Subgroups — #15828572

Order 3328.

836 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123467	C₂	1	1	yes	maximal, characteristic
2	D₁₃×#431	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#6094	C₂	1	1	yes	maximal, characteristic
4	#13113132	C₂	1	2	yes	maximal, complemented
5	#13113130	C₂	1	2	yes	maximal, complemented
6	#13113125	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113124	C₂	1	2	yes	maximal, complemented
8	#13113123	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113117	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#6094	C₂	1	2	yes	maximal, complemented
11	C₈×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#6094	C₄	1	2	yes	—
13	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#431	C₂²	1	1	yes	characteristic
15	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
17	#11718787	C₄	1	2	yes	—
18	#11718779	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	#11718494	C₄	1	2	yes	—
24	D₁₃×C₄⋊C₈	C₄	1	2	yes	—
25	D₁₃×C₂²⋊C₈	C₄	1	2	yes	—
26	#11718379	C₄	1	2	yes	—
27	#11718366	C₄	1	2	yes	—
28	#11718366	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	1	yes	characteristic
34	C₄×#6094	C₂²	1	1	yes	characteristic
35	#11718346	C₂²	1	2	yes	—
36	#11718346	C₂²	1	2	yes	—
37	#11718346	C₂²	1	2	yes	—
38	C₄×C₈×D₁₃	C₂²	1	2	yes	—
39	C₁₃×#322	C₂²	1	2	yes	complemented
40	C₈²×C₁₃	C₂²	1	2	yes	complemented
41	#11718047	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	#11718046	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	C₂×#6094	—	2	8	no	—
59	C₂×#6094	C₂×C₄	1	2	yes	—
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×C₈×D₁₃	C₂×C₄	1	4	yes	—
64	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
65	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
66	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
71	C₄²×D₁₃	C₂³	1	1	yes	characteristic
72	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
73	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
74	C₁₃×#97	C₂×C₄	1	2	yes	—
75	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
76	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₄×C₈×C₁₃	C₂³	1	2	yes	—
78	C₄×C₈×C₁₃	C₂³	1	2	yes	—
79	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²⋊#1055	C₂×C₄	1	2	yes	—
81	#88060	C₂×C₄	1	4	yes	—
82	#88060	C₂×C₄	1	4	yes	—
83	#88060	C₂×C₄	1	4	yes	—
84	#88055	C₂×C₄	1	2	yes	—
85	#88055	C₂×C₄	1	2	yes	—
86	#88055	C₂×C₄	1	2	yes	—
87	#88055	C₂×C₄	1	2	yes	—
88	#88054	C₂×C₄	1	4	yes	—
89	#88054	C₂×C₄	1	4	yes	—
90	#88054	C₂×C₄	1	4	yes	—
91	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
92	C₄⋊#1055	C₂×C₄	1	2	yes	—
93	#88043	C₂×C₄	1	2	yes	—
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	C₄×#1055	C₂³	1	2	yes	—
99	#17327	—	13	1	no	maximal, Sylow
100	C₂³×D₁₃	C₄²	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂²×C₄	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×Dic₁₃	C₄²	1	1	yes	characteristic
105	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
106	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
107	C₂×C₄×D₁₃	—	2	4	no	—
108	C₂×C₄×D₁₃	—	2	4	no	—
109	C₂×C₄×D₁₃	—	4	2	no	—
110	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
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	C₂²×C₄	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	C₁₃×M₁₆	—	2	4	no	—
123	C₂×C₈×C₁₃	—	2	4	no	—
124	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
126	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
127	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
128	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
132	C₄×Dic₁₃	C₄²	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	C₂²×C₄	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	#6099	—	2	4	no	—
145	C₂×#1055	—	2	4	no	—
146	C₂×#1055	C₂²×C₄	1	4	yes	—
147	C₂×#1055	C₂²×C₄	1	2	yes	—
148	C₂×#1055	C₂²×C₄	1	4	yes	—
149	C₂×#1055	C₂²×C₄	1	2	yes	—
150	#6094	—	2	4	no	—
151	#6094	—	2	4	no	—
152	#6094	—	2	4	no	—
153	#6094	M₁₆	1	8	yes	complemented
154	C₈×D₁₃	—	4	4	no	—
155	#2920	—	13	1	no	—
156	C₂×#431	—	13	1	no	—
157	C₂×C₄×M₁₆	—	13	1	no	—
158	#1453	—	13	2	no	—
159	#1453	—	13	2	no	—
160	#1451	—	13	1	no	—
161	#1451	—	13	1	no	—
162	#1451	—	13	2	no	—
163	C₈×M₁₆	—	13	1	no	—
164	C₈×M₁₆	—	13	2	no	—
165	C₈×M₁₆	D₁₃	1	1	yes	characteristic, complemented
166	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
167	C₂²×D₁₃	—	2	2	no	—
168	C₂²×D₁₃	—	2	2	no	—
169	C₂²×D₁₃	—	4	1	no	—
170	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
171	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
177	C₂×C₄×C₁₃	#131	1	4	yes	—
178	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
181	C₂×Dic₁₃	—	2	2	no	—
182	C₂×Dic₁₃	—	2	2	no	—
183	C₂×Dic₁₃	—	4	1	no	—
184	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
185	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
186	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
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	C₄×D₁₃	—	2	2	no	—
191	C₄×D₁₃	—	2	2	no	—
192	C₄×D₁₃	—	2	2	no	—
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	—	4	1	no	—
200	C₄×D₁₃	—	4	1	no	—
201	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
202	C₈×C₁₃	—	2	2	no	—
203	C₈×C₁₃	—	2	4	no	—
204	C₈×C₁₃	—	2	4	no	—
205	C₈×C₁₃	C₂×M₁₆	1	4	yes	—
206	#1055	—	2	2	no	—
207	#1055	—	2	4	no	—
208	#1055	—	2	4	no	—
209	#1055	C₂×M₁₆	1	4	yes	—
210	C₂²×M₁₆	—	13	2	no	—
211	C₂²×C₄²	—	13	1	no	—
212	#432	—	13	2	no	—
213	#432	—	13	2	no	—
214	#431	—	13	1	no	—
215	#431	—	13	2	no	—
216	#431	—	13	2	no	—
217	#431	—	13	2	no	—
218	#431	—	13	2	no	—
219	#431	—	13	2	no	—
220	#431	C₂×D₁₃	1	1	yes	characteristic
221	#423	—	13	2	no	—
222	C₂×C₄⋊C₈	—	13	2	no	—
223	#407	—	13	2	no	—
224	C₂×C₂²⋊C₈	—	13	2	no	—
225	C₄×M₁₆	—	13	1	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	1	no	—
231	C₄×M₁₆	—	13	1	no	—
232	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
233	C₂×#97	—	13	2	no	—
234	C₂×C₄×C₈	—	13	1	no	—
235	C₂×C₄×C₈	—	13	2	no	—
236	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
237	#322	—	13	2	no	—
238	#322	—	13	2	no	—
239	#322	—	13	2	no	—
240	#322	—	13	2	no	—
241	#322	—	13	2	no	—
242	#322	C₂×D₁₃	1	2	yes	complemented
243	C₈²	—	13	2	no	—
244	C₈²	C₂×D₁₃	1	2	yes	complemented
245	C₂²×C₁₃	—	2	1	no	—
246	C₂²×C₁₃	—	2	1	no	—
247	C₂²×C₁₃	#405	1	2	yes	—
248	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
249	C₂×D₁₃	—	2	1	no	—
250	C₂×D₁₃	—	2	1	no	—
251	C₂×D₁₃	—	2	1	no	—
252	C₂×D₁₃	—	2	1	no	—
253	C₂×D₁₃	—	2	1	no	—
254	C₂×D₁₃	—	4	4	no	—
255	C₂×D₁₃	C₄×M₁₆	1	2	yes	—
256	C₄×C₁₃	—	2	1	no	—
257	C₄×C₁₃	—	2	1	no	—
258	C₄×C₁₃	#405	1	2	yes	—
259	C₄×C₁₃	C₂²×M₁₆	1	2	yes	—
260	C₄×C₁₃	C₂×#131	1	2	yes	—
261	C₄×C₁₃	#568	1	2	yes	—
262	Dic₁₃	—	2	1	no	—
263	Dic₁₃	—	2	1	no	—
264	Dic₁₃	—	2	1	no	—
265	Dic₁₃	—	2	1	no	—
266	Dic₁₃	—	2	1	no	—
267	Dic₁₃	C₄×M₁₆	1	2	yes	—
268	C₂³×C₄	—	13	1	no	—
269	C₂³×C₄	—	13	1	no	—
270	C₂³×C₄	—	13	1	no	—
271	C₂×M₁₆	—	13	2	no	—
272	C₂×M₁₆	—	13	2	no	—
273	C₂×M₁₆	—	13	2	no	—
274	C₂×M₁₆	—	13	2	no	—
275	C₂×M₁₆	—	13	2	no	—
276	C₂×M₁₆	—	26	8	no	—
277	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
278	C₂²×C₈	—	13	2	no	—
279	C₂²×C₈	—	13	4	no	—
280	C₂²×C₈	C₄×D₁₃	1	2	yes	—
281	C₂×C₄²	—	13	1	no	—
282	C₂×C₄²	—	13	1	no	—
283	C₂×C₄²	—	13	1	no	—
284	C₂×C₄²	—	13	1	no	—
285	C₂×C₄²	—	13	1	no	—
286	C₂×C₄²	—	13	1	no	—
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	C₂²×D₁₃	1	1	yes	characteristic
293	C₄⋊C₈	—	13	4	no	—
294	C₄⋊C₈	—	13	4	no	—
295	C₄⋊C₈	—	13	4	no	—
296	C₄⋊C₈	—	13	2	no	—
297	C₄⋊C₈	C₄×D₁₃	1	2	yes	—
298	C₂²⋊C₈	—	13	2	no	—
299	C₂²⋊C₈	—	13	4	no	—
300	C₂²⋊C₈	—	13	4	no	—
301	C₂²⋊C₈	—	13	4	no	—
302	C₂²⋊C₈	C₄×D₁₃	1	2	yes	—
303	#97	—	13	2	no	—
304	#97	—	13	2	no	—
305	#97	—	13	2	no	—
306	#97	—	13	2	no	—
307	#97	—	13	2	no	—
308	#97	C₄×D₁₃	1	2	yes	—
309	C₄×C₈	—	13	4	no	—
310	C₄×C₈	—	13	2	no	—
311	C₄×C₈	—	13	1	no	—
312	C₄×C₈	—	13	2	no	—
313	C₄×C₈	—	13	1	no	—
314	C₄×C₈	—	13	2	no	—
315	C₄×C₈	C₄×D₁₃	1	2	yes	—
316	C₄×C₈	C₂²×D₁₃	1	2	yes	—
317	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
318	C₄×C₈	C₂²×D₁₃	1	2	yes	—
319	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
320	C₂×C₁₃	—	2	2	no	—
321	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
322	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
323	C₂×C₁₃	#2873	1	1	yes	characteristic
324	D₁₃	—	2	2	no	—
325	D₁₃	—	4	1	no	—
326	C₂⁴	—	13	1	no	—
327	C₂²×C₄	—	13	1	no	—
328	C₂²×C₄	—	13	1	no	—
329	C₂²×C₄	—	13	1	no	—
330	C₂²×C₄	—	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	—	26	4	no	—
343	C₂²×C₄	—	26	4	no	—
344	C₂²×C₄	—	52	2	no	—
345	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
346	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
347	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
348	M₁₆	—	2	4	no	—
349	M₁₆	—	13	8	no	—
350	M₁₆	—	26	4	no	—
351	M₁₆	—	26	4	no	—
352	M₁₆	—	26	4	no	—
353	M₁₆	—	26	4	no	—
354	C₂×C₈	—	2	4	no	—
355	C₂×C₈	—	13	2	no	—
356	C₂×C₈	—	13	2	no	—
357	C₂×C₈	—	13	4	no	—
358	C₂×C₈	—	13	4	no	—
359	C₂×C₈	—	26	4	no	—
360	C₂×C₈	—	52	4	no	—
361	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
362	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
363	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
364	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
365	C₄²	—	13	1	no	—
366	C₄²	—	13	1	no	—
367	C₄²	—	13	1	no	—
368	C₄²	—	13	1	no	—
369	C₄²	—	13	1	no	—
370	C₄²	—	13	1	no	—
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	C₂×C₄×D₁₃	1	1	yes	characteristic
378	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
379	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
380	C₄²	C₂³×D₁₃	1	1	yes	characteristic
381	C₁₃	#17327	1	1	yes	characteristic, complemented, Sylow
382	C₂³	—	13	1	no	—
383	C₂³	—	13	1	no	—
384	C₂³	—	26	2	no	—
385	C₂³	—	26	2	no	—
386	C₂³	—	52	1	no	—
387	C₂³	C₄²×D₁₃	1	1	yes	characteristic
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	13	1	no	—
391	C₂×C₄	—	13	4	no	—
392	C₂×C₄	—	13	1	no	—
393	C₂×C₄	—	13	1	no	—
394	C₂×C₄	—	13	1	no	—
395	C₂×C₄	—	13	1	no	—
396	C₂×C₄	—	13	1	no	—
397	C₂×C₄	—	26	2	no	—
398	C₂×C₄	—	26	2	no	—
399	C₂×C₄	—	26	2	no	—
400	C₂×C₄	—	26	2	no	—
401	C₂×C₄	—	26	2	no	—
402	C₂×C₄	—	26	2	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	—	52	1	no	—
409	C₂×C₄	—	52	1	no	—
410	C₂×C₄	—	52	1	no	—
411	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
412	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
413	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
414	C₂×C₄	#88155	1	4	yes	—
415	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
416	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
417	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
418	C₈	—	2	4	no	—
419	C₈	—	2	2	no	—
420	C₈	—	2	4	no	—
421	C₈	—	13	4	no	—
422	C₈	—	26	4	no	—
423	C₈	—	26	2	no	—
424	C₈	—	26	4	no	—
425	C₈	M₁₆×D₁₃	1	4	yes	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	13	2	no	—
429	C₂²	—	26	1	no	—
430	C₂²	—	26	1	no	—
431	C₂²	—	26	1	no	—
432	C₂²	—	26	1	no	—
433	C₂²	—	26	1	no	—
434	C₂²	—	52	4	no	—
435	C₂²	#11718350	1	2	yes	—
436	C₂²	C₂×C₄²×D₁₃	1	1	yes	characteristic
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	13	2	no	—
440	C₄	—	26	1	no	—
441	C₄	—	26	1	no	—
442	C₄	—	26	1	no	—
443	C₄	—	26	1	no	—
444	C₄	—	26	1	no	—
445	C₄	#11718350	1	2	yes	—
446	C₄	C₂×#88155	1	2	yes	—
447	C₄	C₂×M₁₆×D₁₃	1	2	yes	—
448	C₄	#11719455	1	2	yes	—
449	C₂	—	2	2	no	—
450	C₂	—	26	2	no	—
451	C₂	—	52	1	no	—
452	C₂	C₄×M₁₆×D₁₃	1	1	yes	characteristic
453	C₂	C₂×#11718350	1	1	yes	characteristic
454	C₂	#13123252	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₈×C₁₃×M₁₆	C₂
prime radical	C₂³×D₁₃	C₄²
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₈×M₁₆	D₁₃
hypocenter	C₁₃	#17327
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
4. #13113132	C₂	semidirect
5. #13113130	C₂	semidirect
6. #13113125	C₂	semidirect
7. #13113124	C₂	semidirect
8. #13113123	C₂	semidirect
9. #13113117	C₂	semidirect
10. C₈×#6094	C₂	semidirect
11. C₈×C₁₃×M₁₆	C₂	semidirect
39. C₁₃×#322	C₂²	semidirect
40. C₈²×C₁₃	C₂²	semidirect
41. #11718047	C₂²	semidirect
42. #11718046	C₂²	semidirect
43. #11718046	C₂²	semidirect
44. #11718046	C₂²	semidirect
45. #11718046	C₂²	semidirect
46. C₈×#1055	C₂²	semidirect
153. #6094	M₁₆	semidirect
165. C₈×M₁₆	D₁₃	semidirect
242. #322	C₂×D₁₃	semidirect
244. C₈²	C₂×D₁₃	semidirect
381. C₁₃	#17327	semidirect

Maximal subgroups

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

subgroup	index
#13123467	2
D₁₃×#431	2
C₂×C₄×#6094	2
#13113132	2
#13113130	2
#13113125	2
#13113124	2
#13113123	2
#13113117	2
C₈×#6094	2
C₈×C₁₃×M₁₆	2
#17327	13