Subgroups — #14577389

Order 2432.

1022 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927264	C₂	1	2	yes	maximal, complemented
2	#11927251	C₂	1	2	yes	maximal, complemented
3	#11927234	C₂	1	2	yes	maximal, complemented
4	#11927234	C₂	1	2	yes	maximal, complemented
5	#11927231	C₂	1	4	yes	maximal, complemented
6	#11927225	C₂	1	4	yes	maximal, complemented
7	#11927172	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927161	C₂	1	2	yes	maximal, complemented
9	#11927154	C₂	1	2	yes	maximal, complemented
10	#11927115	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927096	C₂	1	2	yes	maximal, complemented
12	#11927075	C₂	1	2	yes	maximal, complemented
13	C₂×#10597370	C₂	1	1	yes	maximal, characteristic, complemented
14	#11927027	C₂	1	1	yes	maximal, characteristic, complemented
15	#11927021	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#10597372	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#525	C₂	1	1	yes	maximal, characteristic
18	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
19	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
21	C₁₉×#123	C₂²	1	2	yes	—
22	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₁₉×#121	C₂²	1	1	yes	characteristic
25	C₁₉×#121	C₂²	1	1	yes	characteristic
26	C₁₉×#120	C₂²	1	2	yes	—
27	C₄×D₄×C₁₉	C₂²	1	2	yes	—
28	C₄×D₄×C₁₉	C₂²	1	2	yes	—
29	C₁₉×#117	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
31	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
32	Q₈×Dic₁₉	C₂²	1	2	yes	complemented
33	#10597390	C₂²	1	2	yes	complemented
34	#10597382	C₂²	1	4	yes	—
35	#10597382	C₂²	1	2	yes	complemented
36	#10597381	C₂²	1	4	yes	—
37	#10597381	C₂²	1	4	yes	—
38	#10597381	C₂²	1	4	yes	—
39	D₄×Dic₁₉	C₂²	1	4	yes	—
40	D₄×Dic₁₉	C₂²	1	4	yes	—
41	D₄×Dic₁₉	C₂²	1	2	yes	complemented
42	#10597372	C₂²	1	1	yes	characteristic
43	#10597372	C₂²	1	2	yes	—
44	#10597372	C₂²	1	2	yes	—
45	#10597372	C₂²	1	1	yes	characteristic
46	#10597372	C₂²	1	1	yes	characteristic
47	#10597372	C₂²	1	1	yes	characteristic
48	#10597372	C₂²	1	2	yes	complemented
49	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
50	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
51	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	complemented
53	#10597370	C₂²	1	2	yes	—
54	#10597370	C₂²	1	2	yes	—
55	#10597370	C₂²	1	2	yes	—
56	#10597370	C₂²	1	2	yes	—
57	#10597370	C₂²	1	2	yes	complemented
58	#10597370	C₂²	1	2	yes	complemented
59	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
60	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
61	#10597336	C₂²	1	2	yes	complemented
62	#10597336	C₂²	1	4	yes	complemented
63	#10597335	C₂²	1	4	yes	complemented
64	#10597335	C₂²	1	4	yes	complemented
65	#10597334	C₂²	1	2	yes	complemented
66	#10597333	C₂²	1	2	yes	complemented
67	#10597333	C₂²	1	2	yes	complemented
68	#10597333	C₂²	1	4	yes	complemented
69	#10597325	C₂²	1	4	yes	—
70	#10597325	C₂²	1	4	yes	—
71	#10597325	C₂²	1	4	yes	complemented
72	#10597325	C₂²	1	4	yes	complemented
73	#10597324	C₂²	1	4	yes	—
74	#10597324	C₂²	1	4	yes	—
75	#10597324	C₂²	1	4	yes	complemented
76	#10597323	C₂²	1	4	yes	—
77	#10597323	C₂²	1	4	yes	—
78	#10597323	C₂²	1	4	yes	complemented
79	#10597316	C₂²	1	2	yes	complemented
80	#10597315	C₂²	1	2	yes	complemented
81	C₄×Dic₃₈	C₂²	1	2	yes	complemented
82	C₄×Dic₃₈	C₂²	1	2	yes	complemented
83	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
84	#41×C₁₉	—	2	4	no	—
85	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₁₉	C₂³	1	2	yes	—
87	C₂×D₄×C₁₉	C₂³	1	2	yes	—
88	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×D₄×C₁₉	C₂³	1	2	yes	—
90	C₂²×C₄×C₁₉	—	2	4	no	—
91	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
94	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
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×Dic₁₉	C₂³	1	2	yes	—
99	C₂²×Dic₁₉	C₂³	1	2	yes	—
100	C₂²×Dic₁₉	C₂³	1	4	yes	—
101	C₂²×Dic₁₉	C₂³	1	2	yes	—
102	C₂²×Dic₁₉	C₂³	1	2	yes	—
103	C₂×Dic₃₈	—	2	4	no	—
104	C₂×Dic₃₈	C₂³	1	2	yes	—
105	C₂×Dic₃₈	C₂³	1	2	yes	—
106	C₂×Dic₃₈	C₂³	1	4	yes	—
107	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
108	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
109	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
110	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
111	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
112	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
113	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
114	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
115	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
116	C₄²×C₁₉	C₂³	1	2	yes	—
117	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
118	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
119	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
120	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
121	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
122	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
123	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
124	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
125	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
126	C₄⋊Dic₁₉	C₂³	1	4	yes	—
127	C₄⋊Dic₁₉	C₂³	1	4	yes	—
128	C₄⋊Dic₁₉	C₂³	1	2	yes	—
129	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
130	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
131	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
132	C₄⋊Dic₁₉	C₂³	1	2	yes	—
133	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
134	C₄⋊Dic₁₉	C₂³	1	2	yes	—
135	C₄⋊Dic₁₉	C₂³	1	2	yes	—
136	Dic₁₉⋊C₄	C₂³	1	4	yes	—
137	Dic₁₉⋊C₄	C₂³	1	4	yes	—
138	Dic₁₉⋊C₄	C₂³	1	4	yes	—
139	Dic₁₉⋊C₄	C₂³	1	4	yes	—
140	Dic₁₉⋊C₄	C₂³	1	4	yes	—
141	Dic₁₉⋊C₄	C₂³	1	4	yes	—
142	Dic₁₉⋊C₄	C₂³	1	4	yes	—
143	Dic₁₉⋊C₄	C₂³	1	4	yes	—
144	C₄×Dic₁₉	C₂³	1	4	yes	—
145	C₄×Dic₁₉	C₂³	1	4	yes	—
146	C₄×Dic₁₉	C₂³	1	2	yes	—
147	C₄×Dic₁₉	C₂³	1	4	yes	—
148	C₄×Dic₁₉	C₂³	1	2	yes	—
149	C₄×Dic₁₉	C₂³	1	2	yes	—
150	C₄×Dic₁₉	C₂³	1	2	yes	—
151	C₂³×C₁₉	—	2	2	no	—
152	C₂³×C₁₉	—	2	2	no	—
153	C₂³×C₁₉	—	4	1	no	—
154	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
155	C₂³×C₁₉	C₂⁴	1	2	yes	—
156	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
157	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
158	Q₈×C₁₉	—	2	2	no	—
159	D₄×C₁₉	—	2	4	no	—
160	D₄×C₁₉	—	2	4	no	—
161	D₄×C₁₉	—	2	2	no	—
162	D₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	2	2	no	—
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	2	2	no	—
166	C₂×C₄×C₁₉	—	2	2	no	—
167	C₂×C₄×C₁₉	—	2	2	no	—
168	C₂×C₄×C₁₉	—	2	4	no	—
169	C₂×C₄×C₁₉	#41	1	4	yes	—
170	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
172	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
173	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
174	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
177	C₂×Dic₁₉	—	2	4	no	—
178	C₂×Dic₁₉	—	2	4	no	—
179	C₂×Dic₁₉	—	4	2	no	—
180	C₂×Dic₁₉	—	4	2	no	—
181	C₂×Dic₁₉	—	4	4	no	—
182	C₂×Dic₁₉	C₂⁴	1	2	yes	—
183	C₂×Dic₁₉	C₂⁴	1	2	yes	—
184	C₂×Dic₁₉	C₂⁴	1	2	yes	—
185	C₂×Dic₁₉	C₂⁴	1	4	yes	—
186	C₂×Dic₁₉	C₂⁴	1	2	yes	—
187	C₂×Dic₁₉	C₂⁴	1	4	yes	—
188	Dic₃₈	—	2	4	no	—
189	Dic₃₈	—	2	4	no	—
190	Dic₃₈	—	4	4	no	—
191	#3495	—	19	1	no	maximal, Sylow
192	C₂²×C₁₉	—	2	1	no	—
193	C₂²×C₁₉	—	2	1	no	—
194	C₂²×C₁₉	—	2	1	no	—
195	C₂²×C₁₉	—	2	1	no	—
196	C₂²×C₁₉	—	2	1	no	—
197	C₂²×C₁₉	—	2	2	no	—
198	C₂²×C₁₉	—	2	2	no	—
199	C₂²×C₁₉	—	2	1	no	—
200	C₂²×C₁₉	—	2	2	no	—
201	C₂²×C₁₉	—	2	1	no	—
202	C₂²×C₁₉	—	4	4	no	—
203	C₂²×C₁₉	C₂×#41	1	2	yes	—
204	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
205	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
206	C₄×C₁₉	—	2	1	no	—
207	C₄×C₁₉	—	2	1	no	—
208	C₄×C₁₉	—	2	2	no	—
209	C₄×C₁₉	—	2	2	no	—
210	C₄×C₁₉	—	2	2	no	—
211	C₄×C₁₉	C₂×#41	1	2	yes	—
212	C₄×C₁₉	C₂×#41	1	2	yes	—
213	Dic₁₉	—	2	4	no	—
214	Dic₁₉	—	2	2	no	—
215	Dic₁₉	—	2	2	no	—
216	Dic₁₉	—	2	2	no	—
217	Dic₁₉	—	2	4	no	—
218	Dic₁₉	—	2	2	no	—
219	#556	—	19	2	no	—
220	#554	—	19	2	no	—
221	#552	—	19	4	no	—
222	#552	—	19	2	no	—
223	#552	—	19	2	no	—
224	#551	—	19	4	no	—
225	#544	—	19	1	no	—
226	#542	—	19	2	no	—
227	#541	—	19	2	no	—
228	#536	—	19	1	no	—
229	#533	—	19	2	no	—
230	#529	—	19	2	no	—
231	#525	D₁₉	1	1	yes	characteristic
232	C₂×C₂²⋊Q₈	—	19	1	no	—
233	#520	—	19	1	no	—
234	#519	—	19	1	no	—
235	C₂×#117	—	19	1	no	—
236	C₂×C₁₉	—	2	2	no	—
237	C₂×C₁₉	—	2	2	no	—
238	C₂×C₁₉	—	4	2	no	—
239	C₂×C₁₉	—	4	1	no	—
240	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
241	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
242	C₂×C₁₉	#585	1	1	yes	characteristic
243	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
244	C₂²×Q₈	—	19	1	no	—
245	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
246	C₄⋊Q₈	—	19	2	no	—
247	C₄⋊Q₈	—	19	2	no	—
248	C₄⋊Q₈	—	19	2	no	—
249	#126	—	19	4	no	—
250	#126	—	19	4	no	—
251	#126	—	19	4	no	—
252	#126	—	19	4	no	—
253	#125	—	19	2	no	—
254	#125	—	19	4	no	—
255	#125	—	19	4	no	—
256	#125	—	19	4	no	—
257	#125	—	19	2	no	—
258	#124	—	19	4	no	—
259	#124	—	19	2	no	—
260	#123	—	19	4	no	—
261	#123	—	19	4	no	—
262	#123	—	19	4	no	—
263	#123	C₂×D₁₉	1	2	yes	—
264	C₂²⋊Q₈	—	19	2	no	—
265	C₂²⋊Q₈	—	19	2	no	—
266	C₂²⋊Q₈	—	19	2	no	—
267	C₂²⋊Q₈	—	19	2	no	—
268	C₂²⋊Q₈	—	19	2	no	—
269	C₂²⋊Q₈	—	19	2	no	—
270	C₂²⋊Q₈	—	19	4	no	—
271	C₂²⋊Q₈	—	19	4	no	—
272	C₂²⋊Q₈	—	19	4	no	—
273	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
274	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
275	#121	C₂×D₁₉	1	1	yes	characteristic
276	#121	C₂×D₁₉	1	1	yes	characteristic
277	#120	C₂×D₁₉	1	2	yes	—
278	C₄×Q₈	—	19	2	no	—
279	C₄×Q₈	—	19	2	no	—
280	C₄×Q₈	—	19	2	no	—
281	C₄×Q₈	—	19	4	no	—
282	C₄×Q₈	—	19	2	no	—
283	C₄×Q₈	—	19	2	no	—
284	C₄×D₄	—	19	4	no	—
285	C₄×D₄	—	19	4	no	—
286	C₄×D₄	—	19	2	no	—
287	C₄×D₄	C₂×D₁₉	1	2	yes	—
288	C₄×D₄	C₂×D₁₉	1	2	yes	—
289	#117	—	19	1	no	—
290	#117	—	19	1	no	—
291	#117	—	19	2	no	—
292	#117	—	19	1	no	—
293	#117	—	19	2	no	—
294	#117	—	19	1	no	—
295	#117	—	19	2	no	—
296	#117	—	19	4	no	—
297	#117	—	19	4	no	—
298	#117	—	19	4	no	—
299	#117	C₂×D₁₉	1	1	yes	characteristic
300	C₂×C₄⋊C₄	—	19	1	no	—
301	C₂×C₄⋊C₄	—	19	1	no	—
302	C₂×C₄⋊C₄	—	19	1	no	—
303	C₂×C₄⋊C₄	—	19	2	no	—
304	C₂×C₄⋊C₄	—	19	2	no	—
305	C₂×C₂²⋊C₄	—	19	2	no	—
306	C₂×C₂²⋊C₄	—	19	2	no	—
307	C₂×C₄²	—	19	2	no	—
308	C₁₉	#3495	1	1	yes	characteristic, complemented, Sylow
309	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
310	#41	—	2	4	no	—
311	C₂×Q₈	—	19	2	no	—
312	C₂×Q₈	—	19	2	no	—
313	C₂×Q₈	—	19	4	no	—
314	C₂×Q₈	—	38	4	no	—
315	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
316	C₂×D₄	C₂²×D₁₉	1	2	yes	—
317	C₂×D₄	C₂²×D₁₉	1	2	yes	—
318	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
319	C₂×D₄	C₂²×D₁₉	1	2	yes	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	19	2	no	—
322	C₂²×C₄	—	19	2	no	—
323	C₂²×C₄	—	19	2	no	—
324	C₂²×C₄	—	19	2	no	—
325	C₂²×C₄	—	19	4	no	—
326	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
327	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
328	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
329	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
330	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
331	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
332	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
333	C₄⋊C₄	—	19	4	no	—
334	C₄⋊C₄	—	19	4	no	—
335	C₄⋊C₄	—	19	4	no	—
336	C₄⋊C₄	—	19	4	no	—
337	C₄⋊C₄	—	19	4	no	—
338	C₄⋊C₄	—	19	4	no	—
339	C₄⋊C₄	—	19	4	no	—
340	C₄⋊C₄	—	19	4	no	—
341	C₄⋊C₄	—	19	1	no	—
342	C₄⋊C₄	—	19	2	no	—
343	C₄⋊C₄	—	19	1	no	—
344	C₄⋊C₄	—	19	2	no	—
345	C₄⋊C₄	—	19	1	no	—
346	C₄⋊C₄	—	19	1	no	—
347	C₄⋊C₄	—	19	2	no	—
348	C₄⋊C₄	—	19	2	no	—
349	C₄⋊C₄	—	19	4	no	—
350	C₄⋊C₄	—	19	4	no	—
351	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
352	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
353	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
354	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
355	C₂²⋊C₄	—	19	2	no	—
356	C₂²⋊C₄	—	19	2	no	—
357	C₂²⋊C₄	—	19	2	no	—
358	C₂²⋊C₄	—	19	2	no	—
359	C₂²⋊C₄	—	19	4	no	—
360	C₂²⋊C₄	—	19	4	no	—
361	C₂²⋊C₄	—	19	4	no	—
362	C₂²⋊C₄	—	19	4	no	—
363	C₂²⋊C₄	—	19	4	no	—
364	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
365	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
366	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
367	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
368	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
369	C₄²	—	19	2	no	—
370	C₄²	—	19	2	no	—
371	C₄²	—	19	2	no	—
372	C₄²	—	19	2	no	—
373	C₄²	—	19	4	no	—
374	C₄²	—	19	4	no	—
375	C₄²	—	19	4	no	—
376	C₄²	C₂²×D₁₉	1	2	yes	—
377	C₂³	—	2	2	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	4	1	no	—
380	C₂³	C₂³×D₁₉	1	1	yes	characteristic
381	C₂³	C₂³×D₁₉	1	2	yes	—
382	C₂³	C₂³×D₁₉	1	1	yes	characteristic
383	C₂³	C₂³×D₁₉	1	1	yes	characteristic
384	Q₈	—	2	2	no	—
385	Q₈	—	38	4	no	—
386	Q₈	—	38	4	no	—
387	Q₈	—	76	4	no	—
388	D₄	—	2	4	no	—
389	D₄	—	2	4	no	—
390	D₄	—	2	2	no	—
391	D₄	—	4	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	19	2	no	—
399	C₂×C₄	—	19	2	no	—
400	C₂×C₄	—	19	2	no	—
401	C₂×C₄	—	19	4	no	—
402	C₂×C₄	—	19	2	no	—
403	C₂×C₄	—	19	4	no	—
404	C₂×C₄	—	38	4	no	—
405	C₂×C₄	—	38	4	no	—
406	C₂×C₄	—	76	4	no	—
407	C₂×C₄	—	76	2	no	—
408	C₂×C₄	—	76	2	no	—
409	C₂×C₄	#64543	1	4	yes	—
410	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
411	C₂×C₄	C₂³×D₁₉	1	2	yes	—
412	C₂×C₄	C₂³×D₁₉	1	2	yes	—
413	C₂×C₄	C₂³×D₁₉	1	2	yes	—
414	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
415	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
416	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	2	2	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	4	4	no	—
428	C₂²	C₂×#64543	1	2	yes	—
429	C₂²	#10597436	1	2	yes	—
430	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	2	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	38	4	no	—
437	C₄	—	38	2	no	—
438	C₄	—	38	2	no	—
439	C₄	—	38	2	no	—
440	C₄	—	38	4	no	—
441	C₄	—	38	2	no	—
442	C₄	C₂×#64543	1	2	yes	—
443	C₄	C₂×#64543	1	2	yes	—
444	C₂	—	2	2	no	—
445	C₂	—	2	2	no	—
446	C₂	—	4	1	no	—
447	C₂	—	4	2	no	—
448	C₂	C₂²×#64543	1	1	yes	characteristic
449	C₂	C₂×#10597436	1	1	yes	characteristic
450	C₂	#11927380	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting, prime radical	C₁₉×#525	C₂
hypercenter	#525	D₁₉
hypocenter	C₁₉	#3495
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. #11927264	C₂	semidirect
2. #11927251	C₂	semidirect
3. #11927234	C₂	semidirect
4. #11927234	C₂	semidirect
5. #11927231	C₂	semidirect
6. #11927225	C₂	semidirect
7. #11927172	C₂	semidirect
8. #11927161	C₂	semidirect
9. #11927154	C₂	semidirect
10. #11927115	C₂	semidirect
11. #11927096	C₂	semidirect
12. #11927075	C₂	semidirect
13. C₂×#10597370	C₂	semidirect
14. #11927027	C₂	semidirect
15. #11927021	C₂	semidirect
16. C₂×#10597372	C₂	semidirect
32. Q₈×Dic₁₉	C₂²	semidirect
33. #10597390	C₂²	semidirect
35. #10597382	C₂²	semidirect
41. D₄×Dic₁₉	C₂²	semidirect
48. #10597372	C₂²	semidirect
52. C₂×C₄⋊Dic₁₉	C₂²	semidirect
57. #10597370	C₂²	semidirect
58. #10597370	C₂²	semidirect
61. #10597336	C₂²	semidirect
62. #10597336	C₂²	semidirect
63. #10597335	C₂²	semidirect
64. #10597335	C₂²	semidirect
65. #10597334	C₂²	semidirect
66. #10597333	C₂²	semidirect
67. #10597333	C₂²	semidirect
68. #10597333	C₂²	semidirect
71. #10597325	C₂²	semidirect
72. #10597325	C₂²	semidirect
75. #10597324	C₂²	semidirect
78. #10597323	C₂²	semidirect
79. #10597316	C₂²	semidirect
80. #10597315	C₂²	semidirect
81. C₄×Dic₃₈	C₂²	semidirect
82. C₄×Dic₃₈	C₂²	semidirect
308. C₁₉	#3495	semidirect

Maximal subgroups

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

subgroup	index
#11927264	2
#11927251	2
#11927234	2
#11927231	2
#11927225	2
#11927172	2
#11927161	2
#11927154	2
#11927115	2
#11927096	2
#11927075	2
C₂×#10597370	2
#11927027	2
#11927021	2
C₂×#10597372	2
C₁₉×#525	2
#3495	19