Subgroups — #15832728

Order 3328.

684 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123949	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#88186	C₂	1	1	yes	maximal, characteristic
3	#13113748	C₂	1	2	yes	maximal, complemented
4	#13113738	C₂	1	2	yes	maximal, complemented
5	#13113724	C₂	1	2	yes	maximal, complemented
6	#13113719	C₂	1	2	yes	maximal, complemented
7	#13113589	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113216	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×D₄⋊#1055	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113117	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2975	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×#88186	C₄	1	1	yes	characteristic
14	C₄×#6127	C₂²	1	1	yes	characteristic
15	C₁₃×#436	—	2	1	no	—
16	C₁₃×#436	—	2	1	no	—
17	C₁₃×#436	C₂²	1	2	yes	—
18	C₁₃×#436	C₂²	1	2	yes	—
19	C₁₃×#431	C₂²	1	1	yes	characteristic
20	C₁₃×#431	C₂²	1	1	yes	characteristic
21	C₁₃×#407	—	2	2	no	—
22	#11718876	C₄	1	1	yes	characteristic
23	#11718679	C₄	1	2	yes	—
24	C₄×#6105	C₂²	1	2	yes	—
25	#11718675	C₄	1	2	yes	—
26	C₄×#6104	C₂²	1	2	yes	—
27	#11718627	C₄	1	1	yes	characteristic
28	#11718625	C₄	1	1	yes	characteristic
29	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
30	C₄×#6099	C₂²	1	1	yes	characteristic
31	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
32	#11718498	—	2	1	no	—
33	#11718496	—	2	1	no	—
34	#11718391	—	2	2	no	—
35	#11718349	C₂²	1	2	yes	complemented
36	#11718340	C₂²	1	2	yes	complemented
37	D₄⋊#1055	C₂²	1	2	yes	—
38	D₄⋊#1055	C₂²	1	2	yes	—
39	#11718076	C₂²	1	1	yes	characteristic, complemented
40	#11718076	C₂²	1	1	yes	characteristic, complemented
41	#11718075	C₂²	1	1	yes	characteristic, complemented
42	#11718075	C₂²	1	1	yes	characteristic, complemented
43	#11718072	C₂²	1	2	yes	complemented
44	#11718071	C₂²	1	2	yes	complemented
45	#11718046	C₂²	1	2	yes	complemented
46	C₈×#1055	C₂²	1	2	yes	complemented
47	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	—	2	1	no	—
49	C₂×#6127	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₃×M₁₆	—	2	2	no	—
51	C₂×C₁₃×M₁₆	—	2	2	no	—
52	C₄×D₄×C₁₃	—	2	1	no	—
53	C₄×D₄×C₁₃	—	2	1	no	—
54	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
55	C₄×D₄×C₁₃	C₂³	1	2	yes	—
56	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
57	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
58	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
59	C₂×#6105	C₂×C₄	1	2	yes	—
60	#88186	—	2	4	no	—
61	C₂×#6104	C₂×C₄	1	2	yes	—
62	C₄×C₂²⋊D₁₃	—	2	1	no	—
63	C₄×C₂²⋊D₁₃	—	2	1	no	—
64	#88180	C₂×C₄	1	1	yes	characteristic
65	C₂×#6099	C₂×C₄	1	1	yes	characteristic
66	C₂×#6099	C₂×C₄	1	1	yes	characteristic
67	C₂²×#1055	—	2	1	no	—
68	C₂²×#1055	—	2	1	no	—
69	C₂×#6094	—	2	2	no	—
70	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
71	C₄×D₅₂	C₂³	1	1	yes	characteristic
72	#88126	—	2	1	no	—
73	C₄²×D₁₃	—	2	1	no	—
74	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
75	C₄×Dic₂₆	C₂³	1	1	yes	characteristic
76	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
77	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
78	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
79	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
80	C₁₃×C₂²⋊C₈	—	2	1	no	—
81	C₁₃×C₂²⋊C₈	—	2	2	no	—
82	C₁₃×C₂²⋊C₈	—	2	2	no	—
83	C₁₃×C₂²⋊C₈	D₄	1	2	yes	—
84	C₄×C₈×C₁₃	—	2	1	no	—
85	C₄×C₈×C₁₃	C₂³	1	2	yes	—
86	#88072	C₂×C₄	1	2	yes	—
87	#88072	C₂×C₄	1	2	yes	—
88	#88060	—	2	2	no	—
89	#88055	—	2	2	no	—
90	#88054	—	2	2	no	—
91	#88050	C₂×C₄	1	2	yes	—
92	#88049	C₂×C₄	1	2	yes	—
93	#88048	C₂×C₄	1	2	yes	—
94	#88047	C₂×C₄	1	2	yes	—
95	C₄⋊#1055	—	2	1	no	—
96	C₄⋊#1055	C₂³	1	2	yes	—
97	#88043	C₂×C₄	1	2	yes	—
98	C₄×#1055	—	2	1	no	—
99	C₄×#1055	C₂³	1	1	yes	characteristic
100	C₄×#1055	C₂³	1	1	yes	characteristic
101	C₄×#1055	C₂³	1	2	yes	—
102	#17893	—	13	1	no	maximal, Sylow
103	C₂⁴×C₁₃	—	2	1	no	—
104	C₂×D₄×C₁₃	—	2	1	no	—
105	C₂×D₄×C₁₃	—	2	2	no	—
106	C₂×D₄×C₁₃	—	2	2	no	—
107	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	8	1	no	—
112	C₂²×C₄×C₁₃	—	8	1	no	—
113	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
116	C₂×C₂²⋊D₁₃	—	2	1	no	—
117	#6127	—	2	2	no	—
118	#6127	—	2	2	no	—
119	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₄×D₁₃	—	2	1	no	—
121	C₂×C₄×D₁₃	—	2	1	no	—
122	C₂×C₄×D₁₃	—	2	1	no	—
123	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
124	C₁₃×M₁₆	—	8	2	no	—
125	C₁₃×M₁₆	—	8	2	no	—
126	C₂×C₈×C₁₃	—	2	1	no	—
127	C₂×C₈×C₁₃	—	2	1	no	—
128	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
130	C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
132	C₁₃×C₂²⋊C₄	—	2	2	no	—
133	C₁₃×C₂²⋊C₄	—	2	2	no	—
134	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₁₃	#41	1	1	yes	characteristic
137	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
138	C₂²⋊Dic₁₃	—	2	1	no	—
139	#6105	—	2	4	no	—
140	#6104	—	2	4	no	—
141	#6103	—	2	1	no	—
142	#6103	—	2	1	no	—
143	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
144	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
145	#6101	—	2	1	no	—
146	#6101	—	2	1	no	—
147	C₄×Dic₁₃	—	2	1	no	—
148	C₄×Dic₁₃	—	2	1	no	—
149	C₄×Dic₁₃	—	2	1	no	—
150	#6099	—	2	2	no	—
151	#6099	M₁₆	1	4	yes	complemented
152	C₂×#1055	—	2	1	no	—
153	C₂×#1055	—	2	2	no	—
154	C₂×#1055	—	2	1	no	—
155	C₂×#1055	—	4	2	no	—
156	C₂×#1055	—	8	1	no	—
157	C₂×#1055	C₂²×C₄	1	2	yes	—
158	C₂×#1055	C₂²×C₄	1	2	yes	—
159	#6094	—	8	2	no	—
160	#2989	—	13	1	no	—
161	#2975	D₁₃	1	1	yes	characteristic, complemented
162	C₄×AGL(1,ℤ/8)	—	13	1	no	—
163	#1594	—	13	2	no	—
164	#1592	—	13	2	no	—
165	#1590	—	13	2	no	—
166	#1589	—	13	2	no	—
167	#1565	—	13	1	no	—
168	#1476	—	13	1	no	—
169	C₂×D₄⋊C₈	—	13	1	no	—
170	C₈×M₁₆	—	13	1	no	—
171	C₂³×C₁₃	—	2	2	no	—
172	C₂³×C₁₃	—	4	2	no	—
173	C₂³×C₁₃	—	8	1	no	—
174	C₂³×C₁₃	—	8	1	no	—
175	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
176	C₂²×D₁₃	—	2	1	no	—
177	D₄×C₁₃	—	2	2	no	—
178	D₄×C₁₃	—	2	2	no	—
179	D₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	4	1	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	8	2	no	—
187	C₂×C₄×C₁₃	—	8	1	no	—
188	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
192	C₂×C₄×C₁₃	#131	1	2	yes	—
193	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
196	C₂²⋊D₁₃	—	4	2	no	—
197	C₂×Dic₁₃	—	2	1	no	—
198	C₂×Dic₁₃	—	2	1	no	—
199	C₂×Dic₁₃	—	2	1	no	—
200	D₅₂	—	2	1	no	—
201	D₅₂	—	2	1	no	—
202	C₄×D₁₃	—	4	1	no	—
203	C₄×D₁₃	—	4	1	no	—
204	C₄×D₁₃	—	4	2	no	—
205	C₄×D₁₃	—	8	1	no	—
206	Dic₂₆	—	2	1	no	—
207	Dic₂₆	—	2	1	no	—
208	C₈×C₁₃	—	2	2	no	—
209	C₈×C₁₃	—	2	2	no	—
210	C₈×C₁₃	—	4	1	no	—
211	C₈×C₁₃	—	4	1	no	—
212	#1055	—	2	2	no	—
213	#1055	—	2	2	no	—
214	#1055	—	4	1	no	—
215	#1055	—	4	2	no	—
216	#1055	C₂×M₁₆	1	4	yes	—
217	C₂×AGL(1,ℤ/8)	—	13	1	no	—
218	C₄×#41	—	13	1	no	—
219	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
220	#446	—	13	2	no	—
221	#442	—	13	2	no	—
222	#440	—	13	2	no	—
223	C₄×SD₁₆	—	13	2	no	—
224	C₄×D₈	—	13	2	no	—
225	#436	—	2	1	no	—
226	#436	—	2	1	no	—
227	#436	—	13	2	no	—
228	#436	C₂×D₁₃	1	2	yes	—
229	#436	C₂×D₁₃	1	2	yes	—
230	#435	—	26	2	no	—
231	#432	—	26	1	no	—
232	#431	C₂×D₁₃	1	1	yes	characteristic
233	#431	C₂×D₁₃	1	1	yes	characteristic
234	#428	—	13	1	no	—
235	#423	—	26	1	no	—
236	C₂×C₄⋊C₈	—	13	1	no	—
237	#418	—	13	1	no	—
238	#417	—	13	1	no	—
239	#407	—	2	2	no	—
240	C₄×M₁₆	—	13	1	no	—
241	C₂×C₄×C₈	—	13	1	no	—
242	#335	—	13	2	no	—
243	#334	—	13	2	no	—
244	Q₈⋊C₈	—	13	1	no	—
245	Q₈⋊C₈	—	13	1	no	—
246	D₄⋊C₈	—	13	2	no	—
247	D₄⋊C₈	—	13	2	no	—
248	D₄⋊C₈	—	13	1	no	—
249	D₄⋊C₈	—	13	1	no	—
250	#322	—	13	2	no	—
251	C₈²	—	13	2	no	—
252	C₂²×C₁₃	—	2	1	no	—
253	C₂²×C₁₃	—	2	1	no	—
254	C₂²×C₁₃	—	4	2	no	—
255	C₂²×C₁₃	—	4	2	no	—
256	C₂²×C₁₃	—	4	2	no	—
257	C₂²×C₁₃	—	8	4	no	—
258	C₂²×C₁₃	#436	1	2	yes	—
259	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
260	C₂×D₁₃	—	4	1	no	—
261	C₂×D₁₃	—	4	1	no	—
262	C₂×D₁₃	—	4	1	no	—
263	C₄×C₁₃	—	2	1	no	—
264	C₄×C₁₃	—	2	1	no	—
265	C₄×C₁₃	—	2	1	no	—
266	C₄×C₁₃	—	4	2	no	—
267	C₄×C₁₃	#436	1	2	yes	—
268	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
269	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
270	C₄×C₁₃	#576	1	1	yes	characteristic
271	C₄×C₁₃	#577	1	1	yes	characteristic
272	Dic₁₃	—	4	1	no	—
273	Dic₁₃	—	4	1	no	—
274	Dic₁₃	—	4	1	no	—
275	C₂×#41	—	13	1	no	—
276	C₂²×D₄	C₄×D₁₃	1	1	yes	characteristic
277	C₂³×C₄	—	2	1	no	—
278	AGL(1,ℤ/8)	—	26	4	no	—
279	C₂×SD₁₆	—	13	2	no	—
280	C₂×D₈	—	13	2	no	—
281	C₂×M₁₆	—	2	2	no	—
282	C₂×M₁₆	—	2	2	no	—
283	C₂×M₁₆	—	13	1	no	—
284	C₂×M₁₆	—	13	1	no	—
285	C₂×M₁₆	—	26	2	no	—
286	C₂²×C₈	—	26	1	no	—
287	C₂²×C₈	—	26	1	no	—
288	C₄×Q₈	—	13	1	no	—
289	C₄×Q₈	—	13	1	no	—
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	13	1	no	—
293	C₄×D₄	—	13	1	no	—
294	C₄×D₄	—	26	1	no	—
295	C₄×D₄	—	26	1	no	—
296	C₄×D₄	C₄×D₁₃	1	2	yes	—
297	C₄×D₄	C₂²×D₁₃	1	2	yes	—
298	#117	—	13	1	no	—
299	#117	—	26	1	no	—
300	C₂×C₄⋊C₄	C₄×D₁₃	1	1	yes	characteristic
301	C₂×C₂²⋊C₄	—	2	1	no	—
302	C₂×C₄²	—	26	1	no	—
303	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
304	#107	—	13	2	no	—
305	#106	—	13	2	no	—
306	C₄⋊C₈	—	13	2	no	—
307	C₄⋊C₈	—	26	2	no	—
308	C₄⋊C₈	—	26	1	no	—
309	C₄⋊C₈	C₂²⋊D₁₃	1	1	yes	characteristic
310	C₄⋊C₈	C₂²⋊D₁₃	1	1	yes	characteristic
311	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
312	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
313	#103	—	13	2	no	—
314	#102	—	13	2	no	—
315	#102	—	13	2	no	—
316	#102	—	13	2	no	—
317	C₂²⋊C₈	—	2	1	no	—
318	C₂²⋊C₈	—	2	2	no	—
319	C₂²⋊C₈	—	2	2	no	—
320	C₂²⋊C₈	—	26	2	no	—
321	C₂²⋊C₈	C₂²⋊D₁₃	1	2	yes	—
322	#97	—	13	2	no	—
323	#97	—	26	2	no	—
324	C₄×C₈	—	2	1	no	—
325	C₄×C₈	—	13	2	no	—
326	C₄×C₈	—	13	1	no	—
327	C₄×C₈	—	13	1	no	—
328	C₄×C₈	—	26	1	no	—
329	C₄×C₈	C₂²×D₁₃	1	2	yes	—
330	C₂×C₁₃	—	2	2	no	—
331	C₂×C₁₃	—	8	2	no	—
332	C₂×C₁₃	C₂×#436	1	1	yes	characteristic
333	C₂×C₁₃	#2946	1	1	yes	characteristic
334	C₂×C₁₃	#2956	1	1	yes	characteristic
335	D₁₃	—	8	1	no	—
336	C₂⁴	—	2	1	no	—
337	#41	—	26	2	no	—
338	#41	—	26	2	no	—
339	C₂×Q₈	—	13	1	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	13	1	no	—
344	C₂×D₄	—	26	1	no	—
345	C₂×D₄	C₂×C₄×D₁₃	1	2	yes	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	8	1	no	—
350	C₂²×C₄	—	8	1	no	—
351	C₂²×C₄	—	26	1	no	—
352	C₂²×C₄	—	26	1	no	—
353	C₂²×C₄	—	26	1	no	—
354	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
355	C₂²×C₄	#6127	1	1	yes	characteristic
356	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
357	SD₁₆	—	26	4	no	—
358	D₈	—	26	4	no	—
359	M₁₆	—	8	2	no	—
360	M₁₆	—	8	2	no	—
361	M₁₆	—	13	4	no	—
362	M₁₆	—	26	2	no	—
363	M₁₆	—	104	2	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	13	2	no	—
367	C₂×C₈	—	13	2	no	—
368	C₂×C₈	—	26	1	no	—
369	C₂×C₈	—	26	1	no	—
370	C₂×C₈	—	26	2	no	—
371	C₂×C₈	—	52	2	no	—
372	C₂×C₈	—	104	1	no	—
373	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
374	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	13	1	no	—
377	C₄⋊C₄	—	13	1	no	—
378	C₄⋊C₄	—	26	1	no	—
379	C₄⋊C₄	—	26	1	no	—
380	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
381	C₂²⋊C₄	—	2	2	no	—
382	C₂²⋊C₄	—	2	2	no	—
383	C₂²⋊C₄	—	26	1	no	—
384	C₂²⋊C₄	—	26	1	no	—
385	C₂²⋊C₄	—	26	1	no	—
386	C₄²	—	26	1	no	—
387	C₄²	—	26	1	no	—
388	C₄²	—	26	1	no	—
389	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
390	C₄²	#6127	1	1	yes	characteristic
391	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
392	C₄²	C₂³×D₁₃	1	1	yes	characteristic
393	C₁₃	#17893	1	1	yes	characteristic, complemented, Sylow
394	C₂³	—	2	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	8	1	no	—
397	C₂³	—	8	1	no	—
398	C₂³	—	26	1	no	—
399	C₂³	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
400	Q₈	—	26	1	no	—
401	Q₈	—	26	1	no	—
402	D₄	—	2	2	no	—
403	D₄	—	2	2	no	—
404	D₄	—	4	2	no	—
405	D₄	—	26	1	no	—
406	D₄	—	26	1	no	—
407	D₄	—	52	2	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	8	2	no	—
415	C₂×C₄	—	8	1	no	—
416	C₂×C₄	—	26	1	no	—
417	C₂×C₄	—	26	1	no	—
418	C₂×C₄	—	26	1	no	—
419	C₂×C₄	—	52	1	no	—
420	C₂×C₄	—	52	1	no	—
421	C₂×C₄	—	52	2	no	—
422	C₂×C₄	—	104	1	no	—
423	C₂×C₄	M₁₆×D₁₃	1	2	yes	—
424	C₂×C₄	#88161	1	2	yes	—
425	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
426	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
427	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
428	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
429	C₂×C₄	C₂×#6127	1	1	yes	characteristic
430	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
431	C₈	—	2	2	no	—
432	C₈	—	2	2	no	—
433	C₈	—	4	1	no	—
434	C₈	—	4	1	no	—
435	C₈	—	13	4	no	—
436	C₈	—	26	2	no	—
437	C₈	—	26	2	no	—
438	C₈	—	52	1	no	—
439	C₈	—	52	2	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	8	4	no	—
446	C₂²	—	52	1	no	—
447	C₂²	—	52	1	no	—
448	C₂²	—	52	1	no	—
449	C₂²	#11718789	1	2	yes	—
450	C₂²	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	4	2	no	—
455	C₄	—	52	1	no	—
456	C₄	—	52	1	no	—
457	C₄	—	52	1	no	—
458	C₄	#11718789	1	2	yes	—
459	C₄	C₂×M₁₆×D₁₃	1	1	yes	characteristic
460	C₄	C₂×#88161	1	1	yes	characteristic
461	C₄	#11719540	1	1	yes	characteristic
462	C₄	#11719541	1	1	yes	characteristic
463	C₂	—	2	2	no	—
464	C₂	—	8	2	no	—
465	C₂	—	104	1	no	—
466	C₂	C₂×#11718789	1	1	yes	characteristic
467	C₂	#13123668	1	1	yes	characteristic
468	C₂	#13123743	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×#2975	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×#88186	C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#2975	D₁₃
hypocenter	C₁₃	#17893
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #2975

Complements

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

N	H ≅ G/N	type
1. #13123949	C₂	semidirect
3. #13113748	C₂	semidirect
4. #13113738	C₂	semidirect
5. #13113724	C₂	semidirect
6. #13113719	C₂	semidirect
7. #13113589	C₂	semidirect
8. #13113216	C₂	semidirect
9. C₂×D₄⋊#1055	C₂	semidirect
10. #13113117	C₂	semidirect
11. C₁₃×#2975	C₂	semidirect
35. #11718349	C₂²	semidirect
36. #11718340	C₂²	semidirect
39. #11718076	C₂²	semidirect
40. #11718076	C₂²	semidirect
41. #11718075	C₂²	semidirect
42. #11718075	C₂²	semidirect
43. #11718072	C₂²	semidirect
44. #11718071	C₂²	semidirect
45. #11718046	C₂²	semidirect
46. C₈×#1055	C₂²	semidirect
151. #6099	M₁₆	semidirect
161. #2975	D₁₃	semidirect
393. C₁₃	#17893	semidirect

Maximal subgroups

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

subgroup	index
#13123949	2
C₄×#88186	2
#13113748	2
#13113738	2
#13113724	2
#13113719	2
#13113589	2
#13113216	2
C₂×D₄⋊#1055	2
#13113117	2
C₁₃×#2975	2
#17893	13