Subgroups — #18078218

Order 4864.

568 conjugacy classes of subgroups.

The subgroup lattice has 450 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	#14571988	C₂	1	1	yes	maximal, characteristic
3	#14563612	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926292	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926292	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561518	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10597315	C₂²	1	1	yes	characteristic
9	C₂×#10597343	C₄	1	2	yes	—
10	C₂×C₄²×D₁₉	C₂²	1	1	yes	characteristic
11	#11926600	—	2	2	no	—
12	#11926600	—	2	2	no	—
13	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
16	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
17	C₂×#10597272	—	2	1	no	—
18	#11926449	C₄	1	2	yes	—
19	#11926443	—	2	1	no	—
20	#11926443	—	2	1	no	—
21	#11926401	—	2	1	no	—
22	#11926401	—	2	1	no	—
23	#11926298	—	2	1	no	—
24	#11926292	—	2	2	no	—
25	#11926292	—	2	2	no	—
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₁₉×#384	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×D₁₉	D₄	1	1	yes	characteristic
31	C₂²×C₄×D₁₉	D₄	1	1	yes	characteristic
32	C₂²×Dic₃₈	C₂×C₄	1	2	yes	—
33	C₂²×C₈×C₁₉	—	2	1	no	—
34	C₂²×C₈×C₁₉	—	2	1	no	—
35	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
38	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
39	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
40	C₂×C₄⋊Dic₁₉	—	2	1	no	—
41	C₂×C₄⋊Dic₁₉	—	2	1	no	—
42	C₂×C₄⋊Dic₁₉	—	2	2	no	—
43	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
45	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
46	C₂²×C₁₉⋊C₈	—	2	1	no	—
47	C₂²×C₁₉⋊C₈	—	2	1	no	—
48	#10597343	—	4	4	no	—
49	C₄²×D₁₉	—	2	1	no	—
50	C₄²×D₁₉	—	2	1	no	—
51	C₄²×D₁₉	—	2	1	no	—
52	C₄²×D₁₉	—	2	1	no	—
53	#10597315	—	2	1	no	—
54	#10597315	—	2	1	no	—
55	#10597315	—	2	1	no	—
56	#10597315	—	2	1	no	—
57	C₁₉×C₄⋊C₈	—	2	1	no	—
58	C₁₉×C₄⋊C₈	—	2	1	no	—
59	C₁₉×C₄⋊C₈	—	2	1	no	—
60	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
61	C₁₉⋊#95	—	2	2	no	—
62	C₁₉⋊#95	—	2	2	no	—
63	(C₂×D₁₉)⋊C₈	—	2	4	no	—
64	(C₂×D₁₉)⋊C₈	—	4	2	no	—
65	#10597272	—	2	4	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)	D₄	1	2	yes	—
70	C₂³×D₁₉	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	—	2	2	no	—
72	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₂²×Dic₁₉	—	2	2	no	—
76	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
79	C₂×C₄×D₁₉	—	2	2	no	—
80	C₂×C₄×D₁₉	—	2	1	no	—
81	C₂×C₄×D₁₉	—	2	1	no	—
82	C₂×C₄×D₁₉	—	2	1	no	—
83	C₂×C₄×D₁₉	—	2	1	no	—
84	C₂×C₄×D₁₉	—	2	1	no	—
85	C₂×C₄×D₁₉	—	2	1	no	—
86	C₂×C₄×D₁₉	—	2	1	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	—	4	1	no	—
95	C₂×Dic₃₈	—	2	2	no	—
96	C₂×Dic₃₈	—	2	2	no	—
97	C₂×Dic₃₈	—	4	2	no	—
98	C₂×Dic₃₈	—	4	2	no	—
99	C₂×C₈×C₁₉	—	2	2	no	—
100	C₂×C₈×C₁₉	—	4	1	no	—
101	C₂×C₈×C₁₉	—	4	1	no	—
102	C₂×C₈×C₁₉	—	4	1	no	—
103	C₂×C₈×C₁₉	—	4	1	no	—
104	C₂×C₈×C₁₉	—	4	1	no	—
105	C₄⋊C₄×C₁₉	—	4	2	no	—
106	C₄⋊C₄×C₁₉	—	4	1	no	—
107	C₄⋊C₄×C₁₉	—	4	1	no	—
108	C₄⋊C₄×C₁₉	—	4	1	no	—
109	C₄⋊C₄×C₁₉	—	4	1	no	—
110	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₁₉	#41	1	1	yes	characteristic
113	C₄²×C₁₉	#41	1	1	yes	characteristic
114	(C₂×D₁₉)⋊C₄	—	4	4	no	—
115	C₄⋊Dic₁₉	—	4	4	no	—
116	C₄⋊Dic₁₉	—	4	1	no	—
117	C₄⋊Dic₁₉	—	4	1	no	—
118	C₄⋊Dic₁₉	—	4	1	no	—
119	C₄⋊Dic₁₉	—	4	1	no	—
120	C₄×Dic₁₉	—	2	1	no	—
121	C₄×Dic₁₉	—	2	1	no	—
122	C₄×Dic₁₉	—	2	1	no	—
123	C₄×Dic₁₉	—	2	1	no	—
124	C₄×Dic₁₉	—	2	1	no	—
125	C₄×Dic₁₉	—	2	1	no	—
126	C₂×C₁₉⋊C₈	—	2	2	no	—
127	C₂×C₁₉⋊C₈	—	4	1	no	—
128	C₂×C₁₉⋊C₈	—	4	1	no	—
129	C₂×C₁₉⋊C₈	—	4	1	no	—
130	C₂×C₁₉⋊C₈	—	4	1	no	—
131	C₂×C₁₉⋊C₈	—	4	1	no	—
132	#9136	—	19	1	no	maximal, Sylow
133	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂²×D₁₉	—	2	1	no	—
135	C₂²×D₁₉	—	2	1	no	—
136	C₂²×D₁₉	—	2	1	no	—
137	C₂²×D₁₉	—	2	1	no	—
138	C₂²×D₁₉	—	2	1	no	—
139	C₂²×D₁₉	—	2	1	no	—
140	C₂²×D₁₉	#100	1	2	yes	—
141	C₂×C₄×C₁₉	—	2	1	no	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	4	2	no	—
144	C₂×C₄×C₁₉	—	4	2	no	—
145	C₂×C₄×C₁₉	—	4	2	no	—
146	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
149	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
150	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
151	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
152	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
153	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
154	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
156	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
157	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
159	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
160	C₂×Dic₁₉	—	2	1	no	—
161	C₂×Dic₁₉	—	2	1	no	—
162	C₂×Dic₁₉	—	2	1	no	—
163	C₂×Dic₁₉	—	2	1	no	—
164	C₂×Dic₁₉	—	2	1	no	—
165	C₂×Dic₁₉	—	2	1	no	—
166	C₂×Dic₁₉	—	2	1	no	—
167	C₂×Dic₁₉	—	2	1	no	—
168	C₂×Dic₁₉	—	2	1	no	—
169	C₂×Dic₁₉	—	4	2	no	—
170	C₂×Dic₁₉	—	4	2	no	—
171	C₂×Dic₁₉	—	4	2	no	—
172	C₄×D₁₉	—	4	2	no	—
173	C₄×D₁₉	—	4	2	no	—
174	C₄×D₁₉	—	4	1	no	—
175	C₄×D₁₉	—	4	1	no	—
176	C₄×D₁₉	—	4	1	no	—
177	C₄×D₁₉	—	4	1	no	—
178	C₄×D₁₉	—	4	1	no	—
179	C₄×D₁₉	—	4	1	no	—
180	C₄×D₁₉	—	4	1	no	—
181	C₄×D₁₉	—	4	1	no	—
182	Dic₃₈	—	8	2	no	—
183	Dic₃₈	—	8	2	no	—
184	C₈×C₁₉	—	4	2	no	—
185	C₈×C₁₉	—	8	1	no	—
186	C₁₉⋊C₈	—	4	2	no	—
187	C₁₉⋊C₈	—	8	1	no	—
188	C₂×#432	—	19	1	no	—
189	#2857	—	19	1	no	—
190	#1797	—	19	1	no	—
191	C₂×#333	—	19	1	no	—
192	C₂×#333	—	19	1	no	—
193	#1296	—	19	1	no	—
194	#1296	D₁₉	1	1	yes	characteristic, complemented
195	C₂²×C₁₉	#386	1	1	yes	characteristic
196	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
197	C₂²×C₁₉	#413	1	1	yes	characteristic
198	C₂²×C₁₉	#416	1	1	yes	characteristic
199	C₂²×C₁₉	#417	1	1	yes	characteristic
200	C₂²×C₁₉	#419	1	1	yes	characteristic
201	C₂²×C₁₉	#419	1	1	yes	characteristic
202	C₂×D₁₉	—	2	2	no	—
203	C₂×D₁₉	—	2	2	no	—
204	C₂×D₁₉	—	2	2	no	—
205	C₂×D₁₉	—	4	1	no	—
206	C₂×D₁₉	—	4	1	no	—
207	C₂×D₁₉	—	4	1	no	—
208	C₂×D₁₉	—	4	1	no	—
209	C₄×C₁₉	—	2	1	no	—
210	C₄×C₁₉	—	2	1	no	—
211	C₄×C₁₉	—	8	2	no	—
212	C₄×C₁₉	#452	1	1	yes	characteristic
213	C₄×C₁₉	#452	1	1	yes	characteristic
214	C₄×C₁₉	#468	1	1	yes	characteristic
215	C₄×C₁₉	#468	1	1	yes	characteristic
216	C₄×C₁₉	#470	1	1	yes	characteristic
217	C₄×C₁₉	#470	1	1	yes	characteristic
218	C₄×C₁₉	#485	1	1	yes	characteristic
219	C₄×C₁₉	#485	1	1	yes	characteristic
220	Dic₁₉	—	4	1	no	—
221	Dic₁₉	—	4	1	no	—
222	Dic₁₉	—	4	1	no	—
223	Dic₁₉	—	8	2	no	—
224	C₂×C₄⋊Q₈	—	19	1	no	—
225	C₂×C₂²⋊Q₈	—	19	2	no	—
226	C₂²×C₄²	—	19	1	no	—
227	#432	—	38	2	no	—
228	#432	—	38	2	no	—
229	C₂×C₄⋊C₈	—	19	1	no	—
230	C₂×C₄⋊C₈	—	19	1	no	—
231	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
232	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
233	C₂×C₂²⋊C₈	—	38	1	no	—
234	C₂×C₂²⋊C₈	—	38	1	no	—
235	C₂×#97	—	38	1	no	—
236	#391	—	19	2	no	—
237	#389	—	38	1	no	—
238	#389	—	38	1	no	—
239	#384	C₂×D₁₉	1	1	yes	characteristic
240	#380	—	38	1	no	—
241	#380	—	38	1	no	—
242	#336	—	38	1	no	—
243	#333	—	38	2	no	—
244	#333	—	38	2	no	—
245	C₂×C₁₉	#1551	1	1	yes	characteristic
246	C₂×C₁₉	#1554	1	1	yes	characteristic
247	C₂×C₁₉	#1558	1	1	yes	characteristic
248	C₂×C₁₉	#1559	1	1	yes	characteristic
249	C₂×C₁₉	#1873	1	1	yes	characteristic
250	C₂×C₁₉	#1894	1	1	yes	characteristic
251	C₂×C₁₉	#1900	1	1	yes	characteristic
252	D₁₉	—	4	2	no	—
253	C₂²×Q₈	—	19	2	no	—
254	C₂³×C₄	—	19	1	no	—
255	C₂³×C₄	—	19	1	no	—
256	C₂³×C₄	—	19	1	no	—
257	C₂²×C₈	—	2	1	no	—
258	C₂²×C₈	—	2	1	no	—
259	C₂²×C₈	—	38	1	no	—
260	C₂²×C₈	—	38	1	no	—
261	C₄⋊Q₈	—	38	1	no	—
262	C₄⋊Q₈	—	38	1	no	—
263	C₄⋊Q₈	—	38	1	no	—
264	C₄⋊Q₈	—	38	1	no	—
265	C₂²⋊Q₈	—	76	4	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	38	2	no	—
269	C₂×C₄⋊C₄	—	38	1	no	—
270	C₂×C₄⋊C₄	—	38	1	no	—
271	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
272	C₂×C₂²⋊C₄	—	38	2	no	—
273	C₂×C₄²	—	19	1	no	—
274	C₂×C₄²	—	19	1	no	—
275	C₂×C₄²	—	19	1	no	—
276	C₂×C₄²	—	38	1	no	—
277	C₂×C₄²	—	38	1	no	—
278	C₂×C₄²	—	38	1	no	—
279	C₂×C₄²	—	38	1	no	—
280	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
281	C₄⋊C₈	—	2	1	no	—
282	C₄⋊C₈	—	2	1	no	—
283	C₄⋊C₈	—	2	1	no	—
284	C₄⋊C₈	—	19	2	no	—
285	C₄⋊C₈	—	38	1	no	—
286	C₄⋊C₈	—	38	1	no	—
287	C₄⋊C₈	—	38	1	no	—
288	C₄⋊C₈	D₇₆	1	2	yes	—
289	C₂²⋊C₈	—	38	4	no	—
290	C₂²⋊C₈	—	76	2	no	—
291	#97	—	38	4	no	—
292	#95	—	38	2	no	—
293	#95	—	38	2	no	—
294	C₁₉	#9136	1	1	yes	characteristic, complemented, Sylow
295	C₂⁴	—	19	1	no	—
296	C₂×Q₈	—	38	2	no	—
297	C₂×Q₈	—	38	2	no	—
298	C₂×Q₈	—	76	2	no	—
299	C₂×Q₈	—	76	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	19	1	no	—
302	C₂²×C₄	—	19	1	no	—
303	C₂²×C₄	—	19	1	no	—
304	C₂²×C₄	—	38	2	no	—
305	C₂²×C₄	—	38	1	no	—
306	C₂²×C₄	—	38	1	no	—
307	C₂²×C₄	—	38	1	no	—
308	C₂²×C₄	—	38	1	no	—
309	C₂²×C₄	—	38	1	no	—
310	C₂²×C₄	—	38	1	no	—
311	C₂²×C₄	—	38	1	no	—
312	C₂²×C₄	—	38	1	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	2	no	—
320	C₂²×C₄	—	76	1	no	—
321	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
322	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
323	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	4	1	no	—
326	C₂×C₈	—	4	1	no	—
327	C₂×C₈	—	4	1	no	—
328	C₂×C₈	—	4	1	no	—
329	C₂×C₈	—	4	1	no	—
330	C₂×C₈	—	38	2	no	—
331	C₂×C₈	—	76	1	no	—
332	C₂×C₈	—	76	1	no	—
333	C₂×C₈	—	76	1	no	—
334	C₂×C₈	—	76	1	no	—
335	C₂×C₈	—	76	1	no	—
336	C₄⋊C₄	—	4	2	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₄⋊C₄	—	4	1	no	—
340	C₄⋊C₄	—	4	1	no	—
341	C₄⋊C₄	—	76	4	no	—
342	C₄⋊C₄	—	76	1	no	—
343	C₄⋊C₄	—	76	1	no	—
344	C₄⋊C₄	—	76	1	no	—
345	C₄⋊C₄	—	76	1	no	—
346	C₂²⋊C₄	—	76	4	no	—
347	C₄²	—	38	1	no	—
348	C₄²	—	38	1	no	—
349	C₄²	—	38	1	no	—
350	C₄²	—	38	1	no	—
351	C₄²	—	38	1	no	—
352	C₄²	—	38	1	no	—
353	C₄²	C₂×D₇₆	1	1	yes	characteristic
354	C₄²	#64541	1	1	yes	characteristic
355	C₄²	D₄×D₁₉	1	1	yes	characteristic
356	C₄²	#64545	1	1	yes	characteristic
357	C₂³	—	19	2	no	—
358	C₂³	—	38	1	no	—
359	C₂³	—	38	1	no	—
360	C₂³	—	38	1	no	—
361	C₂³	—	38	1	no	—
362	C₂³	—	38	1	no	—
363	C₂³	—	38	1	no	—
364	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
365	Q₈	—	152	2	no	—
366	Q₈	—	152	2	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	38	1	no	—
373	C₂×C₄	—	38	1	no	—
374	C₂×C₄	—	38	1	no	—
375	C₂×C₄	—	38	1	no	—
376	C₂×C₄	—	38	1	no	—
377	C₂×C₄	—	38	1	no	—
378	C₂×C₄	—	38	1	no	—
379	C₂×C₄	—	38	1	no	—
380	C₂×C₄	—	38	1	no	—
381	C₂×C₄	—	76	2	no	—
382	C₂×C₄	—	76	2	no	—
383	C₂×C₄	—	76	1	no	—
384	C₂×C₄	—	76	1	no	—
385	C₂×C₄	—	76	1	no	—
386	C₂×C₄	—	76	1	no	—
387	C₂×C₄	—	76	1	no	—
388	C₂×C₄	—	76	1	no	—
389	C₂×C₄	—	76	1	no	—
390	C₂×C₄	—	76	1	no	—
391	C₂×C₄	—	76	2	no	—
392	C₂×C₄	—	76	2	no	—
393	C₂×C₄	—	76	2	no	—
394	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
395	C₂×C₄	#10597328	1	1	yes	characteristic
396	C₂×C₄	#10597330	1	1	yes	characteristic
397	C₂×C₄	#10597339	1	1	yes	characteristic
398	C₂×C₄	#10597340	1	1	yes	characteristic
399	C₂×C₄	#10597341	1	1	yes	characteristic
400	C₂×C₄	#10597357	1	1	yes	characteristic
401	C₂×C₄	#10597358	1	1	yes	characteristic
402	C₂×C₄	#10597361	1	1	yes	characteristic
403	C₂×C₄	#10597361	1	1	yes	characteristic
404	C₂×C₄	#10597361	1	1	yes	characteristic
405	C₂×C₄	#10597362	1	1	yes	characteristic
406	C₂×C₄	#10597364	1	1	yes	characteristic
407	C₂×C₄	#10597364	1	1	yes	characteristic
408	C₈	—	4	2	no	—
409	C₈	—	8	1	no	—
410	C₈	—	76	2	no	—
411	C₈	—	152	1	no	—
412	C₂²	—	38	2	no	—
413	C₂²	—	38	2	no	—
414	C₂²	—	38	2	no	—
415	C₂²	—	76	1	no	—
416	C₂²	—	76	1	no	—
417	C₂²	—	76	1	no	—
418	C₂²	—	76	1	no	—
419	C₂²	#11926422	1	1	yes	characteristic
420	C₂²	#100×D₁₉	1	1	yes	characteristic
421	C₂²	#11926527	1	1	yes	characteristic
422	C₂²	#11926537	1	1	yes	characteristic
423	C₂²	#11926542	1	1	yes	characteristic
424	C₂²	#11926551	1	1	yes	characteristic
425	C₂²	#11926551	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	8	2	no	—
429	C₄	—	76	1	no	—
430	C₄	—	76	1	no	—
431	C₄	—	76	1	no	—
432	C₄	—	152	2	no	—
433	C₄	#11926707	1	1	yes	characteristic
434	C₄	#11926709	1	1	yes	characteristic
435	C₄	#11926789	1	1	yes	characteristic
436	C₄	#11926791	1	1	yes	characteristic
437	C₄	#11926801	1	1	yes	characteristic
438	C₄	#11926803	1	1	yes	characteristic
439	C₄	#11926887	1	1	yes	characteristic
440	C₄	#11926888	1	1	yes	characteristic
441	C₂	—	76	2	no	—
442	C₂	#14562327	1	1	yes	characteristic
443	C₂	#14562342	1	1	yes	characteristic
444	C₂	#14562359	1	1	yes	characteristic
445	C₂	#14562364	1	1	yes	characteristic
446	C₂	#14563946	1	1	yes	characteristic
447	C₂	#14564067	1	1	yes	characteristic
448	C₂	#14564097	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1296	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂³×D₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1296	D₁₉
hypocenter	C₁₉	#9136
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

Complements

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

N	H ≅ G/N	type
4. C₂×#11926292	C₂	semidirect
5. C₂×#11926292	C₂	semidirect
6. #14561518	C₂	semidirect
7. C₁₉×#1296	C₂	semidirect
194. #1296	D₁₉	semidirect
294. C₁₉	#9136	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
#14571988	2
#14563612	2
C₂×#11926292	2
#14561518	2
C₁₉×#1296	2
#9136	19