Subgroups — #15829616

Order 3328.

1306 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719182	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718586	C₂	1	1	yes	maximal, characteristic, complemented
3	#13113286	C₂	1	4	yes	maximal, complemented
4	#13113260	C₂	1	4	yes	maximal, complemented
5	#13113234	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#423	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#6127	—	2	1	no	—
8	C₂²×C₁₃×M₁₆	—	2	1	no	—
9	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×#88184	—	2	1	no	—
11	C₂×#88184	C₄	1	2	yes	—
12	#11719182	—	2	1	no	—
13	#11719182	—	2	1	no	—
14	#11719182	—	2	1	no	—
15	#11719182	—	2	1	no	—
16	#11719182	C₄	1	2	yes	—
17	#11719182	C₄	1	2	yes	—
18	#11719182	C₂²	1	2	yes	—
19	#11719182	C₂²	1	2	yes	—
20	C₂×#88129	—	2	1	no	—
21	C₂×#88128	C₄	1	1	yes	characteristic
22	C₂×C₄×D₅₂	—	2	1	no	—
23	C₂×C₄×D₅₂	C₂²	1	2	yes	—
24	C₂×#88123	C₄	1	1	yes	characteristic
25	C₁₃×#423	—	2	1	no	—
26	C₁₃×#423	—	2	1	no	—
27	C₁₃×#423	C₂²	1	2	yes	—
28	C₁₃×#423	C₂²	1	2	yes	complemented
29	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
30	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
31	C₂×C₂²⋊#1055	—	2	1	no	—
32	#11718586	—	2	1	no	—
33	#11718586	—	2	1	no	—
34	#11718586	C₂²	1	2	yes	—
35	#11718586	C₂²	1	2	yes	complemented
36	C₂×C₄⋊#1055	—	2	1	no	—
37	C₂×C₄×#1055	C₂²	1	2	yes	complemented
38	#11718075	C₂²	1	16	yes	complemented
39	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
42	C₂²×C₂²⋊D₁₃	—	2	2	no	—
43	C₂×#6127	—	2	2	no	—
44	C₂×#6127	—	2	2	no	—
45	C₂×#6127	—	2	2	no	—
46	C₂×#6127	—	2	2	no	—
47	C₂×#6127	—	4	4	no	—
48	C₂×#6127	—	4	4	no	—
49	C₂²×D₅₂	—	2	1	no	—
50	C₂²×D₅₂	—	2	1	no	—
51	C₂²×D₅₂	C₂×C₄	1	2	yes	—
52	C₂²×C₄×D₁₃	—	2	2	no	—
53	C₂²×Dic₂₆	—	2	1	no	—
54	C₂×C₁₃×M₁₆	—	2	2	no	—
55	C₂×C₁₃×M₁₆	—	2	2	no	—
56	C₂×C₁₃×M₁₆	—	4	4	no	—
57	C₂²×C₈×C₁₃	—	2	2	no	—
58	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	#88184	—	2	2	no	—
71	#88184	—	2	2	no	—
72	#88184	—	2	2	no	—
73	#88184	—	2	2	no	—
74	#88184	—	2	2	no	—
75	#88184	—	2	2	no	—
76	#88184	C₂×C₄	1	4	yes	—
77	#88184	C₂×C₄	1	4	yes	—
78	C₂×#6103	—	2	2	no	—
79	C₂×#6103	—	2	2	no	—
80	C₂×C₄⋊Dic₁₃	—	2	1	no	—
81	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
82	C₂²×#1055	—	2	2	no	—
83	#88129	—	2	2	no	—
84	#88129	—	2	2	no	—
85	#88129	—	2	2	no	—
86	#88129	—	2	2	no	—
87	#88128	—	2	1	no	—
88	#88128	—	2	1	no	—
89	#88128	C₂×C₄	1	2	yes	—
90	#88128	C₂×C₄	1	2	yes	—
91	C₄×D₅₂	—	2	2	no	—
92	C₄×D₅₂	—	2	2	no	—
93	C₄×D₅₂	—	2	2	no	—
94	C₄×D₅₂	—	2	2	no	—
95	C₄×D₅₂	—	2	2	no	—
96	C₄×D₅₂	—	2	2	no	—
97	C₄×D₅₂	C₂×C₄	1	4	yes	—
98	C₄×D₅₂	C₂³	1	4	yes	—
99	#88123	—	2	1	no	—
100	#88123	—	2	1	no	—
101	#88123	C₂×C₄	1	2	yes	—
102	#88123	C₂×C₄	1	2	yes	—
103	C₁₃×C₄⋊C₈	—	2	2	no	—
104	C₁₃×C₄⋊C₈	—	2	2	no	—
105	C₁₃×C₄⋊C₈	—	2	2	no	—
106	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
107	C₂²⋊#1055	—	2	2	no	—
108	C₂²⋊#1055	—	2	2	no	—
109	C₄⋊#1055	—	2	2	no	—
110	C₄⋊#1055	—	2	2	no	—
111	C₄×#1055	—	2	2	no	—
112	C₄×#1055	C₂³	1	4	yes	—
113	#17485	—	13	1	no	maximal, Sylow
114	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
115	C₂³×D₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₃	—	4	2	no	—
117	C₂²×C₄×C₁₃	—	4	2	no	—
118	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	D₈	1	4	yes	—
128	C₂²×C₄×C₁₃	SD₁₆	1	4	yes	—
129	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₂×C₂²⋊D₁₃	—	2	4	no	—
139	C₂×C₂²⋊D₁₃	—	2	4	no	—
140	C₂×C₂²⋊D₁₃	—	4	8	no	—
141	C₂²×Dic₁₃	—	2	2	no	—
142	#6127	—	4	8	no	—
143	#6127	—	4	8	no	—
144	#6127	—	4	4	no	—
145	#6127	—	4	4	no	—
146	#6127	—	4	4	no	—
147	#6127	—	4	4	no	—
148	C₂×D₅₂	—	2	2	no	—
149	C₂×D₅₂	—	2	2	no	—
150	C₂×D₅₂	—	2	2	no	—
151	C₂×D₅₂	—	2	2	no	—
152	C₂×D₅₂	—	2	2	no	—
153	C₂×D₅₂	—	4	4	no	—
154	C₂×D₅₂	—	4	4	no	—
155	C₂×D₅₂	—	4	4	no	—
156	C₂×D₅₂	C₂²×C₄	1	4	yes	—
157	C₂×C₄×D₁₃	—	2	4	no	—
158	C₂×C₄×D₁₃	—	2	4	no	—
159	C₂×C₄×D₁₃	—	4	4	no	—
160	C₂×C₄×D₁₃	—	4	4	no	—
161	C₂×Dic₂₆	—	2	2	no	—
162	C₂×Dic₂₆	—	2	2	no	—
163	C₂×Dic₂₆	—	4	4	no	—
164	C₁₃×M₁₆	—	4	4	no	—
165	C₁₃×M₁₆	—	4	4	no	—
166	C₂×C₈×C₁₃	—	2	4	no	—
167	C₂×C₈×C₁₃	—	4	4	no	—
168	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
169	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
170	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
171	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
172	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
173	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
174	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
175	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
176	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
177	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
184	#6103	—	2	4	no	—
185	#6103	—	2	4	no	—
186	#6103	—	2	4	no	—
187	#6103	—	2	4	no	—
188	C₄⋊Dic₁₃	—	2	2	no	—
189	C₄⋊Dic₁₃	—	2	2	no	—
190	C₄⋊Dic₁₃	—	2	2	no	—
191	C₄⋊Dic₁₃	C₂²×C₄	1	4	yes	—
192	C₂×#1055	—	2	4	no	—
193	C₂×#1055	—	4	4	no	—
194	C₂×#532	—	13	1	no	—
195	C₂×#431	—	13	1	no	—
196	C₂×#423	D₁₃	1	1	yes	characteristic, complemented
197	#1492	—	13	4	no	—
198	#1486	—	13	4	no	—
199	#1480	—	13	4	no	—
200	C₂³×C₁₃	—	4	1	no	—
201	C₂³×C₁₃	—	4	1	no	—
202	C₂³×C₁₃	#102	1	4	yes	—
203	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂²×D₁₃	—	2	4	no	—
207	C₂²×D₁₃	—	4	4	no	—
208	C₂²×D₁₃	—	4	4	no	—
209	C₂²×D₁₃	—	4	4	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	4	1	no	—
217	C₂×C₄×C₁₃	—	4	1	no	—
218	C₂×C₄×C₁₃	—	4	1	no	—
219	C₂×C₄×C₁₃	—	4	1	no	—
220	C₂×C₄×C₁₃	—	4	1	no	—
221	C₂×C₄×C₁₃	—	4	1	no	—
222	C₂×C₄×C₁₃	#102	1	4	yes	—
223	C₂×C₄×C₁₃	#102	1	4	yes	—
224	C₂×C₄×C₁₃	#102	1	4	yes	—
225	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
235	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
236	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
237	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
238	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
239	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
240	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
241	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
243	C₂²⋊D₁₃	—	4	8	no	—
244	C₂²⋊D₁₃	—	4	8	no	—
245	C₂×Dic₁₃	—	2	4	no	—
246	C₂×Dic₁₃	—	4	4	no	—
247	D₅₂	—	2	8	no	—
248	D₅₂	—	4	4	no	—
249	D₅₂	—	4	4	no	—
250	D₅₂	—	4	4	no	—
251	D₅₂	—	4	4	no	—
252	D₅₂	—	4	4	no	—
253	C₄×D₁₃	—	4	4	no	—
254	C₄×D₁₃	—	4	4	no	—
255	C₄×D₁₃	—	4	8	no	—
256	Dic₂₆	—	4	4	no	—
257	Dic₂₆	—	4	4	no	—
258	C₈×C₁₃	—	4	4	no	—
259	#1055	—	4	4	no	—
260	C₂²×#41	—	26	1	no	—
261	C₂²×M₁₆	—	2	1	no	—
262	#532	—	13	2	no	—
263	#532	—	13	2	no	—
264	#532	—	13	2	no	—
265	#532	—	13	2	no	—
266	#532	—	26	1	no	—
267	#532	—	26	1	no	—
268	#532	—	26	1	no	—
269	#532	—	26	1	no	—
270	C₂×C₄⋊Q₈	—	13	1	no	—
271	C₂×#127	—	13	1	no	—
272	C₂×#124	—	26	1	no	—
273	C₂×#121	—	13	2	no	—
274	C₂×#121	—	26	1	no	—
275	C₂×C₄×D₄	—	13	2	no	—
276	C₂×C₄×D₄	—	26	1	no	—
277	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
278	#431	—	13	2	no	—
279	#431	—	13	2	no	—
280	#431	—	26	1	no	—
281	#431	—	26	1	no	—
282	#423	—	2	1	no	—
283	#423	—	2	1	no	—
284	#423	C₂×D₁₃	1	2	yes	—
285	#423	C₂×D₁₃	1	2	yes	complemented
286	C₂×C₄⋊C₈	—	2	1	no	—
287	C₂×C₄⋊C₈	—	26	1	no	—
288	C₂×C₄⋊C₈	C₂×D₁₃	1	2	yes	complemented
289	C₂×C₂²⋊C₈	—	26	1	no	—
290	C₂×C₄×C₈	—	13	2	no	—
291	D₄⋊C₈	—	13	16	no	—
292	C₂²×C₁₃	—	2	1	no	—
293	C₂²×C₁₃	—	2	1	no	—
294	C₂²×C₁₃	—	2	1	no	—
295	C₂²×C₁₃	—	2	1	no	—
296	C₂²×C₁₃	—	2	1	no	—
297	C₂²×C₁₃	—	2	1	no	—
298	C₂²×C₁₃	—	4	4	no	—
299	C₂²×C₁₃	C₂×#102	1	2	yes	—
300	C₂²×C₁₃	C₂×#102	1	2	yes	—
301	C₂²×C₁₃	C₂×#102	1	2	yes	—
302	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
303	C₂×D₁₃	—	4	4	no	—
304	C₂×D₁₃	—	4	4	no	—
305	C₂×D₁₃	—	4	4	no	—
306	C₂×D₁₃	—	8	8	no	—
307	C₄×C₁₃	—	2	1	no	—
308	C₄×C₁₃	—	2	1	no	—
309	C₄×C₁₃	—	2	1	no	—
310	C₄×C₁₃	—	2	1	no	—
311	C₄×C₁₃	—	2	1	no	—
312	C₄×C₁₃	—	2	1	no	—
313	C₄×C₁₃	C₂×#102	1	2	yes	—
314	C₄×C₁₃	C₂×#102	1	2	yes	—
315	C₄×C₁₃	C₂×#102	1	2	yes	—
316	C₄×C₁₃	#421	1	2	yes	—
317	C₄×C₁₃	#568	1	2	yes	—
318	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
319	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
320	Dic₁₃	—	4	4	no	—
321	C₂×#41	—	26	2	no	—
322	C₂×#41	—	26	2	no	—
323	C₂×#41	—	26	2	no	—
324	C₂×#41	—	26	2	no	—
325	C₂×#41	—	52	4	no	—
326	C₂×#41	—	52	4	no	—
327	C₂²×Q₈	—	26	1	no	—
328	C₂²×D₄	—	13	2	no	—
329	C₂²×D₄	—	26	2	no	—
330	C₂²×D₄	—	26	1	no	—
331	C₂²×D₄	—	26	1	no	—
332	C₂³×C₄	—	26	2	no	—
333	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
334	C₂³×C₄	D₅₂	1	1	yes	characteristic
335	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
336	C₂×M₁₆	—	2	2	no	—
337	C₂×M₁₆	—	2	2	no	—
338	C₂×M₁₆	—	4	4	no	—
339	C₂²×C₈	—	2	2	no	—
340	C₂²×C₈	—	26	2	no	—
341	C₄⋊Q₈	—	13	2	no	—
342	C₄⋊Q₈	—	13	2	no	—
343	C₄⋊Q₈	—	26	1	no	—
344	C₄⋊Q₈	—	26	1	no	—
345	#127	—	13	2	no	—
346	#127	—	13	2	no	—
347	#127	—	26	1	no	—
348	#127	—	26	1	no	—
349	#124	—	26	2	no	—
350	#124	—	26	2	no	—
351	#124	—	26	2	no	—
352	#124	—	26	2	no	—
353	#121	—	13	4	no	—
354	#121	—	13	4	no	—
355	#121	—	26	2	no	—
356	#121	—	26	2	no	—
357	#121	—	26	2	no	—
358	#121	—	26	2	no	—
359	#121	—	26	2	no	—
360	#121	—	26	2	no	—
361	C₄×D₄	—	13	4	no	—
362	C₄×D₄	—	13	4	no	—
363	C₄×D₄	—	26	2	no	—
364	C₄×D₄	—	26	2	no	—
365	C₄×D₄	—	26	2	no	—
366	C₄×D₄	—	26	2	no	—
367	C₄×D₄	—	26	2	no	—
368	C₄×D₄	—	26	2	no	—
369	C₂×C₄⋊C₄	—	13	2	no	—
370	C₂×C₄⋊C₄	—	26	1	no	—
371	C₂×C₂²⋊C₄	—	26	2	no	—
372	C₂×C₂²⋊C₄	—	26	2	no	—
373	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
374	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
375	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
376	C₂×C₄²	D₅₂	1	1	yes	characteristic
377	C₂×C₄²	D₅₂	1	1	yes	characteristic
378	C₂×C₄²	D₅₂	1	1	yes	characteristic
379	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
380	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
381	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
382	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
383	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
384	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
385	C₄⋊C₈	—	2	2	no	—
386	C₄⋊C₈	—	2	2	no	—
387	C₄⋊C₈	—	2	2	no	—
388	C₄⋊C₈	—	26	2	no	—
389	C₄⋊C₈	—	26	2	no	—
390	C₄⋊C₈	C₂²×D₁₃	1	4	yes	—
391	C₂²⋊C₈	—	26	2	no	—
392	C₂²⋊C₈	—	26	2	no	—
393	C₄×C₈	—	13	4	no	—
394	C₄×C₈	—	26	2	no	—
395	C₂×C₁₃	—	2	2	no	—
396	C₂×C₁₃	—	2	2	no	—
397	C₂×C₁₃	—	2	2	no	—
398	C₂×C₁₃	#2879	1	1	yes	characteristic
399	C₂×C₁₃	C₂²×#102	1	1	yes	characteristic
400	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
401	D₁₃	—	8	4	no	—
402	C₂⁴	—	26	2	no	—
403	C₂⁴	#6103	1	1	yes	characteristic
404	#41	—	52	4	no	—
405	#41	—	52	4	no	—
406	#41	—	52	4	no	—
407	#41	—	52	4	no	—
408	#41	—	52	8	no	—
409	#41	—	52	8	no	—
410	C₂×Q₈	—	26	2	no	—
411	C₂×Q₈	—	26	2	no	—
412	C₂×Q₈	—	52	4	no	—
413	C₂×D₄	—	13	4	no	—
414	C₂×D₄	—	26	4	no	—
415	C₂×D₄	—	26	4	no	—
416	C₂×D₄	—	26	2	no	—
417	C₂×D₄	—	26	2	no	—
418	C₂×D₄	—	26	2	no	—
419	C₂×D₄	—	26	2	no	—
420	C₂×D₄	—	26	2	no	—
421	C₂×D₄	—	52	4	no	—
422	C₂×D₄	—	52	4	no	—
423	C₂×D₄	—	52	8	no	—
424	C₂×D₄	—	52	4	no	—
425	C₂²×C₄	—	4	2	no	—
426	C₂²×C₄	—	4	2	no	—
427	C₂²×C₄	—	26	2	no	—
428	C₂²×C₄	—	26	4	no	—
429	C₂²×C₄	—	26	4	no	—
430	C₂²×C₄	—	52	4	no	—
431	C₂²×C₄	—	52	4	no	—
432	C₂²×C₄	#6103	1	1	yes	characteristic
433	C₂²×C₄	#6103	1	1	yes	characteristic
434	C₂²×C₄	#6103	1	1	yes	characteristic
435	C₂²×C₄	#6103	1	1	yes	characteristic
436	C₂²×C₄	#6103	1	1	yes	characteristic
437	C₂²×C₄	#6103	1	1	yes	characteristic
438	C₂²×C₄	#6103	1	1	yes	characteristic
439	C₂²×C₄	#6103	1	1	yes	characteristic
440	C₂²×C₄	#6103	1	1	yes	characteristic
441	C₂²×C₄	#6104	1	4	yes	—
442	C₂²×C₄	#6106	1	4	yes	—
443	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
444	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
445	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
446	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
447	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
448	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
449	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
450	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
451	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
452	M₁₆	—	4	4	no	—
453	M₁₆	—	4	4	no	—
454	C₂×C₈	—	2	4	no	—
455	C₂×C₈	—	4	4	no	—
456	C₂×C₈	—	26	4	no	—
457	C₂×C₈	—	52	4	no	—
458	C₄⋊C₄	—	13	4	no	—
459	C₄⋊C₄	—	26	2	no	—
460	C₄⋊C₄	—	26	2	no	—
461	C₄⋊C₄	—	26	2	no	—
462	C₂²⋊C₄	—	26	4	no	—
463	C₂²⋊C₄	—	26	4	no	—
464	C₂²⋊C₄	—	26	4	no	—
465	C₂²⋊C₄	—	26	4	no	—
466	C₄²	#6103	1	1	yes	characteristic
467	C₄²	#6103	1	1	yes	characteristic
468	C₄²	#6103	1	1	yes	characteristic
469	C₄²	#6103	1	1	yes	characteristic
470	C₄²	#6103	1	1	yes	characteristic
471	C₄²	#6103	1	1	yes	characteristic
472	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
473	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
474	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
475	C₄²	C₂×D₅₂	1	1	yes	characteristic
476	C₄²	C₂×D₅₂	1	1	yes	characteristic
477	C₄²	C₂×D₅₂	1	1	yes	characteristic
478	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
479	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
480	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
481	C₄²	C₂³×D₁₃	1	1	yes	characteristic
482	C₁₃	#17485	1	1	yes	characteristic, complemented, Sylow
483	C₂³	—	4	1	no	—
484	C₂³	—	4	1	no	—
485	C₂³	—	26	4	no	—
486	C₂³	—	52	4	no	—
487	C₂³	—	52	4	no	—
488	C₂³	—	52	4	no	—
489	C₂³	#88049	1	4	yes	—
490	C₂³	C₂×#6103	1	1	yes	characteristic
491	C₂³	C₂×#6103	1	1	yes	characteristic
492	C₂³	C₂×#6103	1	1	yes	characteristic
493	Q₈	—	52	4	no	—
494	Q₈	—	52	4	no	—
495	D₄	—	26	8	no	—
496	D₄	—	52	4	no	—
497	D₄	—	52	4	no	—
498	D₄	—	52	8	no	—
499	D₄	—	52	8	no	—
500	D₄	—	52	4	no	—
501	D₄	—	52	4	no	—
502	D₄	—	52	4	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	26	4	no	—
516	C₂×C₄	—	52	4	no	—
517	C₂×C₄	—	52	4	no	—
518	C₂×C₄	—	52	4	no	—
519	C₂×C₄	—	52	8	no	—
520	C₂×C₄	#88049	1	4	yes	—
521	C₂×C₄	#88049	1	4	yes	—
522	C₂×C₄	#88049	1	4	yes	—
523	C₂×C₄	C₂×#6103	1	1	yes	characteristic
524	C₂×C₄	C₂×#6103	1	1	yes	characteristic
525	C₂×C₄	C₂×#6103	1	1	yes	characteristic
526	C₂×C₄	C₂×#6103	1	1	yes	characteristic
527	C₂×C₄	C₂×#6103	1	1	yes	characteristic
528	C₂×C₄	C₂×#6103	1	1	yes	characteristic
529	C₂×C₄	C₂×#6103	1	1	yes	characteristic
530	C₂×C₄	C₂×#6103	1	1	yes	characteristic
531	C₂×C₄	C₂×#6103	1	1	yes	characteristic
532	C₂×C₄	C₂×#6104	1	2	yes	—
533	C₂×C₄	C₂×#6104	1	2	yes	—
534	C₂×C₄	C₂×#6104	1	2	yes	—
535	C₂×C₄	C₂×#6106	1	2	yes	—
536	C₂×C₄	C₂×#6106	1	2	yes	—
537	C₂×C₄	C₂×#6106	1	2	yes	—
538	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
539	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
540	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
541	C₈	—	4	4	no	—
542	C₈	—	52	4	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	4	4	no	—
550	C₂²	—	52	4	no	—
551	C₂²	—	52	4	no	—
552	C₂²	—	52	4	no	—
553	C₂²	—	104	8	no	—
554	C₂²	C₂×#88049	1	2	yes	—
555	C₂²	C₂×#88049	1	2	yes	—
556	C₂²	C₂×#88049	1	2	yes	—
557	C₂²	C₂²×#6103	1	1	yes	characteristic
558	C₄	—	2	1	no	—
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	2	1	no	—
564	C₄	—	52	4	no	—
565	C₄	C₂×#88049	1	2	yes	—
566	C₄	C₂×#88049	1	2	yes	—
567	C₄	C₂×#88049	1	2	yes	—
568	C₄	#11718800	1	2	yes	—
569	C₄	#11719450	1	2	yes	—
570	C₄	C₂²×#6104	1	1	yes	characteristic
571	C₄	C₂²×#6106	1	1	yes	characteristic
572	C₂	—	2	2	no	—
573	C₂	—	2	2	no	—
574	C₂	—	2	2	no	—
575	C₂	—	104	4	no	—
576	C₂	#13123280	1	1	yes	characteristic
577	C₂	C₂²×#88049	1	1	yes	characteristic
578	C₂	C₂×#11718800	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₂×C₁₃×#423	C₂
socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
prime radical	C₂×#11719182	C₂
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₂×#423	D₁₃
hypocenter	C₁₃	#17485
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#423

Complements

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

N	H ≅ G/N	type
2. C₂×#11718586	C₂	semidirect
3. #13113286	C₂	semidirect
4. #13113260	C₂	semidirect
5. #13113234	C₂	semidirect
6. C₂×C₁₃×#423	C₂	semidirect
28. C₁₃×#423	C₂²	semidirect
30. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
35. #11718586	C₂²	semidirect
37. C₂×C₄×#1055	C₂²	semidirect
38. #11718075	C₂²	semidirect
196. C₂×#423	D₁₃	semidirect
285. #423	C₂×D₁₃	semidirect
288. C₂×C₄⋊C₈	C₂×D₁₃	semidirect
482. C₁₃	#17485	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11719182	2
C₂×#11718586	2
#13113286	2
#13113260	2
#13113234	2
C₂×C₁₃×#423	2
#17485	13