Subgroups — #18077788

Order 4864.

690 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926890	C₂	1	1	yes	maximal, characteristic
2	#14564587	C₂	1	1	yes	maximal, characteristic, complemented
3	#14564558	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926288	C₂	1	1	yes	maximal, characteristic
5	#14561476	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2366	C₂	1	1	yes	maximal, characteristic
8	C₂×#10597315	C₂²	1	1	yes	characteristic
9	#11926890	—	2	2	no	—
10	#11926890	C₄	1	4	yes	complemented
11	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×#10597267	—	2	1	no	—
14	C₂×#10597267	—	2	1	no	—
15	C₂×#10597289	—	2	2	no	—
16	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
17	#11926306	—	2	1	no	—
18	#11926306	—	2	1	no	—
19	#11926288	—	2	2	no	—
20	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₉	—	2	1	no	—
22	C₂×C₄×D₄×C₁₉	—	2	1	no	—
23	C₁₉×#390	—	2	1	no	—
24	C₁₉×#390	—	2	1	no	—
25	C₁₉×#386	—	2	2	no	—
26	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
28	C₂²×D₄×C₁₉	—	2	1	no	—
29	C₂²×D₄×C₁₉	—	2	1	no	—
30	C₂²×D₄×C₁₉	D₄	1	2	yes	—
31	C₂³×C₄×C₁₉	—	2	2	no	—
32	C₂²×Dic₃₈	—	2	1	no	—
33	C₁₉×#127	—	2	1	no	—
34	C₁₉×#127	—	2	1	no	—
35	C₁₉×#127	C₂×C₄	1	2	yes	—
36	C₁₉×#127	D₄	1	2	yes	—
37	C₄×D₄×C₁₉	—	4	2	no	—
38	C₄×D₄×C₁₉	—	4	2	no	—
39	C₄×D₄×C₁₉	—	4	2	no	—
40	C₄×D₄×C₁₉	—	4	2	no	—
41	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
42	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
43	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
45	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
46	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
47	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
48	C₂×C₄²×C₁₉	—	2	1	no	—
49	C₂×C₄²×C₁₉	—	2	1	no	—
50	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
51	C₂×C₄⋊Dic₁₉	—	2	1	no	—
52	C₂×C₄⋊Dic₁₉	—	2	1	no	—
53	C₂²×C₁₉⋊C₈	—	2	1	no	—
54	C₂²×C₁₉⋊C₈	—	2	1	no	—
55	C₂²×C₁₉⋊C₈	—	2	1	no	—
56	#10597315	—	2	1	no	—
57	#10597315	—	2	1	no	—
58	#10597315	—	2	1	no	—
59	#10597315	C₂×C₄	1	2	yes	complemented
60	C₁₉×#95	—	2	1	no	—
61	C₁₉×#95	—	2	1	no	—
62	#10597289	—	2	8	no	—
63	#10597267	—	4	2	no	—
64	#10597267	—	4	2	no	—
65	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
66	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
67	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
68	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
69	C₄×C₁₉⋊C₈	—	2	1	no	—
70	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	complemented
71	C₂⁴×C₁₉	—	2	2	no	—
72	C₂×D₄×C₁₉	—	2	2	no	—
73	C₂×D₄×C₁₉	—	2	2	no	—
74	C₂×D₄×C₁₉	—	2	2	no	—
75	C₂×D₄×C₁₉	—	2	2	no	—
76	C₂×D₄×C₁₉	—	2	2	no	—
77	C₂×D₄×C₁₉	—	4	2	no	—
78	C₂×D₄×C₁₉	—	4	2	no	—
79	C₂×D₄×C₁₉	—	4	1	no	—
80	C₂×D₄×C₁₉	—	4	1	no	—
81	C₂×D₄×C₁₉	—	4	1	no	—
82	C₂×D₄×C₁₉	—	4	1	no	—
83	C₂×D₄×C₁₉	—	4	1	no	—
84	C₂×D₄×C₁₉	—	4	1	no	—
85	C₂×D₄×C₁₉	—	4	1	no	—
86	C₂×D₄×C₁₉	—	4	1	no	—
87	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
88	C₂²×C₄×C₁₉	—	2	1	no	—
89	C₂²×C₄×C₁₉	—	2	1	no	—
90	C₂²×C₄×C₁₉	—	2	1	no	—
91	C₂²×C₄×C₁₉	—	2	1	no	—
92	C₂²×C₄×C₁₉	—	4	4	no	—
93	C₂²×C₄×C₁₉	—	4	4	no	—
94	C₂²×C₄×C₁₉	—	8	2	no	—
95	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×Dic₁₉	—	4	1	no	—
99	C₂×Dic₃₈	—	2	2	no	—
100	C₂×Dic₃₈	—	4	1	no	—
101	C₂×Dic₃₈	—	4	1	no	—
102	C₂×Dic₃₈	—	4	1	no	—
103	C₂×Dic₃₈	—	4	1	no	—
104	C₂×Dic₃₈	—	4	1	no	—
105	C₄⋊C₄×C₁₉	—	2	1	no	—
106	C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₄⋊C₄×C₁₉	—	2	1	no	—
109	C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₄⋊C₄×C₁₉	D₈	1	2	yes	—
112	C₄⋊C₄×C₁₉	SD₁₆	1	2	yes	—
113	C₂²⋊C₄×C₁₉	—	4	4	no	—
114	C₂²⋊C₄×C₁₉	—	4	4	no	—
115	C₂²⋊C₄×C₁₉	—	8	2	no	—
116	C₄²×C₁₉	—	4	1	no	—
117	C₄²×C₁₉	—	4	1	no	—
118	C₄²×C₁₉	—	4	1	no	—
119	C₄²×C₁₉	—	4	1	no	—
120	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₁₉	#41	1	1	yes	characteristic
123	C₄²×C₁₉	#41	1	1	yes	characteristic
124	C₄⋊Dic₁₉	—	2	2	no	—
125	C₄⋊Dic₁₉	—	2	2	no	—
126	C₄⋊Dic₁₉	—	4	1	no	—
127	C₄⋊Dic₁₉	—	4	1	no	—
128	C₂×C₁₉⋊C₈	—	2	2	no	—
129	C₂×C₁₉⋊C₈	—	4	1	no	—
130	C₂×C₁₉⋊C₈	—	4	1	no	—
131	C₂×C₁₉⋊C₈	—	4	1	no	—
132	C₂×C₁₉⋊C₈	—	4	1	no	—
133	C₂×C₁₉⋊C₈	—	4	1	no	—
134	C₂×C₁₉⋊C₈	—	4	1	no	—
135	C₂×C₁₉⋊C₈	—	4	1	no	—
136	C₂×C₁₉⋊C₈	—	4	1	no	—
137	#9057	—	19	1	no	maximal, Sylow
138	C₂³×C₁₉	—	2	4	no	—
139	C₂³×C₁₉	—	4	2	no	—
140	C₂³×C₁₉	—	4	2	no	—
141	C₂³×C₁₉	—	4	2	no	—
142	C₂³×C₁₉	—	4	2	no	—
143	C₂³×C₁₉	—	4	2	no	—
144	C₂³×C₁₉	—	4	2	no	—
145	C₂³×C₁₉	#120	1	1	yes	characteristic
146	D₄×C₁₉	—	4	4	no	—
147	D₄×C₁₉	—	4	2	no	—
148	D₄×C₁₉	—	4	2	no	—
149	D₄×C₁₉	—	4	2	no	—
150	D₄×C₁₉	—	4	2	no	—
151	D₄×C₁₉	—	4	2	no	—
152	D₄×C₁₉	—	4	2	no	—
153	D₄×C₁₉	—	4	2	no	—
154	D₄×C₁₉	—	4	2	no	—
155	D₄×C₁₉	—	8	2	no	—
156	C₂×C₄×C₁₉	—	2	1	no	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	2	2	no	—
159	C₂×C₄×C₁₉	—	2	2	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	8	8	no	—
171	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
181	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
182	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
183	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
185	C₂×Dic₁₉	—	4	2	no	—
186	C₂×Dic₁₉	—	8	1	no	—
187	C₂×Dic₁₉	—	8	1	no	—
188	Dic₃₈	—	4	2	no	—
189	Dic₃₈	—	4	2	no	—
190	Dic₃₈	—	8	1	no	—
191	Dic₃₈	—	8	1	no	—
192	C₁₉⋊C₈	—	4	2	no	—
193	C₁₉⋊C₈	—	8	1	no	—
194	C₁₉⋊C₈	—	8	1	no	—
195	C₂×#486	—	19	1	no	—
196	#2366	D₁₉	1	1	yes	characteristic
197	#1988	—	19	1	no	—
198	#1981	—	19	1	no	—
199	C₂×#331	—	19	1	no	—
200	#1279	—	19	1	no	—
201	#1279	—	19	1	no	—
202	C₂²×C₁₉	—	4	4	no	—
203	C₂²×C₁₉	—	4	4	no	—
204	C₂²×C₁₉	—	4	4	no	—
205	C₂²×C₁₉	—	8	2	no	—
206	C₂²×C₁₉	—	8	2	no	—
207	C₂²×C₁₉	—	8	2	no	—
208	C₂²×C₁₉	—	8	2	no	—
209	C₂²×C₁₉	#386	1	1	yes	characteristic
210	C₂²×C₁₉	#447	1	1	yes	characteristic
211	C₂²×C₁₉	#449	1	1	yes	characteristic
212	C₂²×C₁₉	#450	1	1	yes	characteristic
213	C₂²×C₁₉	#452	1	1	yes	characteristic
214	C₂²×C₁₉	#455	1	1	yes	characteristic
215	C₂²×C₁₉	#455	1	1	yes	characteristic
216	C₄×C₁₉	—	2	1	no	—
217	C₄×C₁₉	—	2	1	no	—
218	C₄×C₁₉	—	4	2	no	—
219	C₄×C₁₉	—	4	2	no	—
220	C₄×C₁₉	—	8	1	no	—
221	C₄×C₁₉	—	8	1	no	—
222	C₄×C₁₉	C₄×D₈	1	1	yes	characteristic
223	C₄×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
224	C₄×C₁₉	#440	1	1	yes	characteristic
225	C₄×C₁₉	#442	1	1	yes	characteristic
226	C₄×C₁₉	#459	1	1	yes	characteristic
227	C₄×C₁₉	#461	1	1	yes	characteristic
228	C₄×C₁₉	#463	1	1	yes	characteristic
229	C₄×C₁₉	#463	1	1	yes	characteristic
230	Dic₁₉	—	8	2	no	—
231	C₂×C₄⋊Q₈	—	19	1	no	—
232	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
233	C₂×C₄×D₄	—	2	1	no	—
234	C₂×C₄×D₄	—	2	1	no	—
235	#486	—	19	4	no	—
236	#486	—	38	2	no	—
237	C₂×C₄⋊C₈	—	19	1	no	—
238	C₂×C₄⋊C₈	—	19	1	no	—
239	C₂×#103	—	38	1	no	—
240	C₂×#103	—	38	1	no	—
241	C₂×#102	—	38	2	no	—
242	C₂×C₄×C₈	—	19	1	no	—
243	#390	—	2	1	no	—
244	#390	—	2	1	no	—
245	#386	—	2	2	no	—
246	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
247	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
248	#340	—	38	1	no	—
249	#340	—	38	1	no	—
250	#331	—	38	2	no	—
251	C₂×C₁₉	—	8	4	no	—
252	C₂×C₁₉	#1639	1	1	yes	characteristic
253	C₂×C₁₉	#1640	1	1	yes	characteristic
254	C₂×C₁₉	#1641	1	1	yes	characteristic
255	C₂×C₁₉	#1642	1	1	yes	characteristic
256	C₂×C₁₉	#1877	1	1	yes	characteristic
257	C₂×C₁₉	#1879	1	1	yes	characteristic
258	C₂×C₁₉	#1885	1	1	yes	characteristic
259	C₂²×Q₈	—	38	1	no	—
260	C₂²×D₄	—	2	1	no	—
261	C₂²×D₄	—	2	1	no	—
262	C₂²×D₄	C₂²⋊D₁₉	1	2	yes	—
263	C₂³×C₄	—	2	2	no	—
264	C₂²×C₈	—	38	1	no	—
265	C₂²×C₈	—	38	1	no	—
266	C₂²×C₈	—	38	1	no	—
267	C₄⋊Q₈	—	19	2	no	—
268	C₄⋊Q₈	—	38	1	no	—
269	C₄⋊Q₈	—	38	1	no	—
270	C₄⋊Q₈	—	38	1	no	—
271	#127	—	2	1	no	—
272	#127	—	2	1	no	—
273	#127	C₄×D₁₉	1	2	yes	—
274	#127	D₇₆	1	2	yes	—
275	C₄×D₄	—	4	2	no	—
276	C₄×D₄	—	4	2	no	—
277	C₄×D₄	—	4	2	no	—
278	C₄×D₄	—	4	2	no	—
279	C₂×C₄⋊C₄	—	38	1	no	—
280	C₂×C₄⋊C₄	—	38	1	no	—
281	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₄²	—	2	1	no	—
289	C₂×C₄²	—	2	1	no	—
290	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
291	C₄⋊C₈	—	38	1	no	—
292	C₄⋊C₈	—	38	1	no	—
293	C₄⋊C₈	—	38	1	no	—
294	C₄⋊C₈	—	38	1	no	—
295	#103	—	76	2	no	—
296	#103	—	76	2	no	—
297	#102	—	38	8	no	—
298	C₄×C₈	—	19	2	no	—
299	C₄×C₈	—	38	1	no	—
300	#95	—	2	1	no	—
301	#95	—	2	1	no	—
302	C₁₉	#9057	1	1	yes	characteristic, complemented, Sylow
303	C₂⁴	—	2	2	no	—
304	C₂×Q₈	—	38	2	no	—
305	C₂×Q₈	—	76	1	no	—
306	C₂×Q₈	—	76	1	no	—
307	C₂×Q₈	—	76	1	no	—
308	C₂×Q₈	—	76	1	no	—
309	C₂×Q₈	—	76	1	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	4	2	no	—
316	C₂×D₄	—	4	2	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂×D₄	—	4	1	no	—
320	C₂×D₄	—	4	1	no	—
321	C₂×D₄	—	4	1	no	—
322	C₂×D₄	—	4	1	no	—
323	C₂×D₄	—	4	1	no	—
324	C₂×D₄	—	4	1	no	—
325	C₂×D₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	4	4	no	—
331	C₂²×C₄	—	4	4	no	—
332	C₂²×C₄	—	8	2	no	—
333	C₂²×C₄	—	76	1	no	—
334	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
335	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
336	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
337	C₂×C₈	—	38	2	no	—
338	C₂×C₈	—	76	1	no	—
339	C₂×C₈	—	76	1	no	—
340	C₂×C₈	—	76	1	no	—
341	C₂×C₈	—	76	1	no	—
342	C₂×C₈	—	76	1	no	—
343	C₂×C₈	—	76	1	no	—
344	C₂×C₈	—	76	1	no	—
345	C₂×C₈	—	76	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	38	2	no	—
353	C₄⋊C₄	—	38	2	no	—
354	C₄⋊C₄	—	76	1	no	—
355	C₄⋊C₄	—	76	1	no	—
356	C₄⋊C₄	#64525	1	2	yes	—
357	C₄⋊C₄	#64526	1	2	yes	—
358	C₂²⋊C₄	—	4	4	no	—
359	C₂²⋊C₄	—	4	4	no	—
360	C₂²⋊C₄	—	8	2	no	—
361	C₄²	—	4	1	no	—
362	C₄²	—	4	1	no	—
363	C₄²	—	4	1	no	—
364	C₄²	—	4	1	no	—
365	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
366	C₄²	C₂×D₇₆	1	1	yes	characteristic
367	C₄²	#64541	1	1	yes	characteristic
368	C₄²	#64541	1	1	yes	characteristic
369	C₂³	—	2	4	no	—
370	C₂³	—	4	2	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	4	2	no	—
373	C₂³	—	4	2	no	—
374	C₂³	—	4	2	no	—
375	C₂³	—	4	2	no	—
376	C₂³	#10597399	1	1	yes	characteristic
377	Q₈	—	76	2	no	—
378	Q₈	—	76	2	no	—
379	Q₈	—	152	1	no	—
380	Q₈	—	152	1	no	—
381	D₄	—	4	4	no	—
382	D₄	—	4	2	no	—
383	D₄	—	4	2	no	—
384	D₄	—	4	2	no	—
385	D₄	—	4	2	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	8	2	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	8	8	no	—
406	C₂×C₄	—	76	2	no	—
407	C₂×C₄	—	152	1	no	—
408	C₂×C₄	—	152	1	no	—
409	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
410	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
411	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
412	C₂×C₄	#10597375	1	1	yes	characteristic
413	C₂×C₄	#10597376	1	1	yes	characteristic
414	C₂×C₄	#10597376	1	1	yes	characteristic
415	C₂×C₄	C₂×#64525	1	1	yes	characteristic
416	C₂×C₄	#10597378	1	1	yes	characteristic
417	C₂×C₄	#10597378	1	1	yes	characteristic
418	C₂×C₄	C₂×#64526	1	1	yes	characteristic
419	C₂×C₄	#10597395	1	1	yes	characteristic
420	C₂×C₄	#10597396	1	1	yes	characteristic
421	C₂×C₄	#10597396	1	1	yes	characteristic
422	C₂×C₄	#10597397	1	1	yes	characteristic
423	C₈	—	76	2	no	—
424	C₈	—	152	1	no	—
425	C₈	—	152	1	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	4	4	no	—
428	C₂²	—	4	4	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	8	2	no	—
431	C₂²	—	8	2	no	—
432	C₂²	—	8	2	no	—
433	C₂²	#11926423	1	1	yes	characteristic
434	C₂²	#11926678	1	1	yes	characteristic
435	C₂²	#11926689	1	1	yes	characteristic
436	C₂²	#11926695	1	1	yes	characteristic
437	C₂²	#11926706	1	1	yes	characteristic
438	C₂²	#11926722	1	1	yes	characteristic
439	C₂²	#11926722	1	1	yes	characteristic
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	4	2	no	—
443	C₄	—	4	2	no	—
444	C₄	—	8	1	no	—
445	C₄	—	8	1	no	—
446	C₄	—	152	2	no	—
447	C₄	C₄×#64525	1	1	yes	characteristic
448	C₄	C₄×#64526	1	1	yes	characteristic
449	C₄	#11926644	1	1	yes	characteristic
450	C₄	#11926654	1	1	yes	characteristic
451	C₄	#11926739	1	1	yes	characteristic
452	C₄	#11926749	1	1	yes	characteristic
453	C₄	#11926759	1	1	yes	characteristic
454	C₄	#11926759	1	1	yes	characteristic
455	C₂	—	8	4	no	—
456	C₂	#14562814	1	1	yes	characteristic
457	C₂	#14562821	1	1	yes	characteristic
458	C₂	#14562828	1	1	yes	characteristic
459	C₂	#14562835	1	1	yes	characteristic
460	C₂	#14563969	1	1	yes	characteristic
461	C₂	#14563983	1	1	yes	characteristic
462	C₂	#14564023	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597399
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2366	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂×C₁₉×#127	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2366	D₁₉
hypocenter	C₁₉	#9057
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2366

Complements

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

N	H ≅ G/N	type
2. #14564587	C₂	semidirect
3. #14564558	C₂	semidirect
5. #14561476	C₂	semidirect
6. #14561476	C₂	semidirect
10. #11926890	C₄	semidirect
59. #10597315	C₂×C₄	semidirect
70. C₄×C₁₉⋊C₈	C₂×C₄	semidirect
302. C₁₉	#9057	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926890	2
#14564587	2
#14564558	2
C₂×#11926288	2
#14561476	2
C₁₉×#2366	2
#9057	19