Subgroups — #18088606

Order 4864.

722 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926567	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926315	C₂	1	1	yes	maximal, characteristic
3	#14563361	C₂	1	1	yes	maximal, characteristic
4	#14563344	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926305	C₂	1	1	yes	maximal, characteristic
6	C₂×#11926303	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#2873	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₂²	1	1	yes	characteristic
9	C₂²×#64520	C₂²	1	1	yes	characteristic
10	C₂×#10597372	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
12	#11926567	—	2	2	no	—
13	#11926567	C₄	1	4	yes	complemented
14	C₂×Dic₁₉⋊C₈	—	2	2	no	—
15	#11926315	—	2	2	no	—
16	#11926308	—	2	2	no	—
17	#11926305	C₄	1	4	yes	complemented
18	#11926303	—	2	2	no	—
19	#11926303	C₄	1	2	yes	complemented
20	#11926303	C₄	1	2	yes	complemented
21	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
24	C₁₉×#405	—	2	2	no	—
25	C₁₉×#405	—	2	2	no	—
26	C₄×M₁₆×C₁₉	—	2	2	no	—
27	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂³×Dic₁₉	—	2	1	no	—
29	C₂×M₁₆×C₁₉	—	2	1	no	—
30	C₂×M₁₆×C₁₉	—	2	1	no	—
31	C₂×M₁₆×C₁₉	—	2	1	no	—
32	C₂×M₁₆×C₁₉	—	2	1	no	—
33	C₂×M₁₆×C₁₉	—	2	1	no	—
34	C₂×M₁₆×C₁₉	—	2	1	no	—
35	C₂×M₁₆×C₁₉	—	2	1	no	—
36	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
37	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
38	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
39	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
40	C₂×M₁₆×C₁₉	Q₈	1	2	yes	—
41	C₂²×C₈×C₁₉	—	2	1	no	—
42	C₂²×C₈×C₁₉	D₄	1	2	yes	—
43	C₁₉×#117	—	2	1	no	—
44	C₁₉×#117	—	2	1	no	—
45	C₁₉×#117	C₂×C₄	1	2	yes	—
46	C₁₉×#117	D₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₁₉	Q₈	1	2	yes	—
48	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₄²×C₁₉	—	2	1	no	—
50	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
51	#10597372	—	2	1	no	—
52	#10597372	—	2	1	no	—
53	#10597372	—	2	1	no	—
54	#10597372	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊Dic₁₉	—	2	1	no	—
56	C₂×C₄×Dic₁₉	—	2	1	no	—
57	C₂×C₄×Dic₁₉	—	2	1	no	—
58	C₂×C₄×Dic₁₉	—	2	1	no	—
59	C₂×C₄×Dic₁₉	—	2	1	no	—
60	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
63	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
64	C₂×#64520	—	2	1	no	—
65	C₂×#64520	—	2	1	no	—
66	C₂×#64520	—	2	1	no	—
67	C₂×#64520	—	2	1	no	—
68	C₂×#64520	—	2	1	no	—
69	C₂×#64520	—	2	1	no	—
70	C₂×#64520	—	2	1	no	—
71	C₂×#64520	—	2	1	no	—
72	C₂×#64520	—	2	1	no	—
73	C₂×#64520	—	2	1	no	—
74	C₂×#64520	C₂×C₄	1	2	yes	—
75	C₂×#64520	C₂×C₄	1	2	yes	—
76	C₂²×C₁₉⋊C₈	—	2	1	no	—
77	C₂²×C₁₉⋊C₈	—	2	1	no	—
78	C₁₉×#97	—	2	4	no	—
79	C₄×C₈×C₁₉	—	2	4	no	—
80	Dic₁₉⋊C₈	—	2	8	no	—
81	C₂⁴×C₁₉	#41	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
97	C₂²×Dic₁₉	—	2	1	no	—
98	C₂²×Dic₁₉	—	2	2	no	—
99	C₂²×Dic₁₉	—	2	2	no	—
100	C₂²×Dic₁₉	—	2	1	no	—
101	C₂²×Dic₁₉	—	4	4	no	—
102	C₂²×Dic₁₉	—	4	1	no	—
103	M₁₆×C₁₉	—	2	2	no	—
104	M₁₆×C₁₉	—	2	2	no	—
105	M₁₆×C₁₉	—	2	2	no	—
106	M₁₆×C₁₉	—	2	2	no	—
107	M₁₆×C₁₉	—	2	2	no	—
108	M₁₆×C₁₉	—	2	2	no	—
109	M₁₆×C₁₉	—	2	2	no	—
110	M₁₆×C₁₉	C₄⋊C₄	1	4	yes	—
111	C₂×C₈×C₁₉	—	2	2	no	—
112	C₂×C₈×C₁₉	—	2	2	no	—
113	C₂×C₈×C₁₉	—	2	2	no	—
114	C₂×C₈×C₁₉	—	2	2	no	—
115	C₂×C₈×C₁₉	—	2	2	no	—
116	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
117	C₄⋊C₄×C₁₉	—	2	2	no	—
118	C₄⋊C₄×C₁₉	C₄⋊C₄	1	4	yes	—
119	C₂²⋊C₄×C₁₉	—	2	2	no	—
120	C₂²⋊C₄×C₁₉	—	2	2	no	—
121	C₄²×C₁₉	—	2	2	no	—
122	C₄²×C₁₉	—	2	2	no	—
123	C₂²⋊Dic₁₉	—	2	2	no	—
124	C₂²⋊Dic₁₉	—	4	1	no	—
125	C₄⋊Dic₁₉	—	2	2	no	—
126	C₄⋊Dic₁₉	—	4	1	no	—
127	C₄×Dic₁₉	—	2	2	no	—
128	C₄×Dic₁₉	—	2	1	no	—
129	C₄×Dic₁₉	—	2	1	no	—
130	C₄×Dic₁₉	—	2	2	no	—
131	C₄×Dic₁₉	—	2	2	no	—
132	C₄×Dic₁₉	—	4	1	no	—
133	C₄×Dic₁₉	C₄²	1	2	yes	—
134	C₄×Dic₁₉	C₄²	1	2	yes	—
135	#64520	—	2	2	no	—
136	#64520	—	2	2	no	—
137	#64520	—	2	2	no	—
138	#64520	—	2	2	no	—
139	#64520	—	4	1	no	—
140	#64520	—	4	1	no	—
141	#64520	—	4	1	no	—
142	#64520	—	4	1	no	—
143	C₂×C₁₉⋊C₈	—	2	2	no	—
144	C₂×C₁₉⋊C₈	—	2	2	no	—
145	C₂×C₁₉⋊C₈	—	4	1	no	—
146	C₂×C₁₉⋊C₈	—	4	1	no	—
147	C₂×C₁₉⋊C₈	—	4	1	no	—
148	C₂×C₁₉⋊C₈	—	4	1	no	—
149	#10894	—	19	1	no	maximal, Sylow
150	C₂³×C₁₉	—	4	2	no	—
151	C₂³×C₁₉	#117	1	1	yes	characteristic
152	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
153	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
154	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
155	C₂³×C₁₉	#123	1	1	yes	characteristic
156	C₂³×C₁₉	#125	1	1	yes	characteristic
157	C₂³×C₁₉	#126	1	1	yes	characteristic
158	C₂×C₄×C₁₉	—	2	4	no	—
159	C₂×C₄×C₁₉	—	8	2	no	—
160	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
161	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
165	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
180	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
182	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
185	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
188	C₂×Dic₁₉	—	2	4	no	—
189	C₂×Dic₁₉	—	2	2	no	—
190	C₂×Dic₁₉	—	2	2	no	—
191	C₂×Dic₁₉	—	4	4	no	—
192	C₂×Dic₁₉	—	4	4	no	—
193	C₂×Dic₁₉	—	4	2	no	—
194	C₂×Dic₁₉	—	4	2	no	—
195	C₂×Dic₁₉	—	8	2	no	—
196	C₈×C₁₉	—	2	4	no	—
197	C₈×C₁₉	—	2	4	no	—
198	C₁₉⋊C₈	—	4	2	no	—
199	C₁₉⋊C₈	—	4	2	no	—
200	C₂×#423	—	19	1	no	—
201	#2873	D₁₉	1	1	yes	characteristic
202	C₂×#344	—	19	1	no	—
203	#1738	—	19	1	no	—
204	#1733	—	19	1	no	—
205	C₂×#339	—	19	1	no	—
206	C₂×#339	—	19	1	no	—
207	C₂²×C₁₉	—	2	2	no	—
208	C₂²×C₁₉	—	2	2	no	—
209	C₂²×C₁₉	—	2	2	no	—
210	C₂²×C₁₉	—	4	1	no	—
211	C₂²×C₁₉	—	4	1	no	—
212	C₂²×C₁₉	—	4	1	no	—
213	C₂²×C₁₉	—	4	1	no	—
214	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
215	C₂²×C₁₉	#385	1	1	yes	characteristic
216	C₂²×C₁₉	#387	1	1	yes	characteristic
217	C₂²×C₁₉	#387	1	1	yes	characteristic
218	C₂²×C₁₉	#387	1	1	yes	characteristic
219	C₂²×C₁₉	#388	1	1	yes	characteristic
220	C₂²×C₁₉	#389	1	1	yes	characteristic
221	C₄×C₁₉	—	4	4	no	—
222	C₄×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
223	C₄×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
224	C₄×C₁₉	#385	1	1	yes	characteristic
225	C₄×C₁₉	#386	1	1	yes	characteristic
226	C₄×C₁₉	#387	1	1	yes	characteristic
227	C₄×C₁₉	#388	1	1	yes	characteristic
228	C₄×C₁₉	#389	1	1	yes	characteristic
229	C₄×C₁₉	#391	1	1	yes	characteristic
230	Dic₁₉	—	2	4	no	—
231	Dic₁₉	—	4	2	no	—
232	Dic₁₉	—	8	2	no	—
233	C₂²×M₁₆	—	19	1	no	—
234	C₂²×M₁₆	—	19	1	no	—
235	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
236	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
237	C₂×#117	—	19	1	no	—
238	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
239	C₂²×C₄²	—	19	1	no	—
240	#423	—	19	4	no	—
241	#423	—	38	2	no	—
242	C₂×C₄⋊C₈	—	38	2	no	—
243	#405	—	2	2	no	—
244	#405	—	2	2	no	—
245	C₄×M₁₆	—	2	2	no	—
246	#344	—	38	2	no	—
247	#341	—	38	2	no	—
248	#339	—	19	4	no	—
249	#339	—	19	2	no	—
250	#339	—	19	2	no	—
251	#339	—	38	2	no	—
252	C₂×C₁₉	—	2	1	no	—
253	C₂×C₁₉	—	2	1	no	—
254	C₂×C₁₉	—	2	1	no	—
255	C₂×C₁₉	—	2	1	no	—
256	C₂×C₁₉	—	2	1	no	—
257	C₂×C₁₉	—	2	1	no	—
258	C₂×C₁₉	#1436	1	1	yes	characteristic
259	C₂×C₁₉	#1861	1	2	yes	—
260	C₂³×C₄	—	38	1	no	—
261	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
262	C₂×M₁₆	—	2	1	no	—
263	C₂×M₁₆	—	2	1	no	—
264	C₂×M₁₆	—	2	1	no	—
265	C₂×M₁₆	—	2	1	no	—
266	C₂×M₁₆	—	2	1	no	—
267	C₂×M₁₆	—	2	1	no	—
268	C₂×M₁₆	—	2	1	no	—
269	C₂×M₁₆	—	19	2	no	—
270	C₂×M₁₆	—	19	2	no	—
271	C₂×M₁₆	—	38	1	no	—
272	C₂×M₁₆	—	38	1	no	—
273	C₂×M₁₆	—	38	1	no	—
274	C₂×M₁₆	—	38	1	no	—
275	C₂×M₁₆	—	38	1	no	—
276	C₂×M₁₆	—	38	1	no	—
277	C₂×M₁₆	—	38	1	no	—
278	C₂×M₁₆	—	38	1	no	—
279	C₂×M₁₆	—	38	1	no	—
280	C₂×M₁₆	—	38	1	no	—
281	C₂×M₁₆	Dic₃₈	1	2	yes	—
282	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
283	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
284	C₂×M₁₆	D₇₆	1	2	yes	—
285	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
286	C₂²×C₈	—	2	1	no	—
287	C₂²×C₈	—	38	1	no	—
288	C₂²×C₈	—	38	1	no	—
289	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
290	#117	—	2	1	no	—
291	#117	—	2	1	no	—
292	#117	—	19	2	no	—
293	#117	—	38	1	no	—
294	#117	—	38	1	no	—
295	#117	—	38	1	no	—
296	#117	C₄×D₁₉	1	2	yes	—
297	#117	C₂²⋊D₁₉	1	2	yes	—
298	C₂×C₄⋊C₄	—	38	1	no	—
299	C₂×C₄⋊C₄	Dic₃₈	1	2	yes	—
300	C₂×C₂²⋊C₄	—	2	1	no	—
301	C₂×C₂²⋊C₄	—	38	1	no	—
302	C₂×C₄²	—	2	1	no	—
303	C₂×C₄²	—	19	1	no	—
304	C₂×C₄²	—	19	1	no	—
305	C₂×C₄²	—	19	2	no	—
306	C₂×C₄²	—	19	2	no	—
307	C₂×C₄²	—	38	1	no	—
308	C₂×C₄²	—	38	1	no	—
309	C₂×C₄²	—	38	1	no	—
310	C₂×C₄²	—	38	1	no	—
311	C₄⋊C₈	—	38	8	no	—
312	#97	—	2	4	no	—
313	C₄×C₈	—	2	4	no	—
314	C₁₉	#10894	1	1	yes	characteristic, complemented, Sylow
315	C₂⁴	#64541	1	1	yes	characteristic
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	38	1	no	—
318	C₂²×C₄	—	38	2	no	—
319	C₂²×C₄	—	38	2	no	—
320	C₂²×C₄	—	38	1	no	—
321	C₂²×C₄	—	76	4	no	—
322	C₂²×C₄	—	76	1	no	—
323	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
324	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
325	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
326	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
327	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
329	C₂²×C₄	#64541	1	1	yes	characteristic
330	C₂²×C₄	#64541	1	1	yes	characteristic
331	C₂²×C₄	#64541	1	1	yes	characteristic
332	C₂²×C₄	#64541	1	1	yes	characteristic
333	C₂²×C₄	#64541	1	1	yes	characteristic
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	M₁₆	—	2	2	no	—
338	M₁₆	—	2	2	no	—
339	M₁₆	—	2	2	no	—
340	M₁₆	—	2	2	no	—
341	M₁₆	—	2	2	no	—
342	M₁₆	—	2	2	no	—
343	M₁₆	—	2	2	no	—
344	M₁₆	—	38	2	no	—
345	M₁₆	—	38	2	no	—
346	M₁₆	—	38	2	no	—
347	M₁₆	—	38	2	no	—
348	M₁₆	—	76	1	no	—
349	M₁₆	—	76	1	no	—
350	M₁₆	—	76	1	no	—
351	M₁₆	—	76	1	no	—
352	M₁₆	Dic₁₉⋊C₄	1	4	yes	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	38	2	no	—
359	C₂×C₈	—	38	2	no	—
360	C₂×C₈	—	76	1	no	—
361	C₂×C₈	—	76	1	no	—
362	C₂×C₈	—	76	1	no	—
363	C₂×C₈	—	76	1	no	—
364	C₂×C₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	38	2	no	—
367	C₄⋊C₄	—	76	1	no	—
368	C₄⋊C₄	Dic₁₉⋊C₄	1	4	yes	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	38	2	no	—
372	C₂²⋊C₄	—	76	1	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	19	2	no	—
376	C₄²	—	19	2	no	—
377	C₄²	—	38	1	no	—
378	C₄²	—	38	1	no	—
379	C₄²	—	38	2	no	—
380	C₄²	—	38	2	no	—
381	C₄²	—	38	2	no	—
382	C₄²	—	76	1	no	—
383	C₂³	—	4	2	no	—
384	C₂³	#10597316	1	1	yes	characteristic
385	C₂³	#10597318	1	1	yes	characteristic
386	C₂³	C₄×D₇₆	1	1	yes	characteristic
387	C₂³	#10597322	1	1	yes	characteristic
388	C₂³	#10597370	1	1	yes	characteristic
389	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
390	C₂³	#10597375	1	1	yes	characteristic
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	8	2	no	—
393	C₂×C₄	—	38	4	no	—
394	C₂×C₄	—	38	2	no	—
395	C₂×C₄	—	38	2	no	—
396	C₂×C₄	—	76	4	no	—
397	C₂×C₄	—	76	4	no	—
398	C₂×C₄	—	76	2	no	—
399	C₂×C₄	—	76	2	no	—
400	C₂×C₄	—	152	2	no	—
401	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
402	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
403	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
404	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
405	C₂×C₄	#10597315	1	1	yes	characteristic
406	C₂×C₄	#10597316	1	1	yes	characteristic
407	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
408	C₂×C₄	#10597318	1	1	yes	characteristic
409	C₂×C₄	#10597318	1	1	yes	characteristic
410	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
411	C₂×C₄	#10597321	1	1	yes	characteristic
412	C₂×C₄	#10597322	1	1	yes	characteristic
413	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
414	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
415	C₂×C₄	#10597370	1	1	yes	characteristic
416	C₂×C₄	#10597370	1	1	yes	characteristic
417	C₂×C₄	#10597370	1	1	yes	characteristic
418	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
419	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
420	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
421	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
422	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
423	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
424	C₂×C₄	#10597375	1	1	yes	characteristic
425	C₂×C₄	#10597375	1	1	yes	characteristic
426	C₂×C₄	#10597376	1	1	yes	characteristic
427	C₂×C₄	#10597376	1	1	yes	characteristic
428	C₂×C₄	#10597399	1	1	yes	characteristic
429	C₈	—	2	4	no	—
430	C₈	—	2	4	no	—
431	C₈	—	76	2	no	—
432	C₈	—	76	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	C₄×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
441	C₂²	#11926417	1	1	yes	characteristic
442	C₂²	#11926428	1	1	yes	characteristic
443	C₂²	#11926428	1	1	yes	characteristic
444	C₂²	#11926428	1	1	yes	characteristic
445	C₂²	#11926435	1	1	yes	characteristic
446	C₂²	#11926442	1	1	yes	characteristic
447	C₄	—	4	4	no	—
448	C₄	—	38	4	no	—
449	C₄	—	76	2	no	—
450	C₄	—	152	2	no	—
451	C₄	C₄×Dic₁₉⋊C₄	1	1	yes	characteristic
452	C₄	C₄×Dic₁₉⋊C₄	1	1	yes	characteristic
453	C₄	#11926417	1	1	yes	characteristic
454	C₄	#11926423	1	1	yes	characteristic
455	C₄	#11926428	1	1	yes	characteristic
456	C₄	#11926435	1	1	yes	characteristic
457	C₄	#11926442	1	1	yes	characteristic
458	C₄	#11926450	1	1	yes	characteristic
459	C₂	—	2	1	no	—
460	C₂	—	2	1	no	—
461	C₂	—	2	1	no	—
462	C₂	—	2	1	no	—
463	C₂	—	2	1	no	—
464	C₂	—	2	1	no	—
465	C₂	#14561868	1	1	yes	characteristic
466	C₂	#14563875	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#10597399
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#2873	C₂
socle	C₂²×C₁₉	#385
prime radical	C₂⁴×C₁₉	#41
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#2873	D₁₉
hypocenter	C₁₉	#10894
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #2873

Complements

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

N	H ≅ G/N	type
13. #11926567	C₄	semidirect
17. #11926305	C₄	semidirect
19. #11926303	C₄	semidirect
20. #11926303	C₄	semidirect
314. C₁₉	#10894	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926567	2
C₂×#11926315	2
#14563361	2
#14563344	2
C₂×#11926305	2
C₂×#11926303	2
C₁₉×#2873	2
#10894	19