Subgroups — #15828630

Order 3328.

900 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123464	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#6094	C₂	1	1	yes	maximal, characteristic
3	C₄×M₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic
4	#13113140	C₂	1	2	yes	maximal, complemented
5	#13113140	C₂	1	2	yes	maximal, complemented
6	#13113124	C₂	1	2	yes	maximal, complemented
7	#13113123	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113117	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×#6099	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113115	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₁₃	C₄	1	2	yes	—
13	C₂²×#6094	C₄	1	2	yes	—
14	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#431	C₂²	1	1	yes	characteristic
16	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
18	M₁₆×Dic₁₃	C₄	1	2	yes	—
19	C₂×#88055	C₄	1	2	yes	—
20	#11718586	C₂²	1	1	yes	characteristic
21	C₄×#6099	C₂²	1	1	yes	characteristic
22	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
23	#11718498	C₄	1	2	yes	—
24	#11718496	C₄	1	2	yes	—
25	#11718387	C₄	1	2	yes	—
26	#11718380	C₄	1	2	yes	—
27	#11718368	C₄	1	2	yes	—
28	D₁₃×#97	C₄	1	2	yes	—
29	C₄×#6094	C₄	1	2	yes	—
30	C₄×#6094	C₄	1	2	yes	—
31	C₄×#6094	C₂²	1	1	yes	characteristic
32	C₄×#6094	C₂²	1	1	yes	characteristic
33	C₄×#6094	C₂²	1	2	yes	—
34	C₄×#6094	C₂²	1	2	yes	—
35	C₄×#6094	C₂²	1	1	yes	characteristic
36	C₄×#6094	C₂²	1	1	yes	characteristic
37	#11718346	C₂²	1	2	yes	—
38	C₄×C₈×D₁₃	C₂²	1	2	yes	—
39	C₁₃×#322	C₂²	1	2	yes	complemented
40	C₁₃×#322	C₂²	1	2	yes	complemented
41	#11718046	C₂²	1	2	yes	complemented
42	#11718046	C₂²	1	2	yes	complemented
43	#11718046	C₂²	1	2	yes	complemented
44	#11718046	C₂²	1	2	yes	complemented
45	C₈×#1055	C₂²	1	2	yes	complemented
46	C₈×#1055	C₂²	1	2	yes	complemented
47	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
51	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
53	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
56	C₂×#6099	C₂×C₄	1	2	yes	—
57	C₂²×#1055	C₂×C₄	1	2	yes	—
58	M₁₆×D₁₃	—	2	8	no	—
59	C₂×#6094	—	2	8	no	—
60	C₂×#6094	C₂×C₄	1	2	yes	—
61	C₂×#6094	C₂×C₄	1	2	yes	—
62	C₂×#6094	C₂×C₄	1	2	yes	—
63	C₂×#6094	C₂×C₄	1	4	yes	—
64	C₂×#6094	C₂×C₄	1	4	yes	—
65	C₂×#6094	C₂×C₄	1	2	yes	—
66	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
67	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
68	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
69	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
70	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
71	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
72	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
73	C₄²×D₁₃	C₂³	1	1	yes	characteristic
74	C₄²×D₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
76	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
77	C₁₃×#97	C₂×C₄	1	2	yes	—
78	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
79	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₁₃	C₂³	1	2	yes	—
82	C₄×C₈×C₁₃	C₂³	1	2	yes	—
83	C₂²⋊#1055	C₂×C₄	1	2	yes	—
84	#88060	C₂×C₄	1	4	yes	—
85	#88055	C₂×C₄	1	4	yes	—
86	#88055	C₂×C₄	1	2	yes	—
87	#88055	C₂×C₄	1	2	yes	—
88	#88055	C₂×C₄	1	2	yes	—
89	#88055	C₂×C₄	1	2	yes	—
90	#88055	C₂×C₄	1	4	yes	—
91	#88054	C₂×C₄	1	4	yes	—
92	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
93	C₄⋊#1055	C₂×C₄	1	2	yes	—
94	#88043	C₂×C₄	1	2	yes	—
95	C₄×#1055	C₂×C₄	1	2	yes	—
96	C₄×#1055	C₂³	1	1	yes	characteristic
97	C₄×#1055	C₂³	1	2	yes	—
98	C₄×#1055	C₂³	1	2	yes	—
99	C₄×#1055	C₂³	1	1	yes	characteristic
100	M₁₆²	—	13	1	no	maximal, Sylow
101	C₂³×D₁₃	C₄²	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
106	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
107	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
108	C₂×C₄×D₁₃	—	2	4	no	—
109	C₂×C₄×D₁₃	—	2	4	no	—
110	C₂×C₄×D₁₃	—	4	2	no	—
111	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
112	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
113	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
114	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
115	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
116	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
117	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₁₃×M₁₆	—	2	4	no	—
124	C₂×C₈×C₁₃	—	2	4	no	—
125	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
127	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
128	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
129	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
133	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
134	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
135	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
136	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
137	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
138	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
139	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
141	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
142	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
143	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
144	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
145	#6099	M₁₆	1	8	yes	complemented
146	C₂×#1055	—	2	4	no	—
147	C₂×#1055	C₂²×C₄	1	4	yes	—
148	C₂×#1055	C₂²×C₄	1	2	yes	—
149	C₂×#1055	C₂²×C₄	1	4	yes	—
150	C₂×#1055	C₂²×C₄	1	2	yes	—
151	#6094	—	2	4	no	—
152	#6094	—	2	4	no	—
153	#6094	—	2	4	no	—
154	#6094	—	2	8	no	—
155	#6094	—	4	4	no	—
156	#6094	M₁₆	1	8	yes	complemented
157	C₈×D₁₃	—	2	8	no	—
158	#2920	—	13	1	no	—
159	C₂×C₄×M₁₆	—	13	1	no	—
160	C₂×C₄×M₁₆	—	13	1	no	—
161	#1455	—	13	2	no	—
162	#1455	—	13	2	no	—
163	#1451	—	13	1	no	—
164	#1451	—	13	2	no	—
165	#1451	D₁₃	1	1	yes	characteristic, complemented
166	C₈×M₁₆	—	13	1	no	—
167	C₈×M₁₆	—	13	1	no	—
168	C₈×M₁₆	—	13	2	no	—
169	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
170	C₂²×D₁₃	—	2	2	no	—
171	C₂²×D₁₃	—	2	2	no	—
172	C₂²×D₁₃	—	4	1	no	—
173	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
174	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
181	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
184	C₂×Dic₁₃	—	2	2	no	—
185	C₂×Dic₁₃	—	2	2	no	—
186	C₂×Dic₁₃	—	4	1	no	—
187	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
188	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
189	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
190	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
191	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
192	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
193	C₄×D₁₃	—	2	2	no	—
194	C₄×D₁₃	—	2	2	no	—
195	C₄×D₁₃	—	2	2	no	—
196	C₄×D₁₃	—	2	2	no	—
197	C₄×D₁₃	—	2	2	no	—
198	C₄×D₁₃	—	2	2	no	—
199	C₄×D₁₃	—	2	2	no	—
200	C₄×D₁₃	—	2	2	no	—
201	C₄×D₁₃	—	2	2	no	—
202	C₄×D₁₃	—	4	1	no	—
203	C₄×D₁₃	—	4	1	no	—
204	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
205	C₈×C₁₃	—	2	4	no	—
206	C₈×C₁₃	—	2	2	no	—
207	C₈×C₁₃	—	2	4	no	—
208	C₈×C₁₃	C₂×M₁₆	1	4	yes	complemented
209	#1055	—	2	2	no	—
210	#1055	—	2	4	no	—
211	#1055	C₂×M₁₆	1	8	yes	complemented
212	#1055	C₂×M₁₆	1	4	yes	complemented
213	C₂²×M₁₆	—	13	2	no	—
214	C₂²×M₁₆	—	13	2	no	—
215	C₂²×C₄²	—	13	1	no	—
216	#432	—	13	2	no	—
217	#432	—	13	2	no	—
218	#431	—	13	1	no	—
219	#431	—	13	2	no	—
220	#431	C₂×D₁₃	1	1	yes	characteristic
221	#423	—	13	2	no	—
222	#407	—	13	2	no	—
223	C₄×M₁₆	—	13	2	no	—
224	C₄×M₁₆	—	13	1	no	—
225	C₄×M₁₆	—	13	2	no	—
226	C₄×M₁₆	—	13	2	no	—
227	C₄×M₁₆	—	13	2	no	—
228	C₄×M₁₆	—	13	1	no	—
229	C₄×M₁₆	—	13	1	no	—
230	C₄×M₁₆	—	13	2	no	—
231	C₄×M₁₆	—	13	1	no	—
232	C₄×M₁₆	—	13	1	no	—
233	C₄×M₁₆	—	13	2	no	—
234	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
235	C₂×#97	—	13	2	no	—
236	C₂×#97	—	13	2	no	—
237	C₂×C₄×C₈	—	13	1	no	—
238	C₂×C₄×C₈	—	13	2	no	—
239	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
240	#322	—	13	2	no	—
241	#322	—	13	2	no	—
242	#322	—	13	2	no	—
243	#322	—	13	2	no	—
244	#322	C₂×D₁₃	1	2	yes	complemented
245	#322	C₂×D₁₃	1	2	yes	complemented
246	C₈²	—	13	2	no	—
247	C₈²	—	13	2	no	—
248	C₂²×C₁₃	—	2	1	no	—
249	C₂²×C₁₃	—	2	1	no	—
250	C₂²×C₁₃	C₄×M₁₆	1	2	yes	—
251	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
252	C₂×D₁₃	—	2	1	no	—
253	C₂×D₁₃	—	2	1	no	—
254	C₂×D₁₃	—	2	1	no	—
255	C₂×D₁₃	—	2	1	no	—
256	C₂×D₁₃	—	2	1	no	—
257	C₂×D₁₃	—	4	4	no	—
258	C₂×D₁₃	C₄×M₁₆	1	2	yes	—
259	C₄×C₁₃	—	2	1	no	—
260	C₄×C₁₃	—	2	1	no	—
261	C₄×C₁₃	C₄×M₁₆	1	2	yes	—
262	C₄×C₁₃	C₂²×M₁₆	1	2	yes	—
263	C₄×C₁₃	C₂²×M₁₆	1	2	yes	—
264	C₄×C₁₃	#568	1	2	yes	—
265	Dic₁₃	—	2	1	no	—
266	Dic₁₃	—	2	1	no	—
267	Dic₁₃	—	2	1	no	—
268	Dic₁₃	—	2	1	no	—
269	Dic₁₃	—	2	1	no	—
270	Dic₁₃	C₄×M₁₆	1	2	yes	—
271	C₂³×C₄	—	13	1	no	—
272	C₂³×C₄	—	13	1	no	—
273	C₂³×C₄	—	13	1	no	—
274	C₂×M₁₆	—	13	2	no	—
275	C₂×M₁₆	—	13	2	no	—
276	C₂×M₁₆	—	13	4	no	—
277	C₂×M₁₆	—	13	2	no	—
278	C₂×M₁₆	—	13	2	no	—
279	C₂×M₁₆	—	13	2	no	—
280	C₂×M₁₆	—	13	4	no	—
281	C₂×M₁₆	—	26	8	no	—
282	C₂×M₁₆	—	26	8	no	—
283	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
284	C₂²×C₈	—	13	2	no	—
285	C₂²×C₈	—	13	4	no	—
286	C₂²×C₈	C₄×D₁₃	1	2	yes	—
287	C₂×C₄²	—	13	1	no	—
288	C₂×C₄²	—	13	1	no	—
289	C₂×C₄²	—	13	1	no	—
290	C₂×C₄²	—	13	1	no	—
291	C₂×C₄²	—	13	1	no	—
292	C₂×C₄²	—	13	1	no	—
293	C₂×C₄²	—	13	1	no	—
294	C₂×C₄²	—	13	1	no	—
295	C₂×C₄²	—	13	1	no	—
296	C₂×C₄²	—	13	1	no	—
297	C₂×C₄²	—	13	1	no	—
298	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
299	C₄⋊C₈	—	13	4	no	—
300	C₄⋊C₈	—	13	2	no	—
301	C₄⋊C₈	C₄×D₁₃	1	2	yes	—
302	C₂²⋊C₈	—	13	2	no	—
303	C₂²⋊C₈	—	13	4	no	—
304	C₂²⋊C₈	C₄×D₁₃	1	2	yes	—
305	#97	—	13	4	no	—
306	#97	—	13	2	no	—
307	#97	—	13	2	no	—
308	#97	—	13	2	no	—
309	#97	—	13	2	no	—
310	#97	—	13	4	no	—
311	#97	—	13	2	no	—
312	#97	C₄×D₁₃	1	2	yes	—
313	C₄×C₈	—	13	4	no	—
314	C₄×C₈	—	13	2	no	—
315	C₄×C₈	—	13	1	no	—
316	C₄×C₈	—	13	2	no	—
317	C₄×C₈	—	13	2	no	—
318	C₄×C₈	—	13	1	no	—
319	C₄×C₈	C₄×D₁₃	1	2	yes	—
320	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
321	C₄×C₈	C₂²×D₁₃	1	2	yes	—
322	C₄×C₈	C₂²×D₁₃	1	2	yes	—
323	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
324	C₂×C₁₃	—	2	2	no	—
325	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
326	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
327	C₂×C₁₃	#2873	1	1	yes	characteristic
328	D₁₃	—	2	2	no	—
329	D₁₃	—	4	1	no	—
330	C₂⁴	—	13	1	no	—
331	C₂²×C₄	—	13	1	no	—
332	C₂²×C₄	—	13	1	no	—
333	C₂²×C₄	—	13	1	no	—
334	C₂²×C₄	—	13	1	no	—
335	C₂²×C₄	—	13	1	no	—
336	C₂²×C₄	—	13	1	no	—
337	C₂²×C₄	—	13	1	no	—
338	C₂²×C₄	—	13	1	no	—
339	C₂²×C₄	—	13	1	no	—
340	C₂²×C₄	—	13	1	no	—
341	C₂²×C₄	—	13	1	no	—
342	C₂²×C₄	—	13	1	no	—
343	C₂²×C₄	—	13	1	no	—
344	C₂²×C₄	—	13	1	no	—
345	C₂²×C₄	—	13	1	no	—
346	C₂²×C₄	—	26	4	no	—
347	C₂²×C₄	—	26	4	no	—
348	C₂²×C₄	—	52	2	no	—
349	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
350	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
352	M₁₆	—	2	4	no	—
353	M₁₆	—	13	8	no	—
354	M₁₆	—	13	8	no	—
355	M₁₆	—	26	4	no	—
356	M₁₆	—	26	8	no	—
357	M₁₆	—	26	4	no	—
358	M₁₆	—	26	4	no	—
359	M₁₆	—	52	4	no	—
360	C₂×C₈	—	2	4	no	—
361	C₂×C₈	—	13	4	no	—
362	C₂×C₈	—	13	2	no	—
363	C₂×C₈	—	13	2	no	—
364	C₂×C₈	—	13	4	no	—
365	C₂×C₈	—	26	8	no	—
366	C₂×C₈	—	26	4	no	—
367	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
368	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
369	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
370	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
371	C₄²	—	13	1	no	—
372	C₄²	—	13	1	no	—
373	C₄²	—	13	1	no	—
374	C₄²	—	13	1	no	—
375	C₄²	—	13	1	no	—
376	C₄²	—	13	1	no	—
377	C₄²	—	13	1	no	—
378	C₄²	—	13	1	no	—
379	C₄²	—	13	1	no	—
380	C₄²	—	13	1	no	—
381	C₄²	—	13	1	no	—
382	C₄²	—	13	1	no	—
383	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
384	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
385	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
386	C₄²	C₂³×D₁₃	1	1	yes	characteristic
387	C₁₃	M₁₆²	1	1	yes	characteristic, complemented, Sylow
388	C₂³	—	13	1	no	—
389	C₂³	—	13	1	no	—
390	C₂³	—	26	2	no	—
391	C₂³	—	26	2	no	—
392	C₂³	—	52	1	no	—
393	C₂³	C₄²×D₁₃	1	1	yes	characteristic
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	13	1	no	—
397	C₂×C₄	—	13	4	no	—
398	C₂×C₄	—	13	1	no	—
399	C₂×C₄	—	13	1	no	—
400	C₂×C₄	—	13	1	no	—
401	C₂×C₄	—	13	1	no	—
402	C₂×C₄	—	13	1	no	—
403	C₂×C₄	—	26	2	no	—
404	C₂×C₄	—	26	2	no	—
405	C₂×C₄	—	26	2	no	—
406	C₂×C₄	—	26	2	no	—
407	C₂×C₄	—	26	2	no	—
408	C₂×C₄	—	26	2	no	—
409	C₂×C₄	—	26	2	no	—
410	C₂×C₄	—	26	2	no	—
411	C₂×C₄	—	26	2	no	—
412	C₂×C₄	—	26	2	no	—
413	C₂×C₄	—	26	2	no	—
414	C₂×C₄	—	52	1	no	—
415	C₂×C₄	—	52	1	no	—
416	C₂×C₄	—	52	1	no	—
417	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
418	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
419	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
420	C₂×C₄	M₁₆×D₁₃	1	4	yes	—
421	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
422	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
423	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
424	C₈	—	2	2	no	—
425	C₈	—	2	4	no	—
426	C₈	—	2	4	no	—
427	C₈	—	13	4	no	—
428	C₈	—	13	8	no	—
429	C₈	—	26	2	no	—
430	C₈	—	26	4	no	—
431	C₈	M₁₆×D₁₃	1	4	yes	complemented
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	13	2	no	—
435	C₂²	—	26	1	no	—
436	C₂²	—	26	1	no	—
437	C₂²	—	26	1	no	—
438	C₂²	—	26	1	no	—
439	C₂²	—	26	1	no	—
440	C₂²	—	52	4	no	—
441	C₂²	#11718368	1	2	yes	—
442	C₂²	C₂×C₄²×D₁₃	1	1	yes	characteristic
443	C₄	—	2	1	no	—
444	C₄	—	2	1	no	—
445	C₄	—	13	2	no	—
446	C₄	—	26	1	no	—
447	C₄	—	26	1	no	—
448	C₄	—	26	1	no	—
449	C₄	—	26	1	no	—
450	C₄	—	26	1	no	—
451	C₄	#11718368	1	2	yes	—
452	C₄	C₂×M₁₆×D₁₃	1	2	yes	—
453	C₄	C₂×M₁₆×D₁₃	1	2	yes	—
454	C₄	#11719455	1	2	yes	—
455	C₂	—	2	2	no	—
456	C₂	—	26	2	no	—
457	C₂	—	52	1	no	—
458	C₂	C₄×M₁₆×D₁₃	1	1	yes	characteristic
459	C₂	C₂×#11718368	1	1	yes	characteristic
460	C₂	#13123252	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#1451	C₂
prime radical	C₂³×D₁₃	C₄²
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1451	D₁₃
hypocenter	C₁₃	M₁₆²
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ #1451

Complements

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

N	H ≅ G/N	type
4. #13113140	C₂	semidirect
5. #13113140	C₂	semidirect
6. #13113124	C₂	semidirect
7. #13113123	C₂	semidirect
8. #13113117	C₂	semidirect
9. C₈×#6099	C₂	semidirect
10. #13113115	C₂	semidirect
11. C₁₃×#1451	C₂	semidirect
39. C₁₃×#322	C₂²	semidirect
40. C₁₃×#322	C₂²	semidirect
41. #11718046	C₂²	semidirect
42. #11718046	C₂²	semidirect
43. #11718046	C₂²	semidirect
44. #11718046	C₂²	semidirect
45. C₈×#1055	C₂²	semidirect
46. C₈×#1055	C₂²	semidirect
145. #6099	M₁₆	semidirect
156. #6094	M₁₆	semidirect
165. #1451	D₁₃	semidirect
208. C₈×C₁₃	C₂×M₁₆	semidirect
211. #1055	C₂×M₁₆	semidirect
212. #1055	C₂×M₁₆	semidirect
244. #322	C₂×D₁₃	semidirect
245. #322	C₂×D₁₃	semidirect
387. C₁₃	M₁₆²	semidirect
431. C₈	M₁₆×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
#13123464	2
C₂×C₄×#6094	2
C₄×M₁₆×D₁₃	2
#13113140	2
#13113124	2
#13113123	2
#13113117	2
C₈×#6099	2
#13113115	2
C₁₃×#1451	2
M₁₆²	13