Subgroups — #18087999

Order 4864.

1164 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11927311	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926518	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926315	C₂	1	2	yes	maximal, complemented
4	#14563373	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#413	C₂	1	1	yes	maximal, characteristic
6	#11927311	—	2	4	no	—
7	#11927311	—	2	4	no	—
8	C₂×#10597394	—	2	2	no	—
9	C₂×#10597394	—	2	2	no	—
10	C₂²×#64520	C₄	1	4	yes	complemented
11	C₂²×#64520	C₂²	1	1	yes	characteristic
12	C₂²×#64520	C₂²	1	1	yes	characteristic
13	C₂×#10597372	C₂²	1	2	yes	—
14	#11926518	—	2	2	no	—
15	#11926518	—	2	2	no	—
16	C₂×#10597291	C₄	1	4	yes	—
17	#11926315	—	2	4	no	—
18	#11926312	—	2	4	no	—
19	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
21	C₁₉×#413	—	2	2	no	—
22	C₁₉×#413	—	2	2	no	—
23	C₂×C₁₉×#101	C₄	1	2	yes	complemented
24	C₂×C₁₉×#100	C₄	1	2	yes	complemented
25	C₂×#41×C₁₉	—	2	2	no	—
26	C₂×#41×C₁₉	—	2	2	no	—
27	C₂×#41×C₁₉	—	2	2	no	—
28	C₂×#41×C₁₉	—	2	2	no	—
29	C₂×#41×C₁₉	D₄	1	2	yes	—
30	C₂×#41×C₁₉	D₄	1	2	yes	—
31	C₂×#41×C₁₉	D₄	1	2	yes	—
32	C₂×#41×C₁₉	Q₈	1	2	yes	—
33	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
35	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
37	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
38	C₂×M₁₆×C₁₉	—	2	2	no	—
39	C₂×M₁₆×C₁₉	—	2	2	no	—
40	C₂×M₁₆×C₁₉	—	2	2	no	—
41	C₂×M₁₆×C₁₉	—	2	2	no	—
42	C₂×M₁₆×C₁₉	—	2	2	no	—
43	C₂×M₁₆×C₁₉	C₂×C₄	1	4	yes	—
44	C₂²×C₈×C₁₉	—	2	2	no	—
45	C₂×C₂²⋊Dic₁₉	C₂×C₄	1	4	yes	—
46	#10597394	—	2	16	no	—
47	#10597394	—	2	16	no	—
48	#10597372	—	2	2	no	—
49	#10597372	—	2	2	no	—
50	#10597372	—	2	2	no	—
51	#10597372	—	2	2	no	—
52	C₂×C₄⋊Dic₁₉	—	2	2	no	—
53	C₂×C₄×Dic₁₉	—	2	2	no	—
54	C₂×#64520	—	2	4	no	—
55	C₂×#64520	—	2	1	no	—
56	C₂×#64520	—	2	1	no	—
57	C₂×#64520	—	2	2	no	—
58	C₂×#64520	—	2	2	no	—
59	C₂×#64520	—	2	8	no	—
60	C₂×#64520	—	2	8	no	—
61	C₂×#64520	C₂×C₄	1	2	yes	—
62	C₂×#64520	C₂×C₄	1	2	yes	—
63	C₂×#64520	D₄	1	4	yes	—
64	C₂×#64520	D₄	1	4	yes	—
65	C₂²×C₁₉⋊C₈	—	2	4	no	—
66	C₂²×C₁₉⋊C₈	—	2	1	no	—
67	C₂²×C₁₉⋊C₈	—	2	1	no	—
68	C₁₉×#101	—	2	4	no	—
69	C₁₉×#100	—	2	4	no	—
70	#10597291	—	2	8	no	—
71	C₂⁴×C₁₉	C₄²	1	2	yes	—
72	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
73	#41×C₁₉	—	2	4	no	—
74	#41×C₁₉	—	2	4	no	—
75	#41×C₁₉	—	2	4	no	—
76	#41×C₁₉	—	2	4	no	—
77	#41×C₁₉	—	2	4	no	—
78	#41×C₁₉	—	2	4	no	—
79	#41×C₁₉	—	2	4	no	—
80	#41×C₁₉	—	2	4	no	—
81	C₂×Q₈×C₁₉	—	2	2	no	—
82	C₂×Q₈×C₁₉	—	2	2	no	—
83	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
84	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
85	C₂×D₄×C₁₉	—	2	4	no	—
86	C₂×D₄×C₁₉	—	2	4	no	—
87	C₂×D₄×C₁₉	—	2	2	no	—
88	C₂×D₄×C₁₉	—	2	2	no	—
89	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
90	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
91	C₂×D₄×C₁₉	C₄⋊C₄	1	4	yes	—
92	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	C₄²	1	2	yes	—
98	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
99	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
100	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	#41	1	2	yes	—
109	C₂²×C₄×C₁₉	#41	1	2	yes	—
110	C₂²×Dic₁₉	—	2	4	no	—
111	M₁₆×C₁₉	—	2	4	no	—
112	M₁₆×C₁₉	—	2	4	no	—
113	M₁₆×C₁₉	—	4	2	no	—
114	M₁₆×C₁₉	—	4	2	no	—
115	C₂×C₈×C₁₉	—	2	4	no	—
116	C₂×C₈×C₁₉	—	4	2	no	—
117	C₂×C₈×C₁₉	—	4	2	no	—
118	C₂²⋊Dic₁₉	—	2	4	no	—
119	C₂²⋊Dic₁₉	—	2	4	no	—
120	C₄⋊Dic₁₉	—	4	2	no	—
121	C₄⋊Dic₁₉	—	4	2	no	—
122	C₄×Dic₁₉	—	4	2	no	—
123	C₄×Dic₁₉	—	4	2	no	—
124	#64520	—	2	16	no	—
125	#64520	—	2	2	no	—
126	#64520	—	2	2	no	—
127	#64520	—	2	4	no	—
128	#64520	—	2	4	no	—
129	#64520	C₂²⋊C₄	1	4	yes	—
130	#64520	C₂²⋊C₄	1	4	yes	—
131	C₂×C₁₉⋊C₈	—	2	16	no	—
132	C₂×C₁₉⋊C₈	—	2	2	no	—
133	C₂×C₁₉⋊C₈	—	2	2	no	—
134	C₂×C₁₉⋊C₈	—	2	4	no	—
135	C₂×C₁₉⋊C₈	—	2	4	no	—
136	#10771	—	19	1	no	maximal, Sylow
137	C₂³×C₁₉	—	2	2	no	—
138	C₂³×C₁₉	—	2	2	no	—
139	C₂³×C₁₉	—	8	1	no	—
140	C₂³×C₁₉	—	8	2	no	—
141	C₂³×C₁₉	#95	1	4	yes	—
142	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
143	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
144	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂³×C₁₉	C₄×D₄	1	2	yes	—
146	C₂³×C₁₉	C₄×D₄	1	2	yes	—
147	Q₈×C₁₉	—	2	4	no	—
148	Q₈×C₁₉	—	2	4	no	—
149	D₄×C₁₉	—	2	8	no	—
150	D₄×C₁₉	—	2	8	no	—
151	D₄×C₁₉	—	2	4	no	—
152	D₄×C₁₉	—	2	4	no	—
153	C₂×C₄×C₁₉	—	2	2	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	2	4	no	—
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	2	4	no	—
158	C₂×C₄×C₁₉	—	2	4	no	—
159	C₂×C₄×C₁₉	#95	1	4	yes	—
160	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
169	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
170	C₂×C₄×C₁₉	#120	1	2	yes	—
171	C₂×C₄×C₁₉	#120	1	2	yes	—
172	C₂×C₄×C₁₉	#121	1	2	yes	—
173	C₂×C₄×C₁₉	#121	1	2	yes	—
174	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
175	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
176	C₂×C₄×C₁₉	#123	1	2	yes	—
177	C₂×C₄×C₁₉	#123	1	2	yes	—
178	C₂×Dic₁₉	—	4	4	no	—
179	C₂×Dic₁₉	—	8	4	no	—
180	C₈×C₁₉	—	4	4	no	—
181	C₁₉⋊C₈	—	2	4	no	—
182	C₁₉⋊C₈	—	2	4	no	—
183	C₂×#568	—	19	1	no	—
184	C₂×#413	D₁₉	1	1	yes	characteristic
185	C₂×#410	—	19	1	no	—
186	C₂×#344	—	19	2	no	—
187	#1742	—	19	2	no	—
188	C₂²×C₁₉	—	2	4	no	—
189	C₂²×C₁₉	—	4	2	no	—
190	C₂²×C₁₉	—	4	1	no	—
191	C₂²×C₁₉	—	4	1	no	—
192	C₂²×C₁₉	—	4	1	no	—
193	C₂²×C₁₉	—	4	2	no	—
194	C₂²×C₁₉	—	4	4	no	—
195	C₂²×C₁₉	—	8	2	no	—
196	C₂²×C₁₉	—	8	2	no	—
197	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
198	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
199	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
200	C₂²×C₁₉	#385	1	2	yes	—
201	C₂²×C₁₉	#386	1	2	yes	—
202	C₄×C₁₉	—	2	4	no	—
203	C₄×C₁₉	#379	1	1	yes	characteristic
204	C₄×C₁₉	#380	1	1	yes	characteristic
205	C₄×C₁₉	#380	1	1	yes	characteristic
206	C₄×C₁₉	#381	1	1	yes	characteristic
207	C₄×C₁₉	#385	1	2	yes	—
208	C₄×C₁₉	#386	1	2	yes	—
209	Dic₁₉	—	8	4	no	—
210	C₂²×#41	C₂×D₁₉	1	1	yes	characteristic
211	#568	—	38	4	no	—
212	#568	—	38	4	no	—
213	C₂×#131	—	38	2	no	—
214	C₂×#131	—	38	2	no	—
215	C₂²×M₁₆	—	19	1	no	—
216	C₂²×M₁₆	—	19	1	no	—
217	C₂²×M₁₆	—	19	4	no	—
218	C₂²×M₁₆	C₂×D₁₉	1	2	yes	—
219	C₂×#117	—	19	2	no	—
220	#413	—	2	2	no	—
221	#413	—	2	2	no	—
222	C₂×#101	Dic₁₉	1	2	yes	complemented
223	C₂×#100	Dic₁₉	1	2	yes	complemented
224	#410	—	38	2	no	—
225	#410	—	38	2	no	—
226	C₂×#99	—	19	4	no	—
227	#344	—	38	4	no	—
228	#343	—	38	4	no	—
229	C₂×C₁₉	—	2	2	no	—
230	C₂×C₁₉	—	2	1	no	—
231	C₂×C₁₉	—	2	1	no	—
232	C₂×C₁₉	—	2	1	no	—
233	C₂×C₁₉	—	2	2	no	—
234	C₂×C₁₉	—	4	4	no	—
235	C₂×C₁₉	C₂²⋊#95	1	1	yes	characteristic
236	C₂×#41	—	2	2	no	—
237	C₂×#41	—	2	2	no	—
238	C₂×#41	—	2	2	no	—
239	C₂×#41	—	2	2	no	—
240	C₂×#41	Dic₃₈	1	2	yes	—
241	C₂×#41	D₇₆	1	2	yes	—
242	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
243	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
244	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
245	C₂²×D₄	C₄×D₁₉	1	2	yes	—
246	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
247	C₂³×C₄	C₄×D₁₉	1	2	yes	—
248	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
249	#131	—	38	16	no	—
250	#131	—	38	16	no	—
251	C₂×M₁₆	—	2	2	no	—
252	C₂×M₁₆	—	2	2	no	—
253	C₂×M₁₆	—	2	2	no	—
254	C₂×M₁₆	—	2	2	no	—
255	C₂×M₁₆	—	2	2	no	—
256	C₂×M₁₆	—	19	2	no	—
257	C₂×M₁₆	—	19	2	no	—
258	C₂×M₁₆	—	19	4	no	—
259	C₂×M₁₆	—	19	4	no	—
260	C₂×M₁₆	—	38	8	no	—
261	C₂×M₁₆	—	38	8	no	—
262	C₂×M₁₆	—	38	4	no	—
263	C₂×M₁₆	—	38	1	no	—
264	C₂×M₁₆	—	38	2	no	—
265	C₂×M₁₆	—	38	2	no	—
266	C₂×M₁₆	—	38	1	no	—
267	C₂×M₁₆	C₂×Dic₁₉	1	4	yes	—
268	C₂²×C₈	—	2	2	no	—
269	C₂²×C₈	—	38	4	no	—
270	C₂²×C₈	—	38	1	no	—
271	C₂²×C₈	—	38	1	no	—
272	#117	—	38	2	no	—
273	#117	—	38	2	no	—
274	#117	—	38	2	no	—
275	#117	—	38	2	no	—
276	C₂×C₄⋊C₄	—	38	2	no	—
277	C₂×C₂²⋊C₄	—	19	4	no	—
278	C₂×C₄²	—	38	2	no	—
279	#101	—	2	4	no	—
280	#100	—	2	4	no	—
281	#99	—	38	8	no	—
282	C₁₉	#10771	1	1	yes	characteristic, complemented, Sylow
283	C₂⁴	C₄×Dic₁₉	1	2	yes	—
284	C₂⁴	C₂×C₄×D₁₉	1	1	yes	characteristic
285	#41	—	2	4	no	—
286	#41	—	2	4	no	—
287	#41	—	2	4	no	—
288	#41	—	2	4	no	—
289	#41	—	2	4	no	—
290	#41	—	2	4	no	—
291	#41	—	2	4	no	—
292	#41	—	2	4	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	C₄⋊Dic₁₉	1	2	yes	—
296	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	Dic₁₉⋊C₄	1	4	yes	—
302	C₂×D₄	C₄⋊Dic₁₉	1	2	yes	—
303	C₂×D₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
304	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	38	4	no	—
310	C₂²×C₄	C₄×Dic₁₉	1	2	yes	—
311	C₂²×C₄	Dic₁₉⋊C₄	1	4	yes	—
312	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
313	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
316	C₂²×C₄	D₄×D₁₉	1	2	yes	—
317	C₂²×C₄	D₄×D₁₉	1	2	yes	—
318	C₂²×C₄	#64543	1	2	yes	—
319	C₂²×C₄	#64543	1	2	yes	—
320	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
321	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
322	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
323	M₁₆	—	2	4	no	—
324	M₁₆	—	2	4	no	—
325	M₁₆	—	4	2	no	—
326	M₁₆	—	4	2	no	—
327	M₁₆	—	19	4	no	—
328	M₁₆	—	19	4	no	—
329	M₁₆	—	38	16	no	—
330	M₁₆	—	38	4	no	—
331	M₁₆	—	38	2	no	—
332	M₁₆	—	38	2	no	—
333	M₁₆	—	38	4	no	—
334	C₂×C₈	—	2	4	no	—
335	C₂×C₈	—	4	2	no	—
336	C₂×C₈	—	4	2	no	—
337	C₂×C₈	—	38	16	no	—
338	C₂×C₈	—	38	4	no	—
339	C₂×C₈	—	38	4	no	—
340	C₂×C₈	—	38	2	no	—
341	C₂×C₈	—	38	2	no	—
342	C₄⋊C₄	—	76	2	no	—
343	C₄⋊C₄	—	76	2	no	—
344	C₂²⋊C₄	—	38	4	no	—
345	C₂²⋊C₄	—	38	4	no	—
346	C₄²	—	76	2	no	—
347	C₄²	—	76	2	no	—
348	C₂³	—	2	2	no	—
349	C₂³	—	2	2	no	—
350	C₂³	—	8	1	no	—
351	C₂³	—	8	2	no	—
352	C₂³	C₁₉⋊#95	1	4	yes	—
353	C₂³	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
354	C₂³	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
355	C₂³	C₂×C₄×Dic₁₉	1	1	yes	characteristic
356	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
357	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
358	Q₈	—	2	4	no	—
359	Q₈	—	2	4	no	—
360	D₄	—	2	8	no	—
361	D₄	—	2	8	no	—
362	D₄	—	2	4	no	—
363	D₄	—	2	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	76	4	no	—
371	C₂×C₄	—	152	4	no	—
372	C₂×C₄	C₁₉⋊#95	1	4	yes	—
373	C₂×C₄	#10597323	1	1	yes	characteristic
374	C₂×C₄	#10597323	1	1	yes	characteristic
375	C₂×C₄	#10597324	1	2	yes	—
376	C₂×C₄	#10597324	1	2	yes	—
377	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
378	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
379	C₂×C₄	#10597328	1	2	yes	—
380	C₂×C₄	#10597332	1	2	yes	—
381	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
382	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
383	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
384	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
385	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
386	C₂×C₄	#10597381	1	2	yes	—
387	C₂×C₄	#10597383	1	2	yes	—
388	C₂×C₄	#10597385	1	2	yes	—
389	C₂×C₄	#10597385	1	2	yes	—
390	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
391	C₈	—	4	4	no	—
392	C₈	—	38	4	no	—
393	C₈	—	38	4	no	—
394	C₂²	—	2	4	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	4	no	—
401	C₂²	—	8	2	no	—
402	C₂²	—	8	2	no	—
403	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
404	C₂²	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
405	C₂²	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
406	C₂²	#11926416	1	2	yes	—
407	C₂²	#11926421	1	2	yes	—
408	C₄	—	2	4	no	—
409	C₄	—	152	4	no	—
410	C₄	#11926399	1	1	yes	characteristic
411	C₄	#11926402	1	1	yes	characteristic
412	C₄	#11926402	1	1	yes	characteristic
413	C₄	#11926405	1	1	yes	characteristic
414	C₄	#11926419	1	2	yes	—
415	C₄	#11926424	1	2	yes	—
416	C₂	—	2	2	no	—
417	C₂	—	2	1	no	—
418	C₂	—	2	1	no	—
419	C₂	—	2	1	no	—
420	C₂	—	2	2	no	—
421	C₂	—	4	4	no	—
422	C₂	#14561857	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11926405
commutator	C₂³×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#413	C₂
socle	C₂×C₁₉	C₂²⋊#95
prime radical	C₂²×#41×C₁₉	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#413	D₁₉
hypocenter	C₁₉	#10771
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ C₂×#413

Complements

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

N	H ≅ G/N	type
3. C₂×#11926315	C₂	semidirect
4. #14563373	C₂	semidirect
10. C₂²×#64520	C₄	semidirect
23. C₂×C₁₉×#101	C₄	semidirect
24. C₂×C₁₉×#100	C₄	semidirect
222. C₂×#101	Dic₁₉	semidirect
223. C₂×#100	Dic₁₉	semidirect
282. C₁₉	#10771	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11927311	2
C₂×#11926518	2
C₂×#11926315	2
#14563373	2
C₂×C₁₉×#413	2
#10771	19