×Dic₁₉	—	4	1	no	—
175	#64520	—	4	1	no	—
176	#64520	—	4	1	no	—
177	C₂×C₁₉⋊C₈	—	4	2	no	—
178	C₂×C₁₉⋊C₈	—	4	1	no	—
179	C₂×C₁₉⋊C₈	—	4	1	no	—
180	C₂×C₁₉⋊C₈	—	4	1	no	—
181	#8421	—	19	1	no	maximal, Sylow
182	C₂³×C₁₉	—	2	1	no	—
183	C₂³×C₁₉	—	2	2	no	—
184	C₂³×C₁₉	#120	1	1	yes	characteristic
185	Q₈×C₁₉	—	2	1	no	—
186	Q₈×C₁₉	—	4	8	no	—
187	Q₈×C₁₉	—	4	2	no	—
188	Q₈×C₁₉	—	4	2	no	—
189	Q₈×C₁₉	—	4	1	no	—
190	Q₈×C₁₉	—	4	2	no	—
191	Q₈×C₁₉	—	4	1	no	—
192	Q₈×C₁₉	—	4	2	no	—
193	Q₈×C₁₉	#102	1	2	yes	—
194	D₄×C₁₉	—	2	2	no	—
195	D₄×C₁₉	—	2	2	no	—
196	D₄×C₁₉	—	2	1	no	—
197	D₄×C₁₉	—	4	2	no	—
198	D₄×C₁₉	—	4	8	no	—
199	D₄×C₁₉	—	4	2	no	—
200	D₄×C₁₉	—	4	2	no	—
201	D₄×C₁₉	—	4	1	no	—
202	D₄×C₁₉	—	4	1	no	—
203	D₄×C₁₉	—	4	1	no	—
204	D₄×C₁₉	—	4	1	no	—
205	D₄×C₁₉	#102	1	2	yes	—
206	C₂×C₄×C₁₉	—	2	1	no	—
207	C₂×C₄×C₁₉	—	2	2	no	—
208	C₂×C₄×C₁₉	—	2	2	no	—
209	C₂×C₄×C₁₉	—	2	1	no	—
210	C₂×C₄×C₁₉	—	2	1	no	—
211	C₂×C₄×C₁₉	—	2	1	no	—
212	C₂×C₄×C₁₉	—	2	1	no	—
213	C₂×C₄×C₁₉	—	2	4	no	—
214	C₂×C₄×C₁₉	—	2	2	no	—
215	C₂×C₄×C₁₉	—	4	1	no	—
216	C₂×C₄×C₁₉	—	4	2	no	—
217	C₂×C₄×C₁₉	—	4	8	no	—
218	C₂×C₄×C₁₉	—	4	8	no	—
219	C₂×C₄×C₁₉	—	4	2	no	—
220	C₂×C₄×C₁₉	—	4	2	no	—
221	C₂×C₄×C₁₉	—	4	2	no	—
222	C₂×C₄×C₁₉	—	4	2	no	—
223	C₂×C₄×C₁₉	—	4	1	no	—
224	C₂×C₄×C₁₉	—	4	1	no	—
225	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
229	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
230	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
231	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
232	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
233	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
234	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
235	C₂×Dic₁₉	—	4	2	no	—
236	C₂×Dic₁₉	—	8	1	no	—
237	C₂×Dic₁₉	—	8	1	no	—
238	C₁₉⋊C₈	—	8	1	no	—
239	C₁₉⋊C₈	—	8	1	no	—
240	C₁₉⋊C₈	—	8	1	no	—
241	#3499	D₁₉	1	1	yes	characteristic
242	#1988	—	19	1	no	—
243	#1806	—	19	1	no	—
244	#1547	—	19	1	no	—
245	#1546	—	19	1	no	—
246	#1502	—	19	1	no	—
247	#1477	—	19	1	no	—
248	C₂²×C₁₉	—	2	1	no	—
249	C₂²×C₁₉	—	2	1	no	—
250	C₂²×C₁₉	—	2	2	no	—
251	C₂²×C₁₉	—	4	1	no	—
252	C₂²×C₁₉	—	4	1	no	—
253	C₂²×C₁₉	—	4	2	no	—
254	C₂²×C₁₉	—	4	2	no	—
255	C₂²×C₁₉	—	4	2	no	—
256	C₂²×C₁₉	#379	1	1	yes	characteristic
257	C₂²×C₁₉	#447	1	1	yes	characteristic
258	C₂²×C₁₉	#450	1	1	yes	characteristic
259	C₄×C₁₉	—	2	1	no	—
260	C₄×C₁₉	—	2	1	no	—
261	C₄×C₁₉	—	2	1	no	—
262	C₄×C₁₉	—	2	2	no	—
263	C₄×C₁₉	—	4	1	no	—
264	C₄×C₁₉	—	4	1	no	—
265	C₄×C₁₉	—	4	4	no	—
266	C₄×C₁₉	—	4	2	no	—
267	C₄×C₁₉	C₂×#102	1	1	yes	characteristic
268	C₄×C₁₉	#418	1	1	yes	characteristic
269	C₄×C₁₉	#447	1	1	yes	characteristic
270	C₄×C₁₉	#450	1	1	yes	characteristic
271	C₄×C₁₉	#454	1	1	yes	characteristic
272	C₄×C₁₉	#456	1	1	yes	characteristic
273	Dic₁₉	—	8	2	no	—
274	C₂×2₋¹⁺⁴	—	2	1	no	—
275	D₄×Q₈	—	2	1	no	—
276	D₄×Q₈	Dic₁₉	1	2	yes	complemented
277	#547	—	2	2	no	—
278	#547	—	2	1	no	—
279	#547	—	2	2	no	—
280	#547	Dic₁₉	1	2	yes	complemented
281	#536	—	2	2	no	—
282	#536	—	2	1	no	—
283	#532	—	2	1	no	—
284	#532	C₂×D₁₉	1	1	yes	characteristic
285	C₂×C₄⋊Q₈	—	2	1	no	—
286	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
287	C₄×#41	C₂×D₁₉	1	1	yes	characteristic
288	#431	—	19	1	no	—
289	#423	—	19	1	no	—
290	C₂×C₄⋊C₈	—	19	1	no	—
291	C₂×#104	—	38	1	no	—
292	C₄×C₄⋊C₄	—	19	1	no	—
293	#340	—	38	2	no	—
294	#339	—	38	1	no	—
295	#332	—	38	2	no	—
296	#332	—	38	1	no	—
297	#331	—	38	1	no	—
298	#327	—	38	2	no	—
299	Q₈⋊C₈	—	38	1	no	—
300	D₄⋊C₈	—	38	1	no	—
301	C₂×C₁₉	—	2	1	no	—
302	C₂×C₁₉	—	2	1	no	—
303	C₂×C₁₉	—	4	2	no	—
304	C₂×C₁₉	—	8	2	no	—
305	C₂×C₁₉	#1786	1	1	yes	characteristic
306	C₂×C₁₉	#1793	1	1	yes	characteristic
307	C₂×C₁₉	#1796	1	1	yes	characteristic
308	2₋¹⁺⁴	—	4	2	no	—
309	2₋¹⁺⁴	—	4	2	no	—
310	2₋¹⁺⁴	—	4	2	no	—
311	2₋¹⁺⁴	—	4	2	no	—
312	C₂×#41	—	2	2	no	—
313	C₂×#41	—	2	4	no	—
314	C₂×#41	—	2	2	no	—
315	C₂×#41	—	2	1	no	—
316	C₂×#41	C₂²⋊D₁₉	1	1	yes	characteristic
317	C₂²×Q₈	—	2	2	no	—
318	C₂²×Q₈	—	2	2	no	—
319	C₂²×Q₈	—	2	1	no	—
320	C₂×M₁₆	—	38	1	no	—
321	C₂²×C₈	—	38	1	no	—
322	C₄⋊Q₈	—	2	2	no	—
323	C₄⋊Q₈	—	2	2	no	—
324	C₄⋊Q₈	—	2	2	no	—
325	C₄⋊Q₈	—	2	1	no	—
326	C₄⋊Q₈	—	2	1	no	—
327	C₄⋊Q₈	C₂×Dic₁₉	1	2	yes	—
328	C₄⋊Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
329	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
330	#127	C₂²⋊D₁₉	1	1	yes	characteristic
331	#124	—	2	2	no	—
332	#124	—	2	1	no	—
333	#123	—	2	4	no	—
334	#123	—	2	4	no	—
335	#123	—	2	4	no	—
336	C₂²⋊Q₈	—	2	4	no	—
337	C₂²⋊Q₈	—	2	2	no	—
338	C₂²⋊Q₈	—	2	4	no	—
339	C₂²⋊Q₈	—	2	2	no	—
340	#121	—	2	2	no	—
341	#121	—	2	2	no	—
342	#121	—	2	1	no	—
343	#121	C₂²⋊D₁₉	1	2	yes	—
344	C₄×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
345	C₄×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
346	C₄×D₄	—	2	2	no	—
347	C₄×D₄	—	2	2	no	—
348	C₄×D₄	—	2	1	no	—
349	C₄×D₄	—	2	1	no	—
350	C₄×D₄	—	2	1	no	—
351	C₄×D₄	C₂×Dic₁₉	1	1	yes	characteristic
352	C₄×D₄	C₂×Dic₁₉	1	2	yes	—
353	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
354	#117	—	2	1	no	—
355	#117	C₂²⋊D₁₉	1	1	yes	characteristic
356	C₂×C₄⋊C₄	—	2	2	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	2	no	—
359	C₂×C₄⋊C₄	—	38	1	no	—
360	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
361	C₂×C₄²	—	2	1	no	—
362	C₂×C₄²	—	38	1	no	—
363	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
364	C₄⋊C₈	—	38	1	no	—
365	C₄⋊C₈	—	38	1	no	—
366	C₄⋊C₈	—	38	1	no	—
367	C₄⋊C₈	—	38	1	no	—
368	C₄⋊C₈	—	38	1	no	—
369	#104	—	76	2	no	—
370	C₂²⋊C₈	—	38	1	no	—
371	C₄×C₈	—	38	1	no	—
372	#95	—	38	1	no	—
373	C₁₉	#8421	1	1	yes	characteristic, complemented, Sylow
374	#41	—	2	1	no	—
375	#41	—	2	1	no	—
376	#41	—	4	4	no	—
377	#41	—	4	4	no	—
378	#41	—	4	8	no	—
379	#41	—	4	8	no	—
380	#41	—	4	4	no	—
381	#41	—	4	4	no	—
382	#41	—	4	1	no	—
383	#41	—	4	1	no	—
384	#41	—	4	1	no	—
385	#41	—	4	1	no	—
386	#41	#64525	1	2	yes	—
387	#41	#64526	1	2	yes	—
388	C₂×Q₈	—	2	4	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	4	4	no	—
393	C₂×Q₈	—	4	4	no	—
394	C₂×Q₈	—	4	4	no	—
395	C₂×Q₈	—	4	4	no	—
396	C₂×Q₈	—	4	1	no	—
397	C₂×Q₈	—	4	1	no	—
398	C₂×Q₈	—	4	1	no	—
399	C₂×Q₈	—	4	1	no	—
400	C₂×Q₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	—	2	4	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
407	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	4	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	76	1	no	—
416	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
417	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
418	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
419	M₁₆	—	76	1	no	—
420	M₁₆	—	76	1	no	—
421	C₂×C₈	—	76	2	no	—
422	C₂×C₈	—	76	1	no	—
423	C₂×C₈	—	76	1	no	—
424	C₂×C₈	—	76	1	no	—
425	C₄⋊C₄	—	2	4	no	—
426	C₄⋊C₄	—	2	4	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	38	2	no	—
434	C₄⋊C₄	—	76	1	no	—
435	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
436	C₄⋊C₄	C₂²⋊Dic₁₉	1	4	yes	—
437	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
438	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
439	C₂²⋊C₄	—	2	4	no	—
440	C₂²⋊C₄	—	2	4	no	—
441	C₂²⋊C₄	—	2	1	no	—
442	C₂²⋊C₄	—	2	1	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	2	1	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₄²	—	2	1	no	—
447	C₄²	—	2	1	no	—
448	C₄²	—	2	1	no	—
449	C₄²	—	76	1	no	—
450	C₄²	—	76	1	no	—
451	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
452	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
453	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
454	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
455	C₂³	—	2	1	no	—
456	C₂³	—	2	2	no	—
457	C₂³	#10597399	1	1	yes	characteristic
458	Q₈	—	2	1	no	—
459	Q₈	—	4	8	no	—
460	Q₈	—	4	2	no	—
461	Q₈	—	4	2	no	—
462	Q₈	—	4	1	no	—
463	Q₈	—	4	2	no	—
464	Q₈	—	4	1	no	—
465	Q₈	—	4	2	no	—
466	Q₈	#10597289	1	2	yes	—
467	D₄	—	2	2	no	—
468	D₄	—	2	2	no	—
469	D₄	—	2	1	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	8	no	—
472	D₄	—	4	2	no	—
473	D₄	—	4	2	no	—
474	D₄	—	4	1	no	—
475	D₄	—	4	1	no	—
476	D₄	—	4	1	no	—
477	D₄	—	4	1	no	—
478	D₄	#10597289	1	2	yes	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	8	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	8	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	76	2	no	—
499	C₂×C₄	—	152	1	no	—
500	C₂×C₄	—	152	1	no	—
501	C₂×C₄	C₂×#64525	1	1	yes	characteristic
502	C₂×C₄	#10597378	1	1	yes	characteristic
503	C₂×C₄	#10597378	1	1	yes	characteristic
504	C₂×C₄	C₂×#64526	1	1	yes	characteristic
505	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
506	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
507	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
508	C₂×C₄	#10597399	1	1	yes	characteristic
509	C₂×C₄	#10597399	1	1	yes	characteristic
510	C₂×C₄	#10597399	1	1	yes	characteristic
511	C₈	—	152	1	no	—
512	C₈	—	152	1	no	—
513	C₈	—	152	1	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	4	1	no	—
518	C₂²	—	4	1	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	#11926400	1	1	yes	characteristic
523	C₂²	#11926678	1	1	yes	characteristic
524	C₂²	#11926695	1	1	yes	characteristic
525	C₄	—	2	1	no	—
526	C₄	—	2	1	no	—
527	C₄	—	2	1	no	—
528	C₄	—	2	2	no	—
529	C₄	—	4	1	no	—
530	C₄	—	4	1	no	—
531	C₄	—	4	4	no	—
532	C₄	—	4	2	no	—
533	C₄	—	152	2	no	—
534	C₄	C₂×#10597289	1	1	yes	characteristic
535	C₄	#11926549	1	1	yes	characteristic
536	C₄	#11926678	1	1	yes	characteristic
537	C₄	#11926695	1	1	yes	characteristic
538	C₄	#11926717	1	1	yes	characteristic
539	C₄	#11926727	1	1	yes	characteristic
540	C₂	—	2	1	no	—
541	C₂	—	2	1	no	—
542	C₂	—	4	2	no	—
543	C₂	—	8	2	no	—
544	C₂	#14563566	1	1	yes	characteristic
545	C₂	#14563594	1	1	yes	characteristic
546	C₂	#14563610	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926400
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#3499	C₂
socle	C₂²×C₁₉	#379
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3499	D₁₉
hypocenter	C₁₉	#8421
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3499

Complements

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

N	H ≅ G/N	type
1. #14564588	C₂	semidirect
2. #14563655	C₂	semidirect
3. #14562312	C₂	semidirect
4. #14562307	C₂	semidirect
5. #14562130	C₂	semidirect
6. #14562022	C₂	semidirect
23. D₄×Q₈×C₁₉	C₄	semidirect
27. C₁₉×#547	C₄	semidirect
276. D₄×Q₈	Dic₁₉	semidirect
280. #547	Dic₁₉	semidirect
373. C₁₉	#8421	semidirect

Maximal subgroups

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

subgroup	index
#14564588	2
#14563655	2
#14562312	2
#14562307	2
#14562130	2
#14562022	2
C₁₉×#3499	2
#8421	19