Subgroups — #28377805

Order 13952.

1424 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	#20295862	C₂	1	2	yes	maximal, complemented
2	#20295842	C₂	1	4	yes	maximal, complemented
3	#20295836	C₂	1	4	yes	maximal, complemented
4	#20295835	C₂	1	4	yes	maximal, complemented
5	#20295830	C₂	1	4	yes	maximal, complemented
6	#20295826	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295823	C₂	1	4	yes	maximal, complemented
8	C₂×#16812719	C₂	1	2	yes	maximal, complemented
9	#135×D₁₀₉	C₂	1	4	yes	maximal, complemented
10	C₂×#16812707	C₂	1	1	yes	maximal, characteristic, complemented
11	#575×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#16812747	C₂²	1	4	yes	complemented
13	#16812746	—	2	2	no	—
14	#16812746	C₂²	1	4	yes	complemented
15	#16812745	—	2	2	no	—
16	#16812745	C₂²	1	4	yes	complemented
17	#16812744	—	2	4	no	—
18	#16812744	C₂²	1	4	yes	complemented
19	C₂×#13182029	—	2	4	no	—
20	C₂×#13182029	C₂²	1	1	yes	characteristic
21	C₂×#13182029	C₂²	1	2	yes	complemented
22	#41×D₁₀₉	—	2	4	no	—
23	#41×D₁₀₉	C₂²	1	8	yes	complemented
24	#16812732	C₂²	1	4	yes	complemented
25	#16812731	C₂²	1	8	yes	complemented
26	#16812728	C₂²	1	8	yes	complemented
27	#16812727	C₂²	1	4	yes	complemented
28	#16812726	C₂²	1	8	yes	complemented
29	#16812723	C₂²	1	8	yes	complemented
30	#16812722	C₂²	1	4	yes	complemented
31	#16812721	C₂²	1	4	yes	complemented
32	#16812720	C₂²	1	8	yes	complemented
33	#16812719	C₂²	1	4	yes	complemented
34	#16812719	C₂²	1	4	yes	complemented
35	#16812719	C₂²	1	4	yes	complemented
36	#16812719	C₂²	1	4	yes	complemented
37	#16812718	C₂²	1	4	yes	complemented
38	C₂×#13182019	C₂²	1	2	yes	complemented
39	Q₁₆×D₁₀₉	C₂²	1	4	yes	complemented
40	C₂×#13182017	C₂²	1	2	yes	complemented
41	C₂×#13182016	C₂²	1	2	yes	complemented
42	SD₁₆×D₁₀₉	C₂²	1	8	yes	complemented
43	C₂×#13182014	C₂²	1	2	yes	complemented
44	D₈×D₁₀₉	C₂²	1	4	yes	complemented
45	#16812707	C₂²	1	4	yes	complemented
46	#16812707	C₂²	1	4	yes	complemented
47	C₂×#13182012	C₂²	1	2	yes	complemented
48	C₂²×#11724784	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₈×D₁₀₉	C₂²	1	2	yes	complemented
50	C₂×#41×C₁₀₉	C₂²	1	2	yes	complemented
51	#137×C₁₀₉	C₂²	1	4	yes	complemented
52	AGL(1,ℤ/8)×C₁₀₉	C₂²	1	4	yes	complemented
53	#135×C₁₀₉	C₂²	1	4	yes	complemented
54	C₂×M₁₆×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
55	#13182030	—	2	4	no	—
56	#13182030	C₂³	1	8	yes	—
57	#13182029	—	2	2	no	—
58	#13182029	—	2	2	no	—
59	#13182029	—	2	8	no	—
60	#13182029	—	2	4	no	—
61	#13182029	—	2	8	no	—
62	#13182029	—	2	4	no	—
63	#13182029	D₄	1	4	yes	—
64	#13182029	C₂³	1	4	yes	—
65	#13182029	C₂³	1	4	yes	—
66	#13182029	C₂³	1	4	yes	—
67	#13182028	—	2	8	no	—
68	#13182028	—	2	8	no	—
69	#13182028	—	2	4	no	—
70	#13182028	C₂³	1	8	yes	—
71	C₂×Dic₂₁₈	—	2	4	no	—
72	C₂×Dic₂₁₈	D₄	1	1	yes	characteristic
73	C₂×Dic₂₁₈	C₂³	1	2	yes	—
74	Q₈×D₁₀₉	—	2	4	no	—
75	Q₈×D₁₀₉	C₂³	1	8	yes	—
76	C₂×D₄₃₆	—	2	4	no	—
77	C₂×D₄₃₆	D₄	1	1	yes	characteristic
78	C₂×D₄₃₆	C₂³	1	2	yes	—
79	C₂×C₂²⋊D₁₀₉	—	2	2	no	—
80	C₂×C₂²⋊D₁₀₉	—	2	8	no	—
81	C₂×C₂²⋊D₁₀₉	D₄	1	2	yes	—
82	D₄×D₁₀₉	—	2	8	no	—
83	D₄×D₁₀₉	—	2	8	no	—
84	D₄×D₁₀₉	—	2	4	no	—
85	D₄×D₁₀₉	C₂³	1	8	yes	—
86	C₂×C₄×D₁₀₉	—	2	2	no	—
87	C₂×C₄×D₁₀₉	—	2	8	no	—
88	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
89	Dic₄₃₆	C₂³	1	4	yes	—
90	#13182019	C₂³	1	4	yes	—
91	#13182019	C₂³	1	4	yes	—
92	#13182018	C₂³	1	8	yes	—
93	#13182017	C₂³	1	4	yes	—
94	#13182017	C₂³	1	4	yes	—
95	#13182016	C₂³	1	4	yes	—
96	#13182016	C₂³	1	4	yes	—
97	D₈₇₂	C₂³	1	4	yes	—
98	#13182014	C₂³	1	4	yes	—
99	#13182014	C₂³	1	4	yes	—
100	#13182012	C₂³	1	8	yes	—
101	C₂×#11724784	C₂³	1	1	yes	characteristic
102	C₂×#11724784	C₂³	1	1	yes	characteristic
103	C₂×#11724784	C₂³	1	2	yes	—
104	C₂×#11724784	C₂³	1	2	yes	—
105	C₈×D₁₀₉	C₂³	1	4	yes	—
106	C₈×D₁₀₉	C₂³	1	4	yes	—
107	#41×C₁₀₉	—	2	2	no	—
108	#41×C₁₀₉	—	2	2	no	—
109	#41×C₁₀₉	C₂³	1	4	yes	—
110	#41×C₁₀₉	C₂³	1	4	yes	—
111	C₂×Q₈×C₁₀₉	C₂³	1	2	yes	—
112	C₂×D₄×C₁₀₉	—	2	2	no	—
113	C₂×D₄×C₁₀₉	C₂³	1	2	yes	—
114	C₂²×C₄×C₁₀₉	—	2	2	no	—
115	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
116	Q₁₆×C₁₀₉	C₂³	1	4	yes	—
117	SD₁₆×C₁₀₉	C₂³	1	8	yes	—
118	D₈×C₁₀₉	C₂³	1	4	yes	—
119	M₁₆×C₁₀₉	C₂³	1	4	yes	—
120	C₂×C₈×C₁₀₉	C₂³	1	2	yes	—
121	C₂³×C₁₀₉	—	2	2	no	—
122	C₂³×C₁₀₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×D₁₀₉	—	2	2	no	—
124	C₂²×D₁₀₉	—	2	8	no	—
125	C₂²×D₁₀₉	C₂×D₄	1	2	yes	—
126	Q₈×C₁₀₉	—	2	2	no	—
127	Q₈×C₁₀₉	C₂⁴	1	4	yes	—
128	D₄×C₁₀₉	—	2	4	no	—
129	D₄×C₁₀₉	—	2	4	no	—
130	D₄×C₁₀₉	—	2	2	no	—
131	D₄×C₁₀₉	C₂⁴	1	4	yes	—
132	C₂×C₄×C₁₀₉	—	2	2	no	—
133	C₂×C₄×C₁₀₉	—	2	4	no	—
134	C₂×C₄×C₁₀₉	—	2	4	no	—
135	C₂×C₄×C₁₀₉	C₂×D₄	1	2	yes	—
136	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
137	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
138	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
139	C₂²⋊D₁₀₉	—	2	4	no	—
140	C₂²⋊D₁₀₉	—	2	4	no	—
141	C₂²⋊D₁₀₉	—	2	8	no	—
142	C₂²⋊D₁₀₉	—	2	8	no	—
143	C₂²⋊D₁₀₉	C₂×D₄	1	8	yes	—
144	C₂×Dic₁₀₉	—	2	2	no	—
145	C₂×Dic₁₀₉	—	2	8	no	—
146	C₂×Dic₁₀₉	C₂×D₄	1	2	yes	—
147	D₄₃₆	—	2	8	no	—
148	D₄₃₆	—	2	2	no	—
149	D₄₃₆	C₂×D₄	1	4	yes	—
150	D₄₃₆	C₂⁴	1	4	yes	—
151	C₄×D₁₀₉	—	2	8	no	—
152	C₄×D₁₀₉	—	2	4	no	—
153	C₄×D₁₀₉	—	2	4	no	—
154	C₄×D₁₀₉	—	2	8	no	—
155	C₄×D₁₀₉	C₂×D₄	1	4	yes	—
156	C₄×D₁₀₉	C₂⁴	1	4	yes	—
157	Dic₂₁₈	—	2	2	no	—
158	Dic₂₁₈	—	2	8	no	—
159	Dic₂₁₈	C₂×D₄	1	4	yes	—
160	Dic₂₁₈	C₂⁴	1	4	yes	—
161	C₈×C₁₀₉	C₂⁴	1	4	yes	—
162	#11724784	C₂⁴	1	1	yes	characteristic
163	#11724784	C₂⁴	1	1	yes	characteristic
164	#11724784	C₂⁴	1	2	yes	—
165	C₂²×C₁₀₉	—	2	4	no	—
166	C₂²×C₁₀₉	—	4	1	no	—
167	C₂²×C₁₀₉	—	8	2	no	—
168	C₂²×C₁₀₉	C₂²×D₄	1	2	yes	—
169	C₂²×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
170	C₂×D₁₀₉	—	2	4	no	—
171	C₂×D₁₀₉	—	4	2	no	—
172	C₂×D₁₀₉	—	8	8	no	—
173	C₂×D₁₀₉	—	8	2	no	—
174	C₂×D₁₀₉	C₂²×D₄	1	4	yes	—
175	C₄×C₁₀₉	—	2	4	no	—
176	C₄×C₁₀₉	C₂²×D₄	1	2	yes	—
177	C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
178	C₄×C₁₀₉	C₂⁵	1	1	yes	characteristic
179	Dic₁₀₉	—	2	4	no	—
180	Dic₁₀₉	C₂²×D₄	1	4	yes	—
181	C₂×C₁₀₉	—	2	1	no	—
182	C₂×C₁₀₉	—	2	2	no	—
183	C₂×C₁₀₉	—	4	4	no	—
184	C₂×C₁₀₉	C₂³×D₄	1	1	yes	characteristic
185	D₁₀₉	—	2	4	no	—
186	D₁₀₉	—	4	4	no	—
187	#3584	—	109	1	no	maximal, Sylow
188	C₁₀₉	#3584	1	1	yes	characteristic, complemented, Sylow
189	#585	—	109	2	no	—
190	#578	—	109	4	no	—
191	#577	—	109	4	no	—
192	#577	—	109	4	no	—
193	#576	—	109	4	no	—
194	#575	—	109	4	no	—
195	#575	—	109	1	no	—
196	#575	D₁₀₉	1	1	yes	characteristic, complemented
197	C₂×#135	—	109	2	no	—
198	C₂×#135	—	109	4	no	—
199	C₂×#131	—	109	1	no	—
200	2₋¹⁺⁴	—	109	4	no	—
201	2₋¹⁺⁴	—	109	4	no	—
202	2₋¹⁺⁴	—	218	2	no	—
203	H(5,𝔽₂)	—	109	4	no	—
204	H(5,𝔽₂)	—	109	4	no	—
205	H(5,𝔽₂)	—	218	4	no	—
206	H(5,𝔽₂)	—	218	2	no	—
207	C₂×#41	—	109	1	no	—
208	C₂×#41	—	109	8	no	—
209	C₂×#41	—	109	2	no	—
210	C₂×#41	—	218	4	no	—
211	C₂×#41	—	218	4	no	—
212	C₂×#41	C₂×D₁₀₉	1	2	yes	complemented
213	#137	—	109	8	no	—
214	#137	—	109	8	no	—
215	#137	—	109	4	no	—
216	#137	C₂×D₁₀₉	1	4	yes	complemented
217	AGL(1,ℤ/8)	—	109	8	no	—
218	AGL(1,ℤ/8)	—	109	8	no	—
219	AGL(1,ℤ/8)	—	109	4	no	—
220	AGL(1,ℤ/8)	C₂×D₁₀₉	1	4	yes	complemented
221	#135	—	109	4	no	—
222	#135	—	109	4	no	—
223	#135	—	109	4	no	—
224	#135	—	109	4	no	—
225	#135	—	109	4	no	—
226	#135	—	109	8	no	—
227	#135	—	109	4	no	—
228	#135	—	109	4	no	—
229	#135	C₂×D₁₀₉	1	4	yes	complemented
230	C₂×Q₁₆	—	109	2	no	—
231	C₂×Q₁₆	—	109	4	no	—
232	C₂×SD₁₆	—	109	2	no	—
233	C₂×SD₁₆	—	109	2	no	—
234	C₂×SD₁₆	—	109	8	no	—
235	C₂×D₈	—	109	2	no	—
236	C₂×D₈	—	109	4	no	—
237	#131	—	109	4	no	—
238	#131	—	109	4	no	—
239	C₂×M₁₆	—	109	2	no	—
240	C₂×M₁₆	C₂×D₁₀₉	1	1	yes	characteristic, complemented
241	C₂²×C₈	—	109	1	no	—
242	C₂²×C₈	—	109	2	no	—
243	#41	—	2	2	no	—
244	#41	—	2	2	no	—
245	#41	—	109	4	no	—
246	#41	—	109	4	no	—
247	#41	—	109	8	no	—
248	#41	—	109	8	no	—
249	#41	—	109	4	no	—
250	#41	—	109	4	no	—
251	#41	—	218	8	no	—
252	#41	—	218	8	no	—
253	#41	—	218	4	no	—
254	#41	—	218	4	no	—
255	#41	—	218	8	no	—
256	#41	—	218	8	no	—
257	#41	—	218	4	no	—
258	#41	—	218	4	no	—
259	#41	—	218	2	no	—
260	#41	—	218	2	no	—
261	#41	C₂²×D₁₀₉	1	4	yes	—
262	#41	C₂²×D₁₀₉	1	4	yes	—
263	C₂×Q₈	—	109	1	no	—
264	C₂×Q₈	—	109	8	no	—
265	C₂×Q₈	—	109	2	no	—
266	C₂×Q₈	—	218	4	no	—
267	C₂×Q₈	—	218	4	no	—
268	C₂×Q₈	C₂²×D₁₀₉	1	2	yes	—
269	C₂×D₄	—	2	2	no	—
270	C₂×D₄	—	109	2	no	—
271	C₂×D₄	—	109	8	no	—
272	C₂×D₄	—	109	1	no	—
273	C₂×D₄	—	109	2	no	—
274	C₂×D₄	—	218	4	no	—
275	C₂×D₄	—	218	8	no	—
276	C₂×D₄	—	218	4	no	—
277	C₂×D₄	—	218	8	no	—
278	C₂×D₄	—	218	8	no	—
279	C₂×D₄	—	218	2	no	—
280	C₂×D₄	C₂²×D₁₀₉	1	2	yes	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	109	2	no	—
283	C₂²×C₄	—	218	8	no	—
284	C₂²×C₄	—	218	2	no	—
285	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
286	Q₁₆	—	109	4	no	—
287	Q₁₆	—	109	4	no	—
288	Q₁₆	—	109	4	no	—
289	Q₁₆	C₂²×D₁₀₉	1	4	yes	—
290	SD₁₆	—	109	4	no	—
291	SD₁₆	—	109	4	no	—
292	SD₁₆	—	109	4	no	—
293	SD₁₆	—	109	4	no	—
294	SD₁₆	—	109	8	no	—
295	SD₁₆	C₂²×D₁₀₉	1	8	yes	—
296	D₈	—	109	4	no	—
297	D₈	—	109	4	no	—
298	D₈	—	109	4	no	—
299	D₈	C₂²×D₁₀₉	1	4	yes	—
300	M₁₆	—	109	8	no	—
301	M₁₆	C₂²×D₁₀₉	1	4	yes	—
302	C₂×C₈	—	109	1	no	—
303	C₂×C₈	—	109	1	no	—
304	C₂×C₈	—	109	2	no	—
305	C₂×C₈	—	109	2	no	—
306	C₂×C₈	—	109	4	no	—
307	C₂×C₈	—	109	4	no	—
308	C₂×C₈	C₂²×D₁₀₉	1	2	yes	—
309	C₂³	—	2	2	no	—
310	C₂³	—	109	2	no	—
311	C₂³	—	218	8	no	—
312	C₂³	—	218	2	no	—
313	C₂³	D₄×D₁₀₉	1	1	yes	characteristic
314	Q₈	—	2	2	no	—
315	Q₈	—	109	4	no	—
316	Q₈	—	109	4	no	—
317	Q₈	—	218	8	no	—
318	Q₈	—	218	2	no	—
319	Q₈	C₂³×D₁₀₉	1	4	yes	—
320	D₄	—	2	4	no	—
321	D₄	—	2	4	no	—
322	D₄	—	2	2	no	—
323	D₄	—	109	8	no	—
324	D₄	—	109	4	no	—
325	D₄	—	109	4	no	—
326	D₄	—	218	8	no	—
327	D₄	—	218	8	no	—
328	D₄	—	218	8	no	—
329	D₄	—	218	4	no	—
330	D₄	—	218	4	no	—
331	D₄	—	218	2	no	—
332	D₄	C₂³×D₁₀₉	1	4	yes	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	109	2	no	—
337	C₂×C₄	—	109	4	no	—
338	C₂×C₄	—	109	4	no	—
339	C₂×C₄	—	218	8	no	—
340	C₂×C₄	—	218	8	no	—
341	C₂×C₄	—	218	8	no	—
342	C₂×C₄	—	218	2	no	—
343	C₂×C₄	—	218	4	no	—
344	C₂×C₄	—	218	4	no	—
345	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
346	C₂×C₄	D₄×D₁₀₉	1	2	yes	—
347	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
348	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
349	C₈	—	109	1	no	—
350	C₈	—	109	1	no	—
351	C₈	—	109	2	no	—
352	C₈	C₂³×D₁₀₉	1	4	yes	—
353	C₂²	—	2	4	no	—
354	C₂²	—	4	1	no	—
355	C₂²	—	8	2	no	—
356	C₂²	—	872	2	no	—
357	C₂²	—	872	8	no	—
358	C₂²	—	109	4	no	—
359	C₂²	—	436	2	no	—
360	C₂²	—	218	4	no	—
361	C₂²	C₂×D₄×D₁₀₉	1	2	yes	—
362	C₂²	C₂×D₄×D₁₀₉	1	1	yes	characteristic
363	C₄	—	2	4	no	—
364	C₄	—	109	4	no	—
365	C₄	—	218	4	no	—
366	C₄	C₂×D₄×D₁₀₉	1	2	yes	—
367	C₄	C₂×D₄×D₁₀₉	1	1	yes	characteristic
368	C₄	C₂⁴×D₁₀₉	1	1	yes	characteristic
369	C₂	—	2	2	no	—
370	C₂	—	2	1	no	—
371	C₂	—	4	4	no	—
372	C₂	—	436	4	no	—
373	C₂	—	218	4	no	—
374	C₂	C₂²×D₄×D₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₄×D₁₀₉
commutator, cosocle	C₄×C₁₀₉	C₂⁵
Frattini	C₄	C₂⁴×D₁₀₉
Fitting	#575×C₁₀₉	C₂
socle	C₂×C₁₀₉	C₂³×D₄
hypercenter	#575	D₁₀₉
hypocenter	C₁₀₉	#3584
LCS	G ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #575

Complements

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

N	H ≅ G/N	type
1. #20295862	C₂	semidirect
2. #20295842	C₂	semidirect
3. #20295836	C₂	semidirect
4. #20295835	C₂	semidirect
5. #20295830	C₂	semidirect
6. #20295826	C₂	semidirect
7. #20295823	C₂	semidirect
8. C₂×#16812719	C₂	semidirect
9. #135×D₁₀₉	C₂	semidirect
10. C₂×#16812707	C₂	semidirect
11. #575×C₁₀₉	C₂	semidirect
12. #16812747	C₂²	semidirect
14. #16812746	C₂²	semidirect
16. #16812745	C₂²	semidirect
18. #16812744	C₂²	semidirect
21. C₂×#13182029	C₂²	semidirect
23. #41×D₁₀₉	C₂²	semidirect
24. #16812732	C₂²	semidirect
25. #16812731	C₂²	semidirect
26. #16812728	C₂²	semidirect
27. #16812727	C₂²	semidirect
28. #16812726	C₂²	semidirect
29. #16812723	C₂²	semidirect
30. #16812722	C₂²	semidirect
31. #16812721	C₂²	semidirect
32. #16812720	C₂²	semidirect
33. #16812719	C₂²	semidirect
34. #16812719	C₂²	semidirect
35. #16812719	C₂²	semidirect
36. #16812719	C₂²	semidirect
37. #16812718	C₂²	semidirect
38. C₂×#13182019	C₂²	semidirect
39. Q₁₆×D₁₀₉	C₂²	semidirect
40. C₂×#13182017	C₂²	semidirect
41. C₂×#13182016	C₂²	semidirect
42. SD₁₆×D₁₀₉	C₂²	semidirect
43. C₂×#13182014	C₂²	semidirect
44. D₈×D₁₀₉	C₂²	semidirect
45. #16812707	C₂²	semidirect
46. #16812707	C₂²	semidirect
47. C₂×#13182012	C₂²	semidirect
48. C₂²×#11724784	C₂²	semidirect
49. C₂×C₈×D₁₀₉	C₂²	semidirect
50. C₂×#41×C₁₀₉	C₂²	semidirect
51. #137×C₁₀₉	C₂²	semidirect
52. AGL(1,ℤ/8)×C₁₀₉	C₂²	semidirect
53. #135×C₁₀₉	C₂²	semidirect
54. C₂×M₁₆×C₁₀₉	C₂²	semidirect
188. C₁₀₉	#3584	semidirect
196. #575	D₁₀₉	semidirect
212. C₂×#41	C₂×D₁₀₉	semidirect
216. #137	C₂×D₁₀₉	semidirect
220. AGL(1,ℤ/8)	C₂×D₁₀₉	semidirect
229. #135	C₂×D₁₀₉	semidirect
240. C₂×M₁₆	C₂×D₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
#20295862	2
#20295842	2
#20295836	2
#20295835	2
#20295830	2
#20295826	2
#20295823	2
C₂×#16812719	2
#135×D₁₀₉	2
C₂×#16812707	2
#575×C₁₀₉	2
#3584	109