Subgroups — #15832147

Order 3328.

610 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×#1055	C₂	1	1	yes	maximal, characteristic
2	#13123502	C₂	1	1	yes	maximal, characteristic
3	#13113617	C₂	1	2	yes	maximal, complemented
4	#13113614	C₂	1	2	yes	maximal, complemented
5	#13113612	C₂	1	1	yes	maximal, characteristic, complemented
6	#13113610	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113597	C₂	1	2	yes	maximal, complemented
8	#13113591	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113582	C₂	1	2	yes	maximal, complemented
10	C₂×#11718072	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2925	C₂	1	1	yes	maximal, characteristic
12	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₁₃×#433	—	2	2	no	—
14	C₁₃×#432	C₂²	1	2	yes	—
15	C₁₃×#431	C₂²	1	2	yes	—
16	C₁₃×#423	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₁₃×#408	—	2	1	no	—
19	C₁₃×#405	—	2	1	no	—
20	#11718895	—	2	1	no	—
21	Q₈×#1055	C₄	1	1	yes	characteristic
22	Q₈×#1055	C₄	1	1	yes	characteristic
23	D₄×#1055	C₄	1	2	yes	—
24	D₄×#1055	C₄	1	1	yes	characteristic
25	D₄×#1055	C₄	1	2	yes	—
26	D₄×#1055	C₄	1	1	yes	characteristic
27	#11718661	—	2	2	no	—
28	#11718658	—	2	1	no	—
29	#11718587	C₂²	1	2	yes	—
30	#11718586	C₂²	1	2	yes	—
31	#11718586	C₂²	1	1	yes	characteristic
32	#11718586	C₂²	1	2	yes	—
33	#11718585	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
35	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
36	C₂×C₄×#1055	C₂²	1	2	yes	—
37	#11718072	C₂²	1	1	yes	characteristic
38	#11718072	C₂²	1	2	yes	—
39	#11718072	C₂²	1	1	yes	characteristic
40	#11718072	C₂²	1	1	yes	characteristic
41	#11718072	C₂²	1	1	yes	characteristic
42	#11718072	C₂²	1	2	yes	—
43	#11718071	C₂²	1	2	yes	—
44	#11718071	C₂²	1	2	yes	—
45	#11718071	C₂²	1	2	yes	—
46	#11718071	C₂²	1	2	yes	—
47	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
48	C₂×C₁₃×M₁₆	—	2	1	no	—
49	C₂²×C₈×C₁₃	—	2	1	no	—
50	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
51	C₄×Q₈×C₁₃	Q₈	1	1	yes	characteristic
52	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
53	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
54	C₄×D₄×C₁₃	Q₈	1	2	yes	—
55	C₄×D₄×C₁₃	Q₈	1	1	yes	characteristic
56	C₁₃×#117	D₄	1	1	yes	characteristic
57	C₁₃×#117	D₄	1	2	yes	—
58	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
60	C₂×#6099	—	2	1	no	—
61	C₂²×#1055	—	2	1	no	—
62	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
63	C₂²×#1055	C₂×C₄	1	2	yes	—
64	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
65	C₂²×#1055	C₂×C₄	1	2	yes	—
66	C₁₃×C₄⋊C₈	—	2	1	no	—
67	C₁₃×C₄⋊C₈	—	2	1	no	—
68	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
69	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
70	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
71	C₁₃×C₂²⋊C₈	—	2	2	no	—
72	C₁₃×C₂²⋊C₈	—	2	2	no	—
73	C₁₃×#97	—	2	2	no	—
74	C₄×C₈×C₁₃	—	2	2	no	—
75	C₂²⋊#1055	—	2	2	no	—
76	C₂²⋊#1055	—	2	2	no	—
77	C₂²⋊#1055	C₂×C₄	1	2	yes	—
78	C₂²⋊#1055	C₂×C₄	1	2	yes	—
79	C₂²⋊#1055	C₂×C₄	1	2	yes	—
80	C₄⋊#1055	—	2	1	no	—
81	C₄⋊#1055	—	2	1	no	—
82	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
83	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
84	C₄⋊#1055	C₂×C₄	1	2	yes	—
85	C₄⋊#1055	C₂×C₄	1	2	yes	—
86	C₄⋊#1055	C₂³	1	1	yes	characteristic
87	C₄⋊#1055	C₂³	1	1	yes	characteristic
88	C₄⋊#1055	C₂³	1	2	yes	—
89	#88043	—	2	2	no	—
90	C₄×#1055	—	2	2	no	—
91	C₄×#1055	C₂×C₄	1	1	yes	characteristic
92	C₄×#1055	C₂×C₄	1	2	yes	—
93	C₄×#1055	C₂×C₄	1	1	yes	characteristic
94	C₄×#1055	C₂×C₄	1	2	yes	—
95	C₄×#1055	C₂³	1	1	yes	characteristic
96	C₄×#1055	C₂³	1	2	yes	—
97	C₄×#1055	C₂³	1	1	yes	characteristic
98	#17827	—	13	1	no	maximal, Sylow
99	C₁₃×#41	—	2	2	no	—
100	C₁₃×#41	—	2	2	no	—
101	C₂×Q₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
102	C₂×D₄×C₁₃	C₄⋊C₄	1	2	yes	—
103	C₂×D₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
109	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
110	C₁₃×M₁₆	—	4	2	no	—
111	C₂×C₈×C₁₃	—	2	1	no	—
112	C₂×C₈×C₁₃	—	2	2	no	—
113	C₂×C₈×C₁₃	—	2	1	no	—
114	C₂×C₈×C₁₃	—	4	2	no	—
115	C₁₃×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
116	C₁₃×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
117	C₁₃×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
118	C₁₃×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
119	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
120	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
121	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
122	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
123	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₁₃	C₂×D₄	1	2	yes	—
125	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
127	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
128	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
129	#6099	—	4	2	no	—
130	C₂×#1055	—	2	2	no	—
131	C₂×#1055	—	2	4	no	—
132	C₂×#1055	—	2	1	no	—
133	C₂×#1055	—	2	1	no	—
134	C₂×#1055	—	2	2	no	—
135	C₂×#1055	—	4	1	no	—
136	C₂×#1055	—	4	2	no	—
137	C₂×#1055	—	4	2	no	—
138	C₂×#1055	C₂²×C₄	1	2	yes	—
139	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
140	C₂×#1055	C₂²×C₄	1	2	yes	—
141	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
142	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
143	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
144	C₈×#41	—	13	1	no	—
145	#2925	—	13	1	no	—
146	#2925	D₁₃	1	1	yes	characteristic
147	#1572	—	13	2	no	—
148	#1572	—	13	2	no	—
149	#1571	—	13	1	no	—
150	#1571	—	13	1	no	—
151	#1568	—	13	2	no	—
152	#1566	—	13	1	no	—
153	#1564	—	13	2	no	—
154	C₂×#334	—	13	1	no	—
155	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
156	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
157	Q₈×C₁₃	—	2	2	no	—
158	D₄×C₁₃	—	2	4	no	—
159	D₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	2	1	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	1	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	4	1	no	—
167	C₂×C₄×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
169	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
171	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
172	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₁₃	#135	1	2	yes	—
175	C₂×C₄×C₁₃	#135	1	2	yes	—
176	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
179	C₈×C₁₃	—	4	1	no	—
180	C₈×C₁₃	—	4	1	no	—
181	C₈×C₁₃	—	4	2	no	—
182	#1055	—	2	2	no	—
183	#1055	—	2	1	no	—
184	#1055	—	2	1	no	—
185	#1055	—	2	2	no	—
186	#1055	—	2	1	no	—
187	#1055	—	4	1	no	—
188	#1055	—	4	1	no	—
189	#1055	—	4	2	no	—
190	#1055	#131	1	2	yes	—
191	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
192	C₈×Q₈	—	13	1	no	—
193	C₈×Q₈	—	13	1	no	—
194	C₈×D₄	—	13	1	no	—
195	C₈×D₄	—	13	2	no	—
196	C₈×D₄	—	13	1	no	—
197	C₈×D₄	—	13	2	no	—
198	#433	—	2	2	no	—
199	#433	—	26	2	no	—
200	#432	—	13	2	no	—
201	#432	C₂×D₁₃	1	2	yes	—
202	#431	—	13	1	no	—
203	#431	—	13	2	no	—
204	#431	—	13	2	no	—
205	#431	C₂×D₁₃	1	2	yes	—
206	#423	—	13	1	no	—
207	#423	C₂×D₁₃	1	1	yes	characteristic
208	C₂×C₄⋊C₈	—	13	1	no	—
209	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
210	#408	—	2	1	no	—
211	#408	—	26	1	no	—
212	#405	—	2	1	no	—
213	#405	—	26	1	no	—
214	C₂×C₄×C₈	—	13	1	no	—
215	C₂×C₄×C₈	—	13	2	no	—
216	#335	—	13	2	no	—
217	#335	—	13	2	no	—
218	#335	—	13	2	no	—
219	#335	—	13	2	no	—
220	#334	—	13	1	no	—
221	#334	—	13	1	no	—
222	#334	—	13	1	no	—
223	#334	—	13	1	no	—
224	#334	—	13	2	no	—
225	#334	—	13	2	no	—
226	C₂²×C₁₃	—	2	1	no	—
227	C₂²×C₁₃	—	2	1	no	—
228	C₂²×C₁₃	—	2	2	no	—
229	C₂²×C₁₃	—	2	2	no	—
230	C₂²×C₁₃	—	2	2	no	—
231	C₂²×C₁₃	#427	1	2	yes	—
232	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
233	C₄×C₁₃	—	2	1	no	—
234	C₄×C₁₃	—	2	2	no	—
235	C₄×C₁₃	—	2	2	no	—
236	C₄×C₁₃	—	2	1	no	—
237	C₄×C₁₃	—	2	1	no	—
238	C₄×C₁₃	—	2	2	no	—
239	C₄×C₁₃	#427	1	2	yes	—
240	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
241	C₄×C₁₃	#568	1	1	yes	characteristic
242	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
243	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
244	C₂×#41	C₂²⋊D₁₃	1	1	yes	characteristic
245	C₂×M₁₆	—	2	1	no	—
246	C₂×M₁₆	—	26	1	no	—
247	C₂²×C₈	—	2	1	no	—
248	C₂²×C₈	—	13	1	no	—
249	C₂²×C₈	—	13	2	no	—
250	C₂²×C₈	—	13	1	no	—
251	C₂²×C₈	—	13	2	no	—
252	C₂²×C₈	—	26	1	no	—
253	C₄×Q₈	Dic₂₆	1	1	yes	characteristic
254	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
255	C₄×D₄	Dic₂₆	1	2	yes	—
256	C₄×D₄	Dic₂₆	1	1	yes	characteristic
257	C₄×D₄	C₄×D₁₃	1	2	yes	—
258	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
259	#117	C₂²⋊D₁₃	1	1	yes	characteristic
260	#117	C₂²⋊D₁₃	1	2	yes	—
261	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
262	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	—	13	1	no	—
266	C₄⋊C₈	—	13	1	no	—
267	C₄⋊C₈	—	13	2	no	—
268	C₄⋊C₈	—	13	2	no	—
269	C₄⋊C₈	—	13	1	no	—
270	C₄⋊C₈	—	13	1	no	—
271	C₄⋊C₈	—	13	2	no	—
272	C₄⋊C₈	—	26	1	no	—
273	C₄⋊C₈	—	26	1	no	—
274	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
275	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
276	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
277	C₂²⋊C₈	—	2	2	no	—
278	C₂²⋊C₈	—	2	2	no	—
279	C₂²⋊C₈	—	13	2	no	—
280	C₂²⋊C₈	—	13	2	no	—
281	C₂²⋊C₈	—	13	2	no	—
282	C₂²⋊C₈	—	26	2	no	—
283	C₂²⋊C₈	—	26	2	no	—
284	#97	—	2	2	no	—
285	#97	—	26	2	no	—
286	C₄×C₈	—	2	2	no	—
287	C₄×C₈	—	13	1	no	—
288	C₄×C₈	—	13	2	no	—
289	C₄×C₈	—	13	1	no	—
290	C₄×C₈	—	13	2	no	—
291	C₄×C₈	—	13	1	no	—
292	C₄×C₈	—	13	1	no	—
293	C₄×C₈	—	13	2	no	—
294	C₄×C₈	—	26	2	no	—
295	C₂×C₁₃	—	2	2	no	—
296	C₂×C₁₃	—	4	2	no	—
297	C₂×C₁₃	#2906	1	1	yes	characteristic
298	C₂×C₁₃	C₂×#427	1	1	yes	characteristic
299	C₂×C₁₃	#2916	1	1	yes	characteristic
300	#41	—	2	2	no	—
301	#41	—	2	2	no	—
302	C₂×Q₈	#6101	1	1	yes	characteristic
303	C₂×D₄	#6101	1	2	yes	—
304	C₂×D₄	#6101	1	1	yes	characteristic
305	C₂²×C₄	C₂×Dic₂₆	1	2	yes	—
306	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
308	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
310	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
311	M₁₆	—	4	2	no	—
312	M₁₆	—	52	2	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	4	2	no	—
317	C₂×C₈	—	13	1	no	—
318	C₂×C₈	—	13	1	no	—
319	C₂×C₈	—	13	1	no	—
320	C₂×C₈	—	13	2	no	—
321	C₂×C₈	—	13	1	no	—
322	C₂×C₈	—	13	2	no	—
323	C₂×C₈	—	26	2	no	—
324	C₂×C₈	—	26	4	no	—
325	C₂×C₈	—	26	1	no	—
326	C₂×C₈	—	26	2	no	—
327	C₂×C₈	—	26	1	no	—
328	C₂×C₈	—	52	1	no	—
329	C₂×C₈	—	52	2	no	—
330	C₂×C₈	—	52	2	no	—
331	C₄⋊C₄	#6101	1	2	yes	—
332	C₄⋊C₄	#6101	1	1	yes	characteristic
333	C₄⋊C₄	#6101	1	2	yes	—
334	C₄⋊C₄	#6101	1	1	yes	characteristic
335	C₂²⋊C₄	#6101	1	2	yes	—
336	C₂²⋊C₄	#6101	1	2	yes	—
337	C₂²⋊C₄	#6101	1	2	yes	—
338	C₄²	C₂×Dic₂₆	1	2	yes	—
339	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
340	C₄²	C₂×C₄×D₁₃	1	2	yes	—
341	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
342	C₄²	C₂×C₂²⋊D₁₃	1	2	yes	—
343	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
344	C₄²	C₂³×D₁₃	1	1	yes	characteristic
345	C₁₃	#17827	1	1	yes	characteristic, complemented, Sylow
346	C₂³	C₂×#6101	1	2	yes	—
347	C₂³	C₂×#6101	1	1	yes	characteristic
348	Q₈	—	2	2	no	—
349	D₄	—	2	4	no	—
350	D₄	—	2	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	C₂×#6101	1	2	yes	—
360	C₂×C₄	C₂×#6101	1	2	yes	—
361	C₂×C₄	C₂×#6101	1	1	yes	characteristic
362	C₂×C₄	C₂×#6101	1	2	yes	—
363	C₂×C₄	C₂×#6101	1	1	yes	characteristic
364	C₂×C₄	C₂×#6101	1	1	yes	characteristic
365	C₂×C₄	#88204	1	2	yes	—
366	C₂×C₄	#88204	1	2	yes	—
367	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
368	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
369	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
370	C₈	—	4	1	no	—
371	C₈	—	4	1	no	—
372	C₈	—	4	2	no	—
373	C₈	—	13	2	no	—
374	C₈	—	26	1	no	—
375	C₈	—	26	2	no	—
376	C₈	—	26	1	no	—
377	C₈	—	26	2	no	—
378	C₈	—	26	1	no	—
379	C₈	—	52	1	no	—
380	C₈	—	52	1	no	—
381	C₈	—	52	2	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	#11718659	1	2	yes	—
388	C₂²	C₂²×#6101	1	1	yes	characteristic
389	C₄	—	2	1	no	—
390	C₄	—	2	2	no	—
391	C₄	—	2	2	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	2	2	no	—
395	C₄	#11718659	1	2	yes	—
396	C₄	D₁₃×#131	1	1	yes	characteristic
397	C₄	#11719455	1	1	yes	characteristic
398	C₄	C₂×#88204	1	1	yes	characteristic
399	C₄	C₂×#88204	1	1	yes	characteristic
400	C₂	—	2	2	no	—
401	C₂	—	4	2	no	—
402	C₂	#13123402	1	1	yes	characteristic
403	C₂	C₂×#11718659	1	1	yes	characteristic
404	C₂	#13123445	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#2925	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂×C₁₃×#41	D₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#2925	D₁₃
hypocenter	C₁₃	#17827
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #2925

Complements

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

N	H ≅ G/N	type
3. #13113617	C₂	semidirect
4. #13113614	C₂	semidirect
5. #13113612	C₂	semidirect
6. #13113610	C₂	semidirect
7. #13113597	C₂	semidirect
8. #13113591	C₂	semidirect
9. #13113582	C₂	semidirect
10. C₂×#11718072	C₂	semidirect
345. C₁₃	#17827	semidirect

Maximal subgroups

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

subgroup	index
#41×#1055	2
#13123502	2
#13113617	2
#13113614	2
#13113612	2
#13113610	2
#13113597	2
#13113591	2
#13113582	2
C₂×#11718072	2
C₁₃×#2925	2
#17827	13