Subgroups — #16792671

Order 3328.

772 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃⋊#431	C₂	1	1	yes	maximal, characteristic
2	D₁₃⋊#431	C₂	1	1	yes	maximal, characteristic
3	#13130057	C₂	1	4	yes	maximal, complemented
4	#13130052	C₂	1	2	yes	maximal, complemented
5	#13130044	C₂	1	2	yes	maximal, complemented
6	#13130042	C₂	1	2	yes	maximal, complemented
7	#13130034	C₂	1	2	yes	maximal, complemented
8	#13123466	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
10	#11719125	C₄	1	2	yes	—
11	#11719125	C₂²	1	2	yes	—
12	D₁₃⋊(C₂²⋊C₈)	C₄	1	2	yes	—
13	D₁₃⋊(C₂²⋊C₈)	C₄	1	2	yes	—
14	#11719119	C₄	1	2	yes	—
15	#11719119	C₂²	1	2	yes	—
16	#11719051	C₄	1	2	yes	—
17	#11719051	C₂²	1	1	yes	characteristic
18	#11719051	C₂²	1	1	yes	characteristic
19	D₁₃⋊(C₄⋊C₈)	C₄	1	2	yes	—
20	D₁₃⋊(C₄⋊C₈)	C₄	1	2	yes	—
21	#11719049	C₄	1	2	yes	—
22	#11719049	C₂²	1	1	yes	characteristic
23	#11719049	C₂²	1	1	yes	characteristic
24	C₄×D₁₃⋊C₈	C₂²	1	2	yes	—
25	C₄×D₁₃⋊C₈	C₂²	1	2	yes	—
26	C₁₃×#432	C₄	1	1	yes	characteristic
27	#11718587	C₄	1	1	yes	characteristic
28	#11718498	C₄	1	2	yes	—
29	#11718494	C₂²	1	2	yes	—
30	#11718387	C₄	1	2	yes	—
31	#11718379	C₂²	1	2	yes	—
32	#11718368	C₂²	1	2	yes	—
33	#11718366	C₄	1	2	yes	—
34	#1057⋊C₈	C₂²	1	4	yes	complemented
35	#1057⋊C₈	C₂²	1	4	yes	complemented
36	#11718251	C₂²	1	4	yes	complemented
37	C₈×#1057	C₂²	1	4	yes	complemented
38	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂×D₁₃⋊C₈	C₂×C₄	1	4	yes	—
42	C₂×D₁₃⋊C₈	C₂×C₄	1	4	yes	—
43	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
47	C₂×#6094	C₂×C₄	1	4	yes	—
48	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
49	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
50	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
51	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
52	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
53	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
54	C₄²×D₁₃	C₂³	1	1	yes	characteristic
55	C₄²×D₁₃	C₂³	1	1	yes	characteristic
56	C₂²⋊#1057	C₂×C₄	1	4	yes	—
57	C₂²⋊#1057	C₂×C₄	1	4	yes	—
58	#88112	C₂×C₄	1	4	yes	—
59	#88112	C₂×C₄	1	2	yes	—
60	#88112	C₂×C₄	1	2	yes	—
61	#88111	C₂×C₄	1	2	yes	—
62	#88111	C₂×C₄	1	2	yes	—
63	#88111	C₂×C₄	1	2	yes	—
64	#88111	C₂×C₄	1	2	yes	—
65	C₄⋊#1057	C₂×C₄	1	4	yes	—
66	C₄⋊#1057	C₂×C₄	1	2	yes	—
67	C₄⋊#1057	C₂×C₄	1	2	yes	—
68	C₄×#1057	C₂×C₄	1	4	yes	—
69	C₄×#1057	C₂×C₄	1	4	yes	—
70	C₄×#1057	C₂³	1	2	yes	—
71	C₄×#1057	C₂³	1	2	yes	—
72	C₄×#1057	C₂³	1	2	yes	—
73	C₄×#1057	C₂³	1	2	yes	—
74	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
75	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
76	C₁₃×#97	C₂×C₄	1	2	yes	—
77	C₂²⋊#1055	C₂×C₄	1	2	yes	—
78	#88060	C₂×C₄	1	4	yes	—
79	#88054	C₂×C₄	1	4	yes	—
80	C₈×Dic₁₃	C₂³	1	4	yes	—
81	C₄⋊#1055	C₂×C₄	1	2	yes	—
82	#88043	C₂×C₄	1	2	yes	—
83	#17326	—	13	1	no	maximal, Sylow
84	C₂³×D₁₃	C₄²	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
88	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
89	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
90	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₄×D₁₃	—	2	4	no	—
92	C₂×C₄×D₁₃	—	2	4	no	—
93	C₂×C₄×D₁₃	—	4	2	no	—
94	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
95	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
96	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
97	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
98	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
99	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
100	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂×#1057	C₂²×C₄	1	4	yes	—
107	C₂×#1057	C₂²×C₄	1	4	yes	—
108	C₂×#1057	C₂²×C₄	1	4	yes	—
109	C₂×#1057	C₂²×C₄	1	4	yes	—
110	D₁₃⋊C₈	—	2	8	no	—
111	D₁₃⋊C₈	—	4	4	no	—
112	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
113	C₄²×C₁₃	C₄²	1	1	yes	characteristic
114	C₄²×C₁₃	C₄²	1	1	yes	characteristic
115	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
118	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
119	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
120	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
121	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
126	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
129	C₂×#1055	C₂²×C₄	1	4	yes	—
130	#6094	—	2	8	no	—
131	#2920	—	13	1	no	—
132	C₂×#431	—	13	1	no	—
133	C₂×#431	—	13	1	no	—
134	#1454	—	13	4	no	—
135	#1452	—	13	2	no	—
136	#1451	—	13	2	no	—
137	#1450	—	13	2	no	—
138	C₈×M₁₆	—	13	2	no	—
139	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
140	C₂²×D₁₃	—	2	2	no	—
141	C₂²×D₁₃	—	2	2	no	—
142	C₂²×D₁₃	—	4	1	no	—
143	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
144	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
145	C₂×C₄×C₁₃	—	2	2	no	—
146	C₂×C₄×C₁₃	—	2	2	no	—
147	C₂×C₄×C₁₃	—	4	1	no	—
148	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
149	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
150	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
151	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
152	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
153	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
154	C₂×Dic₁₃	—	2	2	no	—
155	C₂×Dic₁₃	—	2	2	no	—
156	C₂×Dic₁₃	—	2	2	no	—
157	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
158	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
159	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
160	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
161	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
162	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
163	C₄×D₁₃	—	2	2	no	—
164	C₄×D₁₃	—	2	2	no	—
165	C₄×D₁₃	—	2	2	no	—
166	C₄×D₁₃	—	2	2	no	—
167	C₄×D₁₃	—	2	2	no	—
168	C₄×D₁₃	—	2	2	no	—
169	C₄×D₁₃	—	2	2	no	—
170	C₄×D₁₃	—	2	2	no	—
171	C₄×D₁₃	—	4	1	no	—
172	C₄×D₁₃	—	4	1	no	—
173	C₄×D₁₃	#131	1	4	yes	—
174	C₄×D₁₃	#131	1	4	yes	—
175	#1057	—	2	4	no	—
176	#1057	—	2	4	no	—
177	#1057	—	2	4	no	—
178	#1057	—	2	4	no	—
179	C₈×C₁₃	—	2	4	no	—
180	#1055	—	2	4	no	—
181	C₂²×C₄²	—	13	1	no	—
182	#432	—	13	1	no	—
183	#432	—	13	2	no	—
184	#432	#261	1	1	yes	characteristic
185	#431	—	13	2	no	—
186	#431	—	13	1	no	—
187	#431	—	13	1	no	—
188	#431	—	13	2	no	—
189	#431	—	13	1	no	—
190	#431	—	13	1	no	—
191	#431	—	13	2	no	—
192	#431	—	13	2	no	—
193	#431	—	13	2	no	—
194	#431	—	13	2	no	—
195	#431	—	13	2	no	—
196	#431	—	13	2	no	—
197	#423	—	13	2	no	—
198	C₂×C₄⋊C₈	—	13	2	no	—
199	C₂×C₄⋊C₈	—	13	2	no	—
200	#407	—	13	2	no	—
201	C₂×C₂²⋊C₈	—	13	2	no	—
202	C₂×C₂²⋊C₈	—	13	2	no	—
203	C₄×M₁₆	—	13	2	no	—
204	C₂×C₄×C₈	—	13	2	no	—
205	C₂×C₄×C₈	—	13	2	no	—
206	#322	—	13	4	no	—
207	#322	—	13	4	no	—
208	#322	—	13	4	no	—
209	C₈²	—	13	4	no	—
210	C₂²×C₁₃	—	2	1	no	—
211	C₂²×C₁₃	—	2	1	no	—
212	C₂²×C₁₃	—	2	1	no	—
213	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
214	C₂×D₁₃	—	2	1	no	—
215	C₂×D₁₃	—	2	1	no	—
216	C₂×D₁₃	—	2	1	no	—
217	C₂×D₁₃	—	2	1	no	—
218	C₂×D₁₃	—	4	4	no	—
219	C₂×D₁₃	#405	1	2	yes	—
220	C₂×D₁₃	#405	1	2	yes	—
221	C₄×C₁₃	—	2	1	no	—
222	C₄×C₁₃	—	2	1	no	—
223	C₄×C₁₃	—	2	1	no	—
224	C₄×C₁₃	—	2	1	no	—
225	C₄×C₁₃	#405	1	2	yes	—
226	C₄×C₁₃	C₂×#131	1	2	yes	—
227	Dic₁₃	—	2	1	no	—
228	Dic₁₃	—	2	1	no	—
229	Dic₁₃	—	2	1	no	—
230	Dic₁₃	#405	1	2	yes	—
231	Dic₁₃	C₂×#131	1	2	yes	—
232	Dic₁₃	#568	1	2	yes	—
233	C₂³×C₄	—	13	1	no	—
234	C₂³×C₄	—	13	1	no	—
235	C₂³×C₄	—	13	1	no	—
236	C₂×M₁₆	—	13	4	no	—
237	C₂²×C₈	—	13	4	no	—
238	C₂²×C₈	—	13	4	no	—
239	C₂×C₄²	—	13	1	no	—
240	C₂×C₄²	—	13	1	no	—
241	C₂×C₄²	—	13	1	no	—
242	C₂×C₄²	—	13	1	no	—
243	C₂×C₄²	—	13	1	no	—
244	C₂×C₄²	—	13	1	no	—
245	C₂×C₄²	—	13	1	no	—
246	C₂×C₄²	—	13	1	no	—
247	C₂×C₄²	—	13	1	no	—
248	C₂×C₄²	—	13	1	no	—
249	C₂×C₄²	—	13	1	no	—
250	C₂×C₄²	C₂×#261	1	1	yes	characteristic
251	C₄⋊C₈	—	13	4	no	—
252	C₄⋊C₈	—	13	2	no	—
253	C₄⋊C₈	—	13	2	no	—
254	C₄⋊C₈	—	13	4	no	—
255	C₄⋊C₈	—	13	2	no	—
256	C₄⋊C₈	—	13	2	no	—
257	C₄⋊C₈	—	13	4	no	—
258	C₄⋊C₈	—	13	2	no	—
259	C₄⋊C₈	C₂×#261	1	2	yes	—
260	C₂²⋊C₈	—	13	2	no	—
261	C₂²⋊C₈	—	13	2	no	—
262	C₂²⋊C₈	—	13	2	no	—
263	C₂²⋊C₈	—	13	2	no	—
264	C₂²⋊C₈	—	13	4	no	—
265	C₂²⋊C₈	—	13	4	no	—
266	C₂²⋊C₈	—	13	2	no	—
267	C₂²⋊C₈	—	13	4	no	—
268	C₂²⋊C₈	C₂×#261	1	2	yes	—
269	#97	—	13	2	no	—
270	#97	C₂×#261	1	2	yes	—
271	C₄×C₈	—	13	4	no	—
272	C₄×C₈	—	13	4	no	—
273	C₄×C₈	—	13	2	no	—
274	C₄×C₈	—	13	2	no	—
275	C₄×C₈	—	13	2	no	—
276	C₄×C₈	—	13	2	no	—
277	C₄×C₈	—	13	4	no	—
278	C₂×C₁₃	—	4	1	no	—
279	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
280	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
281	C₂×C₁₃	#2873	1	1	yes	characteristic
282	D₁₃	—	2	2	no	—
283	D₁₃	—	2	2	no	—
284	C₂⁴	—	13	1	no	—
285	C₂²×C₄	—	13	1	no	—
286	C₂²×C₄	—	13	1	no	—
287	C₂²×C₄	—	13	1	no	—
288	C₂²×C₄	—	13	1	no	—
289	C₂²×C₄	—	13	1	no	—
290	C₂²×C₄	—	13	1	no	—
291	C₂²×C₄	—	13	1	no	—
292	C₂²×C₄	—	13	1	no	—
293	C₂²×C₄	—	13	1	no	—
294	C₂²×C₄	—	13	1	no	—
295	C₂²×C₄	—	13	1	no	—
296	C₂²×C₄	—	13	1	no	—
297	C₂²×C₄	—	13	1	no	—
298	C₂²×C₄	—	13	1	no	—
299	C₂²×C₄	—	13	1	no	—
300	C₂²×C₄	—	26	4	no	—
301	C₂²×C₄	—	26	4	no	—
302	C₂²×C₄	—	52	2	no	—
303	C₂²×C₄	C₄×#261	1	1	yes	characteristic
304	C₂²×C₄	C₄×#261	1	1	yes	characteristic
305	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
306	M₁₆	—	26	8	no	—
307	C₂×C₈	—	13	4	no	—
308	C₂×C₈	—	13	4	no	—
309	C₂×C₈	—	13	4	no	—
310	C₂×C₈	—	13	4	no	—
311	C₂×C₈	—	13	4	no	—
312	C₂×C₈	—	26	8	no	—
313	C₂×C₈	—	52	4	no	—
314	C₂×C₈	C₂²×#261	1	4	yes	—
315	C₄²	—	13	1	no	—
316	C₄²	—	13	1	no	—
317	C₄²	—	13	1	no	—
318	C₄²	—	13	1	no	—
319	C₄²	—	13	1	no	—
320	C₄²	—	13	1	no	—
321	C₄²	—	13	1	no	—
322	C₄²	—	13	1	no	—
323	C₄²	—	13	1	no	—
324	C₄²	—	13	1	no	—
325	C₄²	—	13	1	no	—
326	C₄²	—	13	1	no	—
327	C₄²	C₄×#261	1	1	yes	characteristic
328	C₄²	C₄×#261	1	1	yes	characteristic
329	C₄²	C₂²×#261	1	1	yes	characteristic
330	C₄²	C₂²×#261	1	1	yes	characteristic
331	C₁₃	#17326	1	1	yes	characteristic, complemented, Sylow
332	C₂³	—	13	1	no	—
333	C₂³	—	13	1	no	—
334	C₂³	—	26	2	no	—
335	C₂³	—	26	2	no	—
336	C₂³	—	52	1	no	—
337	C₂³	C₂×C₄×#261	1	1	yes	characteristic
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	13	1	no	—
342	C₂×C₄	—	13	1	no	—
343	C₂×C₄	—	13	1	no	—
344	C₂×C₄	—	13	4	no	—
345	C₂×C₄	—	13	4	no	—
346	C₂×C₄	—	13	1	no	—
347	C₂×C₄	—	13	1	no	—
348	C₂×C₄	—	13	1	no	—
349	C₂×C₄	—	26	2	no	—
350	C₂×C₄	—	26	2	no	—
351	C₂×C₄	—	26	2	no	—
352	C₂×C₄	—	26	2	no	—
353	C₂×C₄	—	26	2	no	—
354	C₂×C₄	—	26	2	no	—
355	C₂×C₄	—	26	2	no	—
356	C₂×C₄	—	26	2	no	—
357	C₂×C₄	—	26	2	no	—
358	C₂×C₄	—	26	2	no	—
359	C₂×C₄	—	26	2	no	—
360	C₂×C₄	—	52	1	no	—
361	C₂×C₄	—	52	1	no	—
362	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
363	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
364	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
365	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
366	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
367	C₂×C₄	C₂³×#261	1	1	yes	characteristic
368	C₈	—	2	4	no	—
369	C₈	—	26	4	no	—
370	C₈	—	26	4	no	—
371	C₈	—	26	4	no	—
372	C₈	—	26	4	no	—
373	C₈	—	26	4	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	13	2	no	—
378	C₂²	—	13	2	no	—
379	C₂²	—	26	1	no	—
380	C₂²	—	26	1	no	—
381	C₂²	—	26	1	no	—
382	C₂²	—	26	1	no	—
383	C₂²	—	52	4	no	—
384	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	13	2	no	—
390	C₄	—	13	2	no	—
391	C₄	—	13	2	no	—
392	C₄	—	26	1	no	—
393	C₄	—	26	1	no	—
394	C₄	—	26	1	no	—
395	C₄	#11719099	1	2	yes	—
396	C₄	D₁₃⋊#131	1	2	yes	—
397	C₂	—	4	1	no	—
398	C₂	—	26	2	no	—
399	C₂	—	26	2	no	—
400	C₂	#13131396	1	1	yes	characteristic
401	C₂	C₂×#11719099	1	1	yes	characteristic
402	C₂	#13131399	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#432	C₄
prime radical	C₂³×D₁₃	C₄²
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	#432	#261
hypocenter	C₁₃	#17326
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #432

Complements

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

N	H ≅ G/N	type
3. #13130057	C₂	semidirect
4. #13130052	C₂	semidirect
5. #13130044	C₂	semidirect
6. #13130042	C₂	semidirect
7. #13130034	C₂	semidirect
34. #1057⋊C₈	C₂²	semidirect
35. #1057⋊C₈	C₂²	semidirect
36. #11718251	C₂²	semidirect
37. C₈×#1057	C₂²	semidirect
331. C₁₃	#17326	semidirect

Maximal subgroups

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

subgroup	index
D₁₃⋊#431	2
#13130057	2
#13130052	2
#13130044	2
#13130042	2
#13130034	2
#13123466	2
#17326	13