Subgroups — #18089177

Order 4864.

1306 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926528	C₂	1	2	yes	maximal, complemented
2	C₂×#11926511	C₂	1	2	yes	maximal, complemented
3	#14563374	C₂	1	1	yes	maximal, characteristic, complemented
4	#14563332	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3449	C₂	1	1	yes	maximal, characteristic
6	C₂²×#64520	C₂²	1	1	yes	characteristic
7	C₂²×#64520	C₂²	1	2	yes	—
8	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
9	#11926528	—	2	4	no	—
10	#11926528	—	2	4	no	—
11	C₂×#10597293	—	2	2	no	—
12	C₂×#10597290	—	2	2	no	—
13	#11926511	—	2	4	no	—
14	#11926511	—	2	4	no	—
15	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
16	#11926313	—	2	2	no	—
17	#11926299	—	2	2	no	—
18	C₂²×#41×C₁₉	C₂²	1	2	yes	—
19	C₁₉×#537	—	2	2	no	—
20	C₁₉×#536	—	2	2	no	—
21	C₁₉×#535	—	2	2	no	—
22	C₁₉×#534	C₄	1	4	yes	—
23	C₁₉×#532	—	2	2	no	—
24	C₁₉×#525	—	2	4	no	—
25	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
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	—	2	2	no	—
30	C₂×#41×C₁₉	—	2	2	no	—
31	C₂×#41×C₁₉	—	2	2	no	—
32	C₂×#41×C₁₉	—	2	2	no	—
33	C₂×#41×C₁₉	—	2	2	no	—
34	C₂×#41×C₁₉	—	2	2	no	—
35	C₂×#41×C₁₉	—	2	2	no	—
36	C₂×#41×C₁₉	—	2	2	no	—
37	C₂×#41×C₁₉	—	2	2	no	—
38	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
39	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	—
40	C₂²×D₄×C₁₉	D₄	1	2	yes	—
41	C₂³×C₄×C₁₉	D₄	1	4	yes	—
42	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₁₉×C₄⋊Q₈	—	2	2	no	—
44	C₁₉×#127	—	2	2	no	—
45	C₁₉×#124	—	2	4	no	—
46	C₁₉×#123	—	2	8	no	—
47	C₁₉×C₂²⋊Q₈	—	2	8	no	—
48	C₁₉×#121	—	2	8	no	—
49	C₁₉×#121	—	2	8	no	—
50	C₁₉×#120	—	2	8	no	—
51	C₄×D₄×C₁₉	—	2	8	no	—
52	C₁₉×#117	—	2	2	no	—
53	C₁₉×#117	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
55	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₁₉	D₄	1	2	yes	—
57	C₂×#64520	—	2	2	no	—
58	C₂×#64520	—	2	1	no	—
59	C₂×#64520	—	2	2	no	—
60	C₂×#64520	—	2	2	no	—
61	C₂×#64520	—	2	2	no	—
62	C₂×#64520	—	2	2	no	—
63	C₂×#64520	—	2	2	no	—
64	C₂×#64520	—	2	2	no	—
65	C₂×#64520	D₄	1	2	yes	complemented
66	C₂×#64520	D₄	1	4	yes	complemented
67	C₂²×C₁₉⋊C₈	—	2	1	no	—
68	C₂²×C₁₉⋊C₈	—	2	2	no	—
69	C₂²×C₁₉⋊C₈	—	2	2	no	—
70	C₂²×C₁₉⋊C₈	—	2	1	no	—
71	C₂²×C₁₉⋊C₈	—	2	2	no	—
72	C₂²×C₁₉⋊C₈	—	2	1	no	—
73	C₂²×C₁₉⋊C₈	D₄	1	2	yes	complemented
74	#10597293	—	2	8	no	—
75	#10597290	—	2	8	no	—
76	C₂²⋊(C₁₉⋊C₈)	—	2	16	no	—
77	C₂⁴×C₁₉	C₂²⋊C₄	1	4	yes	—
78	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
79	#41×C₁₉	—	4	2	no	—
80	#41×C₁₉	—	4	2	no	—
81	#41×C₁₉	—	4	2	no	—
82	#41×C₁₉	—	4	2	no	—
83	#41×C₁₉	—	4	2	no	—
84	#41×C₁₉	—	4	2	no	—
85	#41×C₁₉	—	4	2	no	—
86	#41×C₁₉	—	4	2	no	—
87	#41×C₁₉	—	4	2	no	—
88	#41×C₁₉	—	4	2	no	—
89	#41×C₁₉	—	4	2	no	—
90	#41×C₁₉	—	4	2	no	—
91	#41×C₁₉	—	4	2	no	—
92	#41×C₁₉	—	4	2	no	—
93	#41×C₁₉	—	4	2	no	—
94	#41×C₁₉	—	4	2	no	—
95	C₂×Q₈×C₁₉	—	2	2	no	—
96	C₂×Q₈×C₁₉	—	2	2	no	—
97	C₂×Q₈×C₁₉	—	2	2	no	—
98	C₂×Q₈×C₁₉	—	2	2	no	—
99	C₂×Q₈×C₁₉	—	2	2	no	—
100	C₂×Q₈×C₁₉	—	2	2	no	—
101	C₂×D₄×C₁₉	—	2	4	no	—
102	C₂×D₄×C₁₉	—	2	4	no	—
103	C₂×D₄×C₁₉	—	2	4	no	—
104	C₂×D₄×C₁₉	—	2	4	no	—
105	C₂×D₄×C₁₉	—	2	4	no	—
106	C₂×D₄×C₁₉	—	2	4	no	—
107	C₂×D₄×C₁₉	—	2	8	no	—
108	C₂×D₄×C₁₉	—	2	2	no	—
109	C₂×D₄×C₁₉	—	2	2	no	—
110	C₂×D₄×C₁₉	—	2	2	no	—
111	C₂×D₄×C₁₉	—	2	2	no	—
112	C₂×D₄×C₁₉	—	2	2	no	—
113	C₂×D₄×C₁₉	—	2	2	no	—
114	C₂²×C₄×C₁₉	—	2	4	no	—
115	C₂²×C₄×C₁₉	—	2	4	no	—
116	C₂²×C₄×C₁₉	—	2	4	no	—
117	C₂²×C₄×C₁₉	—	2	4	no	—
118	C₂²×C₄×C₁₉	—	2	4	no	—
119	C₂²×C₄×C₁₉	—	2	4	no	—
120	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
121	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
122	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	#41	1	2	yes	—
132	C₄⋊C₄×C₁₉	—	2	8	no	—
133	C₄⋊C₄×C₁₉	—	2	4	no	—
134	C₂²⋊C₄×C₁₉	—	2	16	no	—
135	C₂²⋊C₄×C₁₉	—	2	4	no	—
136	C₄²×C₁₉	—	2	2	no	—
137	C₄²×C₁₉	—	2	2	no	—
138	#64520	—	2	4	no	—
139	#64520	—	2	4	no	—
140	#64520	—	2	4	no	—
141	#64520	—	4	2	no	—
142	#64520	—	4	2	no	—
143	#64520	—	4	2	no	—
144	C₂×C₁₉⋊C₈	—	2	4	no	—
145	C₂×C₁₉⋊C₈	—	2	4	no	—
146	C₂×C₁₉⋊C₈	—	2	2	no	—
147	C₂×C₁₉⋊C₈	—	2	2	no	—
148	C₂×C₁₉⋊C₈	—	4	1	no	—
149	C₂×C₁₉⋊C₈	—	4	1	no	—
150	C₂×C₁₉⋊C₈	—	4	2	no	—
151	C₂×C₁₉⋊C₈	—	4	2	no	—
152	C₂×C₁₉⋊C₈	—	4	2	no	—
153	C₂×C₁₉⋊C₈	—	4	1	no	—
154	C₂×C₁₉⋊C₈	—	4	1	no	—
155	#10996	—	19	1	no	maximal, Sylow
156	C₂³×C₁₉	—	2	4	no	—
157	C₂³×C₁₉	—	2	4	no	—
158	C₂³×C₁₉	—	2	4	no	—
159	C₂³×C₁₉	—	4	2	no	—
160	C₂³×C₁₉	—	4	8	no	—
161	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
162	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂³×C₁₉	C₄×D₄	1	2	yes	—
164	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
165	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
166	Q₈×C₁₉	—	4	2	no	—
167	Q₈×C₁₉	—	4	2	no	—
168	Q₈×C₁₉	—	4	2	no	—
169	Q₈×C₁₉	—	4	2	no	—
170	D₄×C₁₉	—	4	4	no	—
171	D₄×C₁₉	—	4	4	no	—
172	D₄×C₁₉	—	4	4	no	—
173	D₄×C₁₉	—	4	4	no	—
174	D₄×C₁₉	—	4	2	no	—
175	D₄×C₁₉	—	4	2	no	—
176	D₄×C₁₉	—	4	2	no	—
177	D₄×C₁₉	—	4	2	no	—
178	D₄×C₁₉	—	8	8	no	—
179	C₂×C₄×C₁₉	—	2	4	no	—
180	C₂×C₄×C₁₉	—	2	4	no	—
181	C₂×C₄×C₁₉	—	2	4	no	—
182	C₂×C₄×C₁₉	—	2	4	no	—
183	C₂×C₄×C₁₉	—	4	4	no	—
184	C₂×C₄×C₁₉	—	4	4	no	—
185	C₂×C₄×C₁₉	—	4	4	no	—
186	C₂×C₄×C₁₉	—	4	4	no	—
187	C₂×C₄×C₁₉	—	4	4	no	—
188	C₂×C₄×C₁₉	#120	1	2	yes	—
189	C₂×C₄×C₁₉	#120	1	2	yes	—
190	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
191	C₂×C₄×C₁₉	#120	1	2	yes	—
192	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
193	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
194	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
195	C₂×C₄×C₁₉	#121	1	2	yes	—
196	C₂×C₄×C₁₉	#121	1	2	yes	—
197	C₂×C₄×C₁₉	#121	1	2	yes	—
198	C₂×C₄×C₁₉	#121	1	2	yes	—
199	C₂×C₄×C₁₉	#121	1	2	yes	—
200	C₂×C₄×C₁₉	#123	1	2	yes	—
201	C₂×C₄×C₁₉	#123	1	2	yes	—
202	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
203	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
204	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
205	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
206	C₁₉⋊C₈	—	4	2	no	—
207	C₁₉⋊C₈	—	4	4	no	—
208	C₁₉⋊C₈	—	4	2	no	—
209	#3449	D₁₉	1	1	yes	characteristic
210	C₂×#413	—	19	2	no	—
211	C₂×#408	—	19	2	no	—
212	#1742	—	19	1	no	—
213	#1729	—	19	1	no	—
214	C₂²×C₁₉	—	2	2	no	—
215	C₂²×C₁₉	—	2	4	no	—
216	C₂²×C₁₉	—	4	1	no	—
217	C₂²×C₁₉	—	4	2	no	—
218	C₂²×C₁₉	—	4	1	no	—
219	C₂²×C₁₉	—	4	8	no	—
220	C₂²×C₁₉	—	4	4	no	—
221	C₂²×C₁₉	—	4	8	no	—
222	C₂²×C₁₉	—	8	4	no	—
223	C₂²×C₁₉	#379	1	1	yes	characteristic
224	C₂²×C₁₉	#386	1	2	yes	—
225	C₂²×C₁₉	#386	1	2	yes	—
226	C₂²×C₁₉	#390	1	1	yes	characteristic
227	C₂²×C₁₉	#390	1	1	yes	characteristic
228	C₄×C₁₉	—	4	4	no	—
229	C₄×C₁₉	—	4	4	no	—
230	C₄×C₁₉	#392	1	1	yes	characteristic
231	C₄×C₁₉	#392	1	2	yes	—
232	C₄×C₁₉	#392	1	1	yes	characteristic
233	C₄×C₁₉	#394	1	1	yes	characteristic
234	C₄×C₁₉	#394	1	2	yes	—
235	C₄×C₁₉	#394	1	1	yes	characteristic
236	C₂²×#41	C₂×D₁₉	1	2	yes	—
237	C₂²×M₁₆	—	19	2	no	—
238	C₂²×M₁₆	—	19	1	no	—
239	C₂³×C₈	—	19	1	no	—
240	#537	—	2	2	no	—
241	#536	—	2	2	no	—
242	#535	—	2	2	no	—
243	#534	Dic₁₉	1	4	yes	—
244	#532	—	2	2	no	—
245	#525	—	2	4	no	—
246	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
247	#413	—	38	4	no	—
248	#413	—	38	4	no	—
249	C₂×#101	—	38	2	no	—
250	C₂×#100	—	38	2	no	—
251	#408	—	38	4	no	—
252	#408	—	38	4	no	—
253	C₂×C₂²⋊C₈	—	38	4	no	—
254	#343	—	38	2	no	—
255	#336	—	38	2	no	—
256	C₂×C₁₉	—	2	2	no	—
257	C₂×C₁₉	—	2	2	no	—
258	C₂×C₁₉	—	2	1	no	—
259	C₂×C₁₉	—	2	1	no	—
260	C₂×C₁₉	—	8	4	no	—
261	C₂×C₁₉	#1438	1	1	yes	characteristic
262	C₂×C₁₉	#1791	1	2	yes	—
263	C₂×#41	—	2	2	no	—
264	C₂×#41	—	2	2	no	—
265	C₂×#41	—	2	2	no	—
266	C₂×#41	—	2	2	no	—
267	C₂×#41	—	2	2	no	—
268	C₂×#41	—	2	2	no	—
269	C₂×#41	—	2	2	no	—
270	C₂×#41	—	2	2	no	—
271	C₂×#41	—	2	2	no	—
272	C₂×#41	—	2	2	no	—
273	C₂×#41	—	2	2	no	—
274	C₂×#41	—	2	2	no	—
275	C₂²×Q₈	C₂²⋊D₁₉	1	2	yes	—
276	C₂²×D₄	C₂×Dic₁₉	1	4	yes	—
277	C₂²×D₄	C₂²⋊D₁₉	1	2	yes	—
278	C₂³×C₄	C₂²⋊D₁₉	1	4	yes	—
279	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
280	C₂×M₁₆	—	19	4	no	—
281	C₂×M₁₆	—	19	2	no	—
282	C₂×M₁₆	—	38	2	no	—
283	C₂×M₁₆	—	38	1	no	—
284	C₂×M₁₆	—	38	2	no	—
285	C₂×M₁₆	—	38	2	no	—
286	C₂×M₁₆	—	38	2	no	—
287	C₂×M₁₆	—	38	2	no	—
288	C₂×M₁₆	—	38	2	no	—
289	C₂×M₁₆	—	38	2	no	—
290	C₂²×C₈	—	19	2	no	—
291	C₂²×C₈	—	38	2	no	—
292	C₂²×C₈	—	38	1	no	—
293	C₂²×C₈	—	38	1	no	—
294	C₂²×C₈	—	38	2	no	—
295	C₂²×C₈	—	38	1	no	—
296	C₂²×C₈	—	38	2	no	—
297	C₄⋊Q₈	—	2	2	no	—
298	#127	—	2	2	no	—
299	#124	—	2	4	no	—
300	#123	—	2	8	no	—
301	C₂²⋊Q₈	—	2	8	no	—
302	#121	—	2	8	no	—
303	#121	—	2	8	no	—
304	#120	—	2	8	no	—
305	C₄×D₄	—	2	8	no	—
306	#117	—	2	2	no	—
307	#117	—	2	2	no	—
308	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
309	C₂×C₂²⋊C₄	C₂×Dic₁₉	1	2	yes	—
310	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
311	#101	—	38	8	no	—
312	#100	—	38	8	no	—
313	C₂²⋊C₈	—	38	16	no	—
314	C₁₉	#10996	1	1	yes	characteristic, complemented, Sylow
315	C₂⁴	C₂²⋊Dic₁₉	1	4	yes	—
316	C₂⁴	C₂²×Dic₁₉	1	1	yes	characteristic
317	#41	—	4	2	no	—
318	#41	—	4	2	no	—
319	#41	—	4	2	no	—
320	#41	—	4	2	no	—
321	#41	—	4	2	no	—
322	#41	—	4	2	no	—
323	#41	—	4	2	no	—
324	#41	—	4	2	no	—
325	#41	—	4	2	no	—
326	#41	—	4	2	no	—
327	#41	—	4	2	no	—
328	#41	—	4	2	no	—
329	#41	—	4	2	no	—
330	#41	—	4	2	no	—
331	#41	—	4	2	no	—
332	#41	—	4	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×D₄	—	2	4	no	—
340	C₂×D₄	—	2	4	no	—
341	C₂×D₄	—	2	4	no	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	2	4	no	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	2	8	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	C₂²⋊Dic₁₉	1	4	yes	—
359	C₂²×C₄	C₂²⋊Dic₁₉	1	4	yes	—
360	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
361	C₂²×C₄	D₄×D₁₉	1	2	yes	—
362	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
363	C₂²×C₄	#64543	1	1	yes	characteristic
364	C₂²×C₄	#64543	1	1	yes	characteristic
365	C₂²×C₄	#64543	1	2	yes	—
366	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
367	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
368	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
369	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
370	M₁₆	—	38	4	no	—
371	M₁₆	—	38	4	no	—
372	M₁₆	—	38	4	no	—
373	M₁₆	—	76	2	no	—
374	M₁₆	—	76	2	no	—
375	M₁₆	—	76	2	no	—
376	C₂×C₈	—	38	4	no	—
377	C₂×C₈	—	38	4	no	—
378	C₂×C₈	—	38	2	no	—
379	C₂×C₈	—	38	2	no	—
380	C₂×C₈	—	76	2	no	—
381	C₂×C₈	—	76	2	no	—
382	C₂×C₈	—	76	1	no	—
383	C₂×C₈	—	76	1	no	—
384	C₂×C₈	—	76	1	no	—
385	C₂×C₈	—	76	2	no	—
386	C₂×C₈	—	76	1	no	—
387	C₄⋊C₄	—	2	8	no	—
388	C₄⋊C₄	—	2	4	no	—
389	C₂²⋊C₄	—	2	16	no	—
390	C₂²⋊C₄	—	2	4	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	2	2	no	—
393	C₂³	—	2	4	no	—
394	C₂³	—	2	4	no	—
395	C₂³	—	2	4	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	4	8	no	—
398	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
399	C₂³	D₄×Dic₁₉	1	2	yes	—
400	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
401	C₂³	C₂×C₂²⋊Dic₁₉	1	2	yes	—
402	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
403	Q₈	—	4	2	no	—
404	Q₈	—	4	2	no	—
405	Q₈	—	4	2	no	—
406	Q₈	—	4	2	no	—
407	D₄	—	4	4	no	—
408	D₄	—	4	4	no	—
409	D₄	—	4	4	no	—
410	D₄	—	4	4	no	—
411	D₄	—	4	2	no	—
412	D₄	—	4	2	no	—
413	D₄	—	4	2	no	—
414	D₄	—	4	2	no	—
415	D₄	—	8	8	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	4	no	—
425	C₂×C₄	#10597381	1	2	yes	—
426	C₂×C₄	#10597381	1	2	yes	—
427	C₂×C₄	#10597382	1	1	yes	characteristic
428	C₂×C₄	#10597382	1	1	yes	characteristic
429	C₂×C₄	#10597383	1	2	yes	—
430	C₂×C₄	#10597383	1	2	yes	—
431	C₂×C₄	#10597384	1	1	yes	characteristic
432	C₂×C₄	#10597384	1	1	yes	characteristic
433	C₂×C₄	#10597384	1	2	yes	—
434	C₂×C₄	#10597385	1	2	yes	—
435	C₂×C₄	#10597385	1	2	yes	—
436	C₂×C₄	#10597385	1	2	yes	—
437	C₂×C₄	#10597385	1	2	yes	—
438	C₂×C₄	#10597386	1	1	yes	characteristic
439	C₂×C₄	#10597386	1	1	yes	characteristic
440	C₂×C₄	#10597399	1	1	yes	characteristic
441	C₂×C₄	#10597399	1	2	yes	—
442	C₂×C₄	#10597399	1	1	yes	characteristic
443	C₈	—	76	2	no	—
444	C₈	—	76	4	no	—
445	C₈	—	76	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	4	no	—
448	C₂²	—	4	1	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	4	1	no	—
451	C₂²	—	4	8	no	—
452	C₂²	—	4	8	no	—
453	C₂²	—	4	4	no	—
454	C₂²	—	8	4	no	—
455	C₂²	#11926400	1	1	yes	characteristic
456	C₂²	#11926424	1	2	yes	—
457	C₂²	#11926424	1	2	yes	—
458	C₂²	#11926447	1	1	yes	characteristic
459	C₂²	#11926447	1	1	yes	characteristic
460	C₄	—	4	4	no	—
461	C₄	—	4	4	no	—
462	C₄	#11926452	1	1	yes	characteristic
463	C₄	#11926452	1	2	yes	—
464	C₄	#11926452	1	1	yes	characteristic
465	C₄	#11926458	1	1	yes	characteristic
466	C₄	#11926458	1	2	yes	—
467	C₄	#11926458	1	1	yes	characteristic
468	C₂	—	2	2	no	—
469	C₂	—	2	2	no	—
470	C₂	—	2	1	no	—
471	C₂	—	2	1	no	—
472	C₂	—	8	4	no	—
473	C₂	#14561876	1	1	yes	characteristic
474	C₂	#14563586	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#10597399
commutator	C₂⁴×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting, prime radical	C₁₉×#3449	C₂
socle	C₂²×C₁₉	#379
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#3449	D₁₉
hypocenter	C₁₉	#10996
LCS	G ▷ C₂⁴×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #3449

Complements

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

N	H ≅ G/N	type
1. C₂×#11926528	C₂	semidirect
2. C₂×#11926511	C₂	semidirect
3. #14563374	C₂	semidirect
4. #14563332	C₂	semidirect
65. C₂×#64520	D₄	semidirect
66. C₂×#64520	D₄	semidirect
73. C₂²×C₁₉⋊C₈	D₄	semidirect
314. C₁₉	#10996	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926528	2
C₂×#11926511	2
#14563374	2
#14563332	2
C₁₉×#3449	2
#10996	19