Subgroups — #14577307

Order 2432.

1522 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597436	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#64541	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×Dic₃₈	C₂	1	2	yes	maximal, complemented
4	#11927203	C₂	1	2	yes	maximal, complemented
5	#11927199	C₂	1	2	yes	maximal, complemented
6	#11927192	C₂	1	4	yes	maximal, complemented
7	#11927190	C₂	1	2	yes	maximal, complemented
8	#11927181	C₂	1	4	yes	maximal, complemented
9	#11927123	C₂	1	2	yes	maximal, complemented
10	#11927122	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927120	C₂	1	1	yes	maximal, characteristic, complemented
12	#11927117	C₂	1	2	yes	maximal, complemented
13	#11927054	C₂	1	2	yes	maximal, complemented
14	C₂×#10597370	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²⋊Q₈×D₁₉	C₂	1	2	yes	maximal, complemented
16	#11927024	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#525	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic, complemented
19	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊D₁₉	C₂²	1	2	yes	—
21	#10597436	—	2	8	no	—
22	C₂×Q₈×D₁₉	C₂²	1	2	yes	complemented
23	C₂×#64543	C₂²	1	2	yes	complemented
24	C₂×#64543	C₂²	1	4	yes	complemented
25	C₂×#64541	—	2	8	no	—
26	C₂×#64541	C₂²	1	2	yes	—
27	C₂×#64541	C₂²	1	1	yes	characteristic
28	C₂×#64541	C₂²	1	2	yes	—
29	C₂×#64541	C₂²	1	1	yes	characteristic
30	C₂×#64541	C₂²	1	1	yes	characteristic
31	C₂×#64541	C₂²	1	1	yes	characteristic
32	C₂×#64541	C₂²	1	2	yes	complemented
33	C₂²×D₇₆	C₂²	1	1	yes	characteristic
34	C₂²×C₄×D₁₉	C₂²	1	2	yes	—
35	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
36	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
37	C₂²×Dic₃₈	C₂²	1	2	yes	complemented
38	C₁₉×#123	C₂²	1	2	yes	complemented
39	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
40	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
41	C₁₉×#121	C₂²	1	1	yes	characteristic
42	C₁₉×#121	C₂²	1	1	yes	characteristic, complemented
43	C₁₉×#120	C₂²	1	2	yes	—
44	C₄×D₄×C₁₉	C₂²	1	2	yes	—
45	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
46	C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
48	#10597392	C₂²	1	2	yes	complemented
49	#10597385	C₂²	1	4	yes	complemented
50	#10597385	C₂²	1	4	yes	complemented
51	#10597384	C₂²	1	2	yes	complemented
52	#10597384	C₂²	1	4	yes	complemented
53	#10597383	C₂²	1	4	yes	—
54	D₄×Dic₁₉	C₂²	1	4	yes	—
55	#10597376	C₂²	1	2	yes	complemented
56	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic, complemented
57	#10597370	C₂²	1	2	yes	—
58	#10597370	C₂²	1	2	yes	—
59	#10597370	C₂²	1	2	yes	complemented
60	#10597370	C₂²	1	2	yes	complemented
61	#10597370	C₂²	1	2	yes	complemented
62	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	complemented
63	#10597343	C₂²	1	2	yes	complemented
64	#10597343	C₂²	1	2	yes	complemented
65	#10597342	C₂²	1	4	yes	complemented
66	#10597340	C₂²	1	4	yes	complemented
67	#10597338	C₂²	1	2	yes	complemented
68	C₄⋊C₄×D₁₉	C₂²	1	2	yes	complemented
69	C₄⋊C₄×D₁₉	C₂²	1	4	yes	complemented
70	#10597334	C₂²	1	4	yes	complemented
71	#10597332	C₂²	1	4	yes	complemented
72	#10597331	C₂²	1	4	yes	complemented
73	#10597330	C₂²	1	4	yes	complemented
74	#10597329	C₂²	1	4	yes	complemented
75	#10597329	C₂²	1	4	yes	complemented
76	(C₂²⋊D₁₉)⋊C₄	C₂²	1	4	yes	complemented
77	(C₂²⋊D₁₉)⋊C₄	C₂²	1	4	yes	complemented
78	C₂²⋊C₄×D₁₉	C₂²	1	4	yes	—
79	#10597324	C₂²	1	4	yes	—
80	#10597324	C₂²	1	4	yes	complemented
81	#10597321	C₂²	1	2	yes	complemented
82	C₄×D₇₆	C₂²	1	2	yes	complemented
83	#10597315	C₂²	1	2	yes	complemented
84	C₄×Dic₃₈	C₂²	1	2	yes	complemented
85	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
86	C₂³×D₁₉	C₂³	1	2	yes	—
87	#41×C₁₉	—	2	4	no	—
88	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×D₄×C₁₉	C₂³	1	2	yes	—
90	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×D₄×C₁₉	C₂³	1	2	yes	—
92	C₂×D₄×C₁₉	C₂³	1	2	yes	—
93	C₂²×C₄×C₁₉	—	2	4	no	—
94	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
95	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
101	C₂×C₂²⋊D₁₉	—	2	8	no	—
102	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
103	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
104	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
105	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
106	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
107	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
108	C₂²×Dic₁₉	C₂³	1	2	yes	—
109	C₂²×Dic₁₉	C₂³	1	4	yes	—
110	C₂²×Dic₁₉	C₂³	1	2	yes	—
111	C₂²×Dic₁₉	C₂³	1	2	yes	—
112	Q₈×D₁₉	—	2	8	no	—
113	#64543	—	2	16	no	—
114	#64543	—	2	8	no	—
115	#64541	—	2	4	no	—
116	#64541	—	2	8	no	—
117	#64541	—	2	4	no	—
118	#64541	—	2	8	no	—
119	#64541	—	2	8	no	—
120	#64541	—	2	4	no	—
121	#64541	D₄	1	8	yes	complemented
122	C₂×D₇₆	—	2	4	no	—
123	C₂×D₇₆	C₂³	1	1	yes	characteristic
124	C₂×D₇₆	C₂³	1	2	yes	—
125	C₂×D₇₆	C₂³	1	1	yes	characteristic
126	C₂×C₄×D₁₉	—	2	8	no	—
127	C₂×C₄×D₁₉	C₂³	1	2	yes	—
128	C₂×C₄×D₁₉	C₂³	1	2	yes	—
129	C₂×C₄×D₁₉	C₂³	1	2	yes	—
130	C₂×C₄×D₁₉	C₂³	1	4	yes	—
131	C₂×C₄×D₁₉	C₂³	1	4	yes	—
132	C₂×C₄×D₁₉	C₂³	1	2	yes	—
133	C₂×Dic₃₈	—	2	4	no	—
134	C₂×Dic₃₈	—	2	4	no	—
135	C₂×Dic₃₈	—	2	8	no	—
136	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
137	C₂×Dic₃₈	C₂³	1	2	yes	—
138	C₂×Dic₃₈	C₂³	1	2	yes	—
139	C₂×Dic₃₈	C₂³	1	4	yes	—
140	C₂×Dic₃₈	C₂³	1	2	yes	—
141	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
142	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
143	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
144	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
145	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
146	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
147	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
148	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
149	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
150	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
151	C₄²×C₁₉	C₂³	1	2	yes	—
152	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
153	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
154	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
155	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
156	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
157	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
158	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
159	C₄⋊Dic₁₉	C₂³	1	2	yes	—
160	C₄⋊Dic₁₉	C₂³	1	4	yes	—
161	C₄⋊Dic₁₉	C₂³	1	2	yes	—
162	C₄⋊Dic₁₉	C₂³	1	4	yes	—
163	Dic₁₉⋊C₄	C₂³	1	4	yes	—
164	Dic₁₉⋊C₄	C₂³	1	4	yes	—
165	Dic₁₉⋊C₄	C₂³	1	4	yes	—
166	Dic₁₉⋊C₄	C₂³	1	4	yes	—
167	C₄×Dic₁₉	C₂³	1	4	yes	—
168	C₂³×C₁₉	—	2	2	no	—
169	C₂³×C₁₉	—	2	2	no	—
170	C₂³×C₁₉	—	4	1	no	—
171	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
172	C₂³×C₁₉	C₂⁴	1	2	yes	—
173	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
174	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
175	C₂²×D₁₉	—	2	4	no	—
176	C₂²×D₁₉	—	2	4	no	—
177	C₂²×D₁₉	—	4	2	no	—
178	C₂²×D₁₉	C₂⁴	1	2	yes	—
179	C₂²×D₁₉	C₂⁴	1	2	yes	—
180	Q₈×C₁₉	—	2	2	no	—
181	D₄×C₁₉	—	2	4	no	—
182	D₄×C₁₉	—	2	4	no	—
183	D₄×C₁₉	—	2	2	no	—
184	D₄×C₁₉	—	4	2	no	—
185	C₂×C₄×C₁₉	—	2	2	no	—
186	C₂×C₄×C₁₉	—	2	2	no	—
187	C₂×C₄×C₁₉	—	2	4	no	—
188	C₂×C₄×C₁₉	—	2	2	no	—
189	C₂×C₄×C₁₉	—	2	2	no	—
190	C₂×C₄×C₁₉	—	2	2	no	—
191	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
192	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
193	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
194	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
196	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
197	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
198	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
199	C₂²⋊D₁₉	—	2	4	no	—
200	C₂²⋊D₁₉	—	2	4	no	—
201	C₂²⋊D₁₉	—	2	8	no	—
202	C₂²⋊D₁₉	—	2	4	no	—
203	C₂²⋊D₁₉	—	4	4	no	—
204	C₂²⋊D₁₉	C₂×D₄	1	8	yes	—
205	C₂×Dic₁₉	—	2	4	no	—
206	C₂×Dic₁₉	—	2	4	no	—
207	C₂×Dic₁₉	—	2	8	no	—
208	C₂×Dic₁₉	—	4	2	no	—
209	C₂×Dic₁₉	C₂⁴	1	4	yes	—
210	C₂×Dic₁₉	C₂⁴	1	2	yes	—
211	C₂×Dic₁₉	C₂⁴	1	4	yes	—
212	C₂×Dic₁₉	C₂⁴	1	2	yes	—
213	D₇₆	—	2	4	no	—
214	D₇₆	—	2	2	no	—
215	D₇₆	C₂×D₄	1	4	yes	—
216	C₄×D₁₉	—	2	4	no	—
217	C₄×D₁₉	—	2	8	no	—
218	C₄×D₁₉	—	2	4	no	—
219	C₄×D₁₉	—	2	4	no	—
220	C₄×D₁₉	—	4	4	no	—
221	C₄×D₁₉	C₂×D₄	1	8	yes	—
222	Dic₃₈	—	2	4	no	—
223	Dic₃₈	—	2	2	no	—
224	Dic₃₈	—	2	4	no	—
225	Dic₃₈	—	2	4	no	—
226	Dic₃₈	—	2	8	no	—
227	Dic₃₈	C₂×D₄	1	4	yes	—
228	#3489	—	19	1	no	maximal, Sylow
229	C₂²×C₁₉	—	2	1	no	—
230	C₂²×C₁₉	—	2	1	no	—
231	C₂²×C₁₉	—	2	1	no	—
232	C₂²×C₁₉	—	2	1	no	—
233	C₂²×C₁₉	—	2	2	no	—
234	C₂²×C₁₉	—	2	1	no	—
235	C₂²×C₁₉	—	2	2	no	—
236	C₂²×C₁₉	—	2	1	no	—
237	C₂²×C₁₉	—	2	2	no	—
238	C₂²×C₁₉	—	2	1	no	—
239	C₂²×C₁₉	—	4	4	no	—
240	C₂²×C₁₉	C₂²×D₄	1	2	yes	—
241	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	complemented
242	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
243	C₂×D₁₉	—	2	2	no	—
244	C₂×D₁₉	—	2	2	no	—
245	C₂×D₁₉	—	2	2	no	—
246	C₂×D₁₉	—	2	2	no	—
247	C₂×D₁₉	—	2	2	no	—
248	C₂×D₁₉	—	4	8	no	—
249	C₂×D₁₉	C₂²×D₄	1	4	yes	—
250	C₄×C₁₉	—	2	2	no	—
251	C₄×C₁₉	—	2	1	no	—
252	C₄×C₁₉	—	2	1	no	—
253	C₄×C₁₉	—	2	2	no	—
254	C₄×C₁₉	—	2	2	no	—
255	C₄×C₁₉	C₂²×D₄	1	2	yes	—
256	C₄×C₁₉	C₂²×D₄	1	2	yes	—
257	Dic₁₉	—	2	4	no	—
258	Dic₁₉	—	2	2	no	—
259	Dic₁₉	—	2	4	no	—
260	Dic₁₉	C₂²×D₄	1	4	yes	—
261	C₂×2₋¹⁺⁴	—	19	1	no	—
262	C₂²×#41	—	19	1	no	—
263	D₄×Q₈	—	19	2	no	—
264	#548	—	19	2	no	—
265	#547	—	19	4	no	—
266	#547	—	19	2	no	—
267	#546	—	19	4	no	—
268	#546	—	19	2	no	—
269	#537	—	19	1	no	—
270	#537	—	19	2	no	—
271	#536	—	19	2	no	—
272	#536	—	19	1	no	—
273	#525	—	19	2	no	—
274	#525	D₁₉	1	1	yes	characteristic, complemented
275	C₂×C₂²⋊Q₈	—	19	1	no	—
276	C₂×C₂²⋊Q₈	—	19	2	no	—
277	#520	—	19	1	no	—
278	C₂×C₁₉	—	2	2	no	—
279	C₂×C₁₉	—	2	2	no	—
280	C₂×C₁₉	—	4	2	no	—
281	C₂×C₁₉	—	4	1	no	—
282	C₂×C₁₉	C₂³×D₄	1	1	yes	characteristic
283	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
284	C₂×C₁₉	#585	1	1	yes	characteristic
285	D₁₉	—	2	4	no	—
286	D₁₉	—	4	2	no	—
287	2₋¹⁺⁴	—	38	8	no	—
288	C₂×#41	—	19	2	no	—
289	C₂×#41	—	19	4	no	—
290	C₂×#41	—	19	1	no	—
291	C₂×#41	—	19	2	no	—
292	C₂×#41	—	19	1	no	—
293	C₂×#41	—	19	2	no	—
294	C₂×#41	—	19	1	no	—
295	C₂×#41	—	19	2	no	—
296	C₂×#41	—	19	1	no	—
297	C₂×#41	—	38	8	no	—
298	C₂×#41	C₂×D₁₉	1	1	yes	characteristic, complemented
299	C₂²×Q₈	—	19	2	no	—
300	C₂²×Q₈	—	19	1	no	—
301	C₂²×Q₈	—	19	2	no	—
302	C₂²×Q₈	—	19	1	no	—
303	C₂²×D₄	—	19	2	no	—
304	C₂²×D₄	—	19	1	no	—
305	C₂³×C₄	—	19	2	no	—
306	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
307	C₄⋊Q₈	—	19	4	no	—
308	C₄⋊Q₈	—	19	2	no	—
309	#124	—	19	4	no	—
310	#124	—	19	2	no	—
311	#123	—	19	4	no	—
312	#123	—	19	4	no	—
313	#123	—	19	4	no	—
314	#123	—	19	4	no	—
315	#123	C₂×D₁₉	1	2	yes	complemented
316	C₂²⋊Q₈	—	19	2	no	—
317	C₂²⋊Q₈	—	19	2	no	—
318	C₂²⋊Q₈	—	19	2	no	—
319	C₂²⋊Q₈	—	19	2	no	—
320	C₂²⋊Q₈	—	19	2	no	—
321	C₂²⋊Q₈	—	19	2	no	—
322	C₂²⋊Q₈	—	19	2	no	—
323	C₂²⋊Q₈	—	19	4	no	—
324	C₂²⋊Q₈	—	19	2	no	—
325	C₂²⋊Q₈	—	19	4	no	—
326	C₂²⋊Q₈	—	19	4	no	—
327	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
328	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
329	#121	—	19	2	no	—
330	#121	—	19	4	no	—
331	#121	—	19	4	no	—
332	#121	—	19	4	no	—
333	#121	—	19	2	no	—
334	#121	—	19	4	no	—
335	#121	C₂×D₁₉	1	1	yes	characteristic
336	#121	C₂×D₁₉	1	1	yes	characteristic, complemented
337	#120	—	19	4	no	—
338	#120	C₂×D₁₉	1	2	yes	—
339	C₄×Q₈	—	19	2	no	—
340	C₄×D₄	—	19	4	no	—
341	C₄×D₄	—	19	4	no	—
342	C₄×D₄	—	19	4	no	—
343	C₄×D₄	—	19	2	no	—
344	C₄×D₄	C₂×D₁₉	1	2	yes	—
345	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
346	#117	—	19	2	no	—
347	#117	C₂×D₁₉	1	1	yes	characteristic, complemented
348	C₂×C₄⋊C₄	—	19	1	no	—
349	C₂×C₄⋊C₄	—	19	2	no	—
350	C₂×C₄⋊C₄	—	19	2	no	—
351	C₂×C₄⋊C₄	—	19	4	no	—
352	C₂×C₂²⋊C₄	—	19	2	no	—
353	C₂×C₂²⋊C₄	—	19	4	no	—
354	C₁₉	#3489	1	1	yes	characteristic, complemented, Sylow
355	C₂⁴	—	19	2	no	—
356	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
357	#41	—	2	4	no	—
358	#41	—	19	8	no	—
359	#41	—	38	8	no	—
360	#41	—	38	8	no	—
361	#41	—	38	4	no	—
362	#41	—	38	8	no	—
363	#41	—	38	4	no	—
364	#41	—	38	8	no	—
365	#41	—	38	16	no	—
366	#41	—	38	4	no	—
367	C₂×Q₈	—	19	1	no	—
368	C₂×Q₈	—	19	2	no	—
369	C₂×Q₈	—	19	4	no	—
370	C₂×Q₈	—	19	2	no	—
371	C₂×Q₈	—	19	2	no	—
372	C₂×Q₈	—	19	1	no	—
373	C₂×Q₈	—	38	4	no	—
374	C₂×Q₈	—	38	8	no	—
375	C₂×Q₈	—	38	8	no	—
376	C₂×Q₈	—	38	4	no	—
377	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
378	C₂×D₄	—	19	2	no	—
379	C₂×D₄	—	19	4	no	—
380	C₂×D₄	—	19	2	no	—
381	C₂×D₄	—	19	2	no	—
382	C₂×D₄	—	19	2	no	—
383	C₂×D₄	—	19	4	no	—
384	C₂×D₄	—	19	1	no	—
385	C₂×D₄	—	19	2	no	—
386	C₂×D₄	—	19	1	no	—
387	C₂×D₄	—	38	4	no	—
388	C₂×D₄	—	38	8	no	—
389	C₂×D₄	C₂²×D₁₉	1	2	yes	—
390	C₂×D₄	C₂²×D₁₉	1	2	yes	—
391	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
392	C₂×D₄	C₂²×D₁₉	1	2	yes	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	19	2	no	—
395	C₂²×C₄	—	19	2	no	—
396	C₂²×C₄	—	19	4	no	—
397	C₂²×C₄	—	19	2	no	—
398	C₂²×C₄	—	19	2	no	—
399	C₂²×C₄	—	19	4	no	—
400	C₂²×C₄	—	19	2	no	—
401	C₂²×C₄	—	19	2	no	—
402	C₂²×C₄	—	19	2	no	—
403	C₂²×C₄	—	19	4	no	—
404	C₂²×C₄	—	38	8	no	—
405	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
406	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
407	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
408	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
409	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
410	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
411	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
412	C₄⋊C₄	—	19	4	no	—
413	C₄⋊C₄	—	19	4	no	—
414	C₄⋊C₄	—	19	4	no	—
415	C₄⋊C₄	—	19	4	no	—
416	C₄⋊C₄	—	19	2	no	—
417	C₄⋊C₄	—	19	2	no	—
418	C₄⋊C₄	—	19	4	no	—
419	C₄⋊C₄	—	19	4	no	—
420	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
421	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
422	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
423	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
424	C₂²⋊C₄	—	19	4	no	—
425	C₂²⋊C₄	—	19	4	no	—
426	C₂²⋊C₄	—	19	4	no	—
427	C₂²⋊C₄	—	19	4	no	—
428	C₂²⋊C₄	—	19	4	no	—
429	C₂²⋊C₄	—	19	4	no	—
430	C₂²⋊C₄	—	19	4	no	—
431	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
432	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
433	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
434	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
435	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
436	C₄²	—	19	4	no	—
437	C₄²	C₂²×D₁₉	1	2	yes	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	4	1	no	—
441	C₂³	—	19	2	no	—
442	C₂³	—	19	2	no	—
443	C₂³	—	38	4	no	—
444	C₂³	—	38	4	no	—
445	C₂³	—	76	2	no	—
446	C₂³	C₂³×D₁₉	1	1	yes	characteristic
447	C₂³	C₂³×D₁₉	1	2	yes	—
448	C₂³	C₂³×D₁₉	1	1	yes	characteristic
449	C₂³	C₂³×D₁₉	1	1	yes	characteristic
450	Q₈	—	2	2	no	—
451	Q₈	—	19	4	no	—
452	Q₈	—	38	8	no	—
453	Q₈	—	38	4	no	—
454	Q₈	—	38	4	no	—
455	Q₈	—	38	4	no	—
456	Q₈	—	38	2	no	—
457	D₄	—	2	4	no	—
458	D₄	—	2	4	no	—
459	D₄	—	2	2	no	—
460	D₄	—	4	2	no	—
461	D₄	—	19	8	no	—
462	D₄	—	19	4	no	—
463	D₄	—	38	4	no	—
464	D₄	—	38	4	no	—
465	D₄	—	38	4	no	—
466	D₄	—	38	8	no	—
467	D₄	—	38	4	no	—
468	D₄	—	38	2	no	—
469	D₄	—	76	4	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	19	2	no	—
477	C₂×C₄	—	19	8	no	—
478	C₂×C₄	—	19	4	no	—
479	C₂×C₄	—	19	4	no	—
480	C₂×C₄	—	19	2	no	—
481	C₂×C₄	—	38	4	no	—
482	C₂×C₄	—	38	4	no	—
483	C₂×C₄	—	38	8	no	—
484	C₂×C₄	—	38	4	no	—
485	C₂×C₄	—	38	8	no	—
486	C₂×C₄	—	38	4	no	—
487	C₂×C₄	—	38	4	no	—
488	C₂×C₄	—	76	4	no	—
489	C₂×C₄	—	76	2	no	—
490	C₂×C₄	D₄×D₁₉	1	4	yes	—
491	C₂×C₄	C₂³×D₁₉	1	2	yes	—
492	C₂×C₄	C₂³×D₁₉	1	2	yes	—
493	C₂×C₄	C₂³×D₁₉	1	2	yes	—
494	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
495	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
496	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
497	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	2	no	—
504	C₂²	—	2	2	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	1	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	4	4	no	—
509	C₂²	—	19	4	no	—
510	C₂²	—	38	2	no	—
511	C₂²	—	38	2	no	—
512	C₂²	—	38	2	no	—
513	C₂²	—	38	2	no	—
514	C₂²	—	38	2	no	—
515	C₂²	—	76	8	no	—
516	C₂²	C₂×D₄×D₁₉	1	2	yes	—
517	C₂²	#10597436	1	2	yes	complemented
518	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
519	C₄	—	2	1	no	—
520	C₄	—	2	1	no	—
521	C₄	—	2	2	no	—
522	C₄	—	2	2	no	—
523	C₄	—	2	2	no	—
524	C₄	—	19	4	no	—
525	C₄	—	38	2	no	—
526	C₄	—	38	4	no	—
527	C₄	—	38	4	no	—
528	C₄	C₂×D₄×D₁₉	1	2	yes	—
529	C₄	C₂×D₄×D₁₉	1	2	yes	—
530	C₂	—	2	2	no	—
531	C₂	—	2	2	no	—
532	C₂	—	4	1	no	—
533	C₂	—	4	2	no	—
534	C₂	—	38	4	no	—
535	C₂	—	76	2	no	—
536	C₂	C₂²×D₄×D₁₉	1	1	yes	characteristic
537	C₂	C₂×#10597436	1	1	yes	characteristic
538	C₂	#11927380	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#525	C₂
hypercenter	#525	D₁₉
hypocenter	C₁₉	#3489
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #525

Complements

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

N	H ≅ G/N	type
1. C₂×#10597436	C₂	semidirect
2. C₂²×#64541	C₂	semidirect
3. D₄×Dic₃₈	C₂	semidirect
4. #11927203	C₂	semidirect
5. #11927199	C₂	semidirect
6. #11927192	C₂	semidirect
7. #11927190	C₂	semidirect
8. #11927181	C₂	semidirect
9. #11927123	C₂	semidirect
10. #11927122	C₂	semidirect
11. #11927120	C₂	semidirect
12. #11927117	C₂	semidirect
13. #11927054	C₂	semidirect
14. C₂×#10597370	C₂	semidirect
15. C₂²⋊Q₈×D₁₉	C₂	semidirect
16. #11927024	C₂	semidirect
17. C₁₉×#525	C₂	semidirect
18. C₂×#41×C₁₉	C₂²	semidirect
22. C₂×Q₈×D₁₉	C₂²	semidirect
23. C₂×#64543	C₂²	semidirect
24. C₂×#64543	C₂²	semidirect
32. C₂×#64541	C₂²	semidirect
36. C₂²×Dic₃₈	C₂²	semidirect
37. C₂²×Dic₃₈	C₂²	semidirect
38. C₁₉×#123	C₂²	semidirect
40. C₁₉×C₂²⋊Q₈	C₂²	semidirect
42. C₁₉×#121	C₂²	semidirect
45. C₄×D₄×C₁₉	C₂²	semidirect
46. C₁₉×#117	C₂²	semidirect
48. #10597392	C₂²	semidirect
49. #10597385	C₂²	semidirect
50. #10597385	C₂²	semidirect
51. #10597384	C₂²	semidirect
52. #10597384	C₂²	semidirect
55. #10597376	C₂²	semidirect
56. C₂×C₄⋊Dic₁₉	C₂²	semidirect
59. #10597370	C₂²	semidirect
60. #10597370	C₂²	semidirect
61. #10597370	C₂²	semidirect
62. C₂×Dic₁₉⋊C₄	C₂²	semidirect
63. #10597343	C₂²	semidirect
64. #10597343	C₂²	semidirect
65. #10597342	C₂²	semidirect
66. #10597340	C₂²	semidirect
67. #10597338	C₂²	semidirect
68. C₄⋊C₄×D₁₉	C₂²	semidirect
69. C₄⋊C₄×D₁₉	C₂²	semidirect
70. #10597334	C₂²	semidirect
71. #10597332	C₂²	semidirect
72. #10597331	C₂²	semidirect
73. #10597330	C₂²	semidirect
74. #10597329	C₂²	semidirect
75. #10597329	C₂²	semidirect
76. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
77. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
80. #10597324	C₂²	semidirect
81. #10597321	C₂²	semidirect
82. C₄×D₇₆	C₂²	semidirect
83. #10597315	C₂²	semidirect
84. C₄×Dic₃₈	C₂²	semidirect
121. #64541	D₄	semidirect
241. C₂²×C₁₉	2₋¹⁺⁴	semidirect
274. #525	D₁₉	semidirect
298. C₂×#41	C₂×D₁₉	semidirect
315. #123	C₂×D₁₉	semidirect
328. C₂²⋊Q₈	C₂×D₁₉	semidirect
336. #121	C₂×D₁₉	semidirect
345. C₄×D₄	C₂×D₁₉	semidirect
347. #117	C₂×D₁₉	semidirect
354. C₁₉	#3489	semidirect
517. C₂²	#10597436	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10597436	2
C₂²×#64541	2
D₄×Dic₃₈	2
#11927203	2
#11927199	2
#11927192	2
#11927190	2
#11927181	2
#11927123	2
#11927122	2
#11927120	2
#11927117	2
#11927054	2
C₂×#10597370	2
C₂²⋊Q₈×D₁₉	2
#11927024	2
C₁₉×#525	2
#3489	19