Subgroups — #14577862

Order 2432.

1134 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	#11927291	C₂	1	4	yes	maximal, complemented
2	#11927251	C₂	1	2	yes	maximal, complemented
3	#11927203	C₂	1	2	yes	maximal, complemented
4	#11927198	C₂	1	2	yes	maximal, complemented
5	#11927190	C₂	1	2	yes	maximal, complemented
6	#11927181	C₂	1	4	yes	maximal, complemented
7	#11927169	C₂	1	2	yes	maximal, complemented
8	#11927165	C₂	1	2	yes	maximal, complemented
9	#11927143	C₂	1	2	yes	maximal, complemented
10	#11927131	C₂	1	2	yes	maximal, complemented
11	#11927122	C₂	1	2	yes	maximal, complemented
12	#11927121	C₂	1	2	yes	maximal, complemented
13	C₂×#10597370	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#10597376	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#525	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic, complemented
17	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊D₁₉	C₂²	1	2	yes	—
19	C₂×#64543	C₂²	1	4	yes	complemented
20	C₂×#64541	C₂²	1	2	yes	complemented
21	C₂²×D₇₆	C₂²	1	1	yes	characteristic
22	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
23	C₁₉×#123	C₂²	1	2	yes	complemented
24	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₁₉×#121	C₂²	1	1	yes	characteristic
27	C₁₉×#121	C₂²	1	1	yes	characteristic, complemented
28	C₁₉×#120	C₂²	1	2	yes	—
29	C₄×D₄×C₁₉	C₂²	1	2	yes	—
30	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
31	C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
33	#10597392	C₂²	1	4	yes	complemented
34	#10597385	C₂²	1	4	yes	complemented
35	#10597385	C₂²	1	4	yes	complemented
36	#10597385	C₂²	1	4	yes	complemented
37	#10597384	C₂²	1	4	yes	complemented
38	#10597383	C₂²	1	4	yes	—
39	D₄×Dic₁₉	C₂²	1	4	yes	—
40	#10597376	C₂²	1	2	yes	—
41	#10597376	C₂²	1	2	yes	—
42	#10597376	C₂²	1	2	yes	—
43	#10597376	C₂²	1	2	yes	—
44	#10597376	C₂²	1	2	yes	complemented
45	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	—
46	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
47	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	complemented
49	#10597370	C₂²	1	2	yes	—
50	#10597370	C₂²	1	2	yes	—
51	#10597370	C₂²	1	2	yes	complemented
52	#10597370	C₂²	1	2	yes	complemented
53	#10597370	C₂²	1	2	yes	complemented
54	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	complemented
55	#10597344	C₂²	1	4	yes	complemented
56	#10597343	C₂²	1	4	yes	complemented
57	#10597342	C₂²	1	4	yes	complemented
58	#10597342	C₂²	1	4	yes	complemented
59	#10597340	C₂²	1	4	yes	complemented
60	#10597336	C₂²	1	4	yes	complemented
61	#10597332	C₂²	1	4	yes	complemented
62	#10597332	C₂²	1	4	yes	complemented
63	#10597331	C₂²	1	4	yes	complemented
64	#10597331	C₂²	1	4	yes	complemented
65	#10597330	C₂²	1	4	yes	complemented
66	#10597329	C₂²	1	4	yes	complemented
67	(C₂²⋊D₁₉)⋊C₄	C₂²	1	4	yes	complemented
68	C₂²⋊C₄×D₁₉	C₂²	1	4	yes	—
69	#10597324	C₂²	1	4	yes	—
70	#10597324	C₂²	1	4	yes	complemented
71	#10597321	C₂²	1	2	yes	complemented
72	C₄×D₇₆	C₂²	1	2	yes	complemented
73	#10597315	C₂²	1	2	yes	complemented
74	C₄×Dic₃₈	C₂²	1	2	yes	complemented
75	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
76	C₂³×D₁₉	C₂³	1	2	yes	—
77	#41×C₁₉	—	4	2	no	—
78	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
79	C₂×D₄×C₁₉	C₂³	1	2	yes	—
80	C₂×D₄×C₁₉	C₂³	1	2	yes	—
81	C₂×D₄×C₁₉	C₂³	1	2	yes	—
82	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	—	4	2	no	—
84	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
87	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×C₂²⋊D₁₉	—	4	4	no	—
92	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
93	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
94	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
96	C₂²×Dic₁₉	C₂³	1	2	yes	—
97	C₂²×Dic₁₉	C₂³	1	2	yes	—
98	C₂²×Dic₁₉	C₂³	1	4	yes	—
99	C₂²×Dic₁₉	C₂³	1	2	yes	—
100	#64543	—	4	8	no	—
101	#64541	—	4	4	no	—
102	C₂×D₇₆	—	4	2	no	—
103	C₂×D₇₆	C₂³	1	2	yes	—
104	C₂×D₇₆	C₂³	1	2	yes	—
105	C₂×C₄×D₁₉	C₂³	1	4	yes	—
106	C₂×C₄×D₁₉	C₂³	1	4	yes	—
107	C₂×Dic₃₈	—	4	2	no	—
108	C₂×Dic₃₈	C₂³	1	2	yes	—
109	C₂×Dic₃₈	C₂³	1	2	yes	—
110	C₂×Dic₃₈	C₂³	1	4	yes	—
111	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
112	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
113	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
114	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
115	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
116	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
117	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
118	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
119	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
120	C₄²×C₁₉	C₂³	1	2	yes	—
121	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
122	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
123	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
124	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
125	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
126	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
127	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
128	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
129	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
130	C₄⋊Dic₁₉	C₂³	1	2	yes	—
131	C₄⋊Dic₁₉	C₂³	1	2	yes	—
132	C₄⋊Dic₁₉	C₂³	1	2	yes	—
133	C₄⋊Dic₁₉	C₂³	1	4	yes	—
134	C₄⋊Dic₁₉	C₂³	1	4	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	C₄×Dic₁₉	C₂³	1	4	yes	—
141	C₂³×C₁₉	—	2	2	no	—
142	C₂³×C₁₉	—	2	2	no	—
143	C₂³×C₁₉	—	4	1	no	—
144	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
145	C₂³×C₁₉	C₂⁴	1	2	yes	—
146	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
147	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
148	C₂²×D₁₉	—	2	4	no	—
149	C₂²×D₁₉	—	4	2	no	—
150	C₂²×D₁₉	—	4	2	no	—
151	C₂²×D₁₉	C₂⁴	1	4	yes	—
152	Q₈×C₁₉	—	4	1	no	—
153	D₄×C₁₉	—	2	4	no	—
154	D₄×C₁₉	—	2	4	no	—
155	D₄×C₁₉	—	4	2	no	—
156	D₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	2	2	no	—
158	C₂×C₄×C₁₉	—	2	2	no	—
159	C₂×C₄×C₁₉	—	2	4	no	—
160	C₂×C₄×C₁₉	—	2	2	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
165	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
168	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
169	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
171	C₂²⋊D₁₉	—	2	8	no	—
172	C₂²⋊D₁₉	—	4	4	no	—
173	C₂²⋊D₁₉	—	4	4	no	—
174	C₂²⋊D₁₉	—	4	4	no	—
175	C₂×Dic₁₉	—	2	4	no	—
176	C₂×Dic₁₉	—	4	2	no	—
177	C₂×Dic₁₉	—	4	4	no	—
178	C₂×Dic₁₉	—	4	2	no	—
179	C₂×Dic₁₉	C₂⁴	1	4	yes	—
180	C₂×Dic₁₉	C₂⁴	1	4	yes	—
181	C₂×Dic₁₉	C₂⁴	1	4	yes	—
182	D₇₆	—	2	4	no	—
183	D₇₆	—	4	2	no	—
184	C₄×D₁₉	—	4	4	no	—
185	C₄×D₁₉	—	4	4	no	—
186	Dic₃₈	—	2	4	no	—
187	Dic₃₈	—	4	2	no	—
188	Dic₃₈	—	4	4	no	—
189	#3536	—	19	1	no	maximal, Sylow
190	C₂²×C₁₉	—	2	1	no	—
191	C₂²×C₁₉	—	2	1	no	—
192	C₂²×C₁₉	—	2	1	no	—
193	C₂²×C₁₉	—	2	1	no	—
194	C₂²×C₁₉	—	2	2	no	—
195	C₂²×C₁₉	—	2	1	no	—
196	C₂²×C₁₉	—	2	2	no	—
197	C₂²×C₁₉	—	2	1	no	—
198	C₂²×C₁₉	—	2	2	no	—
199	C₂²×C₁₉	—	2	1	no	—
200	C₂²×C₁₉	—	4	4	no	—
201	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
202	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
203	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
204	C₂×D₁₉	—	2	4	no	—
205	C₂×D₁₉	—	2	4	no	—
206	C₂×D₁₉	—	2	4	no	—
207	C₂×D₁₉	—	8	4	no	—
208	C₄×C₁₉	—	2	2	no	—
209	C₄×C₁₉	—	2	1	no	—
210	C₄×C₁₉	—	2	2	no	—
211	C₄×C₁₉	—	2	1	no	—
212	C₄×C₁₉	—	2	1	no	—
213	C₄×C₁₉	—	2	2	no	—
214	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
215	Dic₁₉	—	2	4	no	—
216	Dic₁₉	—	2	4	no	—
217	Dic₁₉	—	2	4	no	—
218	#562	—	19	4	no	—
219	#554	—	19	2	no	—
220	#548	—	19	2	no	—
221	#547	—	19	2	no	—
222	#546	—	19	4	no	—
223	#546	—	19	2	no	—
224	#543	—	19	2	no	—
225	#542	—	19	2	no	—
226	#539	—	19	2	no	—
227	#538	—	19	2	no	—
228	#537	—	19	2	no	—
229	#537	—	19	2	no	—
230	#525	D₁₉	1	1	yes	characteristic, complemented
231	C₂×C₂²⋊Q₈	—	19	1	no	—
232	C₂×#121	—	19	1	no	—
233	C₂×C₁₉	—	2	2	no	—
234	C₂×C₁₉	—	2	2	no	—
235	C₂×C₁₉	—	4	2	no	—
236	C₂×C₁₉	—	4	1	no	—
237	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
238	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
239	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
240	D₁₉	—	4	4	no	—
241	C₂×#41	—	19	4	no	—
242	C₂×#41	—	19	2	no	—
243	C₂×#41	C₂×D₁₉	1	1	yes	characteristic, complemented
244	C₂²×Q₈	—	19	1	no	—
245	C₂²×D₄	—	19	2	no	—
246	C₂²×D₄	—	19	1	no	—
247	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
248	C₄⋊Q₈	—	19	2	no	—
249	#126	—	19	4	no	—
250	#125	—	19	4	no	—
251	#124	—	19	4	no	—
252	#124	—	19	4	no	—
253	#124	—	19	2	no	—
254	#123	—	19	4	no	—
255	#123	—	19	4	no	—
256	#123	—	19	4	no	—
257	#123	—	19	4	no	—
258	#123	C₂×D₁₉	1	2	yes	complemented
259	C₂²⋊Q₈	—	19	4	no	—
260	C₂²⋊Q₈	—	19	2	no	—
261	C₂²⋊Q₈	—	19	2	no	—
262	C₂²⋊Q₈	—	19	2	no	—
263	C₂²⋊Q₈	—	19	2	no	—
264	C₂²⋊Q₈	—	19	2	no	—
265	C₂²⋊Q₈	—	19	4	no	—
266	C₂²⋊Q₈	—	19	4	no	—
267	C₂²⋊Q₈	—	19	4	no	—
268	C₂²⋊Q₈	—	19	4	no	—
269	C₂²⋊Q₈	—	19	4	no	—
270	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
271	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
272	#121	—	19	4	no	—
273	#121	—	19	4	no	—
274	#121	—	19	4	no	—
275	#121	—	19	4	no	—
276	#121	—	19	2	no	—
277	#121	—	19	2	no	—
278	#121	—	19	2	no	—
279	#121	—	19	2	no	—
280	#121	—	19	2	no	—
281	#121	—	19	4	no	—
282	#121	C₂×D₁₉	1	1	yes	characteristic
283	#121	C₂×D₁₉	1	1	yes	characteristic, complemented
284	#120	—	19	4	no	—
285	#120	C₂×D₁₉	1	2	yes	—
286	C₄×Q₈	—	19	2	no	—
287	C₄×D₄	—	19	4	no	—
288	C₄×D₄	—	19	4	no	—
289	C₄×D₄	—	19	2	no	—
290	C₄×D₄	C₂×D₁₉	1	2	yes	—
291	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
292	#117	C₂×D₁₉	1	1	yes	characteristic, complemented
293	C₂×C₄⋊C₄	—	19	1	no	—
294	C₂×C₄⋊C₄	—	19	2	no	—
295	C₂×C₄⋊C₄	—	19	1	no	—
296	C₂×C₄⋊C₄	—	19	2	no	—
297	C₂×C₂²⋊C₄	—	19	2	no	—
298	C₂×C₂²⋊C₄	—	19	2	no	—
299	C₂×C₂²⋊C₄	—	19	4	no	—
300	C₁₉	#3536	1	1	yes	characteristic, complemented, Sylow
301	C₂⁴	—	19	2	no	—
302	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
303	#41	—	4	2	no	—
304	#41	—	76	4	no	—
305	#41	—	76	8	no	—
306	C₂×Q₈	—	19	2	no	—
307	C₂×Q₈	—	19	2	no	—
308	C₂×Q₈	—	19	4	no	—
309	C₂×Q₈	—	76	2	no	—
310	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
311	C₂×D₄	—	19	4	no	—
312	C₂×D₄	—	19	4	no	—
313	C₂×D₄	—	19	4	no	—
314	C₂×D₄	—	19	4	no	—
315	C₂×D₄	—	19	2	no	—
316	C₂×D₄	—	19	2	no	—
317	C₂×D₄	—	76	2	no	—
318	C₂×D₄	—	76	4	no	—
319	C₂×D₄	C₂²×D₁₉	1	2	yes	—
320	C₂×D₄	C₂²×D₁₉	1	2	yes	—
321	C₂×D₄	C₂²×D₁₉	1	2	yes	—
322	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
323	C₂²×C₄	—	4	2	no	—
324	C₂²×C₄	—	19	2	no	—
325	C₂²×C₄	—	19	2	no	—
326	C₂²×C₄	—	19	2	no	—
327	C₂²×C₄	—	19	4	no	—
328	C₂²×C₄	—	19	4	no	—
329	C₂²×C₄	—	19	4	no	—
330	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
331	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
332	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
333	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
334	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
335	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
336	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
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	2	no	—
342	C₄⋊C₄	—	19	2	no	—
343	C₄⋊C₄	—	19	2	no	—
344	C₄⋊C₄	—	19	4	no	—
345	C₄⋊C₄	—	19	2	no	—
346	C₄⋊C₄	—	19	4	no	—
347	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
348	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
349	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
350	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
351	C₂²⋊C₄	—	19	4	no	—
352	C₂²⋊C₄	—	19	4	no	—
353	C₂²⋊C₄	—	19	4	no	—
354	C₂²⋊C₄	—	19	4	no	—
355	C₂²⋊C₄	—	19	4	no	—
356	C₂²⋊C₄	—	19	4	no	—
357	C₂²⋊C₄	—	19	4	no	—
358	C₂²⋊C₄	—	19	4	no	—
359	C₂²⋊C₄	—	19	4	no	—
360	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
361	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
362	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
363	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
364	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
365	C₄²	—	19	4	no	—
366	C₄²	C₂²×D₁₉	1	2	yes	—
367	C₂³	—	2	2	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	4	1	no	—
370	C₂³	—	19	4	no	—
371	C₂³	—	38	4	no	—
372	C₂³	—	76	2	no	—
373	C₂³	—	76	2	no	—
374	C₂³	C₂³×D₁₉	1	1	yes	characteristic
375	C₂³	C₂³×D₁₉	1	2	yes	—
376	C₂³	C₂³×D₁₉	1	1	yes	characteristic
377	C₂³	C₂³×D₁₉	1	1	yes	characteristic
378	Q₈	—	4	1	no	—
379	Q₈	—	38	4	no	—
380	Q₈	—	76	2	no	—
381	Q₈	—	76	4	no	—
382	D₄	—	2	4	no	—
383	D₄	—	2	4	no	—
384	D₄	—	4	1	no	—
385	D₄	—	4	2	no	—
386	D₄	—	38	8	no	—
387	D₄	—	38	4	no	—
388	D₄	—	76	2	no	—
389	D₄	—	76	4	no	—
390	D₄	—	76	4	no	—
391	D₄	—	76	4	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	19	4	no	—
400	C₂×C₄	—	19	4	no	—
401	C₂×C₄	—	19	4	no	—
402	C₂×C₄	—	38	4	no	—
403	C₂×C₄	—	76	4	no	—
404	C₂×C₄	—	76	4	no	—
405	C₂×C₄	—	76	2	no	—
406	C₂×C₄	—	76	2	no	—
407	C₂×C₄	—	76	4	no	—
408	C₂×C₄	C₂³×D₁₉	1	2	yes	—
409	C₂×C₄	C₂³×D₁₉	1	2	yes	—
410	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
411	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
412	C₂×C₄	C₂³×D₁₉	1	2	yes	—
413	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
414	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	2	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	4	4	no	—
426	C₂²	—	38	4	no	—
427	C₂²	—	38	4	no	—
428	C₂²	—	38	4	no	—
429	C₂²	—	152	4	no	—
430	C₂²	#10597435	1	2	yes	—
431	C₂²	#10597436	1	2	yes	—
432	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	2	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	2	no	—
439	C₄	—	38	4	no	—
440	C₄	—	38	4	no	—
441	C₄	—	38	4	no	—
442	C₄	#10597430	1	2	yes	—
443	C₂	—	2	2	no	—
444	C₂	—	2	2	no	—
445	C₂	—	4	1	no	—
446	C₂	—	4	2	no	—
447	C₂	—	76	4	no	—
448	C₂	C₂×#10597430	1	1	yes	characteristic
449	C₂	C₂×#10597435	1	1	yes	characteristic
450	C₂	C₂×#10597436	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	#3536
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. #11927291	C₂	semidirect
2. #11927251	C₂	semidirect
3. #11927203	C₂	semidirect
4. #11927198	C₂	semidirect
5. #11927190	C₂	semidirect
6. #11927181	C₂	semidirect
7. #11927169	C₂	semidirect
8. #11927165	C₂	semidirect
9. #11927143	C₂	semidirect
10. #11927131	C₂	semidirect
11. #11927122	C₂	semidirect
12. #11927121	C₂	semidirect
13. C₂×#10597370	C₂	semidirect
14. C₂×#10597376	C₂	semidirect
15. C₁₉×#525	C₂	semidirect
16. C₂×#41×C₁₉	C₂²	semidirect
19. C₂×#64543	C₂²	semidirect
20. C₂×#64541	C₂²	semidirect
22. C₂²×Dic₃₈	C₂²	semidirect
23. C₁₉×#123	C₂²	semidirect
25. C₁₉×C₂²⋊Q₈	C₂²	semidirect
27. C₁₉×#121	C₂²	semidirect
30. C₄×D₄×C₁₉	C₂²	semidirect
31. C₁₉×#117	C₂²	semidirect
33. #10597392	C₂²	semidirect
34. #10597385	C₂²	semidirect
35. #10597385	C₂²	semidirect
36. #10597385	C₂²	semidirect
37. #10597384	C₂²	semidirect
44. #10597376	C₂²	semidirect
47. C₂×C₄⋊Dic₁₉	C₂²	semidirect
48. C₂×C₄⋊Dic₁₉	C₂²	semidirect
51. #10597370	C₂²	semidirect
52. #10597370	C₂²	semidirect
53. #10597370	C₂²	semidirect
54. C₂×Dic₁₉⋊C₄	C₂²	semidirect
55. #10597344	C₂²	semidirect
56. #10597343	C₂²	semidirect
57. #10597342	C₂²	semidirect
58. #10597342	C₂²	semidirect
59. #10597340	C₂²	semidirect
60. #10597336	C₂²	semidirect
61. #10597332	C₂²	semidirect
62. #10597332	C₂²	semidirect
63. #10597331	C₂²	semidirect
64. #10597331	C₂²	semidirect
65. #10597330	C₂²	semidirect
66. #10597329	C₂²	semidirect
67. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
70. #10597324	C₂²	semidirect
71. #10597321	C₂²	semidirect
72. C₄×D₇₆	C₂²	semidirect
73. #10597315	C₂²	semidirect
74. C₄×Dic₃₈	C₂²	semidirect
230. #525	D₁₉	semidirect
243. C₂×#41	C₂×D₁₉	semidirect
258. #123	C₂×D₁₉	semidirect
271. C₂²⋊Q₈	C₂×D₁₉	semidirect
283. #121	C₂×D₁₉	semidirect
291. C₄×D₄	C₂×D₁₉	semidirect
292. #117	C₂×D₁₉	semidirect
300. C₁₉	#3536	semidirect

Maximal subgroups

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

subgroup	index
#11927291	2
#11927251	2
#11927203	2
#11927198	2
#11927190	2
#11927181	2
#11927169	2
#11927165	2
#11927143	2
#11927131	2
#11927122	2
#11927121	2
C₂×#10597370	2
C₂×#10597376	2
C₁₉×#525	2
#3536	19