Subgroups — #15861770

Order 3328.

890 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718501	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718500	C₂	1	1	yes	maximal, characteristic
3	#13117333	C₂	1	1	yes	maximal, characteristic
4	#13114710	C₂	1	1	yes	maximal, characteristic, complemented
5	#13114707	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×#6101	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114697	C₂	1	1	yes	maximal, characteristic, complemented
8	#13114695	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114695	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₄⋊#1055	C₂	1	1	yes	maximal, characteristic, complemented
11	#13114619	C₂	1	1	yes	maximal, characteristic
12	#13114616	C₂	1	1	yes	maximal, characteristic
13	C₈×#6103	C₂	1	1	yes	maximal, characteristic
14	#13114606	C₂	1	1	yes	maximal, characteristic
15	C₄×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#6094	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
18	C₂×#88126	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₄³×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×#88060	C₂²	1	1	yes	characteristic
25	C₂×#88060	C₂²	1	1	yes	characteristic
26	C₂×#88055	C₂²	1	1	yes	characteristic
27	C₂×#88055	C₂²	1	1	yes	characteristic
28	C₂×#88055	C₂²	1	1	yes	characteristic
29	C₂×#88054	C₂²	1	1	yes	characteristic
30	C₂×#88054	C₂²	1	1	yes	characteristic
31	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
34	#11718601	C₄	1	2	yes	—
35	#11718601	C₄	1	2	yes	—
36	C₄×#6103	C₂²	1	1	yes	characteristic
37	C₄×#6103	C₂²	1	1	yes	characteristic
38	#11718594	C₄	1	2	yes	—
39	#11718594	C₄	1	2	yes	—
40	#11718593	C₂²	1	1	yes	characteristic
41	C₄×#6101	C₂²	1	1	yes	characteristic
42	C₄×#6101	C₂²	1	1	yes	characteristic
43	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
45	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
46	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
47	#11718501	C₄	1	8	yes	complemented
48	#11718500	C₄	1	8	yes	complemented
49	C₁₃×#336	C₂²	1	1	yes	characteristic
50	C₁₃×#336	C₂²	1	1	yes	characteristic
51	#11718142	C₂²	1	1	yes	characteristic
52	#11718142	C₂²	1	1	yes	characteristic
53	#11718142	C₂²	1	1	yes	characteristic
54	#11718142	C₂²	1	1	yes	characteristic
55	#11718116	C₂²	1	1	yes	characteristic
56	#11718116	C₂²	1	1	yes	characteristic
57	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
63	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	C₂×#6103	C₂×C₄	1	2	yes	—
68	C₂×#6103	C₂×C₄	1	2	yes	—
69	C₂×#6103	C₂×C₄	1	1	yes	characteristic
70	C₂×#6103	C₂×C₄	1	1	yes	characteristic
71	C₂×#6101	C₂×C₄	1	2	yes	—
72	C₂×#6101	C₂×C₄	1	2	yes	—
73	C₂×#6101	C₂×C₄	1	1	yes	characteristic
74	C₂×#6101	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
76	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
77	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
78	C₂²×#1055	C₂³	1	1	yes	characteristic
79	C₂²×#1055	C₂³	1	1	yes	characteristic
80	C₂²×#1055	C₂³	1	1	yes	characteristic
81	C₂²×#1055	C₂³	1	1	yes	characteristic
82	C₂×#6094	—	4	1	no	—
83	C₂×#6094	—	4	1	no	—
84	C₂×#6094	C₂×C₄	1	4	yes	—
85	C₂×C₈×D₁₃	—	4	1	no	—
86	C₂×C₈×D₁₃	—	4	1	no	—
87	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
88	#88126	C₂×C₄	1	4	yes	—
89	#88126	C₂×C₄	1	4	yes	—
90	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
91	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
92	C₄×C₈×C₁₃	—	4	1	no	—
93	C₄×C₈×C₁₃	—	4	1	no	—
94	#88071	C₂×C₄	1	2	yes	—
95	#88071	C₂×C₄	1	2	yes	—
96	#88071	C₂×C₄	1	2	yes	—
97	#88071	C₂×C₄	1	2	yes	—
98	#88071	C₂×C₄	1	2	yes	—
99	#88071	C₂×C₄	1	2	yes	—
100	#88060	C₂×C₄	1	4	yes	—
101	#88060	C₂×C₄	1	4	yes	—
102	#88055	—	4	1	no	—
103	#88055	—	4	1	no	—
104	#88055	C₂×C₄	1	4	yes	—
105	#88054	C₂×C₄	1	4	yes	—
106	#88054	C₂×C₄	1	4	yes	—
107	C₈×Dic₁₃	—	4	1	no	—
108	C₈×Dic₁₃	—	4	1	no	—
109	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
110	C₄⋊#1055	C₂×C₄	1	4	yes	—
111	C₄⋊#1055	C₂×C₄	1	4	yes	—
112	C₄×#1055	—	4	1	no	—
113	C₄×#1055	—	4	1	no	—
114	#20552	—	13	1	no	maximal, Sylow
115	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
121	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
122	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
123	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₄×D₁₃	—	2	1	no	—
127	C₂×C₄×D₁₃	—	2	1	no	—
128	C₂×C₄×D₁₃	—	2	1	no	—
129	C₂×C₄×D₁₃	—	2	1	no	—
130	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
131	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
132	C₂×C₈×C₁₃	—	2	1	no	—
133	C₂×C₈×C₁₃	—	2	1	no	—
134	C₂×C₈×C₁₃	—	2	1	no	—
135	C₂×C₈×C₁₃	—	2	1	no	—
136	C₂×C₈×C₁₃	—	2	1	no	—
137	C₂×C₈×C₁₃	—	2	1	no	—
138	C₂×C₈×C₁₃	—	2	1	no	—
139	C₂×C₈×C₁₃	—	2	1	no	—
140	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
141	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
142	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
143	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
144	C₄²×C₁₃	—	2	4	no	—
145	C₄²×C₁₃	—	2	4	no	—
146	C₄²×C₁₃	—	2	1	no	—
147	C₄²×C₁₃	—	2	1	no	—
148	C₄²×C₁₃	—	2	1	no	—
149	C₄²×C₁₃	—	2	1	no	—
150	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
151	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
152	#6103	—	2	4	no	—
153	#6103	—	2	4	no	—
154	#6103	C₄²	1	4	yes	—
155	#6103	C₄²	1	4	yes	—
156	#6101	—	2	4	no	—
157	#6101	—	2	4	no	—
158	#6101	C₄²	1	4	yes	—
159	#6101	C₄²	1	4	yes	—
160	C₄×Dic₁₃	—	2	1	no	—
161	C₄×Dic₁₃	—	2	1	no	—
162	C₄×Dic₁₃	—	2	1	no	—
163	C₄×Dic₁₃	—	2	1	no	—
164	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
165	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
166	C₂×#1055	—	2	1	no	—
167	C₂×#1055	—	2	1	no	—
168	C₂×#1055	—	2	1	no	—
169	C₂×#1055	—	2	1	no	—
170	C₂×#1055	—	2	1	no	—
171	C₂×#1055	—	2	1	no	—
172	C₂×#1055	—	2	1	no	—
173	C₂×#1055	—	2	1	no	—
174	C₂×#1055	C₂²×C₄	1	2	yes	—
175	C₂×#1055	C₂²×C₄	1	2	yes	—
176	C₂×#1055	C₂²×C₄	1	2	yes	—
177	C₂×#1055	C₂²×C₄	1	2	yes	—
178	#6094	—	4	4	no	—
179	C₈×D₁₃	—	4	4	no	—
180	C₂×#433	—	13	1	no	—
181	C₂×#424	—	13	1	no	—
182	#2298	—	13	1	no	—
183	#1771	—	13	1	no	—
184	#1771	—	13	1	no	—
185	C₈×C₄⋊C₄	—	13	1	no	—
186	C₈×C₄⋊C₄	—	13	1	no	—
187	#1768	—	13	1	no	—
188	#1768	—	13	1	no	—
189	C₄×C₄⋊C₈	—	13	1	no	—
190	C₄×C₄⋊C₈	D₁₃	1	1	yes	characteristic, complemented
191	#1753	—	13	1	no	—
192	#1753	—	13	1	no	—
193	C₈×C₂²⋊C₄	—	13	1	no	—
194	C₈×C₂²⋊C₄	—	13	1	no	—
195	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
196	C₂²×D₁₃	—	2	1	no	—
197	C₂²×D₁₃	—	2	1	no	—
198	C₂²×D₁₃	—	2	2	no	—
199	C₂²×D₁₃	—	2	2	no	—
200	C₂²×D₁₃	C₂×C₄²	1	2	yes	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
208	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
209	C₂×C₄×C₁₃	#131	1	4	yes	—
210	C₂×C₄×C₁₃	#131	1	4	yes	—
211	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
212	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
213	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
214	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
215	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
216	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
217	C₂×Dic₁₃	—	2	1	no	—
218	C₂×Dic₁₃	—	2	1	no	—
219	C₂×Dic₁₃	—	2	2	no	—
220	C₂×Dic₁₃	—	2	2	no	—
221	C₂×Dic₁₃	—	2	2	no	—
222	C₂×Dic₁₃	—	2	2	no	—
223	C₂×Dic₁₃	—	2	2	no	—
224	C₂×Dic₁₃	—	2	2	no	—
225	C₂×Dic₁₃	—	2	2	no	—
226	C₂×Dic₁₃	—	2	2	no	—
227	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
228	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
229	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
230	C₄×D₁₃	—	2	2	no	—
231	C₄×D₁₃	—	2	2	no	—
232	C₄×D₁₃	—	2	2	no	—
233	C₄×D₁₃	—	2	2	no	—
234	C₈×C₁₃	—	2	2	no	—
235	C₈×C₁₃	—	2	2	no	—
236	C₈×C₁₃	—	2	2	no	—
237	C₈×C₁₃	—	2	2	no	—
238	#1055	—	2	2	no	—
239	#1055	—	2	2	no	—
240	#1055	—	2	2	no	—
241	#1055	—	2	2	no	—
242	C₂²×M₁₆	—	13	1	no	—
243	C₂³×C₈	—	13	1	no	—
244	C₂×#117	—	13	1	no	—
245	#433	—	13	8	no	—
246	#424	—	13	8	no	—
247	C₂×C₄⋊C₈	—	13	1	no	—
248	C₂×C₄⋊C₈	—	13	1	no	—
249	C₂×C₄⋊C₈	—	13	1	no	—
250	C₂×C₄⋊C₈	—	13	1	no	—
251	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
252	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
253	C₂×C₂²⋊C₈	—	13	1	no	—
254	C₂×C₂²⋊C₈	—	13	1	no	—
255	C₂×#97	—	13	1	no	—
256	C₂×#97	—	13	1	no	—
257	C₂×#97	—	13	1	no	—
258	C₂×C₄×C₈	—	13	1	no	—
259	C₂×C₄×C₈	—	13	1	no	—
260	C₂×C₄×C₈	—	13	1	no	—
261	C₂×C₄×C₈	—	13	1	no	—
262	C₂×C₄×C₈	—	13	1	no	—
263	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
264	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
265	#388	—	13	2	no	—
266	#388	—	13	2	no	—
267	#387	—	13	2	no	—
268	#387	—	13	2	no	—
269	C₄×C₄⋊C₄	—	13	1	no	—
270	C₄×C₄⋊C₄	—	13	1	no	—
271	C₄×C₂²⋊C₄	—	13	1	no	—
272	C₄×C₂²⋊C₄	—	13	1	no	—
273	#376	—	13	1	no	—
274	C₄³	C₂×D₁₃	1	1	yes	characteristic
275	#336	—	13	1	no	—
276	#336	—	13	1	no	—
277	#336	—	13	1	no	—
278	#336	—	13	1	no	—
279	#336	—	13	1	no	—
280	#336	—	13	1	no	—
281	#336	C₂×D₁₃	1	1	yes	characteristic
282	#336	C₂×D₁₃	1	1	yes	characteristic
283	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
284	C₂²×C₁₃	#520	1	1	yes	characteristic
285	C₂²×C₁₃	#520	1	1	yes	characteristic
286	C₂²×C₁₃	C₂×#131	1	2	yes	—
287	C₂²×C₁₃	C₂×#131	1	2	yes	—
288	C₂×D₁₃	—	2	2	no	—
289	C₂×D₁₃	—	2	2	no	—
290	C₂×D₁₃	—	2	2	no	—
291	C₂×D₁₃	—	4	2	no	—
292	C₂×D₁₃	—	4	2	no	—
293	C₄×C₁₃	—	2	2	no	—
294	C₄×C₁₃	—	2	2	no	—
295	C₄×C₁₃	—	2	4	no	—
296	C₄×C₁₃	—	2	4	no	—
297	C₄×C₁₃	#518	1	1	yes	characteristic
298	C₄×C₁₃	#519	1	1	yes	characteristic
299	C₄×C₁₃	#520	1	1	yes	characteristic
300	C₄×C₁₃	#520	1	1	yes	characteristic
301	Dic₁₃	—	2	2	no	—
302	Dic₁₃	—	2	2	no	—
303	Dic₁₃	—	2	2	no	—
304	Dic₁₃	—	4	2	no	—
305	Dic₁₃	—	4	2	no	—
306	C₂³×C₄	—	13	1	no	—
307	C₂×M₁₆	—	13	4	no	—
308	C₂×M₁₆	—	52	1	no	—
309	C₂×M₁₆	—	52	1	no	—
310	C₂²×C₈	—	13	1	no	—
311	C₂²×C₈	—	13	1	no	—
312	C₂²×C₈	—	13	1	no	—
313	C₂²×C₈	—	13	1	no	—
314	C₂²×C₈	—	13	4	no	—
315	C₂²×C₈	—	52	1	no	—
316	C₂²×C₈	—	52	1	no	—
317	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
318	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
319	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
320	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
321	#117	—	13	4	no	—
322	#117	—	13	4	no	—
323	C₂×C₄⋊C₄	—	13	1	no	—
324	C₂×C₄⋊C₄	—	13	1	no	—
325	C₂×C₄⋊C₄	—	13	2	no	—
326	C₂×C₄⋊C₄	—	13	2	no	—
327	C₂×C₂²⋊C₄	—	13	1	no	—
328	C₂×C₂²⋊C₄	—	13	1	no	—
329	C₂×C₂²⋊C₄	—	13	2	no	—
330	C₂×C₂²⋊C₄	—	13	2	no	—
331	C₂×C₄²	—	13	1	no	—
332	C₂×C₄²	—	13	1	no	—
333	C₂×C₄²	—	13	1	no	—
334	C₂×C₄²	C₄×D₁₃	1	2	yes	—
335	C₂×C₄²	C₄×D₁₃	1	2	yes	—
336	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
337	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
338	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
339	C₄⋊C₈	—	13	4	no	—
340	C₄⋊C₈	—	13	4	no	—
341	C₄⋊C₈	—	13	4	no	—
342	C₄⋊C₈	—	13	4	no	—
343	C₄⋊C₈	C₄×D₁₃	1	4	yes	—
344	C₄⋊C₈	C₄×D₁₃	1	4	yes	—
345	C₂²⋊C₈	—	13	4	no	—
346	C₂²⋊C₈	—	13	4	no	—
347	#97	—	13	4	no	—
348	#97	—	52	1	no	—
349	#97	—	52	1	no	—
350	C₄×C₈	—	4	1	no	—
351	C₄×C₈	—	4	1	no	—
352	C₄×C₈	—	13	4	no	—
353	C₄×C₈	—	52	1	no	—
354	C₄×C₈	—	52	1	no	—
355	C₄×C₈	—	52	1	no	—
356	C₄×C₈	—	52	1	no	—
357	#95	—	13	2	no	—
358	#95	—	13	2	no	—
359	#95	—	13	2	no	—
360	#95	—	13	2	no	—
361	#95	—	13	2	no	—
362	#95	—	13	2	no	—
363	C₂×C₁₃	#2274	1	1	yes	characteristic
364	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
365	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
366	C₂×C₁₃	#2994	1	2	yes	—
367	C₂×C₁₃	#2994	1	2	yes	—
368	D₁₃	—	4	2	no	—
369	C₂⁴	—	13	1	no	—
370	C₂²×C₄	—	13	1	no	—
371	C₂²×C₄	—	13	1	no	—
372	C₂²×C₄	—	13	1	no	—
373	C₂²×C₄	—	13	2	no	—
374	C₂²×C₄	—	13	2	no	—
375	C₂²×C₄	—	13	2	no	—
376	C₂²×C₄	—	13	2	no	—
377	C₂²×C₄	—	26	1	no	—
378	C₂²×C₄	—	26	1	no	—
379	C₂²×C₄	—	26	1	no	—
380	C₂²×C₄	—	26	1	no	—
381	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
382	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
383	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
384	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
385	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
386	M₁₆	—	52	4	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	13	2	no	—
396	C₂×C₈	—	13	2	no	—
397	C₂×C₈	—	13	2	no	—
398	C₂×C₈	—	13	2	no	—
399	C₂×C₈	—	26	1	no	—
400	C₂×C₈	—	26	1	no	—
401	C₂×C₈	—	26	1	no	—
402	C₂×C₈	—	26	1	no	—
403	C₂×C₈	—	26	1	no	—
404	C₂×C₈	—	26	1	no	—
405	C₂×C₈	—	26	1	no	—
406	C₂×C₈	—	26	1	no	—
407	C₂×C₈	—	52	4	no	—
408	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
409	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
410	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
411	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
412	C₄⋊C₄	—	13	4	no	—
413	C₄⋊C₄	—	13	4	no	—
414	C₄⋊C₄	—	26	4	no	—
415	C₄⋊C₄	—	26	4	no	—
416	C₂²⋊C₄	—	13	4	no	—
417	C₂²⋊C₄	—	13	4	no	—
418	C₂²⋊C₄	—	26	4	no	—
419	C₂²⋊C₄	—	26	4	no	—
420	C₄²	—	2	4	no	—
421	C₄²	—	2	4	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	1	no	—
425	C₄²	—	2	1	no	—
426	C₄²	—	13	2	no	—
427	C₄²	—	13	2	no	—
428	C₄²	—	26	1	no	—
429	C₄²	—	26	1	no	—
430	C₄²	—	26	1	no	—
431	C₄²	—	26	1	no	—
432	C₄²	C₂×C₄×D₁₃	1	2	yes	—
433	C₄²	C₂×C₄×D₁₃	1	2	yes	—
434	C₁₃	#20552	1	1	yes	characteristic, complemented, Sylow
435	C₂³	—	13	2	no	—
436	C₂³	—	26	2	no	—
437	C₂³	—	26	2	no	—
438	C₂³	—	26	1	no	—
439	C₂³	—	26	1	no	—
440	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	13	2	no	—
448	C₂×C₄	—	13	2	no	—
449	C₂×C₄	—	13	2	no	—
450	C₂×C₄	—	26	2	no	—
451	C₂×C₄	—	26	2	no	—
452	C₂×C₄	—	26	1	no	—
453	C₂×C₄	—	26	1	no	—
454	C₂×C₄	—	26	2	no	—
455	C₂×C₄	—	26	2	no	—
456	C₂×C₄	—	26	2	no	—
457	C₂×C₄	—	26	2	no	—
458	C₂×C₄	—	26	2	no	—
459	C₂×C₄	—	26	2	no	—
460	C₂×C₄	—	26	2	no	—
461	C₂×C₄	—	26	2	no	—
462	C₂×C₄	—	26	2	no	—
463	C₂×C₄	—	26	2	no	—
464	C₂×C₄	C₄²×D₁₃	1	2	yes	—
465	C₂×C₄	C₄²×D₁₃	1	2	yes	—
466	C₂×C₄	#88155	1	4	yes	—
467	C₂×C₄	#88161	1	4	yes	—
468	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
469	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
470	C₂×C₄	#88251	1	1	yes	characteristic
471	C₂×C₄	#88254	1	1	yes	characteristic
472	C₂×C₄	#88256	1	1	yes	characteristic
473	C₂×C₄	#88257	1	1	yes	characteristic
474	C₈	—	2	2	no	—
475	C₈	—	2	2	no	—
476	C₈	—	2	2	no	—
477	C₈	—	2	2	no	—
478	C₈	—	26	2	no	—
479	C₈	—	26	2	no	—
480	C₈	—	26	2	no	—
481	C₈	—	26	2	no	—
482	C₂²	—	26	2	no	—
483	C₂²	—	26	2	no	—
484	C₂²	—	26	2	no	—
485	C₂²	—	52	2	no	—
486	C₂²	—	52	2	no	—
487	C₂²	C₂×C₄²×D₁₃	1	1	yes	characteristic
488	C₂²	#11719209	1	1	yes	characteristic
489	C₂²	#11719228	1	1	yes	characteristic
490	C₂²	C₂×#88155	1	2	yes	—
491	C₂²	C₂×#88161	1	2	yes	—
492	C₄	—	2	4	no	—
493	C₄	—	2	4	no	—
494	C₄	—	2	2	no	—
495	C₄	—	2	2	no	—
496	C₄	—	26	2	no	—
497	C₄	—	26	2	no	—
498	C₄	—	26	2	no	—
499	C₄	—	52	2	no	—
500	C₄	—	52	2	no	—
501	C₄	#11719250	1	1	yes	characteristic
502	C₄	#11719251	1	1	yes	characteristic
503	C₄	#11719277	1	1	yes	characteristic
504	C₄	#11719279	1	1	yes	characteristic
505	C₂	—	52	2	no	—
506	C₂	#13117190	1	1	yes	characteristic
507	C₂	C₄×#88155	1	1	yes	characteristic
508	C₂	C₄×#88161	1	1	yes	characteristic
509	C₂	#13123992	1	2	yes	—
510	C₂	#13123998	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator	C₂²×C₁₃	C₂²×C₄²
Fitting	C₄×C₁₃×C₄⋊C₈	C₂
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂³×D₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₄×C₄⋊C₈	D₁₃
hypocenter	C₁₃	#20552
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
4. #13114710	C₂	semidirect
5. #13114707	C₂	semidirect
6. C₈×#6101	C₂	semidirect
7. #13114697	C₂	semidirect
8. #13114695	C₂	semidirect
9. #13114695	C₂	semidirect
10. C₄×C₄⋊#1055	C₂	semidirect
15. C₄×C₁₃×C₄⋊C₈	C₂	semidirect
47. #11718501	C₄	semidirect
48. #11718500	C₄	semidirect
190. C₄×C₄⋊C₈	D₁₃	semidirect
434. C₁₃	#20552	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718501	2
C₂×#11718500	2
#13117333	2
#13114710	2
#13114707	2
C₈×#6101	2
#13114697	2
#13114695	2
C₄×C₄⋊#1055	2
#13114619	2
#13114616	2
C₈×#6103	2
#13114606	2
C₄×C₁₃×C₄⋊C₈	2
#20552	13