Subgroups — #11753433

Order 960.

560 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₅⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₃×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
3	#91785	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#896	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#4034	C₂	1	1	yes	maximal, characteristic, complemented
6	#91446	C₂	1	1	yes	maximal, characteristic
7	#91436	C₂	1	1	yes	maximal, characteristic, complemented
8	#91429	C₂	1	1	yes	maximal, characteristic, complemented
9	#91411	C₂	1	1	yes	maximal, characteristic, complemented
10	#91410	C₂	1	1	yes	maximal, characteristic, complemented
11	#91406	C₂	1	1	yes	maximal, characteristic
12	#91405	C₂	1	1	yes	maximal, characteristic
13	#91329	C₂	1	1	yes	maximal, characteristic, complemented
14	#91328	C₂	1	1	yes	maximal, characteristic, complemented
15	#91323	C₂	1	1	yes	maximal, characteristic, complemented
16	#65966	—	3	1	no	maximal, Hall
17	C₂×C₄×D₁₅	C₂²	1	1	yes	characteristic
18	C₂×Dic₃₀	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
20	C₂×C₅×Dic₆	C₂²	1	1	yes	characteristic
21	C₂×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
22	C₂×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
23	C₂×#1204	C₂²	1	1	yes	characteristic
24	C₂×#1204	C₂²	1	1	yes	characteristic
25	C₂×#1204	C₂²	1	1	yes	characteristic
26	C₂×#1203	C₂²	1	1	yes	characteristic
27	C₂×#1200	C₂²	1	1	yes	characteristic
28	C₂×#1200	C₂²	1	1	yes	characteristic
29	C₂×D₃×Dic₅	C₂²	1	1	yes	characteristic
30	C₂×D₃×Dic₅	C₂²	1	1	yes	characteristic
31	D₁₅⋊Q₈	—	2	4	no	—
32	D₃×Dic₁₀	—	2	4	no	—
33	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	#6714	C₂²	1	1	yes	characteristic
35	#6714	C₂²	1	1	yes	characteristic
36	#6712	C₂²	1	1	yes	characteristic
37	#6712	C₂²	1	1	yes	characteristic
38	C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
39	C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
40	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
41	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
42	C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
43	C₃×#683	C₂²	1	1	yes	characteristic
44	C₃×#683	C₂²	1	1	yes	characteristic
45	C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
46	Dic₃⋊Dic₅	C₂²	1	1	yes	characteristic
47	#6669	C₂²	1	1	yes	characteristic
48	#6668	C₂²	1	1	yes	characteristic
49	#6668	C₂²	1	1	yes	characteristic
50	#6667	C₂²	1	1	yes	characteristic
51	(C₂×D₃)⋊Dic₅	C₂²	1	1	yes	characteristic
52	Dic₃×Dic₅	C₂²	1	1	yes	characteristic
53	Dic₃×Dic₅	C₂²	1	1	yes	characteristic
54	#5727	—	5	1	no	maximal, Hall
55	C₂×Q₈×D₅	—	3	1	no	—
56	C₂²×Dic₁₀	—	3	1	no	—
57	C₅×C₂²⋊Q₈	—	3	1	no	—
58	#4090	—	3	1	no	—
59	C₄×C₂²⋊D₅	—	3	1	no	—
60	#4043	—	3	1	no	—
61	#4042	—	3	1	no	—
62	#4042	—	3	1	no	—
63	#4034	—	3	1	no	—
64	#4034	D₃	1	1	yes	characteristic, complemented
65	#4033	—	3	1	no	—
66	#4027	—	3	1	no	—
67	#4027	—	3	1	no	—
68	#4024	—	3	1	no	—
69	#4024	—	3	1	no	—
70	C₂²×D₁₅	C₂³	1	1	yes	characteristic
71	C₂²×C₅×D₃	C₂³	1	1	yes	characteristic
72	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
73	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
75	C₂×Dic₁₅	C₂³	1	1	yes	characteristic
76	C₂×Dic₁₅	C₂³	1	1	yes	characteristic
77	C₂×Dic₁₅	C₂³	1	1	yes	characteristic
78	C₄×D₁₅	—	2	2	no	—
79	Dic₃₀	—	2	2	no	—
80	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
81	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
82	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
83	C₄×C₅×D₃	—	2	2	no	—
84	C₅×Dic₆	—	2	2	no	—
85	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
86	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
87	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
88	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
89	C₃×Dic₁₀	—	2	2	no	—
90	C₃×Dic₁₀	—	2	2	no	—
91	#1204	—	2	2	no	—
92	#1204	—	2	2	no	—
93	#1204	D₄	1	4	yes	complemented
94	#1203	Q₈	1	4	yes	complemented
95	#1200	—	2	2	no	—
96	#1200	—	2	2	no	—
97	D₃×Dic₅	—	2	2	no	—
98	D₃×Dic₅	—	2	2	no	—
99	C₂×D₃×Q₈	—	5	1	no	—
100	C₂×D₃×Q₈	—	5	1	no	—
101	C₃×C₄⋊Q₈	—	5	1	no	—
102	#946	—	5	1	no	—
103	#946	—	5	1	no	—
104	#896	—	5	1	no	—
105	#896	—	5	1	no	—
106	#896	—	5	1	no	—
107	#896	D₅	1	1	yes	characteristic, complemented
108	#893	—	5	1	no	—
109	#893	—	5	1	no	—
110	#888	—	5	1	no	—
111	#888	—	5	1	no	—
112	C₄×D₁₂	—	5	1	no	—
113	C₄×Dic₆	—	5	1	no	—
114	C₂×C₅×Q₈	—	3	1	no	—
115	C₂²×C₄×C₅	—	3	1	no	—
116	C₂×C₂²⋊D₅	—	3	1	no	—
117	C₂²×Dic₅	—	3	1	no	—
118	C₂²×Dic₅	—	3	1	no	—
119	Q₈×D₅	—	6	4	no	—
120	C₂×C₄×D₅	—	3	1	no	—
121	C₂×C₄×D₅	—	3	1	no	—
122	C₂×C₄×D₅	—	3	1	no	—
123	C₂×Dic₁₀	—	3	1	no	—
124	C₂×Dic₁₀	—	3	1	no	—
125	C₂×Dic₁₀	—	3	1	no	—
126	C₂×Dic₁₀	—	3	1	no	—
127	C₂×Dic₁₀	—	6	4	no	—
128	C₂×Dic₁₀	C₂×D₃	1	1	yes	characteristic
129	C₂×Dic₁₀	C₂×D₃	1	1	yes	characteristic
130	C₅×C₄⋊C₄	—	3	1	no	—
131	C₅×C₄⋊C₄	—	3	1	no	—
132	C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
133	C₅×C₂²⋊C₄	—	3	1	no	—
134	C₅×C₂²⋊C₄	—	3	1	no	—
135	C₂²⋊Dic₅	—	3	1	no	—
136	#685	—	3	1	no	—
137	#685	—	3	1	no	—
138	#685	—	3	1	no	—
139	C₄⋊Dic₅	—	3	1	no	—
140	C₄⋊Dic₅	C₂×D₃	1	1	yes	characteristic
141	#683	—	3	1	no	—
142	#683	—	3	1	no	—
143	#683	—	3	1	no	—
144	#683	—	3	1	no	—
145	#683	—	3	1	no	—
146	#683	C₂×D₃	1	1	yes	characteristic
147	#683	C₂×D₃	1	1	yes	characteristic
148	C₄×Dic₅	—	3	1	no	—
149	C₄×Dic₅	—	3	1	no	—
150	C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
151	D₄×Q₈	—	15	1	no	Sylow
152	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
153	C₂×D₁₅	—	2	1	no	—
154	C₂×D₁₅	—	2	1	no	—
155	C₂×D₁₅	C₂×Q₈	1	2	yes	complemented
156	C₂×C₅×D₃	—	2	1	no	—
157	C₂×C₅×D₃	—	2	1	no	—
158	C₂×C₅×D₃	C₂×Q₈	1	2	yes	complemented
159	C₃×C₄×C₅	—	2	1	no	—
160	C₃×C₄×C₅	—	2	1	no	—
161	C₃×C₄×C₅	—	2	1	no	—
162	Dic₁₅	—	2	1	no	—
163	Dic₁₅	—	2	1	no	—
164	Dic₁₅	C₂×D₄	1	2	yes	—
165	C₃×Dic₅	—	2	1	no	—
166	C₃×Dic₅	—	2	1	no	—
167	C₃×Dic₅	C₂×D₄	1	2	yes	—
168	C₃×Dic₅	C₂×Q₈	1	2	yes	complemented
169	C₅×Dic₃	—	2	1	no	—
170	C₅×Dic₃	—	2	1	no	—
171	C₅×Dic₃	C₂×D₄	1	2	yes	—
172	C₂×C₃×Q₈	—	5	1	no	—
173	C₂×C₃×Q₈	—	5	1	no	—
174	D₃×Q₈	—	10	4	no	—
175	D₃×Q₈	—	10	4	no	—
176	C₂×D₁₂	—	5	1	no	—
177	C₂×C₄×D₃	—	5	1	no	—
178	C₂×C₄×D₃	—	5	1	no	—
179	C₂×C₄×D₃	—	5	1	no	—
180	C₂×C₄×D₃	—	5	1	no	—
181	C₂×C₄×D₃	—	5	1	no	—
182	C₂×C₄×D₃	C₂×D₅	1	1	yes	characteristic
183	C₂×Dic₆	—	5	1	no	—
184	C₂×Dic₆	—	5	1	no	—
185	C₂×Dic₆	—	5	1	no	—
186	C₂×Dic₆	—	5	1	no	—
187	C₂×Dic₆	C₂×D₅	1	1	yes	characteristic
188	C₃×C₄⋊C₄	—	5	1	no	—
189	C₃×C₄⋊C₄	—	5	1	no	—
190	C₃×C₄⋊C₄	—	5	1	no	—
191	C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
192	C₃×C₄²	—	5	1	no	—
193	(C₂×D₃)⋊C₄	—	5	1	no	—
194	(C₂×D₃)⋊C₄	—	5	1	no	—
195	(C₂×D₃)⋊C₄	—	5	1	no	—
196	(C₂×D₃)⋊C₄	—	5	1	no	—
197	(C₂×D₃)⋊C₄	C₂×D₅	1	1	yes	characteristic
198	(C₂×D₃)⋊C₄	C₂×D₅	1	1	yes	characteristic
199	C₄⋊Dic₃	—	5	1	no	—
200	C₄⋊Dic₃	—	5	1	no	—
201	Dic₃⋊C₄	—	5	1	no	—
202	Dic₃⋊C₄	—	5	1	no	—
203	Dic₃⋊C₄	—	5	1	no	—
204	Dic₃⋊C₄	—	5	1	no	—
205	Dic₃⋊C₄	C₂×D₅	1	1	yes	characteristic
206	Dic₃⋊C₄	C₂×D₅	1	1	yes	characteristic
207	C₄×Dic₃	—	5	1	no	—
208	C₄×Dic₃	—	5	1	no	—
209	C₂³×C₅	—	3	1	no	—
210	C₂²×D₅	—	3	1	no	—
211	C₅×Q₈	—	6	2	no	—
212	C₂×C₄×C₅	—	3	1	no	—
213	C₂×C₄×C₅	—	3	1	no	—
214	C₂×C₄×C₅	—	3	1	no	—
215	C₂×C₄×C₅	—	6	2	no	—
216	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
217	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
218	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
219	C₂²⋊D₅	—	3	4	no	—
220	C₂×Dic₅	—	3	1	no	—
221	C₂×Dic₅	—	3	1	no	—
222	C₂×Dic₅	—	3	1	no	—
223	C₂×Dic₅	—	6	2	no	—
224	C₂×Dic₅	—	6	2	no	—
225	C₂×Dic₅	C₂²×D₃	1	1	yes	characteristic
226	C₂×Dic₅	C₂²×D₃	1	1	yes	characteristic
227	C₂×Dic₅	C₂²×D₃	1	1	yes	characteristic
228	C₂×Dic₅	C₂²×D₃	1	1	yes	characteristic
229	C₄×D₅	—	6	2	no	—
230	C₄×D₅	—	6	2	no	—
231	C₄×D₅	—	6	2	no	—
232	Dic₁₀	—	2	2	no	—
233	Dic₁₀	—	2	2	no	—
234	Dic₁₀	—	3	4	no	—
235	Dic₁₀	—	6	2	no	—
236	Dic₁₀	—	6	2	no	—
237	Dic₁₀	—	6	2	no	—
238	C₂²×Q₈	—	15	1	no	—
239	C₂²×Q₈	—	15	1	no	—
240	C₄⋊Q₈	—	5	1	no	—
241	C₄⋊Q₈	—	15	1	no	—
242	C₄⋊Q₈	—	15	1	no	—
243	C₂²⋊Q₈	—	3	1	no	—
244	C₂²⋊Q₈	—	15	1	no	—
245	C₂²⋊Q₈	—	15	1	no	—
246	C₂²⋊Q₈	—	15	1	no	—
247	C₂²⋊Q₈	—	15	1	no	—
248	C₂²⋊Q₈	—	15	1	no	—
249	C₄×Q₈	—	15	1	no	—
250	C₄×D₄	—	15	1	no	—
251	C₄×D₄	—	15	1	no	—
252	C₄×D₄	—	15	1	no	—
253	C₂×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
255	C₂×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
256	D₁₅	—	2	2	no	—
257	C₅×D₃	—	2	2	no	—
258	C₂²×D₃	—	5	1	no	—
259	C₂²×D₃	C₂²×D₅	1	1	yes	characteristic
260	C₃×Q₈	—	10	2	no	—
261	C₃×Q₈	—	10	2	no	—
262	C₂×C₃×C₄	—	5	1	no	—
263	C₂×C₃×C₄	—	5	1	no	—
264	C₂×C₃×C₄	—	5	1	no	—
265	C₂×C₃×C₄	—	5	1	no	—
266	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
269	C₂×Dic₃	—	5	1	no	—
270	C₂×Dic₃	—	5	1	no	—
271	C₂×Dic₃	—	5	1	no	—
272	C₂×Dic₃	C₂²×D₅	1	1	yes	characteristic
273	C₂×Dic₃	C₂²×D₅	1	1	yes	characteristic
274	C₂×Dic₃	C₂²×D₅	1	1	yes	characteristic
275	D₁₂	—	5	4	no	—
276	C₄×D₃	—	2	2	no	—
277	C₄×D₃	—	10	2	no	—
278	C₄×D₃	—	10	2	no	—
279	C₄×D₃	—	10	2	no	—
280	C₄×D₃	—	10	2	no	—
281	C₄×D₃	—	10	2	no	—
282	Dic₆	—	2	2	no	—
283	Dic₆	—	5	4	no	—
284	Dic₆	—	10	2	no	—
285	Dic₆	—	10	2	no	—
286	Dic₆	—	10	2	no	—
287	C₂²×C₅	—	3	2	no	—
288	C₂²×C₅	—	6	1	no	—
289	C₂²×C₅	—	6	1	no	—
290	C₂²×C₅	C₂³×D₃	1	1	yes	characteristic
291	C₂×D₅	—	3	2	no	—
292	C₂×D₅	—	6	1	no	—
293	C₂×D₅	—	6	1	no	—
294	C₄×C₅	—	2	1	no	—
295	C₄×C₅	—	2	1	no	—
296	C₄×C₅	—	2	1	no	—
297	C₄×C₅	—	3	2	no	—
298	C₄×C₅	—	6	1	no	—
299	C₄×C₅	—	6	1	no	—
300	Dic₅	—	2	1	no	—
301	Dic₅	—	2	1	no	—
302	Dic₅	—	3	2	no	—
303	Dic₅	—	6	1	no	—
304	Dic₅	—	6	1	no	—
305	Dic₅	D₃×D₄	1	2	yes	—
306	Dic₅	D₃×Q₈	1	2	yes	complemented
307	C₂×Q₈	—	3	1	no	—
308	C₂×Q₈	—	5	1	no	—
309	C₂×Q₈	—	5	1	no	—
310	C₂×Q₈	—	15	1	no	—
311	C₂×Q₈	—	15	1	no	—
312	C₂×Q₈	—	15	1	no	—
313	C₂×Q₈	—	15	1	no	—
314	C₂×Q₈	—	30	4	no	—
315	C₂×Q₈	—	30	4	no	—
316	C₂×D₄	—	15	1	no	—
317	C₂²×C₄	—	3	1	no	—
318	C₂²×C₄	—	15	1	no	—
319	C₂²×C₄	—	15	1	no	—
320	C₂²×C₄	—	15	1	no	—
321	C₂²×C₄	—	15	1	no	—
322	C₂²×C₄	—	15	1	no	—
323	C₄⋊C₄	—	3	1	no	—
324	C₄⋊C₄	—	3	1	no	—
325	C₄⋊C₄	—	5	1	no	—
326	C₄⋊C₄	—	5	1	no	—
327	C₄⋊C₄	—	5	1	no	—
328	C₄⋊C₄	—	15	1	no	—
329	C₄⋊C₄	—	15	1	no	—
330	C₄⋊C₄	—	15	1	no	—
331	C₄⋊C₄	—	15	1	no	—
332	C₄⋊C₄	—	15	1	no	—
333	C₄⋊C₄	—	15	1	no	—
334	C₄⋊C₄	D₃×D₅	1	1	yes	characteristic
335	C₂²⋊C₄	—	3	1	no	—
336	C₂²⋊C₄	—	3	1	no	—
337	C₂²⋊C₄	—	15	1	no	—
338	C₂²⋊C₄	—	15	1	no	—
339	C₂²⋊C₄	—	15	1	no	—
340	C₂²⋊C₄	—	15	1	no	—
341	C₄²	—	5	1	no	—
342	C₄²	—	15	1	no	—
343	C₄²	—	15	1	no	—
344	C₃×C₅	D₄×Q₈	1	1	yes	characteristic, complemented, Hall
345	C₂²×C₃	C₂³×D₅	1	1	yes	characteristic
346	C₂×D₃	—	2	1	no	—
347	C₂×D₃	—	2	1	no	—
348	C₂×D₃	—	5	2	no	—
349	C₂×D₃	—	10	1	no	—
350	C₂×D₃	—	10	1	no	—
351	C₂×D₃	Q₈×D₅	1	2	yes	complemented
352	C₃×C₄	—	2	1	no	—
353	C₃×C₄	—	2	1	no	—
354	C₃×C₄	—	2	1	no	—
355	C₃×C₄	—	5	2	no	—
356	C₃×C₄	—	5	2	no	—
357	C₃×C₄	—	10	1	no	—
358	C₃×C₄	—	10	1	no	—
359	Dic₃	—	2	1	no	—
360	Dic₃	—	2	1	no	—
361	Dic₃	—	5	2	no	—
362	Dic₃	—	10	1	no	—
363	Dic₃	—	10	1	no	—
364	Dic₃	D₄×D₅	1	2	yes	—
365	C₂×C₅	—	6	2	no	—
366	C₂×C₅	C₂×D₃×D₄	1	1	yes	characteristic
367	C₂×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
368	C₂×C₅	#1007	1	1	yes	characteristic
369	D₅	—	6	2	no	—
370	C₂³	—	3	1	no	—
371	C₂³	—	15	1	no	—
372	Q₈	—	6	2	no	—
373	Q₈	—	10	2	no	—
374	Q₈	—	10	2	no	—
375	Q₈	—	15	4	no	—
376	Q₈	—	30	2	no	—
377	Q₈	—	30	2	no	—
378	Q₈	—	30	2	no	—
379	D₄	—	15	4	no	—
380	C₂×C₄	—	3	1	no	—
381	C₂×C₄	—	3	1	no	—
382	C₂×C₄	—	3	1	no	—
383	C₂×C₄	—	5	1	no	—
384	C₂×C₄	—	5	1	no	—
385	C₂×C₄	—	5	1	no	—
386	C₂×C₄	—	5	1	no	—
387	C₂×C₄	—	6	2	no	—
388	C₂×C₄	—	15	1	no	—
389	C₂×C₄	—	15	1	no	—
390	C₂×C₄	—	15	1	no	—
391	C₂×C₄	—	30	2	no	—
392	C₂×C₄	—	30	2	no	—
393	C₂×C₄	—	30	2	no	—
394	C₂×C₄	—	30	2	no	—
395	C₂×C₄	—	30	2	no	—
396	C₂×C₄	C₂×D₃×D₅	1	1	yes	characteristic
397	C₂×C₄	C₂×D₃×D₅	1	1	yes	characteristic
398	C₂×C₄	C₂×D₃×D₅	1	1	yes	characteristic
399	C₂×C₃	C₂×D₄×D₅	1	1	yes	characteristic
400	C₂×C₃	C₂×Q₈×D₅	1	1	yes	characteristic
401	C₂×C₃	#4150	1	1	yes	characteristic
402	D₃	—	2	2	no	—
403	D₃	—	10	2	no	—
404	C₅	#5727	1	1	yes	characteristic, complemented, Sylow
405	C₂²	—	3	2	no	—
406	C₂²	—	6	1	no	—
407	C₂²	—	6	1	no	—
408	C₂²	—	15	2	no	—
409	C₂²	—	30	1	no	—
410	C₂²	—	30	1	no	—
411	C₂²	C₂²×D₃×D₅	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	3	2	no	—
416	C₄	—	5	2	no	—
417	C₄	—	5	2	no	—
418	C₄	—	6	1	no	—
419	C₄	—	6	1	no	—
420	C₄	—	10	1	no	—
421	C₄	—	10	1	no	—
422	C₄	—	15	2	no	—
423	C₄	—	30	1	no	—
424	C₄	—	30	1	no	—
425	C₃	#65966	1	1	yes	characteristic, complemented, Sylow
426	C₂	—	6	2	no	—
427	C₂	—	30	2	no	—
428	C₂	#92004	1	1	yes	characteristic
429	C₂	D₃×D₄×D₅	1	1	yes	characteristic
430	C₂	D₃×Q₈×D₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₃×D₅
commutator, socle, cosocle	C₂²×C₃×C₅	C₂⁴
Fitting	C₃×C₅×C₄⋊C₄	C₂²
prime radical	C₂×#1203	C₂²
hypercenter	C₄⋊C₄	D₃×D₅
hypocenter	C₃×C₅	D₄×Q₈
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂×D₁₅⋊Q₈	C₂	semidirect
2. C₂×D₃×Dic₁₀	C₂	semidirect
3. #91785	C₂	semidirect
4. C₅×#896	C₂	semidirect
5. C₃×#4034	C₂	semidirect
7. #91436	C₂	semidirect
8. #91429	C₂	semidirect
9. #91411	C₂	semidirect
10. #91410	C₂	semidirect
13. #91329	C₂	semidirect
14. #91328	C₂	semidirect
15. #91323	C₂	semidirect
64. #4034	D₃	semidirect
93. #1204	D₄	semidirect
94. #1203	Q₈	semidirect
107. #896	D₅	semidirect
155. C₂×D₁₅	C₂×Q₈	semidirect
158. C₂×C₅×D₃	C₂×Q₈	semidirect
168. C₃×Dic₅	C₂×Q₈	semidirect
306. Dic₅	D₃×Q₈	semidirect
344. C₃×C₅	D₄×Q₈	semidirect
351. C₂×D₃	Q₈×D₅	semidirect
404. C₅	#5727	semidirect
425. C₃	#65966	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₅⋊Q₈	2
C₂×D₃×Dic₁₀	2
#91785	2
C₅×#896	2
C₃×#4034	2
#91446	2
#91436	2
#91429	2
#91411	2
#91410	2
#91406	2
#91405	2
#91329	2
#91328	2
#91323	2
#65966	3
#5727	5