Subgroups — #14295331

Order 1920.

696 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#6650	C₂	1	1	yes	maximal, characteristic
2	C₂×#91087	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₂×(C₂×D₃)⋊#168	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₃×#168	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64744	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745967	C₂	1	1	yes	maximal, characteristic, complemented
8	#10600241	—	3	1	no	maximal, Hall
9	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
12	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
13	C₂×C₅×(C₂×D₃)⋊C₄	C₄	1	2	yes	—
14	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
15	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
16	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
17	C₂×#6650	—	2	2	no	—
18	C₂×#6650	—	2	2	no	—
19	C₂×#6650	C₄	1	4	yes	complemented
20	#91087	—	2	2	no	—
21	C₅×C₃⋊#95	C₄	1	2	yes	—
22	(C₂×D₃)⋊#168	C₄	1	4	yes	complemented
23	Dic₃×#168	—	2	2	no	—
24	#68650	—	5	1	no	maximal, Hall
25	C₂²×#681	—	3	1	no	—
26	C₄×C₅×C₂²⋊C₄	—	3	1	no	—
27	C₂×C₂²⋊#168	—	3	1	no	—
28	C₂×#3935	—	3	1	no	—
29	C₂×C₄×#168	—	3	1	no	—
30	#64744	—	3	1	no	—
31	#64744	D₃	1	1	yes	characteristic, complemented
32	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
34	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
37	C₂×C₄×C₅×D₃	—	2	1	no	—
38	C₂×C₄×C₅×D₃	—	2	1	no	—
39	C₂×C₄×C₅×D₃	—	2	1	no	—
40	C₂×C₄×C₅×D₃	—	2	1	no	—
41	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
42	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
43	C₃×C₄²×C₅	—	2	1	no	—
44	C₃×C₄²×C₅	—	2	1	no	—
45	C₂×C₃⋊#168	—	2	1	no	—
46	C₂×C₃⋊#168	—	2	1	no	—
47	C₂×C₃⋊#168	C₂×C₄	1	2	yes	—
48	C₂×C₃⋊#168	C₂×C₄	1	2	yes	—
49	C₂×C₃⋊#168	D₄	1	2	yes	—
50	C₂×C₃⋊#168	D₄	1	2	yes	—
51	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
52	C₄×C₅×Dic₃	—	2	1	no	—
53	C₄×C₅×Dic₃	—	2	1	no	—
54	C₂×C₃×#168	—	2	1	no	—
55	C₂×C₃×#168	—	2	1	no	—
56	C₂×C₃×#168	—	2	1	no	—
57	C₂×C₃×#168	—	2	1	no	—
58	C₂×C₃×#168	C₂×C₄	1	2	yes	—
59	C₂×C₃×#168	C₂×C₄	1	2	yes	—
60	#6650	—	2	8	no	—
61	C₂²×ΓL(1,𝔽₂₅)	—	5	1	no	—
62	C₂×(C₂×D₃)⋊C₈	—	5	1	no	—
63	C₂×C₈×Dic₃	—	5	1	no	—
64	C₄×(C₂×D₃)⋊C₄	D₅	1	1	yes	characteristic
65	C₂×#803	—	5	1	no	—
66	C₃×#336	—	5	1	no	—
67	#4550	—	5	1	no	—
68	C₂³×C₄×C₅	—	3	1	no	—
69	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
70	C₂×C₄²×C₅	—	3	1	no	—
71	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
72	C₂×#681	—	3	4	no	—
73	C₂×#681	—	6	2	no	—
74	C₂×#681	—	6	2	no	—
75	C₂²×#168	—	3	1	no	—
76	C₂²×#168	—	3	1	no	—
77	C₂²×#168	C₂×D₃	1	1	yes	characteristic
78	C₂²×#168	C₂×D₃	1	1	yes	characteristic
79	C₅×#95	—	3	2	no	—
80	C₂²⋊#168	—	3	4	no	—
81	#3935	—	6	2	no	—
82	C₄×#168	—	6	2	no	—
83	#1753	—	15	1	no	Sylow
84	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₅×D₃	—	2	1	no	—
86	C₂²×C₅×D₃	—	2	1	no	—
87	C₂²×C₅×D₃	—	2	2	no	—
88	C₂²×C₅×D₃	—	2	2	no	—
89	C₂²×C₅×D₃	C₄²	1	2	yes	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	—	2	2	no	—
92	C₂×C₃×C₄×C₅	—	2	2	no	—
93	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
99	C₂×C₅×Dic₃	—	2	2	no	—
100	C₂×C₅×Dic₃	—	2	1	no	—
101	C₂×C₅×Dic₃	—	2	1	no	—
102	C₂×C₅×Dic₃	—	2	2	no	—
103	C₂×C₅×Dic₃	C₄²	1	2	yes	—
104	C₂×C₅×Dic₃	M₁₆	1	4	yes	complemented
105	C₄×C₅×D₃	—	2	2	no	—
106	C₄×C₅×D₃	—	2	2	no	—
107	C₄×C₅×D₃	—	2	2	no	—
108	C₄×C₅×D₃	—	2	2	no	—
109	C₃⋊#168	—	2	2	no	—
110	C₃⋊#168	C₂²⋊C₄	1	4	yes	complemented
111	C₃×#168	—	2	2	no	—
112	C₃×#168	—	2	2	no	—
113	C₂²×C₄×D₃	C₂×D₅	1	1	yes	characteristic
114	C₂²×C₃×C₈	—	5	1	no	—
115	C₂²×C₃×C₈	—	5	1	no	—
116	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
117	C₂×(C₂×D₃)⋊C₄	Dic₅	1	2	yes	—
118	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
119	C₂²×C₃⋊C₈	—	5	1	no	—
120	C₂²×C₃⋊C₈	—	5	1	no	—
121	C₂×ΓL(1,𝔽₂₅)	—	5	4	no	—
122	C₂×ΓL(1,𝔽₂₅)	—	10	2	no	—
123	C₂×ΓL(1,𝔽₂₅)	—	10	2	no	—
124	C₃⋊#95	Dic₅	1	2	yes	—
125	(C₂×D₃)⋊C₈	—	5	4	no	—
126	C₈×Dic₃	—	10	2	no	—
127	#803	—	10	2	no	—
128	C₂⁴×C₅	—	3	1	no	—
129	C₂²×C₄×C₅	—	3	2	no	—
130	C₂²×C₄×C₅	—	3	1	no	—
131	C₂²×C₄×C₅	—	3	2	no	—
132	C₂²×C₄×C₅	—	3	2	no	—
133	C₂²×C₄×C₅	—	6	1	no	—
134	C₂²×C₄×C₅	—	6	1	no	—
135	C₂²×C₄×C₅	—	6	1	no	—
136	C₂²×C₄×C₅	—	6	1	no	—
137	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
138	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
139	C₅×C₂²⋊C₄	—	6	4	no	—
140	C₄²×C₅	—	2	1	no	—
141	C₄²×C₅	—	2	1	no	—
142	C₄²×C₅	—	6	1	no	—
143	C₄²×C₅	—	6	1	no	—
144	#681	—	6	8	no	—
145	C₂×#168	—	2	1	no	—
146	C₂×#168	—	2	1	no	—
147	C₂×#168	—	2	1	no	—
148	C₂×#168	—	2	1	no	—
149	C₂×#168	—	3	2	no	—
150	C₂×#168	—	3	2	no	—
151	C₂×#168	—	3	2	no	—
152	C₂×#168	—	3	2	no	—
153	C₂×#168	—	6	1	no	—
154	C₂×#168	—	6	1	no	—
155	C₂×#168	C₄×D₃	1	2	yes	—
156	C₂×#168	C₄×D₃	1	2	yes	—
157	C₂²×M₁₆	—	15	1	no	—
158	C₂×C₂²⋊C₈	—	15	1	no	—
159	C₂×#97	—	15	1	no	—
160	C₂×C₄×C₈	—	15	1	no	—
161	C₄×C₂²⋊C₄	—	3	1	no	—
162	#336	—	5	1	no	—
163	#336	—	15	1	no	—
164	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
165	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
166	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
167	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
168	C₂²×C₃×C₅	#131	1	2	yes	—
169	C₂×C₅×D₃	—	2	2	no	—
170	C₂×C₅×D₃	—	2	2	no	—
171	C₂×C₅×D₃	—	2	2	no	—
172	C₂×C₅×D₃	—	4	2	no	—
173	C₂×C₅×D₃	—	4	2	no	—
174	C₃×C₄×C₅	—	4	2	no	—
175	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₃×C₄×C₅	#117	1	1	yes	characteristic
177	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
178	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
179	C₅×Dic₃	—	2	2	no	—
180	C₅×Dic₃	—	2	4	no	—
181	C₂³×D₃	C₂×Dic₅	1	1	yes	characteristic
182	C₂²×C₃×C₄	C₂×Dic₅	1	2	yes	—
183	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
184	C₂²×Dic₃	C₂×Dic₅	1	2	yes	—
185	C₂²×Dic₃	C₂×Dic₅	1	1	yes	characteristic
186	C₂×C₄×D₃	—	2	1	no	—
187	C₂×C₄×D₃	—	2	1	no	—
188	C₂×C₄×D₃	—	2	1	no	—
189	C₂×C₄×D₃	—	2	1	no	—
190	C₂×C₄×D₃	C₄×D₅	1	2	yes	—
191	C₂×C₄×D₃	C₄×D₅	1	2	yes	—
192	C₂×C₃×C₈	—	5	2	no	—
193	C₂×C₃×C₈	—	5	2	no	—
194	C₂×C₃×C₈	—	10	1	no	—
195	C₂×C₃×C₈	—	10	1	no	—
196	C₂×C₃×C₈	—	10	1	no	—
197	C₂×C₃×C₈	—	10	1	no	—
198	C₃×C₄²	—	2	1	no	—
199	C₃×C₄²	—	2	1	no	—
200	(C₂×D₃)⋊C₄	—	2	4	no	—
201	C₄×Dic₃	—	2	1	no	—
202	C₄×Dic₃	—	2	1	no	—
203	C₂×C₃⋊C₈	—	5	2	no	—
204	C₂×C₃⋊C₈	—	5	2	no	—
205	C₂×C₃⋊C₈	—	5	2	no	—
206	C₂×C₃⋊C₈	—	5	2	no	—
207	C₂×C₃⋊C₈	—	10	1	no	—
208	C₂×C₃⋊C₈	—	10	1	no	—
209	ΓL(1,𝔽₂₅)	—	10	8	no	—
210	C₂³×C₅	—	3	2	no	—
211	C₂³×C₅	—	6	1	no	—
212	C₂³×C₅	—	6	1	no	—
213	C₂³×C₅	—	6	2	no	—
214	C₂³×C₅	—	6	2	no	—
215	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	2	no	—
218	C₂×C₄×C₅	—	2	2	no	—
219	C₂×C₄×C₅	—	3	2	no	—
220	C₂×C₄×C₅	—	3	4	no	—
221	C₂×C₄×C₅	—	6	1	no	—
222	C₂×C₄×C₅	—	6	2	no	—
223	C₂×C₄×C₅	—	6	1	no	—
224	C₂×C₄×C₅	—	6	2	no	—
225	C₂×C₄×C₅	—	6	2	no	—
226	C₂×C₄×C₅	—	6	2	no	—
227	C₂×C₄×C₅	—	6	2	no	—
228	C₂×C₄×C₅	—	6	2	no	—
229	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
231	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
232	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
233	C₂×C₄×C₅	#237	1	1	yes	characteristic
234	C₂×C₄×C₅	#239	1	1	yes	characteristic
235	#168	—	2	2	no	—
236	#168	—	2	2	no	—
237	#168	—	3	4	no	—
238	#168	—	6	2	no	—
239	C₂³×C₄	—	3	1	no	—
240	C₂×M₁₆	—	15	4	no	—
241	C₂×M₁₆	—	30	2	no	—
242	C₂×M₁₆	—	30	2	no	—
243	C₂²×C₈	—	5	1	no	—
244	C₂²×C₈	—	5	1	no	—
245	C₂²×C₈	—	15	1	no	—
246	C₂²×C₈	—	15	1	no	—
247	C₂×C₂²⋊C₄	—	3	2	no	—
248	C₂×C₄²	—	3	1	no	—
249	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
250	C₂²⋊C₈	—	15	4	no	—
251	#97	—	30	2	no	—
252	C₄×C₈	—	30	2	no	—
253	#95	—	3	2	no	—
254	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
255	C₂×C₃×C₅	C₄×M₁₆	1	1	yes	characteristic
256	C₂×C₃×C₅	#405	1	1	yes	characteristic
257	C₂×C₃×C₅	#435	1	2	yes	—
258	C₂×C₃×C₅	#436	1	2	yes	—
259	C₅×D₃	—	4	2	no	—
260	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
261	C₂²×D₃	—	2	2	no	—
262	C₂²×D₃	—	2	1	no	—
263	C₂²×D₃	—	2	1	no	—
264	C₂²×D₃	—	2	2	no	—
265	C₂²×D₃	C₄×Dic₅	1	2	yes	—
266	C₂×C₃×C₄	—	2	2	no	—
267	C₂×C₃×C₄	—	2	2	no	—
268	C₂×C₃×C₄	—	2	2	no	—
269	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
270	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
271	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
272	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
273	C₂×C₃×C₄	#711	1	1	yes	characteristic
274	C₂×C₃×C₄	#711	1	1	yes	characteristic
275	C₂×Dic₃	—	2	2	no	—
276	C₂×Dic₃	—	2	1	no	—
277	C₂×Dic₃	—	2	1	no	—
278	C₂×Dic₃	—	2	2	no	—
279	C₂×Dic₃	#681	1	4	yes	complemented
280	C₂×Dic₃	C₄×Dic₅	1	2	yes	—
281	C₄×D₃	—	2	2	no	—
282	C₄×D₃	—	2	2	no	—
283	C₄×D₃	—	2	2	no	—
284	C₄×D₃	—	2	2	no	—
285	C₃×C₈	—	10	2	no	—
286	C₃×C₈	—	10	2	no	—
287	C₃⋊C₈	—	5	4	no	—
288	C₃⋊C₈	—	10	2	no	—
289	C₂²×C₅	—	6	2	no	—
290	C₂²×C₅	—	6	2	no	—
291	C₂²×C₅	—	6	2	no	—
292	C₂²×C₅	—	12	2	no	—
293	C₂²×C₅	—	12	2	no	—
294	C₂²×C₅	C₄²×D₃	1	1	yes	characteristic
295	C₂²×C₅	#67⋊C₄	1	1	yes	characteristic
296	C₂²×C₅	#893	1	1	yes	characteristic
297	C₂²×C₅	#901	1	2	yes	—
298	C₂²×C₅	D₃×M₁₆	1	2	yes	—
299	C₄×C₅	—	4	2	no	—
300	C₄×C₅	—	6	2	no	—
301	C₄×C₅	—	6	4	no	—
302	C₄×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
303	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
304	C₄×C₅	#892	1	1	yes	characteristic
305	C₄×C₅	#893	1	1	yes	characteristic
306	C₂⁴	—	3	1	no	—
307	C₂²×C₄	—	3	1	no	—
308	C₂²×C₄	—	3	2	no	—
309	C₂²×C₄	—	3	2	no	—
310	C₂²×C₄	—	3	2	no	—
311	C₂²×C₄	—	6	1	no	—
312	C₂²×C₄	—	6	1	no	—
313	C₂²×C₄	—	6	1	no	—
314	C₂²×C₄	—	6	1	no	—
315	C₂²×C₄	D₃×Dic₅	1	2	yes	—
316	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
317	M₁₆	—	30	8	no	—
318	C₂×C₈	—	5	2	no	—
319	C₂×C₈	—	5	2	no	—
320	C₂×C₈	—	10	1	no	—
321	C₂×C₈	—	10	1	no	—
322	C₂×C₈	—	10	1	no	—
323	C₂×C₈	—	10	1	no	—
324	C₂×C₈	—	15	2	no	—
325	C₂×C₈	—	15	2	no	—
326	C₂×C₈	—	15	2	no	—
327	C₂×C₈	—	15	2	no	—
328	C₂×C₈	—	30	1	no	—
329	C₂×C₈	—	30	1	no	—
330	C₂²⋊C₄	—	6	4	no	—
331	C₄²	—	2	1	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	6	1	no	—
334	C₄²	—	6	1	no	—
335	C₃×C₅	#1753	1	1	yes	characteristic, complemented, Hall
336	C₂²×C₃	C₂×#681	1	2	yes	—
337	C₂²×C₃	C₂×C₄×Dic₅	1	1	yes	characteristic
338	C₂²×C₃	D₄×Dic₅	1	1	yes	characteristic
339	C₂²×C₃	D₄×Dic₅	1	1	yes	characteristic
340	C₂²×C₃	#4094	1	2	yes	—
341	C₂×D₃	—	2	2	no	—
342	C₂×D₃	—	2	2	no	—
343	C₂×D₃	—	2	2	no	—
344	C₂×D₃	—	4	2	no	—
345	C₂×D₃	—	4	2	no	—
346	C₃×C₄	—	4	2	no	—
347	C₃×C₄	#4023	1	1	yes	characteristic
348	C₃×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
349	C₃×C₄	#4027	1	1	yes	characteristic
350	C₃×C₄	#4027	1	1	yes	characteristic
351	Dic₃	—	2	4	no	—
352	Dic₃	—	2	2	no	—
353	C₂×C₅	—	12	2	no	—
354	C₂×C₅	#4666	1	1	yes	characteristic
355	C₂×C₅	#4689	1	1	yes	characteristic
356	C₂×C₅	#4707	1	1	yes	characteristic
357	C₂×C₅	#4729	1	2	yes	—
358	C₂×C₅	#4836	1	2	yes	—
359	C₂³	—	3	2	no	—
360	C₂³	—	6	1	no	—
361	C₂³	—	6	2	no	—
362	C₂³	—	6	2	no	—
363	C₂³	—	6	1	no	—
364	C₂³	C₂×D₃×Dic₅	1	1	yes	characteristic
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	3	2	no	—
369	C₂×C₄	—	3	4	no	—
370	C₂×C₄	—	6	2	no	—
371	C₂×C₄	—	6	1	no	—
372	C₂×C₄	—	6	2	no	—
373	C₂×C₄	—	6	1	no	—
374	C₂×C₄	—	6	2	no	—
375	C₂×C₄	—	6	2	no	—
376	C₂×C₄	—	6	2	no	—
377	C₂×C₄	—	6	2	no	—
378	C₂×C₄	#6768	1	1	yes	characteristic
379	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
380	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
381	C₂×C₄	#6777	1	1	yes	characteristic
382	C₂×C₄	#6780	1	1	yes	characteristic
383	C₂×C₄	#6790	1	1	yes	characteristic
384	C₈	—	10	2	no	—
385	C₈	—	10	2	no	—
386	C₈	—	15	4	no	—
387	C₈	—	30	2	no	—
388	C₂×C₃	C₄×#681	1	1	yes	characteristic
389	C₂×C₃	C₂²⋊C₄×Dic₅	1	1	yes	characteristic
390	C₂×C₃	#65286	1	1	yes	characteristic
391	C₂×C₃	#65300	1	2	yes	—
392	C₂×C₃	#65301	1	2	yes	—
393	D₃	—	4	2	no	—
394	C₅	#68650	1	1	yes	characteristic, complemented, Sylow
395	C₂²	—	6	2	no	—
396	C₂²	—	6	2	no	—
397	C₂²	—	6	2	no	—
398	C₂²	—	12	2	no	—
399	C₂²	—	12	2	no	—
400	C₂²	#91286	1	2	yes	—
401	C₂²	D₃×#681	1	2	yes	—
402	C₂²	C₄×D₃×Dic₅	1	1	yes	characteristic
403	C₂²	#91435	1	1	yes	characteristic
404	C₂²	#67⋊Dic₅	1	1	yes	characteristic
405	C₄	—	4	2	no	—
406	C₄	—	6	2	no	—
407	C₄	—	6	4	no	—
408	C₄	#91400	1	1	yes	characteristic
409	C₄	#91406	1	1	yes	characteristic
410	C₄	#91442	1	1	yes	characteristic
411	C₄	#91473	1	1	yes	characteristic
412	C₃	#10600241	1	1	yes	characteristic, complemented, Sylow
413	C₂	—	12	2	no	—
414	C₂	#11746977	1	1	yes	characteristic
415	C₂	#11746999	1	2	yes	—
416	C₂	#11747005	1	1	yes	characteristic
417	C₂	#11748314	1	2	yes	—
418	C₂	#11748886	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂×D₃×D₅
commutator	C₂²×C₃×C₅	C₂×C₄²
Fitting	C₂×C₃×C₄²×C₅	C₂²
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂³×C₅×D₃	C₂×C₄
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	#1753
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×#91087	C₂	semidirect
5. C₂×Dic₃×#168	C₂	semidirect
6. C₃×#64744	C₂	semidirect
7. #11745967	C₂	semidirect
19. C₂×#6650	C₄	semidirect
22. (C₂×D₃)⋊#168	C₄	semidirect
31. #64744	D₃	semidirect
104. C₂×C₅×Dic₃	M₁₆	semidirect
110. C₃⋊#168	C₂²⋊C₄	semidirect
279. C₂×Dic₃	#681	semidirect
335. C₃×C₅	#1753	semidirect
394. C₅	#68650	semidirect
412. C₃	#10600241	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#6650	2
C₂×#91087	2
C₄×C₅×(C₂×D₃)⋊C₄	2
C₂×(C₂×D₃)⋊#168	2
C₂×Dic₃×#168	2
C₃×#64744	2
#11745967	2
#10600241	3
#68650	5