Subgroups — #11752699

Order 960.

468 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₆₀	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#4018	C₂	1	1	yes	maximal, characteristic, complemented
4	#91459	C₂	1	1	yes	maximal, characteristic
5	#91455	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×#1202	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×#1202	C₂	1	1	yes	maximal, characteristic, complemented
8	#91433	C₂	1	1	yes	maximal, characteristic, complemented
9	#91424	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#1200	C₂	1	1	yes	maximal, characteristic, complemented
11	#91386	C₂	1	1	yes	maximal, characteristic, complemented
12	#91362	C₂	1	1	yes	maximal, characteristic, complemented
13	#91356	C₂	1	1	yes	maximal, characteristic, complemented
14	#91343	C₂	1	1	yes	maximal, characteristic, complemented
15	#91337	C₂	1	1	yes	maximal, characteristic, complemented
16	#65914	—	3	1	no	maximal, Hall
17	C₂×D₆₀	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₁₅	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₁₅	C₂²	1	1	yes	characteristic
20	C₂×C₅×Dic₆	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
22	C₂×#1202	C₂²	1	1	yes	characteristic
23	C₂×#1202	C₂²	1	1	yes	characteristic
24	C₂×#1200	C₂²	1	1	yes	characteristic
25	C₂×#1200	C₂²	1	1	yes	characteristic
26	C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
27	#6714	C₂²	1	1	yes	characteristic
28	#6714	C₂²	1	1	yes	characteristic
29	C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
30	C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
31	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
32	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
34	C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
35	C₃×#685	C₂²	1	1	yes	characteristic
36	C₃×#685	C₂²	1	1	yes	characteristic
37	C₃×#683	C₂²	1	1	yes	characteristic
38	C₃×#683	C₂²	1	1	yes	characteristic
39	C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
40	Dic₃⋊Dic₅	C₂²	1	1	yes	characteristic
41	Dic₃⋊Dic₅	C₂²	1	1	yes	characteristic
42	#6669	C₂²	1	1	yes	characteristic
43	#6669	C₂²	1	1	yes	characteristic
44	#6667	C₂²	1	1	yes	characteristic
45	#6667	C₂²	1	1	yes	characteristic
46	#6667	C₂²	1	1	yes	characteristic
47	#6667	C₂²	1	1	yes	characteristic
48	#6665	C₂²	1	1	yes	characteristic
49	#6665	C₂²	1	1	yes	characteristic
50	Dic₃×Dic₅	C₂²	1	1	yes	characteristic
51	Dic₃×Dic₅	C₂²	1	1	yes	characteristic
52	#5528	—	5	1	no	maximal, Hall
53	C₄×C₅×Q₈	—	3	1	no	—
54	#4093	—	3	1	no	—
55	#4092	—	3	1	no	—
56	#4044	—	3	1	no	—
57	#4044	—	3	1	no	—
58	#4041	—	3	1	no	—
59	#4040	—	3	1	no	—
60	#4040	—	3	1	no	—
61	#4036	—	3	1	no	—
62	C₄×D₂₀	—	3	1	no	—
63	C₄×D₂₀	—	3	1	no	—
64	C₄×D₂₀	—	3	1	no	—
65	#4018	—	3	1	no	—
66	#4018	D₃	1	1	yes	characteristic, complemented
67	C₄²×D₅	—	3	1	no	—
68	C₂²×D₁₅	C₂³	1	1	yes	characteristic
69	C₂²×D₁₅	C₂³	1	1	yes	characteristic
70	C₂²×C₃×D₅	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₄×C₅	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×Dic₁₅	C₂³	1	1	yes	characteristic
75	C₂×Dic₁₅	C₂³	1	1	yes	characteristic
76	D₆₀	—	2	2	no	—
77	C₄×D₁₅	—	2	2	no	—
78	C₄×D₁₅	—	2	2	no	—
79	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
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	C₅×Dic₆	—	2	2	no	—
84	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
85	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
86	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
87	C₃×C₄×D₅	—	2	2	no	—
88	#1202	—	2	2	no	—
89	#1202	—	2	2	no	—
90	#1200	—	2	2	no	—
91	#1200	—	2	2	no	—
92	C₃×#117	—	5	1	no	—
93	C₄×#67	—	5	1	no	—
94	C₄×#67	—	5	1	no	—
95	#898	—	5	1	no	—
96	#896	—	5	1	no	—
97	#894	—	5	1	no	—
98	#889	—	5	1	no	—
99	#885	—	5	1	no	—
100	#884	—	5	1	no	—
101	#883	—	5	1	no	—
102	#879	—	5	1	no	—
103	C₄×D₁₂	—	5	1	no	—
104	#872	—	5	1	no	—
105	C₄²×D₃	—	5	1	no	—
106	C₄×Dic₆	D₅	1	1	yes	characteristic, complemented
107	C₂×C₅×Q₈	—	3	1	no	—
108	C₂×D₂₀	—	3	1	no	—
109	C₂×D₂₀	—	3	1	no	—
110	C₂×D₂₀	—	3	1	no	—
111	C₂×C₄×D₅	—	3	1	no	—
112	C₂×C₄×D₅	—	3	1	no	—
113	C₂×C₄×D₅	—	3	1	no	—
114	C₂×C₄×D₅	—	3	1	no	—
115	C₂×C₄×D₅	C₂×D₃	1	1	yes	characteristic
116	C₅×C₄⋊C₄	—	3	1	no	—
117	C₅×C₄⋊C₄	—	3	1	no	—
118	C₅×C₄⋊C₄	—	3	1	no	—
119	C₄²×C₅	—	3	1	no	—
120	C₄²×C₅	—	3	1	no	—
121	C₄²×C₅	C₂×D₃	1	1	yes	characteristic
122	#685	—	3	1	no	—
123	#685	—	3	1	no	—
124	#685	—	3	1	no	—
125	#685	—	3	1	no	—
126	#685	—	3	1	no	—
127	#685	—	3	1	no	—
128	#685	—	3	1	no	—
129	#685	—	3	1	no	—
130	#685	C₂×D₃	1	1	yes	characteristic
131	#685	C₂×D₃	1	1	yes	characteristic
132	C₄⋊Dic₅	—	3	1	no	—
133	C₄⋊Dic₅	—	3	1	no	—
134	C₄⋊Dic₅	—	3	1	no	—
135	#683	—	3	1	no	—
136	#683	—	3	1	no	—
137	#683	C₂×D₃	1	1	yes	characteristic
138	#683	C₂×D₃	1	1	yes	characteristic
139	C₄×Dic₅	—	3	1	no	—
140	C₄×Dic₅	—	3	1	no	—
141	C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
142	#529	—	15	1	no	Sylow
143	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
144	C₂×D₁₅	—	2	1	no	—
145	C₂×D₁₅	—	2	1	no	—
146	C₂×D₁₅	—	2	1	no	—
147	C₂×D₁₅	—	2	1	no	—
148	C₂×D₁₅	—	2	1	no	—
149	C₂×D₁₅	#41	1	2	yes	—
150	C₂×C₃×D₅	—	2	1	no	—
151	C₂×C₃×D₅	—	2	1	no	—
152	C₂×C₃×D₅	—	2	1	no	—
153	C₃×C₄×C₅	—	2	1	no	—
154	C₃×C₄×C₅	—	2	1	no	—
155	C₃×C₄×C₅	#41	1	2	yes	—
156	Dic₁₅	—	2	1	no	—
157	Dic₁₅	—	2	1	no	—
158	C₃×Dic₅	—	2	1	no	—
159	C₃×Dic₅	—	2	1	no	—
160	C₃×Dic₅	—	2	1	no	—
161	C₅×Dic₃	—	2	1	no	—
162	C₅×Dic₃	—	2	1	no	—
163	C₅×Dic₃	—	2	1	no	—
164	C₅×Dic₃	#41	1	2	yes	—
165	C₂²×C₃×C₄	—	5	1	no	—
166	C₂×#67	—	5	1	no	—
167	C₂×#67	—	5	1	no	—
168	C₂×D₁₂	—	5	1	no	—
169	C₂×C₄×D₃	—	5	1	no	—
170	C₂×C₄×D₃	—	5	1	no	—
171	C₂×C₄×D₃	—	5	1	no	—
172	C₂×C₄×D₃	—	5	1	no	—
173	C₂×Dic₆	C₂×D₅	1	1	yes	characteristic
174	C₃×C₄⋊C₄	—	5	1	no	—
175	C₃×C₄⋊C₄	—	5	1	no	—
176	C₃×C₂²⋊C₄	—	5	1	no	—
177	C₃×C₂²⋊C₄	—	5	1	no	—
178	C₃×C₄²	—	5	1	no	—
179	C₃×C₄²	C₂×D₅	1	1	yes	characteristic
180	#217	—	5	1	no	—
181	#217	—	5	1	no	—
182	(C₂×D₃)⋊C₄	—	5	1	no	—
183	(C₂×D₃)⋊C₄	—	5	1	no	—
184	(C₂×D₃)⋊C₄	—	5	1	no	—
185	(C₂×D₃)⋊C₄	—	5	1	no	—
186	(C₂×D₃)⋊C₄	—	5	1	no	—
187	(C₂×D₃)⋊C₄	—	5	1	no	—
188	C₄⋊Dic₃	—	5	1	no	—
189	C₄⋊Dic₃	C₂×D₅	1	1	yes	characteristic
190	Dic₃⋊C₄	—	5	1	no	—
191	Dic₃⋊C₄	—	5	1	no	—
192	Dic₃⋊C₄	—	5	1	no	—
193	Dic₃⋊C₄	—	5	1	no	—
194	Dic₃⋊C₄	C₂×D₅	1	1	yes	characteristic
195	Dic₃⋊C₄	C₂×D₅	1	1	yes	characteristic
196	C₄×Dic₃	—	5	1	no	—
197	C₄×Dic₃	—	5	1	no	—
198	C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
199	C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
200	C₂²×D₅	—	3	1	no	—
201	C₂²×D₅	—	3	1	no	—
202	C₂²×D₅	C₂²×D₃	1	1	yes	characteristic
203	C₅×Q₈	—	6	2	no	—
204	C₂×C₄×C₅	—	3	1	no	—
205	C₂×C₄×C₅	—	3	1	no	—
206	C₂×C₄×C₅	—	3	1	no	—
207	C₂×C₄×C₅	—	3	1	no	—
208	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
209	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
211	C₂×Dic₅	—	3	1	no	—
212	C₂×Dic₅	—	3	1	no	—
213	C₂×Dic₅	C₂²×D₃	1	1	yes	characteristic
214	C₂×Dic₅	C₂²×D₃	1	1	yes	characteristic
215	C₂×Dic₅	C₂²×D₃	1	1	yes	characteristic
216	D₂₀	—	6	2	no	—
217	D₂₀	—	6	2	no	—
218	D₂₀	—	6	2	no	—
219	C₄×D₅	—	2	2	no	—
220	C₄×D₅	—	6	2	no	—
221	C₄×D₅	—	6	2	no	—
222	C₄×D₅	—	6	2	no	—
223	C₄×D₅	—	6	2	no	—
224	#126	—	15	1	no	—
225	#126	—	15	1	no	—
226	#125	—	15	1	no	—
227	#124	—	15	1	no	—
228	#123	—	15	1	no	—
229	#123	—	15	1	no	—
230	C₂²⋊Q₈	—	15	1	no	—
231	#121	—	15	1	no	—
232	C₄×Q₈	—	3	1	no	—
233	C₄×D₄	—	15	1	no	—
234	C₄×D₄	—	15	1	no	—
235	C₄×D₄	—	15	1	no	—
236	#117	—	5	1	no	—
237	#117	—	15	1	no	—
238	C₂×C₄²	—	15	1	no	—
239	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
240	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
241	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
242	D₁₅	—	2	2	no	—
243	D₁₅	—	4	1	no	—
244	C₃×D₅	—	4	1	no	—
245	C₂³×C₃	—	5	1	no	—
246	C₂²×D₃	—	5	1	no	—
247	C₂²×D₃	—	5	1	no	—
248	C₂×C₃×C₄	—	5	1	no	—
249	C₂×C₃×C₄	—	5	1	no	—
250	C₂×C₃×C₄	—	5	1	no	—
251	C₂×C₃×C₄	—	10	2	no	—
252	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
254	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
255	#67	—	10	2	no	—
256	#67	—	10	2	no	—
257	C₂×Dic₃	—	5	1	no	—
258	C₂×Dic₃	—	5	1	no	—
259	C₂×Dic₃	C₂²×D₅	1	1	yes	characteristic
260	C₂×Dic₃	C₂²×D₅	1	1	yes	characteristic
261	C₂×Dic₃	C₂²×D₅	1	1	yes	characteristic
262	C₂×Dic₃	C₂²×D₅	1	1	yes	characteristic
263	D₁₂	—	10	2	no	—
264	C₄×D₃	—	10	2	no	—
265	C₄×D₃	—	10	2	no	—
266	C₄×D₃	—	10	2	no	—
267	C₄×D₃	—	10	2	no	—
268	Dic₆	—	2	2	no	—
269	C₂²×C₅	C₂³×D₃	1	1	yes	characteristic
270	C₂×D₅	—	2	1	no	—
271	C₂×D₅	—	2	1	no	—
272	C₂×D₅	—	2	1	no	—
273	C₂×D₅	—	3	2	no	—
274	C₂×D₅	—	6	1	no	—
275	C₂×D₅	—	6	1	no	—
276	C₂×D₅	—	6	1	no	—
277	C₂×D₅	—	6	1	no	—
278	C₂×D₅	—	6	1	no	—
279	C₄×C₅	—	2	1	no	—
280	C₄×C₅	—	2	1	no	—
281	C₄×C₅	—	3	2	no	—
282	C₄×C₅	—	6	1	no	—
283	C₄×C₅	—	6	1	no	—
284	C₄×C₅	—	6	1	no	—
285	C₄×C₅	#235	1	2	yes	—
286	Dic₅	—	2	1	no	—
287	Dic₅	—	2	1	no	—
288	Dic₅	—	2	1	no	—
289	Dic₅	—	6	1	no	—
290	Dic₅	—	6	1	no	—
291	C₂×Q₈	—	3	1	no	—
292	C₂×D₄	—	15	1	no	—
293	C₂×D₄	—	15	1	no	—
294	C₂×D₄	—	15	1	no	—
295	C₂²×C₄	—	5	1	no	—
296	C₂²×C₄	—	15	1	no	—
297	C₂²×C₄	—	15	1	no	—
298	C₂²×C₄	—	15	1	no	—
299	C₂²×C₄	—	15	1	no	—
300	C₄⋊C₄	—	3	1	no	—
301	C₄⋊C₄	—	3	1	no	—
302	C₄⋊C₄	—	3	1	no	—
303	C₄⋊C₄	—	5	1	no	—
304	C₄⋊C₄	—	5	1	no	—
305	C₄⋊C₄	—	15	1	no	—
306	C₄⋊C₄	—	15	1	no	—
307	C₄⋊C₄	—	15	1	no	—
308	C₄⋊C₄	—	15	1	no	—
309	C₄⋊C₄	—	15	1	no	—
310	C₂²⋊C₄	—	5	1	no	—
311	C₂²⋊C₄	—	5	1	no	—
312	C₂²⋊C₄	—	15	1	no	—
313	C₂²⋊C₄	—	15	1	no	—
314	C₂²⋊C₄	—	15	1	no	—
315	C₂²⋊C₄	—	15	1	no	—
316	C₂²⋊C₄	—	15	1	no	—
317	C₂²⋊C₄	—	15	1	no	—
318	C₂²⋊C₄	—	15	1	no	—
319	C₂²⋊C₄	—	15	1	no	—
320	C₄²	—	3	1	no	—
321	C₄²	—	3	1	no	—
322	C₄²	—	5	1	no	—
323	C₄²	—	15	1	no	—
324	C₄²	—	15	1	no	—
325	C₄²	D₃×D₅	1	1	yes	characteristic
326	C₃×C₅	#529	1	1	yes	characteristic, complemented, Hall
327	C₂²×C₃	—	10	1	no	—
328	C₂²×C₃	—	10	1	no	—
329	C₂²×C₃	—	10	1	no	—
330	C₂²×C₃	C₂³×D₅	1	1	yes	characteristic
331	C₂×D₃	—	5	2	no	—
332	C₂×D₃	—	10	1	no	—
333	C₂×D₃	—	10	1	no	—
334	C₂×D₃	—	10	1	no	—
335	C₂×D₃	—	10	1	no	—
336	C₂×D₃	—	10	1	no	—
337	C₃×C₄	—	2	1	no	—
338	C₃×C₄	—	2	1	no	—
339	C₃×C₄	—	10	1	no	—
340	C₃×C₄	—	10	1	no	—
341	C₃×C₄	—	10	1	no	—
342	C₃×C₄	#713	1	2	yes	—
343	Dic₃	—	2	1	no	—
344	Dic₃	—	2	1	no	—
345	Dic₃	—	2	1	no	—
346	Dic₃	—	10	1	no	—
347	Dic₃	—	10	1	no	—
348	Dic₃	#709	1	2	yes	—
349	C₂×C₅	C₂×#235	1	1	yes	characteristic
350	C₂×C₅	D₃×#41	1	1	yes	characteristic
351	C₂×C₅	D₃×#41	1	1	yes	characteristic
352	D₅	—	4	1	no	—
353	D₅	—	6	2	no	—
354	D₅	—	12	1	no	—
355	C₂³	—	5	1	no	—
356	C₂³	—	15	1	no	—
357	C₂³	—	15	1	no	—
358	Q₈	—	6	2	no	—
359	D₄	—	30	2	no	—
360	D₄	—	30	2	no	—
361	D₄	—	30	2	no	—
362	C₂×C₄	—	3	1	no	—
363	C₂×C₄	—	3	1	no	—
364	C₂×C₄	—	3	1	no	—
365	C₂×C₄	—	3	1	no	—
366	C₂×C₄	—	5	1	no	—
367	C₂×C₄	—	5	1	no	—
368	C₂×C₄	—	5	1	no	—
369	C₂×C₄	—	10	2	no	—
370	C₂×C₄	—	15	1	no	—
371	C₂×C₄	—	15	1	no	—
372	C₂×C₄	—	30	2	no	—
373	C₂×C₄	—	30	2	no	—
374	C₂×C₄	—	30	2	no	—
375	C₂×C₄	—	30	2	no	—
376	C₂×C₄	C₂×D₃×D₅	1	1	yes	characteristic
377	C₂×C₄	C₂×D₃×D₅	1	1	yes	characteristic
378	C₂×C₄	C₂×D₃×D₅	1	1	yes	characteristic
379	C₂×C₃	—	20	1	no	—
380	C₂×C₃	C₂×#709	1	1	yes	characteristic
381	C₂×C₃	C₂×#713	1	1	yes	characteristic
382	C₂×C₃	D₅×#41	1	1	yes	characteristic
383	D₃	—	10	2	no	—
384	D₃	—	20	1	no	—
385	C₅	#5528	1	1	yes	characteristic, complemented, Sylow
386	C₂²	—	10	1	no	—
387	C₂²	—	10	1	no	—
388	C₂²	—	10	1	no	—
389	C₂²	—	15	2	no	—
390	C₂²	—	30	1	no	—
391	C₂²	—	30	1	no	—
392	C₂²	—	30	1	no	—
393	C₂²	—	30	1	no	—
394	C₂²	—	30	1	no	—
395	C₂²	C₂²×D₃×D₅	1	1	yes	characteristic
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	3	2	no	—
399	C₄	—	6	1	no	—
400	C₄	—	6	1	no	—
401	C₄	—	6	1	no	—
402	C₄	—	10	1	no	—
403	C₄	—	10	1	no	—
404	C₄	—	10	1	no	—
405	C₄	—	30	1	no	—
406	C₄	—	30	1	no	—
407	C₄	#6773	1	2	yes	—
408	C₃	#65914	1	1	yes	characteristic, complemented, Sylow
409	C₂	—	20	1	no	—
410	C₂	—	30	2	no	—
411	C₂	—	60	1	no	—
412	C₂	C₂×#6773	1	1	yes	characteristic
413	C₂	D₃×#709	1	1	yes	characteristic
414	C₂	#92016	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₃×D₅
commutator, socle, cosocle	C₂²×C₃×C₅	C₂⁴
Frattini	C₂²	C₂²×D₃×D₅
Fitting	C₃×C₄²×C₅	C₂²
prime radical	#91459	C₂
hypercenter	C₄²	D₃×D₅
hypocenter	C₃×C₅	#529
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
1. C₄×D₆₀	C₂	semidirect
2. C₄×C₅×Dic₆	C₂	semidirect
3. C₃×#4018	C₂	semidirect
5. #91455	C₂	semidirect
6. C₄×#1202	C₂	semidirect
7. C₄×#1202	C₂	semidirect
8. #91433	C₂	semidirect
9. #91424	C₂	semidirect
10. C₄×#1200	C₂	semidirect
11. #91386	C₂	semidirect
12. #91362	C₂	semidirect
13. #91356	C₂	semidirect
14. #91343	C₂	semidirect
15. #91337	C₂	semidirect
66. #4018	D₃	semidirect
106. C₄×Dic₆	D₅	semidirect
326. C₃×C₅	#529	semidirect
385. C₅	#5528	semidirect
408. C₃	#65914	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₆₀	2
C₄×C₅×Dic₆	2
C₃×#4018	2
#91459	2
#91455	2
C₄×#1202	2
#91433	2
#91424	2
C₄×#1200	2
#91386	2
#91362	2
#91356	2
#91343	2
#91337	2
#65914	3
#5528	5