Subgroups — #14295666

Order 1920.

640 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₃×#709	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3957	C₂	1	1	yes	maximal, characteristic
4	#11748611	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#90976	C₂	1	1	yes	maximal, characteristic
6	#11746376	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745978	C₂	1	1	yes	maximal, characteristic, complemented
8	#10600659	—	3	1	no	maximal, Hall
9	C₂×C₃×#709	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	#91815	C₂²	1	1	yes	characteristic
12	C₂×C₄×Dic₁₅	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
14	C₂×C₅×#208	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
16	Dic₃×C₂²⋊D₅	—	2	2	no	—
17	Dic₃×D₂₀	C₄	1	2	yes	complemented
18	C₄×D₅×Dic₃	—	2	1	no	—
19	#91357	—	2	1	no	—
20	Dic₃×Dic₁₀	C₄	1	2	yes	complemented
21	C₅×#815	—	2	1	no	—
22	C₅×C₈×Dic₃	—	2	1	no	—
23	C₃×#3957	C₄	1	4	yes	complemented
24	#90994	—	2	2	no	—
25	#90976	C₄	1	4	yes	complemented
26	#70354	—	5	1	no	maximal, Hall
27	C₄×#709	—	3	1	no	—
28	C₄×C₅×M₁₆	—	3	1	no	—
29	C₂×#3957	—	3	1	no	—
30	C₂×#3957	D₃	1	1	yes	characteristic
31	#65221	—	3	1	no	—
32	#64775	—	3	1	no	—
33	#64775	—	3	1	no	—
34	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₂²×Dic₁₅	—	2	1	no	—
36	C₂²×C₅×Dic₃	D₄	1	2	yes	—
37	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
38	C₂²×C₃×Dic₅	—	2	1	no	—
39	C₃×#709	—	2	1	no	—
40	C₃×#709	—	2	1	no	—
41	C₃×#709	C₂×C₄	1	2	yes	—
42	C₃×#709	C₂×C₄	1	2	yes	—
43	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃×C₄×D₅	—	2	1	no	—
45	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
46	C₂×D₅×Dic₃	—	2	2	no	—
47	C₃×C₅×M₁₆	—	2	1	no	—
48	C₃×C₅×M₁₆	C₂×C₄	1	2	yes	complemented
49	C₂×C₃×C₅×C₈	—	2	1	no	—
50	#6719	—	2	1	no	—
51	C₄⋊Dic₁₅	C₂×C₄	1	2	yes	—
52	C₄×Dic₁₅	—	2	1	no	—
53	C₄×Dic₁₅	—	2	1	no	—
54	C₄×Dic₁₅	C₂×C₄	1	2	yes	complemented
55	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
56	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
57	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
58	C₅×#208	—	2	1	no	—
59	C₅×#208	C₂×C₄	1	2	yes	complemented
60	C₂×C₅×C₃⋊C₈	—	2	1	no	—
61	C₃×C₄×Dic₅	—	2	1	no	—
62	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	complemented
63	#6668	—	2	2	no	—
64	#6665	—	2	2	no	—
65	Dic₃×Dic₅	—	2	2	no	—
66	Dic₃×#41	—	5	1	no	—
67	C₂×C₃×#104	—	5	1	no	—
68	C₂×#837	—	5	1	no	—
69	Dic₃×M₁₆	D₅	1	1	yes	characteristic, complemented
70	#4932	—	5	1	no	—
71	#4555	—	5	1	no	—
72	#4523	—	5	1	no	—
73	C₂×#709	C₂×D₃	1	1	yes	characteristic
74	C₂×C₅×M₁₆	—	3	1	no	—
75	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
76	C₂×C₄²×C₅	—	3	1	no	—
77	C₄×C₂²⋊D₅	—	6	2	no	—
78	#4072	—	3	1	no	—
79	C₂×C₄×Dic₅	—	3	1	no	—
80	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
81	C₄×D₂₀	—	3	2	no	—
82	#4018	—	6	1	no	—
83	C₄²×D₅	—	6	1	no	—
84	C₄×Dic₁₀	—	3	2	no	—
85	C₅×#97	—	6	1	no	—
86	C₄×C₅×C₈	—	6	1	no	—
87	#3963	—	6	2	no	—
88	#3957	—	3	4	no	—
89	#3957	Dic₃	1	4	yes	complemented
90	#1759	—	15	1	no	Sylow
91	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₃×D₅	—	2	1	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	C₂²×C₄	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×Dic₁₅	—	2	2	no	—
100	C₂×Dic₁₅	—	2	2	no	—
101	C₂×Dic₁₅	—	4	2	no	—
102	C₂×C₅×Dic₃	—	4	2	no	—
103	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
104	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
105	C₃×C₂²⋊D₅	—	2	2	no	—
106	C₃×C₂²⋊D₅	—	2	2	no	—
107	C₂×C₃×Dic₅	—	2	1	no	—
108	C₂×C₃×Dic₅	—	2	2	no	—
109	C₂×C₃×Dic₅	—	4	2	no	—
110	C₃×D₂₀	—	2	1	no	—
111	C₃×D₂₀	C₄²	1	2	yes	—
112	C₃×C₄×D₅	—	2	2	no	—
113	C₃×C₄×D₅	—	2	2	no	—
114	C₃×Dic₁₀	—	2	1	no	—
115	C₃×Dic₁₀	C₄²	1	2	yes	—
116	D₅×Dic₃	—	4	4	no	—
117	C₃×C₅×C₈	—	2	2	no	—
118	C₅×C₃⋊C₈	—	2	2	no	—
119	C₂×C₃×#41	—	5	1	no	—
120	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
121	C₂×C₃×C₄²	—	5	1	no	—
122	Q₈×Dic₃	—	5	2	no	—
123	D₄×Dic₃	—	5	2	no	—
124	D₄×Dic₃	—	10	2	no	—
125	#926	—	5	1	no	—
126	#926	—	10	1	no	—
127	C₂×C₄×Dic₃	—	5	1	no	—
128	C₂×C₄×Dic₃	—	10	1	no	—
129	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
130	C₂×#208	C₂×D₅	1	1	yes	characteristic
131	C₃×#104	—	5	4	no	—
132	#837	—	5	4	no	—
133	C₃⋊#95	—	10	2	no	—
134	#815	—	2	1	no	—
135	C₈×Dic₃	—	2	1	no	—
136	C₂²×C₄×C₅	—	3	2	no	—
137	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
138	C₂×C₂²⋊D₅	—	2	1	no	—
139	C₂²×Dic₅	—	2	1	no	—
140	C₂²×Dic₅	—	6	1	no	—
141	#709	—	2	1	no	—
142	#709	—	2	1	no	—
143	#709	C₄×D₃	1	2	yes	—
144	#709	C₂×Dic₃	1	2	yes	—
145	C₂×D₂₀	C₄×D₃	1	1	yes	characteristic
146	C₂×C₄×D₅	—	2	1	no	—
147	C₂×C₄×D₅	—	6	2	no	—
148	C₂×Dic₁₀	C₄×D₃	1	1	yes	characteristic
149	C₅×M₁₆	—	2	1	no	—
150	C₅×M₁₆	—	3	2	no	—
151	C₅×M₁₆	—	6	1	no	—
152	C₅×M₁₆	C₂×Dic₃	1	2	yes	complemented
153	C₂×C₅×C₈	—	2	1	no	—
154	C₂×C₅×C₈	—	6	1	no	—
155	C₄²×C₅	—	3	2	no	—
156	C₄²×C₅	—	3	1	no	—
157	C₄²×C₅	—	3	1	no	—
158	C₂²⋊Dic₅	—	6	1	no	—
159	#685	—	6	2	no	—
160	C₄⋊Dic₅	—	3	2	no	—
161	#683	—	6	2	no	—
162	C₄×Dic₅	—	2	1	no	—
163	C₄×Dic₅	—	3	2	no	—
164	C₄×Dic₅	—	6	2	no	—
165	C₄×Dic₅	—	6	1	no	—
166	C₄×Dic₅	—	6	1	no	—
167	C₄×Dic₅	C₂×Dic₃	1	2	yes	complemented
168	C₄×#41	—	15	1	no	—
169	C₂×#104	—	5	1	no	—
170	C₂×#104	—	15	1	no	—
171	C₄×M₁₆	—	3	1	no	—
172	#376	—	15	1	no	—
173	#339	—	15	1	no	—
174	#339	—	15	1	no	—
175	C₂²×C₃×C₅	—	2	2	no	—
176	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
178	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
179	C₂×C₃×D₅	—	2	2	no	—
180	C₂×C₃×D₅	—	4	2	no	—
181	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
182	C₃×C₄×C₅	#117	1	1	yes	characteristic
183	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
184	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
185	Dic₁₅	—	4	2	no	—
186	Dic₁₅	—	4	2	no	—
187	C₃×Dic₅	—	2	2	no	—
188	C₃×Dic₅	—	4	2	no	—
189	C₅×Dic₃	—	2	2	no	—
190	C₅×Dic₃	—	2	2	no	—
191	C₃×#41	—	5	2	no	—
192	C₃×#41	—	5	2	no	—
193	C₃×#41	—	10	1	no	—
194	C₃×#41	—	10	1	no	—
195	C₂×C₃×Q₈	—	5	1	no	—
196	C₂×C₃×D₄	—	5	1	no	—
197	C₂×C₃×D₄	—	10	1	no	—
198	C₂²×C₃×C₄	—	10	1	no	—
199	C₂²×C₃×C₄	—	10	1	no	—
200	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
201	C₂²×Dic₃	—	10	1	no	—
202	C₂²×Dic₃	—	10	2	no	—
203	C₂²×Dic₃	D₂₀	1	2	yes	—
204	C₃×M₁₆	—	2	1	no	—
205	C₃×M₁₆	C₄×D₅	1	2	yes	complemented
206	C₂×C₃×C₈	—	2	1	no	—
207	C₃×C₄²	—	5	2	no	—
208	C₃×C₄²	—	10	1	no	—
209	#217	—	10	1	no	—
210	#217	—	10	2	no	—
211	C₄⋊Dic₃	—	5	2	no	—
212	C₄⋊Dic₃	—	10	2	no	—
213	C₄×Dic₃	—	5	2	no	—
214	C₄×Dic₃	—	10	1	no	—
215	C₄×Dic₃	—	10	1	no	—
216	C₄×Dic₃	—	10	2	no	—
217	C₄×Dic₃	C₄×D₅	1	2	yes	—
218	C₄×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
219	C₄×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
220	#208	—	2	1	no	—
221	#208	C₄×D₅	1	2	yes	complemented
222	C₂×C₃⋊C₈	—	2	1	no	—
223	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
224	C₂²×D₅	—	2	1	no	—
225	C₂×C₄×C₅	—	3	2	no	—
226	C₂×C₄×C₅	—	3	2	no	—
227	C₂×C₄×C₅	—	12	2	no	—
228	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
229	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
230	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
231	C₂×C₄×C₅	#237	1	1	yes	characteristic
232	C₂×C₄×C₅	#237	1	1	yes	characteristic
233	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
234	C₂²⋊D₅	—	2	2	no	—
235	C₂²⋊D₅	—	2	2	no	—
236	C₂×Dic₅	—	2	1	no	—
237	C₂×Dic₅	—	2	2	no	—
238	C₂×Dic₅	—	4	2	no	—
239	C₂×Dic₅	—	6	2	no	—
240	C₂×Dic₅	—	6	2	no	—
241	C₂×Dic₅	—	12	2	no	—
242	D₂₀	—	2	1	no	—
243	D₂₀	C₄×Dic₃	1	2	yes	—
244	C₄×D₅	—	2	2	no	—
245	C₄×D₅	—	2	2	no	—
246	C₄×D₅	—	12	4	no	—
247	Dic₁₀	—	2	1	no	—
248	Dic₁₀	C₄×Dic₃	1	2	yes	—
249	C₅×C₈	—	2	2	no	—
250	C₅×C₈	—	6	2	no	—
251	C₂×#41	—	5	1	no	—
252	C₂×M₁₆	—	3	1	no	—
253	C₂×M₁₆	D₃×D₅	1	1	yes	characteristic
254	C₄×Q₈	—	15	2	no	—
255	C₄×D₄	—	15	2	no	—
256	C₄×D₄	—	30	2	no	—
257	#117	—	15	1	no	—
258	#117	—	30	1	no	—
259	C₂×C₄²	—	3	1	no	—
260	C₂×C₄²	—	5	1	no	—
261	C₂×C₄²	—	15	1	no	—
262	C₂×C₄²	—	30	1	no	—
263	#104	—	5	4	no	—
264	#104	—	15	4	no	—
265	#97	—	6	1	no	—
266	C₄×C₈	—	6	1	no	—
267	#95	—	30	2	no	—
268	C₂×C₃×C₅	—	2	1	no	—
269	C₂×C₃×C₅	—	2	1	no	—
270	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
271	C₂×C₃×C₅	#421	1	2	yes	—
272	C₃×D₅	—	4	2	no	—
273	C₂³×C₃	—	10	1	no	—
274	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
275	C₃×Q₈	—	5	2	no	—
276	C₃×Q₈	—	10	1	no	—
277	C₃×D₄	—	5	2	no	—
278	C₃×D₄	—	10	2	no	—
279	C₃×D₄	—	10	2	no	—
280	C₃×D₄	—	10	1	no	—
281	C₂×C₃×C₄	—	10	1	no	—
282	C₂×C₃×C₄	—	10	2	no	—
283	C₂×C₃×C₄	—	10	2	no	—
284	C₂×C₃×C₄	—	10	2	no	—
285	C₂×C₃×C₄	—	20	2	no	—
286	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
289	C₂×C₃×C₄	#709	1	1	yes	characteristic
290	C₂×C₃×C₄	#709	1	1	yes	characteristic
291	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
292	C₂×Dic₃	—	4	2	no	—
293	C₂×Dic₃	—	10	2	no	—
294	C₂×Dic₃	—	10	2	no	—
295	C₂×Dic₃	—	20	4	no	—
296	C₂×Dic₃	—	20	2	no	—
297	C₂×Dic₃	#685	1	2	yes	—
298	C₂×Dic₃	#685	1	2	yes	—
299	C₃×C₈	—	2	2	no	—
300	C₃⋊C₈	—	2	2	no	—
301	C₂²×C₅	—	2	2	no	—
302	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
303	C₂²×C₅	#67⋊C₄	1	1	yes	characteristic
304	C₂²×C₅	D₄×Dic₃	1	1	yes	characteristic
305	C₂×D₅	—	2	2	no	—
306	C₂×D₅	—	4	2	no	—
307	C₄×C₅	—	6	2	no	—
308	C₄×C₅	—	6	2	no	—
309	C₄×C₅	#877	1	1	yes	characteristic
310	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
311	C₄×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
312	C₄×C₅	D₄×Dic₃	1	1	yes	characteristic
313	Dic₅	—	2	2	no	—
314	Dic₅	—	4	2	no	—
315	Dic₅	—	12	2	no	—
316	Dic₅	—	12	2	no	—
317	#41	—	5	2	no	—
318	#41	—	5	2	no	—
319	#41	—	10	1	no	—
320	#41	—	10	1	no	—
321	C₂×Q₈	—	5	1	no	—
322	C₂×D₄	—	5	1	no	—
323	C₂×D₄	—	10	1	no	—
324	C₂²×C₄	—	3	2	no	—
325	C₂²×C₄	—	10	1	no	—
326	C₂²×C₄	—	10	1	no	—
327	C₂²×C₄	—	30	2	no	—
328	C₂²×C₄	—	30	1	no	—
329	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
330	M₁₆	—	2	1	no	—
331	M₁₆	—	3	2	no	—
332	M₁₆	—	6	1	no	—
333	M₁₆	D₅×Dic₃	1	2	yes	complemented
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	6	1	no	—
336	C₄⋊C₄	—	15	2	no	—
337	C₄⋊C₄	—	30	2	no	—
338	C₂²⋊C₄	—	30	2	no	—
339	C₂²⋊C₄	—	30	1	no	—
340	C₄²	—	3	2	no	—
341	C₄²	—	3	1	no	—
342	C₄²	—	3	1	no	—
343	C₄²	—	5	2	no	—
344	C₄²	—	10	1	no	—
345	C₄²	—	15	2	no	—
346	C₄²	—	30	2	no	—
347	C₄²	—	30	1	no	—
348	C₄²	—	30	1	no	—
349	C₃×C₅	#1759	1	1	yes	characteristic, complemented, Hall
350	C₂²×C₃	—	2	2	no	—
351	C₂²×C₃	—	10	2	no	—
352	C₂²×C₃	—	20	2	no	—
353	C₂²×C₃	C₄×D₂₀	1	1	yes	characteristic
354	C₂²×C₃	C₄×D₂₀	1	1	yes	characteristic
355	C₂²×C₃	C₂×#685	1	1	yes	characteristic
356	C₃×C₄	—	10	2	no	—
357	C₃×C₄	—	20	2	no	—
358	C₃×C₄	C₄²×D₅	1	1	yes	characteristic
359	C₃×C₄	#4018	1	1	yes	characteristic
360	C₃×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
361	C₃×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
362	Dic₃	—	2	2	no	—
363	Dic₃	—	2	2	no	—
364	Dic₃	—	20	2	no	—
365	Dic₃	—	20	2	no	—
366	C₂×C₅	—	2	1	no	—
367	C₂×C₅	—	2	1	no	—
368	C₂×C₅	#4821	1	2	yes	—
369	C₂×C₅	Dic₃×C₂²⋊C₄	1	1	yes	characteristic
370	D₅	—	4	2	no	—
371	C₂³	—	10	1	no	—
372	C₂³	D₃×D₂₀	1	1	yes	characteristic
373	Q₈	—	5	2	no	—
374	Q₈	—	10	1	no	—
375	D₄	—	5	2	no	—
376	D₄	—	10	2	no	—
377	D₄	—	10	2	no	—
378	D₄	—	10	1	no	—
379	C₂×C₄	—	3	2	no	—
380	C₂×C₄	—	3	2	no	—
381	C₂×C₄	—	10	1	no	—
382	C₂×C₄	—	10	2	no	—
383	C₂×C₄	—	10	2	no	—
384	C₂×C₄	—	10	2	no	—
385	C₂×C₄	—	12	2	no	—
386	C₂×C₄	—	20	2	no	—
387	C₂×C₄	—	30	2	no	—
388	C₂×C₄	—	30	2	no	—
389	C₂×C₄	—	60	4	no	—
390	C₂×C₄	—	60	2	no	—
391	C₂×C₄	#6765	1	1	yes	characteristic
392	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
393	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
394	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
395	C₂×C₄	#6779	1	1	yes	characteristic
396	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
397	C₈	—	2	2	no	—
398	C₈	—	6	2	no	—
399	C₂×C₃	—	2	1	no	—
400	C₂×C₃	—	2	1	no	—
401	C₂×C₃	—	20	2	no	—
402	C₂×C₃	C₄×#685	1	1	yes	characteristic
403	C₂×C₃	#65428	1	2	yes	—
404	C₅	#70354	1	1	yes	characteristic, complemented, Sylow
405	C₂²	—	2	2	no	—
406	C₂²	—	10	2	no	—
407	C₂²	—	20	2	no	—
408	C₂²	#91395	1	1	yes	characteristic
409	C₂²	Dic₃×D₂₀	1	1	yes	characteristic
410	C₂²	D₃×#685	1	1	yes	characteristic
411	C₄	—	6	2	no	—
412	C₄	—	6	2	no	—
413	C₄	—	10	2	no	—
414	C₄	—	20	2	no	—
415	C₄	—	60	2	no	—
416	C₄	—	60	2	no	—
417	C₄	C₄×D₅×Dic₃	1	1	yes	characteristic
418	C₄	#91393	1	1	yes	characteristic
419	C₄	#91441	1	1	yes	characteristic
420	C₄	Dic₃×C₂²⋊D₅	1	1	yes	characteristic
421	C₃	#10600659	1	1	yes	characteristic, complemented, Sylow
422	C₂	—	2	1	no	—
423	C₂	—	2	1	no	—
424	C₂	—	20	2	no	—
425	C₂	#11748233	1	2	yes	—
426	C₂	Dic₃×#685	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₃×C₂²⋊D₅
commutator	C₃×C₄×C₅	C₂×C₄²
Frattini	C₂²×C₄	C₂×D₃×D₅
Fitting	C₂×C₃×C₅×M₁₆	C₂²
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₃×#709	C₂²
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂×M₁₆	D₃×D₅
hypocenter	C₃×C₅	#1759
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₅×Dic₃×M₁₆	C₂	semidirect
4. #11748611	C₂	semidirect
6. #11746376	C₂	semidirect
7. #11745978	C₂	semidirect
17. Dic₃×D₂₀	C₄	semidirect
20. Dic₃×Dic₁₀	C₄	semidirect
23. C₃×#3957	C₄	semidirect
25. #90976	C₄	semidirect
48. C₃×C₅×M₁₆	C₂×C₄	semidirect
54. C₄×Dic₁₅	C₂×C₄	semidirect
59. C₅×#208	C₂×C₄	semidirect
62. C₃×C₄×Dic₅	C₂×C₄	semidirect
69. Dic₃×M₁₆	D₅	semidirect
89. #3957	Dic₃	semidirect
152. C₅×M₁₆	C₂×Dic₃	semidirect
167. C₄×Dic₅	C₂×Dic₃	semidirect
205. C₃×M₁₆	C₄×D₅	semidirect
221. #208	C₄×D₅	semidirect
333. M₁₆	D₅×Dic₃	semidirect
349. C₃×C₅	#1759	semidirect
404. C₅	#70354	semidirect
421. C₃	#10600659	semidirect

Maximal subgroups

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

subgroup	index
Dic₃×#709	2
C₅×Dic₃×M₁₆	2
C₂×C₃×#3957	2
#11748611	2
C₂×#90976	2
#11746376	2
#11745978	2
#10600659	3
#70354	5