Subgroups — #13126530

Order 1664.

546 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×#6105	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×SD₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719337	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#450	C₂	1	1	yes	maximal, characteristic, complemented
6	#11718836	C₂	1	1	yes	maximal, characteristic, complemented
7	#11718831	C₂	1	1	yes	maximal, characteristic, complemented
8	#11718823	C₂	1	1	yes	maximal, characteristic, complemented
9	#11718709	C₂	1	1	yes	maximal, characteristic, complemented
10	#11718439	C₂	1	1	yes	maximal, characteristic, complemented
11	#11718437	C₂	1	1	yes	maximal, characteristic, complemented
12	#11718423	C₂	1	1	yes	maximal, characteristic, complemented
13	#11718419	C₂	1	1	yes	maximal, characteristic, complemented
14	#11718399	C₂	1	1	yes	maximal, characteristic, complemented
15	#11718386	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂²×C₂²⋊D₁₃	—	2	1	no	—
18	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic, complemented
19	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
20	C₂²×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
23	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	#88207	—	2	1	no	—
25	#88198	C₂²	1	1	yes	characteristic, complemented
26	C₂×#6106	C₂²	1	1	yes	characteristic, complemented
27	#88194	C₂²	1	1	yes	characteristic
28	#88193	—	2	1	no	—
29	#88192	C₂²	1	1	yes	characteristic
30	#88191	—	2	1	no	—
31	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
32	C₂×#6105	—	2	4	no	—
33	C₂×#6105	C₂²	1	1	yes	characteristic
34	C₂×#6105	C₂²	1	1	yes	characteristic
35	C₂×#6105	C₂²	1	1	yes	characteristic, complemented
36	C₂×#6105	C₂²	1	1	yes	characteristic, complemented
37	#88184	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
39	C₂²×#1055	C₂²	1	1	yes	characteristic, complemented
40	SD₁₆×D₁₃	—	2	4	no	—
41	C₂×#6095	C₂²	1	1	yes	characteristic, complemented
42	C₂×#6095	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic, complemented
44	#88151	C₂²	1	1	yes	characteristic, complemented
45	#88150	—	2	1	no	—
46	#88142	—	2	1	no	—
47	#88141	C₂²	1	1	yes	characteristic, complemented
48	#88135	—	2	1	no	—
49	#88132	—	2	1	no	—
50	C₁₃×#102	C₂²	1	1	yes	characteristic
51	C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	#88075	C₂²	1	1	yes	characteristic, complemented
54	#88060	C₂²	1	1	yes	characteristic, complemented
55	#88056	C₂²	1	1	yes	characteristic, complemented
56	#88056	C₂²	1	1	yes	characteristic, complemented
57	#88054	C₂²	1	1	yes	characteristic, complemented
58	C₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
59	#88049	C₂²	1	1	yes	characteristic, complemented
60	#88048	C₂²	1	1	yes	characteristic, complemented
61	C₂⁴×C₁₃	—	2	1	no	—
62	C₂³×D₁₃	—	2	1	no	—
63	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×D₄×C₁₃	—	2	2	no	—
65	C₂×D₄×C₁₃	—	2	1	no	—
66	C₂×D₄×C₁₃	—	4	1	no	—
67	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊D₁₃	—	2	1	no	—
71	C₂×C₂²⋊D₁₃	—	2	1	no	—
72	C₂×C₂²⋊D₁₃	—	2	1	no	—
73	C₂×C₂²⋊D₁₃	—	2	1	no	—
74	C₂×C₂²⋊D₁₃	—	2	1	no	—
75	C₂×C₂²⋊D₁₃	—	4	4	no	—
76	C₂×C₂²⋊D₁₃	D₄	1	1	yes	characteristic
77	C₂²×Dic₁₃	—	2	1	no	—
78	C₂²×Dic₁₃	—	2	1	no	—
79	Q₈×D₁₃	—	2	2	no	—
80	Q₈×D₁₃	—	4	1	no	—
81	D₄×D₁₃	—	2	2	no	—
82	D₄×D₁₃	—	4	1	no	—
83	C₂×D₅₂	C₂³	1	1	yes	characteristic
84	C₂×C₄×D₁₃	—	2	1	no	—
85	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
86	C₂×Dic₂₆	—	2	2	no	—
87	C₂×Dic₂₆	—	2	1	no	—
88	C₂×Dic₂₆	—	2	1	no	—
89	C₂×Dic₂₆	—	4	1	no	—
90	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
91	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
92	C₁₃×SD₁₆	—	2	2	no	—
93	C₁₃×SD₁₆	—	4	1	no	—
94	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₁₃×C₄⋊C₄	—	2	1	no	—
97	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₁₃×C₂²⋊C₄	—	2	1	no	—
99	C₂²⋊Dic₁₃	—	2	1	no	—
100	C₂²⋊Dic₁₃	—	2	1	no	—
101	C₂²⋊Dic₁₃	D₄	1	1	yes	characteristic
102	#6106	—	2	2	no	—
103	#6105	—	2	2	no	—
104	#6105	—	2	2	no	—
105	#6105	—	2	2	no	—
106	#6105	D₄	1	4	yes	complemented
107	#6103	—	2	1	no	—
108	#6103	—	2	1	no	—
109	#6103	D₄	1	1	yes	characteristic
110	C₄⋊Dic₁₃	—	2	1	no	—
111	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
112	#6101	—	2	1	no	—
113	#6101	—	2	1	no	—
114	#6101	—	2	1	no	—
115	#6101	D₄	1	1	yes	characteristic
116	C₄×Dic₁₃	—	2	1	no	—
117	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
118	C₂×#1055	—	2	2	no	—
119	C₂×#1055	C₂³	1	1	yes	characteristic
120	C₂×#1055	C₂³	1	1	yes	characteristic
121	#6095	—	2	2	no	—
122	#6095	—	4	1	no	—
123	C₈×D₁₃	—	2	2	no	—
124	D₄×SD₁₆	—	13	1	no	maximal, Sylow
125	C₂³×C₁₃	—	2	1	no	—
126	C₂³×C₁₃	—	2	1	no	—
127	C₂³×C₁₃	—	4	2	no	—
128	C₂³×C₁₃	—	4	2	no	—
129	C₂³×C₁₃	—	8	1	no	—
130	C₂³×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×D₁₃	—	2	1	no	—
132	C₂²×D₁₃	—	4	2	no	—
133	C₂²×D₁₃	—	4	2	no	—
134	C₂²×D₁₃	—	8	1	no	—
135	C₂²×D₁₃	C₂×D₄	1	1	yes	characteristic
136	Q₈×C₁₃	—	2	1	no	—
137	Q₈×C₁₃	—	2	1	no	—
138	D₄×C₁₃	—	2	1	no	—
139	D₄×C₁₃	—	2	1	no	—
140	D₄×C₁₃	—	2	1	no	—
141	D₄×C₁₃	—	4	2	no	—
142	D₄×C₁₃	C₂×D₄	1	2	yes	—
143	C₂×C₄×C₁₃	—	2	1	no	—
144	C₂×C₄×C₁₃	—	2	1	no	—
145	C₂×C₄×C₁₃	—	2	1	no	—
146	C₂×C₄×C₁₃	—	2	1	no	—
147	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
149	C₂²⋊D₁₃	—	4	2	no	—
150	C₂²⋊D₁₃	—	4	2	no	—
151	C₂²⋊D₁₃	—	4	2	no	—
152	C₂²⋊D₁₃	—	4	2	no	—
153	C₂²⋊D₁₃	—	8	1	no	—
154	C₂²⋊D₁₃	SD₁₆	1	4	yes	complemented
155	C₂×Dic₁₃	—	2	1	no	—
156	C₂×Dic₁₃	—	2	1	no	—
157	C₂×Dic₁₃	—	2	1	no	—
158	C₂×Dic₁₃	—	4	2	no	—
159	C₂×Dic₁₃	—	4	2	no	—
160	C₂×Dic₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂×Dic₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂×Dic₁₃	C₂×D₄	1	1	yes	characteristic
163	D₅₂	—	2	1	no	—
164	D₅₂	—	2	1	no	—
165	C₄×D₁₃	—	2	1	no	—
166	C₄×D₁₃	—	2	1	no	—
167	C₄×D₁₃	—	4	2	no	—
168	Dic₂₆	—	2	1	no	—
169	Dic₂₆	—	2	1	no	—
170	Dic₂₆	—	2	1	no	—
171	Dic₂₆	—	4	2	no	—
172	Dic₂₆	—	4	2	no	—
173	Dic₂₆	C₂×D₄	1	2	yes	complemented
174	C₈×C₁₃	—	2	1	no	—
175	C₈×C₁₃	—	2	1	no	—
176	#1055	—	2	1	no	—
177	#1055	C₂×D₄	1	2	yes	complemented
178	C₂²×SD₁₆	—	13	1	no	—
179	C₂²×SD₁₆	—	13	1	no	—
180	D₄×Q₈	—	13	1	no	—
181	D₄²	—	13	1	no	—
182	#492	—	13	1	no	—
183	#465	—	13	1	no	—
184	#465	—	13	1	no	—
185	#461	—	13	1	no	—
186	#460	—	13	1	no	—
187	#450	—	13	1	no	—
188	#450	D₁₃	1	1	yes	characteristic, complemented
189	#448	—	13	1	no	—
190	#448	—	13	1	no	—
191	C₄×SD₁₆	—	13	1	no	—
192	C₈×D₄	—	13	1	no	—
193	C₂²×C₁₃	—	2	1	no	—
194	C₂²×C₁₃	—	2	1	no	—
195	C₂²×C₁₃	—	2	2	no	—
196	C₂²×C₁₃	—	4	1	no	—
197	C₂²×C₁₃	—	4	1	no	—
198	C₂²×C₁₃	—	4	1	no	—
199	C₂²×C₁₃	—	4	1	no	—
200	C₂²×C₁₃	—	4	1	no	—
201	C₂²×C₁₃	—	8	4	no	—
202	C₂²×C₁₃	C₂×SD₁₆	1	2	yes	complemented
203	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
204	C₂×D₁₃	—	2	1	no	—
205	C₂×D₁₃	—	2	1	no	—
206	C₂×D₁₃	—	4	1	no	—
207	C₂×D₁₃	—	4	1	no	—
208	C₂×D₁₃	—	4	1	no	—
209	C₂×D₁₃	—	8	4	no	—
210	C₂×D₁₃	C₂×SD₁₆	1	2	yes	complemented
211	C₄×C₁₃	—	2	1	no	—
212	C₄×C₁₃	—	4	1	no	—
213	C₄×C₁₃	—	4	1	no	—
214	C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
215	C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
216	Dic₁₃	—	2	2	no	—
217	Dic₁₃	—	2	1	no	—
218	Dic₁₃	—	2	1	no	—
219	Dic₁₃	—	4	1	no	—
220	Dic₁₃	—	4	1	no	—
221	Dic₁₃	C₂×SD₁₆	1	2	yes	complemented
222	C₂²×Q₈	—	13	1	no	—
223	C₂²×Q₈	—	13	1	no	—
224	C₂²×D₄	—	13	1	no	—
225	C₂²×D₄	—	26	1	no	—
226	C₂²×D₄	C₂×D₁₃	1	1	yes	characteristic
227	C₂×SD₁₆	—	13	1	no	—
228	C₂×SD₁₆	—	13	1	no	—
229	C₂×SD₁₆	—	13	1	no	—
230	C₂×SD₁₆	—	13	1	no	—
231	C₂×SD₁₆	—	13	1	no	—
232	C₂×SD₁₆	—	13	1	no	—
233	C₂×SD₁₆	—	13	1	no	—
234	C₂×SD₁₆	—	26	4	no	—
235	C₂×SD₁₆	—	26	4	no	—
236	C₂×SD₁₆	C₂×D₁₃	1	1	yes	characteristic
237	C₂×SD₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
238	C₂²×C₈	—	13	1	no	—
239	C₂²×C₈	—	13	1	no	—
240	C₄⋊Q₈	—	13	1	no	—
241	C₄⋊Q₈	—	26	1	no	—
242	#127	—	13	1	no	—
243	C₂²⋊Q₈	—	13	1	no	—
244	C₂²⋊Q₈	—	26	1	no	—
245	C₂²⋊Q₈	—	26	1	no	—
246	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
247	#121	—	13	1	no	—
248	#121	—	13	1	no	—
249	#121	—	26	1	no	—
250	#120	—	26	1	no	—
251	#120	—	26	1	no	—
252	C₄×Q₈	—	13	1	no	—
253	C₄×D₄	—	13	1	no	—
254	C₄×D₄	—	13	1	no	—
255	C₄×D₄	—	26	1	no	—
256	#106	—	13	1	no	—
257	C₄⋊C₈	—	13	1	no	—
258	#103	—	13	1	no	—
259	#103	—	13	1	no	—
260	#103	—	13	1	no	—
261	#102	—	13	1	no	—
262	#102	C₂×D₁₃	1	1	yes	characteristic
263	#102	C₂×D₁₃	1	1	yes	characteristic, complemented
264	C₂²⋊C₈	—	13	1	no	—
265	C₂²⋊C₈	C₂×D₁₃	1	1	yes	characteristic, complemented
266	C₄×C₈	—	13	1	no	—
267	C₂×C₁₃	—	2	2	no	—
268	C₂×C₁₃	—	4	2	no	—
269	C₂×C₁₃	—	8	1	no	—
270	C₂×C₁₃	D₄²	1	1	yes	characteristic
271	C₂×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
272	C₂×C₁₃	#577	1	1	yes	characteristic
273	D₁₃	—	2	2	no	—
274	D₁₃	—	8	1	no	—
275	C₂⁴	—	2	1	no	—
276	C₂⁴	—	26	1	no	—
277	C₂×Q₈	—	13	1	no	—
278	C₂×Q₈	—	13	1	no	—
279	C₂×Q₈	—	26	1	no	—
280	C₂×Q₈	—	26	2	no	—
281	C₂×Q₈	—	26	1	no	—
282	C₂×Q₈	—	26	2	no	—
283	C₂×Q₈	—	52	1	no	—
284	C₂×Q₈	—	52	1	no	—
285	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	1	no	—
288	C₂×D₄	—	4	1	no	—
289	C₂×D₄	—	13	1	no	—
290	C₂×D₄	—	13	1	no	—
291	C₂×D₄	—	26	1	no	—
292	C₂×D₄	—	26	1	no	—
293	C₂×D₄	—	26	1	no	—
294	C₂×D₄	—	26	2	no	—
295	C₂×D₄	—	26	1	no	—
296	C₂×D₄	—	26	1	no	—
297	C₂×D₄	—	52	1	no	—
298	C₂×D₄	—	52	4	no	—
299	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
300	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
301	C₂²×C₄	—	13	1	no	—
302	C₂²×C₄	—	26	1	no	—
303	C₂²×C₄	—	26	1	no	—
304	C₂²×C₄	—	26	1	no	—
305	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
306	SD₁₆	—	2	2	no	—
307	SD₁₆	—	4	1	no	—
308	SD₁₆	—	13	4	no	—
309	SD₁₆	—	26	2	no	—
310	SD₁₆	—	26	2	no	—
311	SD₁₆	—	26	2	no	—
312	SD₁₆	—	26	2	no	—
313	SD₁₆	—	26	2	no	—
314	SD₁₆	—	52	1	no	—
315	C₂×C₈	—	13	1	no	—
316	C₂×C₈	—	13	1	no	—
317	C₂×C₈	—	26	2	no	—
318	C₂×C₈	—	26	2	no	—
319	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
320	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	13	1	no	—
323	C₄⋊C₄	—	13	1	no	—
324	C₄⋊C₄	—	26	1	no	—
325	C₄⋊C₄	—	26	1	no	—
326	C₄⋊C₄	—	26	1	no	—
327	C₄⋊C₄	—	26	1	no	—
328	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
329	C₂²⋊C₄	—	2	1	no	—
330	C₂²⋊C₄	—	13	1	no	—
331	C₂²⋊C₄	—	13	1	no	—
332	C₂²⋊C₄	—	26	1	no	—
333	C₂²⋊C₄	—	26	1	no	—
334	C₂²⋊C₄	—	26	1	no	—
335	C₂²⋊C₄	—	26	1	no	—
336	C₄²	—	13	1	no	—
337	C₄²	—	26	1	no	—
338	C₁₃	D₄×SD₁₆	1	1	yes	characteristic, complemented, Sylow
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	8	1	no	—
344	C₂³	—	13	1	no	—
345	C₂³	—	26	1	no	—
346	C₂³	—	52	2	no	—
347	C₂³	—	52	2	no	—
348	C₂³	—	104	1	no	—
349	C₂³	D₄×D₁₃	1	1	yes	characteristic
350	Q₈	—	2	1	no	—
351	Q₈	—	2	1	no	—
352	Q₈	—	13	2	no	—
353	Q₈	—	26	1	no	—
354	Q₈	—	26	1	no	—
355	Q₈	—	26	1	no	—
356	Q₈	—	52	2	no	—
357	Q₈	—	52	2	no	—
358	D₄	—	2	1	no	—
359	D₄	—	2	1	no	—
360	D₄	—	2	1	no	—
361	D₄	—	4	2	no	—
362	D₄	—	13	4	no	—
363	D₄	—	26	1	no	—
364	D₄	—	26	1	no	—
365	D₄	—	52	2	no	—
366	D₄	—	52	2	no	—
367	D₄	—	52	2	no	—
368	D₄	—	52	2	no	—
369	D₄	—	104	1	no	—
370	D₄	D₄×D₁₃	1	2	yes	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	13	1	no	—
376	C₂×C₄	—	13	1	no	—
377	C₂×C₄	—	13	1	no	—
378	C₂×C₄	—	26	1	no	—
379	C₂×C₄	—	26	1	no	—
380	C₂×C₄	—	26	1	no	—
381	C₂×C₄	—	26	1	no	—
382	C₂×C₄	—	26	1	no	—
383	C₂×C₄	—	52	2	no	—
384	C₂×C₄	—	52	2	no	—
385	C₂×C₄	—	52	2	no	—
386	C₂×C₄	D₄×D₁₃	1	1	yes	characteristic
387	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
388	C₈	—	2	1	no	—
389	C₈	—	2	1	no	—
390	C₈	—	13	2	no	—
391	C₈	—	26	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	8	4	no	—
401	C₂²	—	13	2	no	—
402	C₂²	—	26	1	no	—
403	C₂²	—	26	1	no	—
404	C₂²	—	52	1	no	—
405	C₂²	—	52	1	no	—
406	C₂²	—	52	1	no	—
407	C₂²	—	104	4	no	—
408	C₂²	SD₁₆×D₁₃	1	2	yes	complemented
409	C₂²	C₂×D₄×D₁₃	1	1	yes	characteristic
410	C₄	—	2	1	no	—
411	C₄	—	4	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	13	2	no	—
414	C₄	—	26	1	no	—
415	C₄	—	26	1	no	—
416	C₄	—	26	2	no	—
417	C₄	—	52	1	no	—
418	C₄	—	52	1	no	—
419	C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
420	C₄	#88251	1	1	yes	characteristic
421	C₂	—	2	2	no	—
422	C₂	—	4	2	no	—
423	C₂	—	8	1	no	—
424	C₂	—	26	2	no	—
425	C₂	—	104	1	no	—
426	C₂	#11719295	1	1	yes	characteristic
427	C₂	C₂×SD₁₆×D₁₃	1	1	yes	characteristic
428	C₂	#11719480	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₃
commutator, cosocle	C₂×C₄×C₁₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₃
Fitting	C₁₃×#450	C₂
socle	C₂²×C₁₃	C₂²×D₄
prime radical	D₄×C₂²⋊D₁₃	C₂
hypercenter	#450	D₁₃
hypocenter	C₁₃	D₄×SD₁₆
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #450

Complements

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

N	H ≅ G/N	type
2. C₂²×#6105	C₂	semidirect
3. C₂×SD₁₆×D₁₃	C₂	semidirect
4. #11719337	C₂	semidirect
5. C₁₃×#450	C₂	semidirect
6. #11718836	C₂	semidirect
7. #11718831	C₂	semidirect
8. #11718823	C₂	semidirect
9. #11718709	C₂	semidirect
10. #11718439	C₂	semidirect
11. #11718437	C₂	semidirect
12. #11718423	C₂	semidirect
13. #11718419	C₂	semidirect
14. #11718399	C₂	semidirect
15. #11718386	C₂	semidirect
18. C₂×Q₈×D₁₃	C₂²	semidirect
20. C₂²×Dic₂₆	C₂²	semidirect
22. C₂×C₁₃×SD₁₆	C₂²	semidirect
23. C₁₃×C₂²⋊Q₈	C₂²	semidirect
25. #88198	C₂²	semidirect
26. C₂×#6106	C₂²	semidirect
35. C₂×#6105	C₂²	semidirect
36. C₂×#6105	C₂²	semidirect
39. C₂²×#1055	C₂²	semidirect
41. C₂×#6095	C₂²	semidirect
42. C₂×#6095	C₂²	semidirect
43. C₂×C₈×D₁₃	C₂²	semidirect
44. #88151	C₂²	semidirect
47. #88141	C₂²	semidirect
51. C₁₃×#102	C₂²	semidirect
52. C₁₃×C₂²⋊C₈	C₂²	semidirect
53. #88075	C₂²	semidirect
54. #88060	C₂²	semidirect
55. #88056	C₂²	semidirect
56. #88056	C₂²	semidirect
57. #88054	C₂²	semidirect
58. C₈×Dic₁₃	C₂²	semidirect
59. #88049	C₂²	semidirect
60. #88048	C₂²	semidirect
106. #6105	D₄	semidirect
154. C₂²⋊D₁₃	SD₁₆	semidirect
173. Dic₂₆	C₂×D₄	semidirect
177. #1055	C₂×D₄	semidirect
188. #450	D₁₃	semidirect
202. C₂²×C₁₃	C₂×SD₁₆	semidirect
210. C₂×D₁₃	C₂×SD₁₆	semidirect
221. Dic₁₃	C₂×SD₁₆	semidirect
237. C₂×SD₁₆	C₂×D₁₃	semidirect
246. C₂²⋊Q₈	C₂×D₁₃	semidirect
263. #102	C₂×D₁₃	semidirect
265. C₂²⋊C₈	C₂×D₁₃	semidirect
338. C₁₃	D₄×SD₁₆	semidirect
408. C₂²	SD₁₆×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
D₄×C₂²⋊D₁₃	2
C₂²×#6105	2
C₂×SD₁₆×D₁₃	2
#11719337	2
C₁₃×#450	2
#11718836	2
#11718831	2
#11718823	2
#11718709	2
#11718439	2
#11718437	2
#11718423	2
#11718419	2
#11718399	2
#11718386	2
D₄×SD₁₆	13