Subgroups — #18074761

Order 4864.

754 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14564625	C₂	1	1	yes	maximal, characteristic, complemented
2	#14564480	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562370	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562227	C₂	1	1	yes	maximal, characteristic, complemented
5	#14562074	C₂	1	1	yes	maximal, characteristic, complemented
6	#14562074	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3511	C₂	1	1	yes	maximal, characteristic
8	#11926568	C₂²	1	1	yes	characteristic
9	#11926568	C₂²	1	1	yes	characteristic
10	C₂×#10597293	—	2	2	no	—
11	C₄×#64520	C₂²	1	1	yes	characteristic
12	C₄×#64520	C₂²	1	1	yes	characteristic
13	#11926313	—	2	2	no	—
14	#11926293	—	2	1	no	—
15	#11926288	—	2	1	no	—
16	#11926284	—	2	2	no	—
17	Q₈⋊(C₁₉⋊C₈)	—	2	1	no	—
18	Q₈⋊(C₁₉⋊C₈)	—	2	1	no	—
19	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
20	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
21	C₁₉×#556	—	2	1	no	—
22	C₁₉×#555	—	2	1	no	—
23	C₁₉×#554	—	2	1	no	—
24	C₁₉×#553	—	2	2	no	—
25	C₁₉×#548	—	2	2	no	—
26	C₁₉×#547	—	2	1	no	—
27	C₁₉×#542	—	2	2	no	—
28	C₁₉×#537	C₄	1	2	yes	—
29	C₁₉×#533	—	2	1	no	—
30	C₁₉×#532	—	2	1	no	—
31	C₁₉×#532	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
33	C₁₉×#520	C₄	1	2	yes	—
34	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
35	C₂×#41×C₁₉	—	2	2	no	—
36	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
38	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
39	C₁₉×C₄⋊Q₈	—	2	1	no	—
40	C₁₉×C₄⋊Q₈	—	2	1	no	—
41	C₁₉×C₄⋊Q₈	—	2	1	no	—
42	C₁₉×C₄⋊Q₈	—	2	1	no	—
43	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
44	C₁₉×#127	D₄	1	1	yes	characteristic
45	C₁₉×#126	—	2	4	no	—
46	C₁₉×#125	—	2	2	no	—
47	C₁₉×#124	—	2	2	no	—
48	C₁₉×#124	—	2	4	no	—
49	C₁₉×#124	D₄	1	2	yes	—
50	C₁₉×#123	—	2	4	no	—
51	C₁₉×C₂²⋊Q₈	—	2	2	no	—
52	C₁₉×C₂²⋊Q₈	—	2	4	no	—
53	C₁₉×C₂²⋊Q₈	—	2	2	no	—
54	C₁₉×C₂²⋊Q₈	—	2	2	no	—
55	C₁₉×#121	—	2	2	no	—
56	C₁₉×#121	—	2	2	no	—
57	C₁₉×#121	—	2	2	no	—
58	C₁₉×#121	—	2	4	no	—
59	C₁₉×#121	—	2	1	no	—
60	C₁₉×#121	—	2	1	no	—
61	C₄×Q₈×C₁₉	—	2	2	no	—
62	C₄×Q₈×C₁₉	—	2	2	no	—
63	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
64	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
65	C₄×D₄×C₁₉	—	2	2	no	—
66	C₄×D₄×C₁₉	—	2	2	no	—
67	C₄×D₄×C₁₉	—	2	4	no	—
68	C₄×D₄×C₁₉	—	2	1	no	—
69	C₄×D₄×C₁₉	—	2	1	no	—
70	C₄×D₄×C₁₉	—	2	1	no	—
71	C₄×D₄×C₁₉	—	2	1	no	—
72	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
73	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
74	C₁₉×#117	—	2	2	no	—
75	C₁₉×#117	—	2	2	no	—
76	C₁₉×#117	—	2	1	no	—
77	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
79	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
80	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
81	C₂×C₄²×C₁₉	—	2	1	no	—
82	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
83	C₂×#64520	—	2	1	no	—
84	C₂×#64520	—	2	1	no	—
85	C₂×#64520	—	2	1	no	—
86	C₂×#64520	—	2	1	no	—
87	#10597293	—	4	4	no	—
88	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
89	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
90	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
91	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
92	#10597260	—	2	1	no	—
93	#10597260	—	2	1	no	—
94	C₄×C₁₉⋊C₈	—	2	1	no	—
95	C₄×C₁₉⋊C₈	—	2	1	no	—
96	#41×C₁₉	—	4	2	no	—
97	#41×C₁₉	—	4	4	no	—
98	#41×C₁₉	—	8	2	no	—
99	#41×C₁₉	—	8	2	no	—
100	C₂×Q₈×C₁₉	—	2	2	no	—
101	C₂×Q₈×C₁₉	—	2	2	no	—
102	C₂×Q₈×C₁₉	—	4	2	no	—
103	C₂×Q₈×C₁₉	—	4	2	no	—
104	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
105	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
106	C₂×D₄×C₁₉	—	2	2	no	—
107	C₂×D₄×C₁₉	—	2	1	no	—
108	C₂×D₄×C₁₉	—	2	4	no	—
109	C₂×D₄×C₁₉	—	2	1	no	—
110	C₂×D₄×C₁₉	—	2	1	no	—
111	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
112	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
113	C₂²×C₄×C₁₉	—	2	4	no	—
114	C₂²×C₄×C₁₉	—	2	1	no	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	2	1	no	—
117	C₂²×C₄×C₁₉	—	2	1	no	—
118	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
119	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₄⋊C₄×C₁₉	—	2	4	no	—
123	C₄⋊C₄×C₁₉	—	2	4	no	—
124	C₄⋊C₄×C₁₉	—	2	2	no	—
125	C₄⋊C₄×C₁₉	—	2	2	no	—
126	C₄⋊C₄×C₁₉	—	2	2	no	—
127	C₄⋊C₄×C₁₉	—	2	2	no	—
128	C₄⋊C₄×C₁₉	—	2	1	no	—
129	C₄⋊C₄×C₁₉	—	2	1	no	—
130	C₄⋊C₄×C₁₉	—	2	1	no	—
131	C₄⋊C₄×C₁₉	—	2	1	no	—
132	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
133	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
134	C₂²⋊C₄×C₁₉	—	2	4	no	—
135	C₂²⋊C₄×C₁₉	—	2	4	no	—
136	C₂²⋊C₄×C₁₉	—	2	4	no	—
137	C₂²⋊C₄×C₁₉	—	2	1	no	—
138	C₂²⋊C₄×C₁₉	—	2	1	no	—
139	C₂²⋊C₄×C₁₉	—	2	1	no	—
140	C₂²⋊C₄×C₁₉	—	2	2	no	—
141	C₂²⋊C₄×C₁₉	—	2	2	no	—
142	C₄²×C₁₉	—	2	4	no	—
143	C₄²×C₁₉	—	2	1	no	—
144	C₄²×C₁₉	—	2	1	no	—
145	C₄²×C₁₉	—	2	1	no	—
146	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
150	#64520	—	2	2	no	—
151	#64520	—	2	2	no	—
152	#64520	—	4	1	no	—
153	#64520	—	4	1	no	—
154	#64520	—	4	2	no	—
155	#64520	—	4	2	no	—
156	C₂×C₁₉⋊C₈	—	4	1	no	—
157	C₂×C₁₉⋊C₈	—	4	1	no	—
158	C₂×C₁₉⋊C₈	—	4	1	no	—
159	C₂×C₁₉⋊C₈	—	4	1	no	—
160	#8470	—	19	1	no	maximal, Sylow
161	C₂³×C₁₉	—	2	1	no	—
162	C₂³×C₁₉	—	2	2	no	—
163	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	Q₈×C₁₉	—	2	2	no	—
165	Q₈×C₁₉	—	4	2	no	—
166	Q₈×C₁₉	—	4	2	no	—
167	Q₈×C₁₉	—	4	2	no	—
168	Q₈×C₁₉	—	8	2	no	—
169	D₄×C₁₉	—	2	2	no	—
170	D₄×C₁₉	—	4	2	no	—
171	D₄×C₁₉	—	4	2	no	—
172	D₄×C₁₉	—	4	4	no	—
173	D₄×C₁₉	—	4	1	no	—
174	D₄×C₁₉	—	4	1	no	—
175	D₄×C₁₉	—	4	1	no	—
176	D₄×C₁₉	—	4	1	no	—
177	D₄×C₁₉	—	8	4	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	2	1	no	—
180	C₂×C₄×C₁₉	—	2	1	no	—
181	C₂×C₄×C₁₉	—	2	1	no	—
182	C₂×C₄×C₁₉	—	2	1	no	—
183	C₂×C₄×C₁₉	—	2	1	no	—
184	C₂×C₄×C₁₉	—	2	1	no	—
185	C₂×C₄×C₁₉	—	2	2	no	—
186	C₂×C₄×C₁₉	—	2	1	no	—
187	C₂×C₄×C₁₉	—	2	4	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	4	no	—
190	C₂×C₄×C₁₉	—	4	1	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	4	1	no	—
193	C₂×C₄×C₁₉	—	4	1	no	—
194	C₂×C₄×C₁₉	—	4	4	no	—
195	C₂×C₄×C₁₉	—	8	4	no	—
196	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
198	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
199	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
200	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
201	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
202	C₁₉⋊C₈	—	4	2	no	—
203	C₁₉⋊C₈	—	4	2	no	—
204	C₁₉⋊C₈	—	8	1	no	—
205	C₁₉⋊C₈	—	8	1	no	—
206	#3511	D₁₉	1	1	yes	characteristic
207	#1997	—	19	1	no	—
208	#1966	—	19	1	no	—
209	#1560	—	19	1	no	—
210	#1525	—	19	1	no	—
211	#1489	—	19	1	no	—
212	#1489	—	19	1	no	—
213	C₂²×C₁₉	—	2	1	no	—
214	C₂²×C₁₉	—	2	1	no	—
215	C₂²×C₁₉	—	2	1	no	—
216	C₂²×C₁₉	—	4	1	no	—
217	C₂²×C₁₉	—	4	2	no	—
218	C₂²×C₁₉	—	4	1	no	—
219	C₂²×C₁₉	—	4	2	no	—
220	C₂²×C₁₉	—	4	1	no	—
221	C₂²×C₁₉	—	4	2	no	—
222	C₂²×C₁₉	#379	1	1	yes	characteristic
223	C₄×C₁₉	—	2	1	no	—
224	C₄×C₁₉	—	2	1	no	—
225	C₄×C₁₉	—	2	1	no	—
226	C₄×C₁₉	—	4	1	no	—
227	C₄×C₁₉	—	4	4	no	—
228	C₄×C₁₉	—	4	1	no	—
229	C₄×C₁₉	—	4	1	no	—
230	C₄×C₁₉	—	4	2	no	—
231	C₄×C₁₉	#413	1	2	yes	—
232	C₄×C₁₉	#453	1	1	yes	characteristic
233	C₄×C₁₉	#454	1	1	yes	characteristic
234	C₄×C₁₉	#455	1	1	yes	characteristic
235	C₄×C₁₉	#456	1	1	yes	characteristic
236	#556	—	2	1	no	—
237	#555	—	2	1	no	—
238	#554	—	2	1	no	—
239	#553	—	2	2	no	—
240	#548	—	2	2	no	—
241	#547	—	2	1	no	—
242	#542	—	2	2	no	—
243	#537	Dic₁₉	1	2	yes	—
244	#533	—	2	1	no	—
245	#532	—	2	1	no	—
246	#532	C₂×D₁₉	1	1	yes	characteristic
247	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
248	#520	Dic₁₉	1	2	yes	—
249	C₄×#41	C₂×D₁₉	1	1	yes	characteristic
250	#423	—	19	1	no	—
251	#423	—	19	1	no	—
252	C₂×#101	—	38	2	no	—
253	C₄×M₁₆	—	19	1	no	—
254	C₄×M₁₆	—	19	1	no	—
255	#343	—	38	2	no	—
256	#333	—	38	1	no	—
257	#331	—	38	1	no	—
258	#329	—	38	2	no	—
259	Q₈⋊C₈	—	38	1	no	—
260	Q₈⋊C₈	—	38	1	no	—
261	D₄⋊C₈	—	38	1	no	—
262	D₄⋊C₈	—	38	1	no	—
263	C₂×C₁₉	—	4	1	no	—
264	C₂×C₁₉	—	8	1	no	—
265	C₂×C₁₉	—	8	2	no	—
266	C₂×C₁₉	#1785	1	1	yes	characteristic
267	C₂×C₁₉	#1792	1	1	yes	characteristic
268	C₂×C₁₉	#1793	1	1	yes	characteristic
269	C₂×#41	—	2	2	no	—
270	C₂×#41	C₂×Dic₁₉	1	1	yes	characteristic
271	C₂×#41	C₂×Dic₁₉	1	2	yes	—
272	C₂²×Q₈	C₂²⋊D₁₉	1	2	yes	—
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	C₄⋊Q₈	—	2	1	no	—
278	C₄⋊Q₈	—	2	1	no	—
279	C₄⋊Q₈	—	2	1	no	—
280	C₄⋊Q₈	—	2	1	no	—
281	C₄⋊Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
282	#127	C₂²⋊D₁₉	1	1	yes	characteristic
283	#126	—	2	4	no	—
284	#125	—	2	2	no	—
285	#124	—	2	2	no	—
286	#124	—	2	4	no	—
287	#124	C₂²⋊D₁₉	1	2	yes	—
288	#123	—	2	4	no	—
289	C₂²⋊Q₈	—	2	2	no	—
290	C₂²⋊Q₈	—	2	4	no	—
291	C₂²⋊Q₈	—	2	2	no	—
292	C₂²⋊Q₈	—	2	2	no	—
293	#121	—	2	2	no	—
294	#121	—	2	2	no	—
295	#121	—	2	2	no	—
296	#121	—	2	4	no	—
297	#121	—	2	1	no	—
298	#121	—	2	1	no	—
299	C₄×Q₈	—	2	2	no	—
300	C₄×Q₈	—	2	2	no	—
301	C₄×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
302	C₄×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
303	C₄×D₄	—	2	2	no	—
304	C₄×D₄	—	2	2	no	—
305	C₄×D₄	—	2	4	no	—
306	C₄×D₄	—	2	1	no	—
307	C₄×D₄	—	2	1	no	—
308	C₄×D₄	—	2	1	no	—
309	C₄×D₄	—	2	1	no	—
310	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
311	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
312	#117	—	2	2	no	—
313	#117	—	2	2	no	—
314	#117	—	2	1	no	—
315	#117	C₂×Dic₁₉	1	1	yes	characteristic
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
318	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
319	C₂×C₄²	—	2	1	no	—
320	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
321	C₄⋊C₈	—	38	1	no	—
322	C₄⋊C₈	—	38	1	no	—
323	C₄⋊C₈	—	38	1	no	—
324	C₄⋊C₈	—	38	1	no	—
325	#101	—	76	4	no	—
326	#97	—	38	1	no	—
327	#97	—	38	1	no	—
328	C₄×C₈	—	38	1	no	—
329	C₄×C₈	—	38	1	no	—
330	C₁₉	#8470	1	1	yes	characteristic, complemented, Sylow
331	#41	—	4	2	no	—
332	#41	—	4	4	no	—
333	#41	—	8	2	no	—
334	#41	—	8	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	4	2	no	—
338	C₂×Q₈	—	4	2	no	—
339	C₂×Q₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
340	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	4	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
347	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	C₂²⋊Dic₁₉	1	4	yes	—
354	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
355	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
356	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
357	M₁₆	—	38	2	no	—
358	M₁₆	—	38	2	no	—
359	M₁₆	—	76	1	no	—
360	M₁₆	—	76	1	no	—
361	M₁₆	—	76	2	no	—
362	M₁₆	—	76	2	no	—
363	C₂×C₈	—	76	1	no	—
364	C₂×C₈	—	76	1	no	—
365	C₂×C₈	—	76	1	no	—
366	C₂×C₈	—	76	1	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
378	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
379	C₂²⋊C₄	—	2	4	no	—
380	C₂²⋊C₄	—	2	4	no	—
381	C₂²⋊C₄	—	2	4	no	—
382	C₂²⋊C₄	—	2	1	no	—
383	C₂²⋊C₄	—	2	1	no	—
384	C₂²⋊C₄	—	2	1	no	—
385	C₂²⋊C₄	—	2	2	no	—
386	C₂²⋊C₄	—	2	2	no	—
387	C₄²	—	2	4	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	—	2	1	no	—
391	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
392	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
393	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
394	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
395	C₂³	—	2	1	no	—
396	C₂³	—	2	2	no	—
397	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
398	Q₈	—	2	2	no	—
399	Q₈	—	4	2	no	—
400	Q₈	—	4	2	no	—
401	Q₈	—	4	2	no	—
402	Q₈	—	8	2	no	—
403	D₄	—	2	2	no	—
404	D₄	—	4	2	no	—
405	D₄	—	4	2	no	—
406	D₄	—	4	4	no	—
407	D₄	—	4	1	no	—
408	D₄	—	4	1	no	—
409	D₄	—	4	1	no	—
410	D₄	—	4	1	no	—
411	D₄	—	8	4	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	8	4	no	—
430	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
431	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
432	C₂×C₄	#10597399	1	1	yes	characteristic
433	C₂×C₄	#10597399	1	1	yes	characteristic
434	C₂×C₄	#10597399	1	1	yes	characteristic
435	C₂×C₄	#10597399	1	1	yes	characteristic
436	C₈	—	76	2	no	—
437	C₈	—	76	2	no	—
438	C₈	—	152	1	no	—
439	C₈	—	152	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	4	2	no	—
449	C₂²	#11926400	1	1	yes	characteristic
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	4	1	no	—
454	C₄	—	4	4	no	—
455	C₄	—	4	1	no	—
456	C₄	—	4	1	no	—
457	C₄	—	4	2	no	—
458	C₄	#11926528	1	2	yes	—
459	C₄	#11926712	1	1	yes	characteristic
460	C₄	#11926717	1	1	yes	characteristic
461	C₄	#11926722	1	1	yes	characteristic
462	C₄	#11926727	1	1	yes	characteristic
463	C₂	—	4	1	no	—
464	C₂	—	8	1	no	—
465	C₂	—	8	2	no	—
466	C₂	#14563563	1	1	yes	characteristic
467	C₂	#14563589	1	1	yes	characteristic
468	C₂	#14563594	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926400
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#3511	C₂
socle	C₂²×C₁₉	#379
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3511	D₁₉
hypocenter	C₁₉	#8470
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3511

Complements

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

N	H ≅ G/N	type
1. #14564625	C₂	semidirect
2. #14564480	C₂	semidirect
3. #14562370	C₂	semidirect
4. #14562227	C₂	semidirect
5. #14562074	C₂	semidirect
6. #14562074	C₂	semidirect
330. C₁₉	#8470	semidirect

Maximal subgroups

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

subgroup	index
#14564625	2
#14564480	2
#14562370	2
#14562227	2
#14562074	2
C₁₉×#3511	2
#8470	19