Subgroups — #14413526

Order 1920.

952 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4047	C₂	1	1	yes	maximal, characteristic
2	#11754509	C₂	1	2	yes	maximal
3	C₂×#91102	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5106	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748460	C₂	1	2	yes	maximal, complemented
6	#11747672	C₂	1	2	yes	maximal, complemented
7	#11747618	C₂	1	4	yes	maximal, complemented
8	D₅×#818	C₂	1	2	yes	maximal, complemented
9	#10610910	—	3	1	no	maximal, Hall
10	C₂×C₃×#709	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₅	C₂²	1	2	yes	—
13	C₅×#926	C₂²	1	2	yes	—
14	C₂×C₃×#681	C₂²	1	1	yes	characteristic
15	C₃×#4047	C₄	1	8	yes	complemented
16	C₂×C₃×#676	C₂²	1	2	yes	—
17	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
18	#91559	—	2	4	no	—
19	Dic₃×D₂₀	—	2	2	no	—
20	D₅×C₄⋊Dic₃	C₂²	1	4	yes	—
21	#91358	C₂²	1	4	yes	—
22	Dic₃×Dic₁₀	—	2	2	no	—
23	#91102	C₂²	1	2	yes	—
24	#91102	C₂²	1	2	yes	—
25	C₅×#818	C₂²	1	1	yes	characteristic
26	C₅×#818	C₂²	1	1	yes	characteristic
27	C₅×#817	C₂²	1	2	yes	—
28	#90988	C₂²	1	4	yes	—
29	#90985	C₂²	1	4	yes	—
30	#83785	—	5	1	no	maximal, Hall
31	C₂×#4047	D₃	1	1	yes	characteristic
32	#65857	—	3	2	no	—
33	C₅×#427	—	3	1	no	—
34	C₂×#3950	—	3	1	no	—
35	#65284	—	3	2	no	—
36	#65169	—	3	2	no	—
37	D₅×#107	—	3	2	no	—
38	#65150	—	3	4	no	—
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂²×Dic₁₅	—	2	2	no	—
41	C₂×C₃×C₂²⋊D₅	D₄	1	2	yes	—
42	C₃×#709	C₂×C₄	1	4	yes	—
43	C₃×#709	Q₈	1	4	yes	—
44	C₂×C₃×D₂₀	D₄	1	1	yes	characteristic
45	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
46	C₂×C₃×Dic₁₀	D₄	1	1	yes	characteristic
47	C₂×D₅×Dic₃	—	2	4	no	—
48	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
49	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
50	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
51	C₄⋊Dic₁₅	—	2	2	no	—
52	C₄⋊Dic₁₅	C₂³	1	4	yes	—
53	C₅×#217	—	2	2	no	—
54	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
55	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
56	C₄×C₅×Dic₃	—	2	2	no	—
57	C₃×#681	C₂×C₄	1	4	yes	complemented
58	C₂×C₃×#168	C₂³	1	2	yes	—
59	C₃×#676	C₂×C₄	1	8	yes	complemented
60	C₃×C₈×D₅	C₂×C₄	1	8	yes	complemented
61	#6668	—	2	4	no	—
62	#6665	—	2	4	no	—
63	Dic₃×Dic₅	—	2	4	no	—
64	C₂×C₃×#131	—	5	1	no	—
65	#5827	—	5	2	no	—
66	#5121	—	5	2	no	—
67	#5121	—	5	4	no	—
68	#5106	—	5	2	no	—
69	#5106	D₅	1	1	yes	characteristic, complemented
70	C₂×#818	—	5	1	no	—
71	C₂×#818	—	5	2	no	—
72	C₂×#709	C₂×D₃	1	1	yes	characteristic
73	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
74	C₅×#117	—	3	2	no	—
75	C₂×C₄⋊Dic₅	—	3	2	no	—
76	C₂×#681	C₂×D₃	1	1	yes	characteristic
77	#4047	Dic₃	1	8	yes	complemented
78	C₂×#676	C₂×D₃	1	2	yes	—
79	C₂×C₈×D₅	C₂×D₃	1	2	yes	—
80	#4038	—	3	4	no	—
81	D₅×C₄⋊C₄	—	3	4	no	—
82	#4027	—	6	4	no	—
83	C₄×D₂₀	—	6	2	no	—
84	C₄×Dic₁₀	—	6	2	no	—
85	C₅×#107	—	3	1	no	—
86	C₅×#107	—	3	1	no	—
87	C₅×#106	—	3	2	no	—
88	#3950	—	3	2	no	—
89	#3950	—	3	2	no	—
90	#3940	—	3	4	no	—
91	#3939	—	3	4	no	—
92	#2913	—	15	1	no	Sylow
93	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₃×D₅	C₂×D₄	1	2	yes	—
95	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
96	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
99	C₂×Dic₁₅	—	2	4	no	—
100	C₂×Dic₁₅	—	8	2	no	—
101	C₂×C₅×Dic₃	—	2	2	no	—
102	C₂×C₅×Dic₃	—	2	2	no	—
103	C₃×C₂²⋊D₅	C₄⋊C₄	1	8	yes	—
104	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
105	C₃×D₂₀	C₄⋊C₄	1	4	yes	—
106	C₃×C₄×D₅	C₂²×C₄	1	4	yes	—
107	C₃×C₄×D₅	C₂×Q₈	1	4	yes	—
108	C₃×Dic₁₀	C₄⋊C₄	1	4	yes	—
109	D₅×Dic₃	—	8	4	no	—
110	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
111	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
112	C₃×#168	C₂²×C₄	1	4	yes	—
113	C₂×C₃×#41	—	5	1	no	—
114	C₃×#131	—	5	8	no	—
115	C₂×C₃×M₁₆	—	5	1	no	—
116	C₂×C₃×M₁₆	—	5	2	no	—
117	C₂²×C₃×C₈	—	5	2	no	—
118	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
119	Q₈×Dic₃	—	10	2	no	—
120	D₄×Dic₃	—	10	2	no	—
121	D₄×Dic₃	—	10	4	no	—
122	#926	—	5	4	no	—
123	#926	C₂×D₅	1	2	yes	—
124	C₂×C₄⋊Dic₃	—	5	2	no	—
125	C₂×C₄⋊Dic₃	—	5	4	no	—
126	#818	—	5	2	no	—
127	#818	—	5	2	no	—
128	#818	—	5	4	no	—
129	#818	C₂×D₅	1	1	yes	characteristic
130	#818	C₂×D₅	1	1	yes	characteristic
131	#817	—	5	4	no	—
132	#817	C₂×D₅	1	2	yes	—
133	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
134	C₂×C₂²⋊D₅	D₁₂	1	2	yes	—
135	C₂²×Dic₅	—	6	2	no	—
136	#709	Dic₆	1	4	yes	—
137	#709	C₂×Dic₃	1	4	yes	—
138	C₂×D₂₀	D₁₂	1	1	yes	characteristic
139	C₂×C₄×D₅	—	6	4	no	—
140	C₂×C₄×D₅	C₂²×D₃	1	2	yes	—
141	C₂×Dic₁₀	D₁₂	1	1	yes	characteristic
142	C₂×C₅×C₈	C₂×Dic₃	1	4	yes	complemented
143	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
144	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
145	C₅×C₄⋊C₄	—	3	2	no	—
146	C₅×C₄⋊C₄	—	3	2	no	—
147	C₅×C₂²⋊C₄	—	6	2	no	—
148	C₄²×C₅	—	6	2	no	—
149	#685	—	6	4	no	—
150	C₄⋊Dic₅	—	3	4	no	—
151	C₄⋊Dic₅	—	6	2	no	—
152	#683	—	6	4	no	—
153	C₄×Dic₅	—	6	4	no	—
154	#681	C₂×Dic₃	1	4	yes	complemented
155	C₂×#168	C₂²×D₃	1	2	yes	—
156	#676	C₂×Dic₃	1	8	yes	complemented
157	C₈×D₅	C₂×Dic₃	1	8	yes	complemented
158	C₂×#131	—	5	1	no	—
159	#520	—	15	2	no	—
160	#428	—	15	4	no	—
161	#428	—	15	2	no	—
162	#427	—	3	1	no	—
163	#427	—	15	2	no	—
164	C₂×#107	—	15	2	no	—
165	C₂×#107	—	15	1	no	—
166	C₂²×C₃×C₅	—	2	1	no	—
167	C₂²×C₃×C₅	—	2	1	no	—
168	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	2	yes	—
169	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₃×D₅	—	2	2	no	—
171	C₂×C₃×D₅	—	2	2	no	—
172	C₂×C₃×D₅	C₂×C₄⋊C₄	1	4	yes	—
173	C₃×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
174	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
175	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
176	Dic₁₅	—	4	4	no	—
177	C₃×Dic₅	C₂×C₄⋊C₄	1	4	yes	—
178	C₅×Dic₃	—	4	2	no	—
179	C₅×Dic₃	—	4	2	no	—
180	C₃×#41	—	5	4	no	—
181	C₃×#41	—	5	4	no	—
182	C₂×C₃×Q₈	—	5	1	no	—
183	C₂×C₃×D₄	—	5	2	no	—
184	C₂×C₃×D₄	—	5	1	no	—
185	C₂²×C₃×C₄	—	5	2	no	—
186	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
187	C₂²×Dic₃	—	10	4	no	—
188	C₂²×Dic₃	—	10	2	no	—
189	C₃×M₁₆	—	5	4	no	—
190	C₃×M₁₆	—	5	8	no	—
191	C₂×C₃×C₈	—	5	2	no	—
192	C₂×C₃×C₈	—	5	8	no	—
193	C₂×C₃×C₈	C₄×D₅	1	4	yes	complemented
194	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
195	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
196	#217	—	2	2	no	—
197	#217	—	10	4	no	—
198	C₄⋊Dic₃	—	5	4	no	—
199	C₄⋊Dic₃	—	10	4	no	—
200	C₄⋊Dic₃	—	10	2	no	—
201	C₄⋊Dic₃	C₂²×D₅	1	2	yes	—
202	C₄⋊Dic₃	C₂²×D₅	1	2	yes	—
203	C₄×Dic₃	—	2	2	no	—
204	C₄×Dic₃	—	10	4	no	—
205	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
206	C₂²×D₅	C₂×D₁₂	1	2	yes	—
207	C₂×C₄×C₅	—	6	2	no	—
208	C₂×C₄×C₅	—	6	2	no	—
209	C₂×C₄×C₅	C₂×Dic₆	1	2	yes	—
210	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
212	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
213	C₂²⋊D₅	C₄⋊Dic₃	1	8	yes	—
214	C₂×Dic₅	—	6	4	no	—
215	C₂×Dic₅	—	24	2	no	—
216	C₂×Dic₅	C₂×D₁₂	1	2	yes	—
217	D₂₀	C₄⋊Dic₃	1	4	yes	—
218	C₄×D₅	—	24	4	no	—
219	C₄×D₅	C₂×Dic₆	1	4	yes	—
220	C₄×D₅	C₂²×Dic₃	1	4	yes	—
221	Dic₁₀	C₄⋊Dic₃	1	4	yes	—
222	C₅×C₈	C₂²×Dic₃	1	2	yes	—
223	C₅×C₈	C₂²×Dic₃	1	2	yes	—
224	#168	C₂²×Dic₃	1	4	yes	—
225	C₂×#41	—	5	1	no	—
226	#131	—	5	8	no	—
227	C₂×M₁₆	—	5	1	no	—
228	C₂×M₁₆	—	5	2	no	—
229	C₂²×C₈	—	5	2	no	—
230	C₂²×C₈	D₃×D₅	1	1	yes	characteristic
231	C₄×Q₈	—	30	2	no	—
232	C₄×D₄	—	30	2	no	—
233	C₄×D₄	—	30	4	no	—
234	#117	—	3	2	no	—
235	#117	—	15	4	no	—
236	C₂×C₄⋊C₄	—	15	4	no	—
237	C₂×C₄⋊C₄	—	15	2	no	—
238	#107	—	3	1	no	—
239	#107	—	3	1	no	—
240	#107	—	15	4	no	—
241	#107	—	15	2	no	—
242	#107	—	15	2	no	—
243	#106	—	3	2	no	—
244	#106	—	15	4	no	—
245	C₂×C₃×C₅	—	2	2	no	—
246	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
247	C₂×C₃×C₅	#576	1	1	yes	characteristic
248	C₂×C₃×C₅	#578	1	1	yes	characteristic
249	C₃×D₅	—	2	4	no	—
250	C₂³×C₃	—	5	2	no	—
251	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
252	C₃×Q₈	—	5	4	no	—
253	C₃×D₄	—	5	8	no	—
254	C₃×D₄	—	5	4	no	—
255	C₂×C₃×C₄	—	5	2	no	—
256	C₂×C₃×C₄	—	5	4	no	—
257	C₂×C₃×C₄	—	5	4	no	—
258	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
259	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
260	C₂×C₃×C₄	Q₈×D₅	1	2	yes	—
261	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
262	C₂×Dic₃	—	2	2	no	—
263	C₂×Dic₃	—	2	2	no	—
264	C₂×Dic₃	—	10	4	no	—
265	C₂×Dic₃	—	40	4	no	—
266	C₂×Dic₃	—	40	2	no	—
267	C₃×C₈	—	5	4	no	—
268	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
269	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
270	C₂²×C₅	—	2	1	no	—
271	C₂²×C₅	—	2	1	no	—
272	C₂²×C₅	C₂×C₄⋊Dic₃	1	2	yes	—
273	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
274	C₂×D₅	—	2	2	no	—
275	C₂×D₅	—	2	2	no	—
276	C₂×D₅	C₂×C₄⋊Dic₃	1	4	yes	—
277	C₄×C₅	—	12	2	no	—
278	C₄×C₅	—	12	2	no	—
279	C₄×C₅	C₂×C₄⋊Dic₃	1	2	yes	—
280	C₄×C₅	C₂²×Dic₆	1	1	yes	characteristic
281	C₄×C₅	C₂³×Dic₃	1	1	yes	characteristic
282	Dic₅	—	12	4	no	—
283	Dic₅	C₂×C₄⋊Dic₃	1	4	yes	—
284	#41	—	5	4	no	—
285	#41	—	5	4	no	—
286	C₂×Q₈	—	5	1	no	—
287	C₂×D₄	—	5	2	no	—
288	C₂×D₄	—	5	1	no	—
289	C₂²×C₄	—	5	2	no	—
290	C₂²×C₄	—	30	4	no	—
291	C₂²×C₄	—	30	2	no	—
292	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
293	M₁₆	—	5	4	no	—
294	M₁₆	—	5	8	no	—
295	C₂×C₈	—	5	2	no	—
296	C₂×C₈	—	5	8	no	—
297	C₂×C₈	D₅×Dic₃	1	4	yes	complemented
298	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
299	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
300	C₄⋊C₄	—	3	2	no	—
301	C₄⋊C₄	—	3	2	no	—
302	C₄⋊C₄	—	15	4	no	—
303	C₄⋊C₄	—	30	4	no	—
304	C₄⋊C₄	—	30	2	no	—
305	C₂²⋊C₄	—	6	2	no	—
306	C₂²⋊C₄	—	30	4	no	—
307	C₄²	—	6	2	no	—
308	C₄²	—	30	4	no	—
309	C₃×C₅	#2913	1	1	yes	characteristic, complemented, Hall
310	C₂²×C₃	—	2	1	no	—
311	C₂²×C₃	—	2	1	no	—
312	C₂²×C₃	—	5	4	no	—
313	C₂²×C₃	—	10	2	no	—
314	C₂²×C₃	—	10	2	no	—
315	C₂²×C₃	D₅×C₄⋊C₄	1	2	yes	—
316	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
317	C₃×C₄	—	5	4	no	—
318	C₃×C₄	D₅×C₄⋊C₄	1	2	yes	—
319	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
320	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
321	Dic₃	—	4	2	no	—
322	Dic₃	—	4	2	no	—
323	Dic₃	—	20	4	no	—
324	C₂×C₅	—	2	2	no	—
325	C₂×C₅	#5752	1	1	yes	characteristic
326	C₂×C₅	#5753	1	1	yes	characteristic
327	C₂×C₅	C₂²×C₄⋊Dic₃	1	1	yes	characteristic
328	D₅	—	2	4	no	—
329	C₂³	—	5	2	no	—
330	C₂³	D₅×D₁₂	1	1	yes	characteristic
331	Q₈	—	5	4	no	—
332	D₄	—	5	8	no	—
333	D₄	—	5	4	no	—
334	C₂×C₄	—	5	2	no	—
335	C₂×C₄	—	5	4	no	—
336	C₂×C₄	—	5	4	no	—
337	C₂×C₄	—	6	2	no	—
338	C₂×C₄	—	6	2	no	—
339	C₂×C₄	—	30	4	no	—
340	C₂×C₄	—	120	4	no	—
341	C₂×C₄	—	120	2	no	—
342	C₂×C₄	D₅×Dic₆	1	2	yes	—
343	C₂×C₄	D₅×D₁₂	1	1	yes	characteristic
344	C₂×C₄	C₂×D₅×Dic₃	1	2	yes	—
345	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
346	C₈	—	5	4	no	—
347	C₈	C₂×D₅×Dic₃	1	2	yes	—
348	C₈	C₂×D₅×Dic₃	1	2	yes	—
349	C₂×C₃	—	2	2	no	—
350	C₂×C₃	—	10	4	no	—
351	C₂×C₃	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
352	C₂×C₃	#66103	1	1	yes	characteristic
353	C₂×C₃	#66105	1	1	yes	characteristic
354	C₅	#83785	1	1	yes	characteristic, complemented, Sylow
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	5	4	no	—
358	C₂²	—	10	2	no	—
359	C₂²	—	10	2	no	—
360	C₂²	D₅×C₄⋊Dic₃	1	2	yes	—
361	C₂²	C₂×D₅×D₁₂	1	1	yes	characteristic
362	C₄	—	5	4	no	—
363	C₄	—	12	2	no	—
364	C₄	—	12	2	no	—
365	C₄	—	60	4	no	—
366	C₄	D₅×C₄⋊Dic₃	1	2	yes	—
367	C₄	C₂×D₅×Dic₆	1	1	yes	characteristic
368	C₄	C₂²×D₅×Dic₃	1	1	yes	characteristic
369	C₃	#10610910	1	1	yes	characteristic, complemented, Sylow
370	C₂	—	2	2	no	—
371	C₂	—	10	4	no	—
372	C₂	#11753963	1	1	yes	characteristic
373	C₂	#11753988	1	1	yes	characteristic
374	C₂	C₂×D₅×C₄⋊Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₅×D₁₂
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₂²×C₃×C₅×C₈	C₂²
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×#709	C₂²
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂²×C₈	D₃×D₅
hypocenter	C₃×C₅	#2913
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. C₂×#91102	C₂	semidirect
4. C₅×#5106	C₂	semidirect
5. #11748460	C₂	semidirect
6. #11747672	C₂	semidirect
7. #11747618	C₂	semidirect
8. D₅×#818	C₂	semidirect
15. C₃×#4047	C₄	semidirect
48. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
57. C₃×#681	C₂×C₄	semidirect
59. C₃×#676	C₂×C₄	semidirect
60. C₃×C₈×D₅	C₂×C₄	semidirect
69. #5106	D₅	semidirect
77. #4047	Dic₃	semidirect
142. C₂×C₅×C₈	C₂×Dic₃	semidirect
154. #681	C₂×Dic₃	semidirect
156. #676	C₂×Dic₃	semidirect
157. C₈×D₅	C₂×Dic₃	semidirect
193. C₂×C₃×C₈	C₄×D₅	semidirect
297. C₂×C₈	D₅×Dic₃	semidirect
309. C₃×C₅	#2913	semidirect
354. C₅	#83785	semidirect
369. C₃	#10610910	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#4047	2
#11754509	2
C₂×#91102	2
C₅×#5106	2
#11748460	2
#11747672	2
#11747618	2
D₅×#818	2
#10610910	3
#83785	5