Subgroups — #18078226

Order 4864.

568 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926600	C₂	1	1	yes	maximal, characteristic
2	#14571982	C₂	1	1	yes	maximal, characteristic
3	#14563612	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926290	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561519	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561519	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#332	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10597392	—	2	1	no	—
9	C₂×C₄²×D₁₉	C₂²	1	1	yes	characteristic
10	#11926600	—	2	2	no	—
11	#11926600	—	2	2	no	—
12	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
15	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
16	C₂×#10597272	—	2	1	no	—
17	#11926451	—	2	1	no	—
18	#11926440	—	2	1	no	—
19	#11926440	C₄	1	2	yes	—
20	#11926414	C₂²	1	1	yes	characteristic
21	#11926401	—	2	1	no	—
22	#11926401	C₄	1	2	yes	—
23	#11926298	—	2	1	no	—
24	#11926290	—	2	2	no	—
25	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₁₉×#332	—	2	2	no	—
29	C₂²×Q₈×C₁₉	—	2	1	no	—
30	C₂²×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₄×D₁₉	D₄	1	1	yes	characteristic
32	C₂²×C₄×D₁₉	D₄	1	1	yes	characteristic
33	C₂²×C₈×C₁₉	—	2	1	no	—
34	C₂²×C₈×C₁₉	—	2	1	no	—
35	C₁₉×C₄⋊Q₈	—	2	1	no	—
36	C₁₉×C₄⋊Q₈	—	2	1	no	—
37	C₁₉×C₄⋊Q₈	—	2	1	no	—
38	C₁₉×C₄⋊Q₈	—	2	1	no	—
39	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
40	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
41	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
42	#10597392	—	4	2	no	—
43	#10597392	—	4	2	no	—
44	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
45	C₂×C₄⋊Dic₁₉	—	2	1	no	—
46	C₂×C₄⋊Dic₁₉	—	2	1	no	—
47	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
48	C₂×Dic₁₉⋊C₄	—	2	2	no	—
49	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
51	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
52	C₂²×C₁₉⋊C₈	—	2	1	no	—
53	C₂²×C₁₉⋊C₈	—	2	1	no	—
54	C₄²×D₁₉	—	2	1	no	—
55	C₄²×D₁₉	—	2	1	no	—
56	C₄²×D₁₉	—	2	1	no	—
57	C₄²×D₁₉	—	2	1	no	—
58	C₁₉×C₄⋊C₈	—	2	1	no	—
59	C₁₉×C₄⋊C₈	—	2	1	no	—
60	C₁₉×C₄⋊C₈	—	2	1	no	—
61	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
62	C₁₉⋊#95	—	2	2	no	—
63	C₁₉⋊#95	—	2	2	no	—
64	(C₂×D₁₉)⋊C₈	—	2	4	no	—
65	(C₂×D₁₉)⋊C₈	—	4	2	no	—
66	#10597272	—	2	4	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)	D₄	1	2	yes	—
71	C₂³×D₁₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂×Q₈×C₁₉	—	4	1	no	—
73	C₂×Q₈×C₁₉	—	4	1	no	—
74	C₂×Q₈×C₁₉	—	4	1	no	—
75	C₂×Q₈×C₁₉	—	4	1	no	—
76	C₂×Q₈×C₁₉	—	4	1	no	—
77	C₂×Q₈×C₁₉	—	4	1	no	—
78	C₂²×C₄×C₁₉	—	2	2	no	—
79	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₂²×Dic₁₉	—	2	2	no	—
83	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₄×D₁₉	—	2	2	no	—
87	C₂×C₄×D₁₉	—	2	1	no	—
88	C₂×C₄×D₁₉	—	2	1	no	—
89	C₂×C₄×D₁₉	—	2	1	no	—
90	C₂×C₄×D₁₉	—	2	1	no	—
91	C₂×C₄×D₁₉	—	2	1	no	—
92	C₂×C₄×D₁₉	—	2	1	no	—
93	C₂×C₄×D₁₉	—	2	1	no	—
94	C₂×C₄×D₁₉	—	2	1	no	—
95	C₂×C₄×D₁₉	—	2	1	no	—
96	C₂×C₄×D₁₉	—	2	1	no	—
97	C₂×C₄×D₁₉	—	2	1	no	—
98	C₂×C₄×D₁₉	—	2	1	no	—
99	C₂×C₄×D₁₉	—	2	1	no	—
100	C₂×C₄×D₁₉	—	2	1	no	—
101	C₂×C₄×D₁₉	—	4	1	no	—
102	C₂×C₈×C₁₉	—	2	2	no	—
103	C₂×C₈×C₁₉	—	4	1	no	—
104	C₂×C₈×C₁₉	—	4	1	no	—
105	C₂×C₈×C₁₉	—	4	1	no	—
106	C₂×C₈×C₁₉	—	4	1	no	—
107	C₂×C₈×C₁₉	—	4	1	no	—
108	C₄⋊C₄×C₁₉	—	2	2	no	—
109	C₄⋊C₄×C₁₉	—	2	2	no	—
110	C₄⋊C₄×C₁₉	—	4	1	no	—
111	C₄⋊C₄×C₁₉	—	4	1	no	—
112	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₁₉	#41	1	1	yes	characteristic
115	C₄²×C₁₉	#41	1	1	yes	characteristic
116	(C₂×D₁₉)⋊C₄	—	4	4	no	—
117	C₄⋊Dic₁₉	—	4	1	no	—
118	C₄⋊Dic₁₉	—	4	1	no	—
119	C₄⋊Dic₁₉	—	4	1	no	—
120	C₄⋊Dic₁₉	—	4	1	no	—
121	C₄⋊Dic₁₉	—	4	2	no	—
122	Dic₁₉⋊C₄	—	4	4	no	—
123	C₄×Dic₁₉	—	2	1	no	—
124	C₄×Dic₁₉	—	2	1	no	—
125	C₄×Dic₁₉	—	2	1	no	—
126	C₄×Dic₁₉	—	2	1	no	—
127	C₄×Dic₁₉	—	2	1	no	—
128	C₄×Dic₁₉	—	2	1	no	—
129	C₂×C₁₉⋊C₈	—	2	2	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	#9138	—	19	1	no	maximal, Sylow
136	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
137	C₂²×D₁₉	—	2	1	no	—
138	C₂²×D₁₉	—	2	1	no	—
139	C₂²×D₁₉	—	2	1	no	—
140	C₂²×D₁₉	—	2	1	no	—
141	C₂²×D₁₉	—	2	1	no	—
142	C₂²×D₁₉	—	2	1	no	—
143	C₂²×D₁₉	#101	1	2	yes	—
144	Q₈×C₁₉	—	8	1	no	—
145	Q₈×C₁₉	—	8	1	no	—
146	Q₈×C₁₉	—	8	1	no	—
147	Q₈×C₁₉	—	8	1	no	—
148	C₂×C₄×C₁₉	—	2	1	no	—
149	C₂×C₄×C₁₉	—	2	1	no	—
150	C₂×C₄×C₁₉	—	4	2	no	—
151	C₂×C₄×C₁₉	—	4	2	no	—
152	C₂×C₄×C₁₉	—	4	2	no	—
153	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
156	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
157	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
159	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
160	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
161	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
162	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
163	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
164	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
165	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
166	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
167	C₂×Dic₁₉	—	2	1	no	—
168	C₂×Dic₁₉	—	2	1	no	—
169	C₂×Dic₁₉	—	2	1	no	—
170	C₂×Dic₁₉	—	2	1	no	—
171	C₂×Dic₁₉	—	2	1	no	—
172	C₂×Dic₁₉	—	2	1	no	—
173	C₂×Dic₁₉	—	2	1	no	—
174	C₂×Dic₁₉	—	2	1	no	—
175	C₂×Dic₁₉	—	2	1	no	—
176	C₂×Dic₁₉	—	4	2	no	—
177	C₂×Dic₁₉	—	4	2	no	—
178	C₂×Dic₁₉	—	4	2	no	—
179	C₄×D₁₉	—	4	2	no	—
180	C₄×D₁₉	—	4	2	no	—
181	C₄×D₁₉	—	4	1	no	—
182	C₄×D₁₉	—	4	1	no	—
183	C₄×D₁₉	—	4	1	no	—
184	C₄×D₁₉	—	4	1	no	—
185	C₄×D₁₉	—	4	1	no	—
186	C₄×D₁₉	—	4	1	no	—
187	C₄×D₁₉	—	4	1	no	—
188	C₄×D₁₉	—	4	1	no	—
189	C₈×C₁₉	—	4	2	no	—
190	C₈×C₁₉	—	8	1	no	—
191	C₁₉⋊C₈	—	4	2	no	—
192	C₁₉⋊C₈	—	8	1	no	—
193	C₂×#432	—	19	1	no	—
194	#2857	—	19	1	no	—
195	#1797	—	19	1	no	—
196	C₂×#332	—	19	1	no	—
197	C₂×#332	D₁₉	1	1	yes	characteristic, complemented
198	#1296	—	19	1	no	—
199	#1296	—	19	1	no	—
200	C₂²×C₁₉	#386	1	1	yes	characteristic
201	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
202	C₂²×C₁₉	#413	1	1	yes	characteristic
203	C₂²×C₁₉	#416	1	1	yes	characteristic
204	C₂²×C₁₉	#417	1	1	yes	characteristic
205	C₂²×C₁₉	#418	1	1	yes	characteristic
206	C₂²×C₁₉	#419	1	1	yes	characteristic
207	C₂×D₁₉	—	2	2	no	—
208	C₂×D₁₉	—	2	2	no	—
209	C₂×D₁₉	—	2	2	no	—
210	C₂×D₁₉	—	4	1	no	—
211	C₂×D₁₉	—	4	1	no	—
212	C₂×D₁₉	—	4	1	no	—
213	C₂×D₁₉	—	4	1	no	—
214	C₄×C₁₉	—	2	1	no	—
215	C₄×C₁₉	—	2	1	no	—
216	C₄×C₁₉	—	8	2	no	—
217	C₄×C₁₉	#452	1	1	yes	characteristic
218	C₄×C₁₉	#452	1	1	yes	characteristic
219	C₄×C₁₉	#468	1	1	yes	characteristic
220	C₄×C₁₉	#468	1	1	yes	characteristic
221	C₄×C₁₉	#469	1	1	yes	characteristic
222	C₄×C₁₉	#469	1	1	yes	characteristic
223	C₄×C₁₉	#485	1	1	yes	characteristic
224	C₄×C₁₉	#485	1	1	yes	characteristic
225	Dic₁₉	—	4	1	no	—
226	Dic₁₉	—	4	1	no	—
227	Dic₁₉	—	4	1	no	—
228	Dic₁₉	—	8	2	no	—
229	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
230	C₂×C₂²⋊Q₈	—	38	1	no	—
231	C₂²×C₄²	—	19	1	no	—
232	#432	—	38	2	no	—
233	#432	—	38	2	no	—
234	C₂×C₄⋊C₈	—	19	1	no	—
235	C₂×C₄⋊C₈	—	19	1	no	—
236	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
237	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
238	C₂×C₂²⋊C₈	—	38	1	no	—
239	C₂×C₂²⋊C₈	—	38	1	no	—
240	C₂×#97	—	38	1	no	—
241	#391	—	38	1	no	—
242	#389	—	19	2	no	—
243	#389	—	38	1	no	—
244	#384	—	19	1	no	—
245	#380	—	19	2	no	—
246	#380	—	38	1	no	—
247	#336	—	38	1	no	—
248	#332	—	2	2	no	—
249	#332	—	38	2	no	—
250	C₂×C₁₉	#1552	1	1	yes	characteristic
251	C₂×C₁₉	#1553	1	1	yes	characteristic
252	C₂×C₁₉	#1556	1	1	yes	characteristic
253	C₂×C₁₉	#1559	1	1	yes	characteristic
254	C₂×C₁₉	#1873	1	1	yes	characteristic
255	C₂×C₁₉	#1895	1	1	yes	characteristic
256	C₂×C₁₉	#1901	1	1	yes	characteristic
257	D₁₉	—	4	2	no	—
258	C₂²×Q₈	—	2	1	no	—
259	C₂³×C₄	—	19	1	no	—
260	C₂³×C₄	—	19	1	no	—
261	C₂³×C₄	—	19	1	no	—
262	C₂²×C₈	—	2	1	no	—
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	—	38	1	no	—
265	C₂²×C₈	—	38	1	no	—
266	C₄⋊Q₈	—	2	1	no	—
267	C₄⋊Q₈	—	2	1	no	—
268	C₄⋊Q₈	—	2	1	no	—
269	C₄⋊Q₈	—	2	1	no	—
270	C₂²⋊Q₈	—	76	2	no	—
271	C₂²⋊Q₈	—	76	2	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	19	2	no	—
274	C₂×C₄⋊C₄	—	38	2	no	—
275	C₂×C₄⋊C₄	—	38	1	no	—
276	C₂×C₄⋊C₄	—	38	1	no	—
277	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
278	C₂×C₂²⋊C₄	—	38	2	no	—
279	C₂×C₄²	—	19	1	no	—
280	C₂×C₄²	—	19	1	no	—
281	C₂×C₄²	—	19	1	no	—
282	C₂×C₄²	—	38	1	no	—
283	C₂×C₄²	—	38	1	no	—
284	C₂×C₄²	—	38	1	no	—
285	C₂×C₄²	—	38	1	no	—
286	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
287	C₄⋊C₈	—	2	1	no	—
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	—	2	1	no	—
290	C₄⋊C₈	—	19	2	no	—
291	C₄⋊C₈	—	38	1	no	—
292	C₄⋊C₈	—	38	1	no	—
293	C₄⋊C₈	—	38	1	no	—
294	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
295	C₂²⋊C₈	—	38	4	no	—
296	C₂²⋊C₈	—	76	2	no	—
297	#97	—	38	4	no	—
298	#95	—	38	2	no	—
299	#95	—	38	2	no	—
300	C₁₉	#9138	1	1	yes	characteristic, complemented, Sylow
301	C₂⁴	—	19	1	no	—
302	C₂×Q₈	—	4	1	no	—
303	C₂×Q₈	—	4	1	no	—
304	C₂×Q₈	—	4	1	no	—
305	C₂×Q₈	—	4	1	no	—
306	C₂×Q₈	—	4	1	no	—
307	C₂×Q₈	—	4	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	19	1	no	—
310	C₂²×C₄	—	19	1	no	—
311	C₂²×C₄	—	19	1	no	—
312	C₂²×C₄	—	38	2	no	—
313	C₂²×C₄	—	38	1	no	—
314	C₂²×C₄	—	38	1	no	—
315	C₂²×C₄	—	38	1	no	—
316	C₂²×C₄	—	38	1	no	—
317	C₂²×C₄	—	38	1	no	—
318	C₂²×C₄	—	38	1	no	—
319	C₂²×C₄	—	38	1	no	—
320	C₂²×C₄	—	38	1	no	—
321	C₂²×C₄	—	38	1	no	—
322	C₂²×C₄	—	38	1	no	—
323	C₂²×C₄	—	38	1	no	—
324	C₂²×C₄	—	38	1	no	—
325	C₂²×C₄	—	38	1	no	—
326	C₂²×C₄	—	38	1	no	—
327	C₂²×C₄	—	38	2	no	—
328	C₂²×C₄	—	76	1	no	—
329	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
330	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
331	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	—	4	1	no	—
338	C₂×C₈	—	38	2	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	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	4	1	no	—
347	C₄⋊C₄	—	4	1	no	—
348	C₄⋊C₄	—	76	2	no	—
349	C₄⋊C₄	—	76	4	no	—
350	C₄⋊C₄	—	76	1	no	—
351	C₄⋊C₄	—	76	1	no	—
352	C₄⋊C₄	—	76	1	no	—
353	C₄⋊C₄	—	76	1	no	—
354	C₂²⋊C₄	—	76	4	no	—
355	C₄²	—	38	1	no	—
356	C₄²	—	38	1	no	—
357	C₄²	—	38	1	no	—
358	C₄²	—	38	1	no	—
359	C₄²	—	38	1	no	—
360	C₄²	—	38	1	no	—
361	C₄²	#64541	1	1	yes	characteristic
362	C₄²	D₄×D₁₉	1	1	yes	characteristic
363	C₄²	#64543	1	1	yes	characteristic
364	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
365	C₂³	—	19	2	no	—
366	C₂³	—	38	1	no	—
367	C₂³	—	38	1	no	—
368	C₂³	—	38	1	no	—
369	C₂³	—	38	1	no	—
370	C₂³	—	38	1	no	—
371	C₂³	—	38	1	no	—
372	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
373	Q₈	—	8	1	no	—
374	Q₈	—	8	1	no	—
375	Q₈	—	8	1	no	—
376	Q₈	—	8	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	38	1	no	—
383	C₂×C₄	—	38	1	no	—
384	C₂×C₄	—	38	1	no	—
385	C₂×C₄	—	38	1	no	—
386	C₂×C₄	—	38	1	no	—
387	C₂×C₄	—	38	1	no	—
388	C₂×C₄	—	38	1	no	—
389	C₂×C₄	—	38	1	no	—
390	C₂×C₄	—	38	1	no	—
391	C₂×C₄	—	76	2	no	—
392	C₂×C₄	—	76	2	no	—
393	C₂×C₄	—	76	1	no	—
394	C₂×C₄	—	76	1	no	—
395	C₂×C₄	—	76	1	no	—
396	C₂×C₄	—	76	1	no	—
397	C₂×C₄	—	76	1	no	—
398	C₂×C₄	—	76	1	no	—
399	C₂×C₄	—	76	1	no	—
400	C₂×C₄	—	76	1	no	—
401	C₂×C₄	—	76	2	no	—
402	C₂×C₄	—	76	2	no	—
403	C₂×C₄	—	76	2	no	—
404	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
405	C₂×C₄	#10597329	1	1	yes	characteristic
406	C₂×C₄	#10597330	1	1	yes	characteristic
407	C₂×C₄	#10597357	1	1	yes	characteristic
408	C₂×C₄	#10597357	1	1	yes	characteristic
409	C₂×C₄	#10597360	1	1	yes	characteristic
410	C₂×C₄	#10597361	1	1	yes	characteristic
411	C₂×C₄	#10597361	1	1	yes	characteristic
412	C₂×C₄	#10597362	1	1	yes	characteristic
413	C₂×C₄	#10597364	1	1	yes	characteristic
414	C₂×C₄	#10597365	1	1	yes	characteristic
415	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
416	C₂×C₄	#10597383	1	1	yes	characteristic
417	C₂×C₄	#10597384	1	1	yes	characteristic
418	C₈	—	4	2	no	—
419	C₈	—	8	1	no	—
420	C₈	—	76	2	no	—
421	C₈	—	152	1	no	—
422	C₂²	—	38	2	no	—
423	C₂²	—	38	2	no	—
424	C₂²	—	38	2	no	—
425	C₂²	—	76	1	no	—
426	C₂²	—	76	1	no	—
427	C₂²	—	76	1	no	—
428	C₂²	—	76	1	no	—
429	C₂²	#11926420	1	1	yes	characteristic
430	C₂²	#101×D₁₉	1	1	yes	characteristic
431	C₂²	#11926527	1	1	yes	characteristic
432	C₂²	#11926539	1	1	yes	characteristic
433	C₂²	#11926542	1	1	yes	characteristic
434	C₂²	#11926547	1	1	yes	characteristic
435	C₂²	#11926551	1	1	yes	characteristic
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	8	2	no	—
439	C₄	—	76	1	no	—
440	C₄	—	76	1	no	—
441	C₄	—	76	1	no	—
442	C₄	—	152	2	no	—
443	C₄	#11926703	1	1	yes	characteristic
444	C₄	#11926705	1	1	yes	characteristic
445	C₄	#11926787	1	1	yes	characteristic
446	C₄	#11926789	1	1	yes	characteristic
447	C₄	#11926794	1	1	yes	characteristic
448	C₄	#11926796	1	1	yes	characteristic
449	C₄	#11926883	1	1	yes	characteristic
450	C₄	#11926884	1	1	yes	characteristic
451	C₂	—	76	2	no	—
452	C₂	#14562334	1	1	yes	characteristic
453	C₂	#14562339	1	1	yes	characteristic
454	C₂	#14562350	1	1	yes	characteristic
455	C₂	#14562364	1	1	yes	characteristic
456	C₂	#14563944	1	1	yes	characteristic
457	C₂	#14564070	1	1	yes	characteristic
458	C₂	#14564100	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#332	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂³×D₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#332	D₁₉
hypocenter	C₁₉	#9138
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#332

Complements

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

N	H ≅ G/N	type
4. C₂×#11926290	C₂	semidirect
5. #14561519	C₂	semidirect
6. #14561519	C₂	semidirect
7. C₂×C₁₉×#332	C₂	semidirect
197. C₂×#332	D₁₉	semidirect
300. C₁₉	#9138	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926600	2
#14571982	2
#14563612	2
C₂×#11926290	2
#14561519	2
C₂×C₁₉×#332	2
#9138	19