Subgroups — #15830097

Order 3328.

1364 conjugacy classes of subgroups.

The subgroup lattice has 570 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	C₄×#88180	C₂	1	1	yes	maximal, characteristic, complemented
3	#13113353	C₂	1	4	yes	maximal, complemented
4	#13113345	C₂	1	4	yes	maximal, complemented
5	#13113332	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#6127	—	2	1	no	—
8	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×#88184	—	2	1	no	—
10	C₂×#88184	C₂²	1	2	yes	—
11	C₂×#88180	—	2	1	no	—
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	complemented
17	#11719182	C₄	1	2	yes	complemented
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, complemented
22	C₂×C₄×D₅₂	—	2	1	no	—
23	C₂×C₄×D₅₂	C₄	1	2	yes	complemented
24	C₂×#88123	C₄	1	1	yes	characteristic, complemented
25	C₁₃×#432	—	2	1	no	—
26	C₁₃×#432	C₂²	1	2	yes	complemented
27	C₁₃×#431	—	2	1	no	—
28	C₁₃×#431	C₂²	1	2	yes	complemented
29	C₁₃×#423	—	2	1	no	—
30	C₁₃×#407	C₂²	1	2	yes	—
31	C₄×C₁₃×M₁₆	—	2	1	no	—
32	C₄×C₂²⋊Dic₁₃	—	2	1	no	—
33	C₄×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
34	C₄×C₄⋊Dic₁₃	—	2	1	no	—
35	C₄×C₄⋊Dic₁₃	C₂²	1	2	yes	complemented
36	#11718593	C₂²	1	2	yes	complemented
37	C₄²×Dic₁₃	—	2	1	no	—
38	#11718062	C₂²	1	16	yes	complemented
39	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₃	C₂³	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	8	no	—
48	C₂²×D₅₂	—	2	1	no	—
49	C₂²×D₅₂	—	2	1	no	—
50	C₂²×D₅₂	C₂×C₄	1	2	yes	—
51	C₂²×C₄×D₁₃	—	2	2	no	—
52	C₂²×Dic₂₆	—	2	1	no	—
53	C₂×C₁₃×M₁₆	—	2	2	no	—
54	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₃	D₄	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	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊Dic₁₃	—	2	2	no	—
67	#88184	—	2	2	no	—
68	#88184	—	2	2	no	—
69	#88184	—	2	2	no	—
70	#88184	—	2	2	no	—
71	#88184	—	2	2	no	—
72	#88184	—	2	2	no	—
73	#88184	C₂×C₄	1	4	yes	—
74	#88184	C₂³	1	4	yes	—
75	C₂×#6103	—	2	2	no	—
76	C₂×#6103	—	2	2	no	—
77	#88180	—	2	8	no	—
78	C₂×C₄⋊Dic₁₃	—	2	1	no	—
79	C₂×C₄⋊Dic₁₃	—	2	2	no	—
80	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
81	C₂×C₄×Dic₁₃	—	2	2	no	—
82	C₂×C₄×Dic₁₃	—	2	2	no	—
83	C₂×C₄×Dic₁₃	—	2	2	no	—
84	#88129	—	2	2	no	—
85	#88129	—	2	2	no	—
86	#88129	—	2	2	no	—
87	#88129	—	2	2	no	—
88	#88128	—	2	1	no	—
89	#88128	—	2	1	no	—
90	#88128	C₂×C₄	1	2	yes	—
91	#88128	C₂×C₄	1	2	yes	—
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	—	2	2	no	—
98	C₄×D₅₂	C₂×C₄	1	4	yes	—
99	C₄×D₅₂	C₂×C₄	1	4	yes	—
100	#88123	—	2	1	no	—
101	#88123	—	2	1	no	—
102	#88123	C₂×C₄	1	2	yes	—
103	#88123	C₂×C₄	1	2	yes	—
104	C₁₃×C₄⋊C₈	—	2	2	no	—
105	C₁₃×C₄⋊C₈	—	2	2	no	—
106	C₁₃×C₂²⋊C₈	—	2	2	no	—
107	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
108	C₁₃×#97	—	2	2	no	—
109	C₄×C₈×C₁₃	—	2	2	no	—
110	#88071	—	2	2	no	—
111	#88071	C₂³	1	4	yes	—
112	#17544	—	13	1	no	maximal, Sylow
113	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂³×D₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	2	4	no	—
116	C₂²×C₄×C₁₃	—	2	4	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	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂×D₄	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	C₂⁴	1	1	yes	characteristic
136	C₂×C₂²⋊D₁₃	—	2	4	no	—
137	C₂×C₂²⋊D₁₃	—	2	4	no	—
138	C₂×C₂²⋊D₁₃	—	4	8	no	—
139	C₂²×Dic₁₃	—	2	2	no	—
140	C₂²×Dic₁₃	—	2	4	no	—
141	#6127	—	4	8	no	—
142	#6127	—	4	8	no	—
143	#6127	—	4	8	no	—
144	#6127	—	4	8	no	—
145	C₂×D₅₂	—	2	2	no	—
146	C₂×D₅₂	—	2	2	no	—
147	C₂×D₅₂	—	2	2	no	—
148	C₂×D₅₂	—	2	2	no	—
149	C₂×D₅₂	—	2	2	no	—
150	C₂×D₅₂	—	4	4	no	—
151	C₂×D₅₂	—	4	4	no	—
152	C₂×D₅₂	—	4	4	no	—
153	C₂×D₅₂	C₂²×C₄	1	4	yes	—
154	C₂×C₄×D₁₃	—	2	4	no	—
155	C₂×C₄×D₁₃	—	2	4	no	—
156	C₂×C₄×D₁₃	—	4	8	no	—
157	C₂×Dic₂₆	—	2	2	no	—
158	C₂×Dic₂₆	—	2	2	no	—
159	C₂×Dic₂₆	—	4	4	no	—
160	C₁₃×M₁₆	—	4	4	no	—
161	C₂×C₈×C₁₃	—	2	4	no	—
162	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
163	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
164	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
165	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
166	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
167	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₂²⋊Dic₁₃	—	2	8	no	—
179	#6103	—	2	4	no	—
180	#6103	—	2	4	no	—
181	#6103	—	2	4	no	—
182	#6103	—	2	4	no	—
183	C₄⋊Dic₁₃	—	2	8	no	—
184	C₄⋊Dic₁₃	—	2	2	no	—
185	C₄⋊Dic₁₃	—	2	2	no	—
186	C₄⋊Dic₁₃	—	2	2	no	—
187	C₄⋊Dic₁₃	C₂²×C₄	1	4	yes	—
188	C₄×Dic₁₃	—	2	8	no	—
189	C₄×Dic₁₃	—	4	4	no	—
190	C₄×Dic₁₃	—	4	4	no	—
191	C₂×#532	—	13	1	no	—
192	#2920	D₁₃	1	1	yes	characteristic, complemented
193	C₄×#117	—	13	1	no	—
194	#1507	—	13	4	no	—
195	#1505	—	13	4	no	—
196	#1502	—	13	4	no	—
197	C₂³×C₁₃	—	2	2	no	—
198	C₂³×C₁₃	—	2	2	no	—
199	C₂³×C₁₃	—	4	1	no	—
200	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
201	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
202	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
203	C₂²×D₁₃	—	2	4	no	—
204	C₂²×D₁₃	—	4	4	no	—
205	C₂²×D₁₃	—	4	4	no	—
206	C₂²×D₁₃	—	4	4	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	2	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	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	4	1	no	—
221	C₂×C₄×C₁₃	—	4	1	no	—
222	C₂×C₄×C₁₃	—	4	1	no	—
223	C₂×C₄×C₁₃	#104	1	4	yes	—
224	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
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	AGL(1,ℤ/8)	1	4	yes	—
235	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
237	C₂²⋊D₁₃	—	4	8	no	—
238	C₂²⋊D₁₃	—	4	8	no	—
239	C₂×Dic₁₃	—	2	8	no	—
240	C₂×Dic₁₃	—	2	4	no	—
241	C₂×Dic₁₃	—	4	4	no	—
242	C₂×Dic₁₃	—	4	4	no	—
243	C₂×Dic₁₃	—	4	4	no	—
244	D₅₂	—	4	4	no	—
245	D₅₂	—	4	4	no	—
246	D₅₂	—	4	4	no	—
247	D₅₂	—	4	4	no	—
248	D₅₂	—	4	4	no	—
249	D₅₂	—	4	4	no	—
250	C₄×D₁₃	—	4	8	no	—
251	C₄×D₁₃	—	4	8	no	—
252	Dic₂₆	—	4	4	no	—
253	Dic₂₆	—	4	4	no	—
254	C₈×C₁₃	—	4	4	no	—
255	C₂²×#41	—	26	1	no	—
256	#532	—	13	2	no	—
257	#532	—	13	2	no	—
258	#532	—	13	2	no	—
259	#532	—	13	2	no	—
260	#532	—	26	1	no	—
261	#532	—	26	1	no	—
262	#532	—	26	1	no	—
263	#532	—	26	1	no	—
264	C₂×C₄⋊Q₈	—	13	1	no	—
265	C₂×#127	—	13	1	no	—
266	C₂×#124	—	26	1	no	—
267	C₂×#121	—	13	2	no	—
268	C₂×#121	—	26	1	no	—
269	C₂×C₄×D₄	—	13	2	no	—
270	C₂×C₄×D₄	—	26	1	no	—
271	C₂×#117	—	26	1	no	—
272	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
273	#432	—	2	1	no	—
274	#432	C₂×D₁₃	1	2	yes	complemented
275	#431	—	2	1	no	—
276	#431	C₂×D₁₃	1	2	yes	complemented
277	#423	—	2	1	no	—
278	#407	C₂×D₁₃	1	2	yes	—
279	C₄×M₁₆	—	2	1	no	—
280	C₄×C₄⋊C₄	—	13	2	no	—
281	C₄×C₄⋊C₄	—	26	1	no	—
282	C₄×C₂²⋊C₄	—	13	2	no	—
283	C₄×C₂²⋊C₄	—	26	1	no	—
284	#376	—	13	2	no	—
285	C₄³	—	26	1	no	—
286	#327	—	13	16	no	—
287	C₂²×C₁₃	—	2	1	no	—
288	C₂²×C₁₃	—	2	1	no	—
289	C₂²×C₁₃	—	2	1	no	—
290	C₂²×C₁₃	—	2	1	no	—
291	C₂²×C₁₃	—	2	1	no	—
292	C₂²×C₁₃	—	2	1	no	—
293	C₂²×C₁₃	—	2	1	no	—
294	C₂²×C₁₃	—	4	4	no	—
295	C₂²×C₁₃	C₂×#104	1	2	yes	—
296	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
297	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
298	C₂×D₁₃	—	4	4	no	—
299	C₂×D₁₃	—	4	4	no	—
300	C₂×D₁₃	—	4	4	no	—
301	C₂×D₁₃	—	8	8	no	—
302	C₄×C₁₃	—	2	1	no	—
303	C₄×C₁₃	—	2	1	no	—
304	C₄×C₁₃	—	2	1	no	—
305	C₄×C₁₃	—	2	1	no	—
306	C₄×C₁₃	—	2	1	no	—
307	C₄×C₁₃	—	2	1	no	—
308	C₄×C₁₃	—	2	1	no	—
309	C₄×C₁₃	#410	1	2	yes	—
310	C₄×C₁₃	#418	1	2	yes	—
311	C₄×C₁₃	#418	1	2	yes	—
312	C₄×C₁₃	C₂×#104	1	2	yes	—
313	C₄×C₁₃	C₂×#104	1	2	yes	—
314	Dic₁₃	—	4	8	no	—
315	Dic₁₃	—	4	4	no	—
316	C₂×#41	—	26	2	no	—
317	C₂×#41	—	26	2	no	—
318	C₂×#41	—	26	2	no	—
319	C₂×#41	—	26	2	no	—
320	C₂×#41	—	52	8	no	—
321	C₂²×Q₈	—	26	1	no	—
322	C₂²×D₄	—	13	2	no	—
323	C₂²×D₄	—	26	2	no	—
324	C₂²×D₄	—	26	1	no	—
325	C₂²×D₄	—	26	1	no	—
326	C₂³×C₄	—	26	2	no	—
327	C₂³×C₄	D₅₂	1	1	yes	characteristic
328	C₂³×C₄	D₅₂	1	1	yes	characteristic
329	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
330	C₂×M₁₆	—	2	2	no	—
331	C₄⋊Q₈	—	13	2	no	—
332	C₄⋊Q₈	—	13	2	no	—
333	C₄⋊Q₈	—	26	1	no	—
334	C₄⋊Q₈	—	26	1	no	—
335	#127	—	13	2	no	—
336	#127	—	13	2	no	—
337	#127	—	26	1	no	—
338	#127	—	26	1	no	—
339	#124	—	26	2	no	—
340	#124	—	26	2	no	—
341	#124	—	26	2	no	—
342	#124	—	26	2	no	—
343	#121	—	13	4	no	—
344	#121	—	13	4	no	—
345	#121	—	26	2	no	—
346	#121	—	26	2	no	—
347	#121	—	26	2	no	—
348	#121	—	26	2	no	—
349	#121	—	26	2	no	—
350	#121	—	26	2	no	—
351	C₄×D₄	—	13	4	no	—
352	C₄×D₄	—	13	4	no	—
353	C₄×D₄	—	26	2	no	—
354	C₄×D₄	—	26	2	no	—
355	C₄×D₄	—	26	2	no	—
356	C₄×D₄	—	26	2	no	—
357	C₄×D₄	—	26	2	no	—
358	C₄×D₄	—	26	2	no	—
359	#117	—	26	8	no	—
360	C₂×C₄⋊C₄	—	13	2	no	—
361	C₂×C₄⋊C₄	—	26	1	no	—
362	C₂×C₄⋊C₄	—	26	2	no	—
363	C₂×C₂²⋊C₄	—	26	2	no	—
364	C₂×C₂²⋊C₄	—	26	2	no	—
365	C₂×C₂²⋊C₄	—	26	2	no	—
366	C₂×C₄²	—	26	2	no	—
367	C₂×C₄²	—	26	2	no	—
368	C₂×C₄²	—	26	2	no	—
369	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
370	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
371	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
372	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
373	C₂×C₄²	D₅₂	1	1	yes	characteristic
374	C₂×C₄²	D₅₂	1	1	yes	characteristic
375	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
376	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
377	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
378	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
379	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
380	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
381	C₄⋊C₈	—	2	2	no	—
382	C₄⋊C₈	—	2	2	no	—
383	C₂²⋊C₈	—	2	2	no	—
384	C₂²⋊C₈	C₂²×D₁₃	1	4	yes	—
385	#97	—	2	2	no	—
386	C₄×C₈	—	2	2	no	—
387	#95	—	13	4	no	—
388	#95	—	26	2	no	—
389	C₂×C₁₃	—	2	2	no	—
390	C₂×C₁₃	—	2	2	no	—
391	C₂×C₁₃	—	4	1	no	—
392	C₂×C₁₃	C₂×#410	1	1	yes	characteristic
393	C₂×C₁₃	C₂×#418	1	1	yes	characteristic
394	C₂×C₁₃	C₂²×#104	1	1	yes	characteristic
395	D₁₃	—	8	4	no	—
396	C₂⁴	—	26	2	no	—
397	C₂⁴	C₂×D₅₂	1	1	yes	characteristic
398	#41	—	52	8	no	—
399	#41	—	52	8	no	—
400	#41	—	52	8	no	—
401	#41	—	52	8	no	—
402	C₂×Q₈	—	26	2	no	—
403	C₂×Q₈	—	26	2	no	—
404	C₂×Q₈	—	52	4	no	—
405	C₂×D₄	—	13	4	no	—
406	C₂×D₄	—	26	4	no	—
407	C₂×D₄	—	26	4	no	—
408	C₂×D₄	—	26	2	no	—
409	C₂×D₄	—	26	2	no	—
410	C₂×D₄	—	26	2	no	—
411	C₂×D₄	—	26	2	no	—
412	C₂×D₄	—	26	2	no	—
413	C₂×D₄	—	52	4	no	—
414	C₂×D₄	—	52	4	no	—
415	C₂×D₄	—	52	8	no	—
416	C₂×D₄	—	52	4	no	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	4	2	no	—
420	C₂²×C₄	—	26	2	no	—
421	C₂²×C₄	—	26	4	no	—
422	C₂²×C₄	—	26	4	no	—
423	C₂²×C₄	—	26	4	no	—
424	C₂²×C₄	—	52	8	no	—
425	C₂²×C₄	#6103	1	1	yes	characteristic
426	C₂²×C₄	#6103	1	1	yes	characteristic
427	C₂²×C₄	#6103	1	1	yes	characteristic
428	C₂²×C₄	#6103	1	1	yes	characteristic
429	C₂²×C₄	#6103	1	1	yes	characteristic
430	C₂²×C₄	#6103	1	1	yes	characteristic
431	C₂²×C₄	#6103	1	1	yes	characteristic
432	C₂²×C₄	#6103	1	1	yes	characteristic
433	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
434	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
436	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
440	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
441	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
442	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
443	M₁₆	—	4	4	no	—
444	C₂×C₈	—	2	4	no	—
445	C₄⋊C₄	—	13	4	no	—
446	C₄⋊C₄	—	26	8	no	—
447	C₄⋊C₄	—	26	2	no	—
448	C₄⋊C₄	—	26	2	no	—
449	C₄⋊C₄	—	26	2	no	—
450	C₂²⋊C₄	—	26	8	no	—
451	C₂²⋊C₄	—	26	4	no	—
452	C₂²⋊C₄	—	26	4	no	—
453	C₂²⋊C₄	—	26	4	no	—
454	C₂²⋊C₄	—	26	4	no	—
455	C₄²	—	26	8	no	—
456	C₄²	—	52	4	no	—
457	C₄²	—	52	4	no	—
458	C₄²	#6103	1	1	yes	characteristic
459	C₄²	#6103	1	1	yes	characteristic
460	C₄²	#6103	1	1	yes	characteristic
461	C₄²	#6103	1	1	yes	characteristic
462	C₄²	#6103	1	1	yes	characteristic
463	C₄²	#6103	1	1	yes	characteristic
464	C₄²	#6103	1	1	yes	characteristic
465	C₄²	#6103	1	1	yes	characteristic
466	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
467	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
468	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
469	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
470	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
471	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
472	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
473	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
474	C₁₃	#17544	1	1	yes	characteristic, complemented, Sylow
475	C₂³	—	2	2	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	4	1	no	—
478	C₂³	—	26	4	no	—
479	C₂³	—	52	4	no	—
480	C₂³	—	52	4	no	—
481	C₂³	—	52	4	no	—
482	C₂³	C₂×#6103	1	1	yes	characteristic
483	C₂³	C₂×#6103	1	1	yes	characteristic
484	C₂³	C₂²×D₅₂	1	1	yes	characteristic
485	Q₈	—	52	4	no	—
486	Q₈	—	52	4	no	—
487	D₄	—	52	4	no	—
488	D₄	—	52	4	no	—
489	D₄	—	52	8	no	—
490	D₄	—	52	8	no	—
491	D₄	—	52	4	no	—
492	D₄	—	52	4	no	—
493	D₄	—	52	4	no	—
494	D₄	—	52	4	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	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	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	26	8	no	—
512	C₂×C₄	—	26	4	no	—
513	C₂×C₄	—	52	8	no	—
514	C₂×C₄	—	52	4	no	—
515	C₂×C₄	—	52	4	no	—
516	C₂×C₄	—	52	4	no	—
517	C₂×C₄	—	52	8	no	—
518	C₂×C₄	#88065	1	4	yes	—
519	C₂×C₄	#88162	1	4	yes	—
520	C₂×C₄	C₂×#6103	1	1	yes	characteristic
521	C₂×C₄	C₂×#6103	1	1	yes	characteristic
522	C₂×C₄	C₂×#6103	1	1	yes	characteristic
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	C₂²×C₄×D₁₃	1	1	yes	characteristic
531	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
532	C₈	—	4	4	no	—
533	C₂²	—	2	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	4	4	no	—
541	C₂²	—	52	4	no	—
542	C₂²	—	52	4	no	—
543	C₂²	—	52	4	no	—
544	C₂²	—	104	8	no	—
545	C₂²	C₂×#88065	1	2	yes	—
546	C₂²	C₂×#88162	1	2	yes	—
547	C₂²	C₂²×#6103	1	1	yes	characteristic
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	2	1	no	—
554	C₄	—	2	1	no	—
555	C₄	—	52	8	no	—
556	C₄	—	52	4	no	—
557	C₄	#11718667	1	2	yes	—
558	C₄	#11718792	1	2	yes	—
559	C₄	#11718792	1	2	yes	—
560	C₄	C₂×#88065	1	2	yes	—
561	C₄	C₂×#88065	1	2	yes	—
562	C₂	—	2	2	no	—
563	C₂	—	2	2	no	—
564	C₂	—	4	1	no	—
565	C₂	—	104	4	no	—
566	C₂	C₂×#11718667	1	1	yes	characteristic
567	C₂	C₂×#11718792	1	1	yes	characteristic
568	C₂	C₂²×#88065	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#6103
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#2920	C₂
socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
prime radical	C₂×#11719182	C₂
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#2920	D₁₃
hypocenter	C₁₃	#17544
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
2. C₄×#88180	C₂	semidirect
3. #13113353	C₂	semidirect
4. #13113345	C₂	semidirect
5. #13113332	C₂	semidirect
6. C₁₃×#2920	C₂	semidirect
16. #11719182	C₄	semidirect
17. #11719182	C₄	semidirect
21. C₂×#88128	C₄	semidirect
23. C₂×C₄×D₅₂	C₄	semidirect
24. C₂×#88123	C₄	semidirect
26. C₁₃×#432	C₂²	semidirect
28. C₁₃×#431	C₂²	semidirect
35. C₄×C₄⋊Dic₁₃	C₂²	semidirect
36. #11718593	C₂²	semidirect
38. #11718062	C₂²	semidirect
192. #2920	D₁₃	semidirect
274. #432	C₂×D₁₃	semidirect
276. #431	C₂×D₁₃	semidirect
474. C₁₃	#17544	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
C₄×#88180	2
#13113353	2
#13113345	2
#13113332	2
C₁₃×#2920	2
#17544	13