Subgroups — #16796737

Order 3328.

1470 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719099	C₂	1	1	yes	maximal, characteristic
2	#13131396	C₂	1	1	yes	maximal, characteristic
3	C₂×#11719089	C₂	1	1	yes	maximal, characteristic
4	C₂×M₁₆×#261	C₂	1	1	yes	maximal, characteristic
5	C₂²×#88100	C₂	1	1	yes	maximal, characteristic
6	#117×#261	C₂	1	1	yes	maximal, characteristic
7	#13130494	C₂	1	2	yes	maximal, complemented
8	#13130492	C₂	1	2	yes	maximal, complemented
9	C₄×#88100	C₂	1	2	yes	maximal, complemented
10	#97×#261	C₂	1	2	yes	maximal, complemented
11	D₁₃×#405	C₂	1	1	yes	maximal, characteristic
12	C₂×#88237	C₂²	1	1	yes	characteristic
13	C₂²×C₄×#261	C₂²	1	1	yes	characteristic
14	C₂×D₁₃⋊M₁₆	C₂²	1	1	yes	characteristic
15	C₂²×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×M₁₆×D₁₃	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
18	D₁₃×#117	C₂²	1	1	yes	characteristic
19	#11719099	C₄	1	8	yes	complemented
20	M₁₆×#261	C₄	1	8	yes	complemented
21	#11719089	C₄	1	8	yes	complemented
22	C₂×#88100	C₄	1	8	yes	complemented
23	C₂×#88100	C₂²	1	1	yes	characteristic
24	C₂×#88100	C₂²	1	1	yes	characteristic
25	C₂×#88100	C₂²	1	1	yes	characteristic
26	C₂×#88100	C₂²	1	1	yes	characteristic
27	C₂×#88100	C₂²	1	2	yes	—
28	C₂×#88100	C₂²	1	2	yes	—
29	C₂×#88100	C₂²	1	2	yes	—
30	C₂×C₈×#261	C₂²	1	2	yes	—
31	C₂×C₈×#261	C₂²	1	2	yes	—
32	C₂×C₈×#261	C₂²	1	2	yes	—
33	C₄⋊C₄×#261	C₄	1	4	yes	—
34	#11719072	C₄	1	4	yes	complemented
35	C₂²⋊C₄×#261	C₄	1	4	yes	—
36	#11719062	C₄	1	4	yes	complemented
37	#11719057	C₂²	1	2	yes	—
38	C₄²×#261	C₂²	1	2	yes	—
39	#11719047	C₂²	1	2	yes	—
40	C₄×D₁₃⋊C₈	C₂²	1	2	yes	—
41	C₁₃×#405	C₄	1	1	yes	characteristic, complemented
42	#11718783	C₄	1	1	yes	characteristic, complemented
43	#11718762	C₄	1	1	yes	characteristic, complemented
44	#11718658	C₄	1	1	yes	characteristic, complemented
45	#11718369	C₄	1	2	yes	complemented
46	D₁₃×#97	C₂²	1	2	yes	—
47	#11718350	C₄	1	2	yes	complemented
48	C₄×C₈×D₁₃	C₂²	1	2	yes	—
49	C₂³×#261	C₂×C₄	1	2	yes	—
50	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
51	C₂×C₂²⋊#261	C₂×C₄	1	2	yes	—
52	C₂×#6122	C₂×C₄	1	2	yes	—
53	C₂²×#1057	C₂×C₄	1	2	yes	—
54	#88237	C₂×C₄	1	4	yes	—
55	#88237	C₂×C₄	1	4	yes	—
56	C₂×C₄⋊#261	C₂×C₄	1	2	yes	—
57	C₂×C₄×#261	C₂×C₄	1	8	yes	—
58	C₂×C₄×#261	C₂×C₄	1	2	yes	—
59	C₂×C₄×#261	C₂×C₄	1	4	yes	—
60	C₂×C₄×#261	C₂×C₄	1	4	yes	—
61	C₂×C₄×#261	C₂³	1	1	yes	characteristic
62	C₂×C₄×#261	C₂³	1	2	yes	—
63	C₂×C₄×#261	C₂³	1	1	yes	characteristic
64	D₁₃⋊M₁₆	C₂×C₄	1	4	yes	—
65	D₁₃⋊M₁₆	C₂×C₄	1	4	yes	—
66	C₂×#6118	C₂×C₄	1	2	yes	—
67	C₂×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
68	C₂×D₁₃⋊C₈	C₂×C₄	1	4	yes	—
69	C₂×D₁₃⋊C₈	C₂×C₄	1	4	yes	—
70	C₂×D₁₃⋊C₈	C₂³	1	1	yes	characteristic
71	C₂×D₁₃⋊C₈	C₂³	1	2	yes	—
72	C₂×D₁₃⋊C₈	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
74	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
75	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
76	#88180	C₂×C₄	1	1	yes	characteristic
77	C₂×#6099	C₂×C₄	1	1	yes	characteristic
78	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
79	M₁₆×D₁₃	C₂×C₄	1	4	yes	—
80	M₁₆×D₁₃	C₂×C₄	1	4	yes	—
81	C₂×#6094	C₂×C₄	1	2	yes	—
82	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
83	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
84	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
85	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
86	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
88	C₂×C₈×D₁₃	C₂³	1	2	yes	—
89	#88146	C₂×C₄	1	2	yes	—
90	C₄⋊C₄×D₁₃	C₂×C₄	1	2	yes	—
91	C₂²⋊C₄×D₁₃	C₂×C₄	1	2	yes	—
92	#88131	C₂×C₄	1	2	yes	—
93	#88126	C₂×C₄	1	2	yes	—
94	C₄²×D₁₃	C₂³	1	2	yes	—
95	(C₂×#261)⋊C₄	C₂×C₄	1	8	yes	—
96	#88110	C₂×C₄	1	8	yes	complemented
97	C₄×#1057	C₂×C₄	1	8	yes	complemented
98	#88100	C₂×C₄	1	4	yes	—
99	#88100	C₂×C₄	1	4	yes	—
100	#88100	C₂×C₄	1	4	yes	—
101	#88100	C₂×C₄	1	4	yes	—
102	#88100	C₂×C₄	1	8	yes	—
103	#88100	C₂×C₄	1	8	yes	complemented
104	#88100	C₂×C₄	1	8	yes	complemented
105	C₈×#261	C₂×C₄	1	8	yes	—
106	C₈×#261	C₂×C₄	1	8	yes	complemented
107	C₈×#261	C₂×C₄	1	8	yes	complemented
108	C₁₃×#97	C₂×C₄	1	2	yes	complemented
109	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	complemented
110	#88055	C₂×C₄	1	2	yes	complemented
111	#88055	C₂×C₄	1	2	yes	complemented
112	C₈×Dic₁₃	C₂×C₄	1	2	yes	complemented
113	C₈×Dic₁₃	C₂×C₄	1	2	yes	complemented
114	#88043	C₂×C₄	1	2	yes	complemented
115	C₄×#1055	C₂×C₄	1	2	yes	complemented
116	#20331	—	13	1	no	maximal, Sylow
117	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂²×#261	—	4	4	no	—
119	C₂²×#261	C₄²	1	8	yes	—
120	C₂²×#261	C₂²×C₄	1	2	yes	—
121	C₂²×#261	C₂²×C₄	1	4	yes	—
122	C₂²×#261	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₄×D₁₃	C₂²×C₄	1	4	yes	—
126	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
130	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
131	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
132	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
133	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
134	C₂²⋊#261	C₄²	1	8	yes	—
135	#6122	C₄²	1	8	yes	complemented
136	C₂×#1057	C₄²	1	8	yes	complemented
137	C₂×#1057	C₂²×C₄	1	2	yes	—
138	C₂×#1057	C₂²×C₄	1	4	yes	—
139	C₂×#1057	C₂²×C₄	1	2	yes	—
140	C₄⋊#261	C₄²	1	8	yes	—
141	C₄×#261	—	4	8	no	—
142	C₄×#261	C₄²	1	8	yes	—
143	C₄×#261	C₂²×C₄	1	2	yes	—
144	C₄×#261	C₂²×C₄	1	4	yes	—
145	C₄×#261	C₂²×C₄	1	4	yes	—
146	C₄×#261	C₂²×C₄	1	2	yes	—
147	C₄×#261	C₂²×C₄	1	2	yes	—
148	C₄×#261	C₂²×C₄	1	2	yes	—
149	#6118	C₄²	1	8	yes	complemented
150	D₁₃⋊C₈	C₄²	1	8	yes	complemented
151	D₁₃⋊C₈	C₂²×C₄	1	4	yes	—
152	D₁₃⋊C₈	C₂²×C₄	1	2	yes	—
153	D₁₃⋊C₈	C₂²×C₄	1	4	yes	—
154	D₁₃⋊C₈	C₂²×C₄	1	2	yes	—
155	D₁₃⋊C₈	C₂²×C₄	1	2	yes	—
156	D₁₃⋊C₈	C₂²×C₄	1	2	yes	—
157	C₁₃×M₁₆	C₄²	1	4	yes	complemented
158	C₂×C₈×C₁₃	C₄²	1	4	yes	complemented
159	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
161	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
162	C₁₃×C₄⋊C₄	C₄²	1	2	yes	—
163	C₁₃×C₂²⋊C₄	C₄²	1	2	yes	—
164	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
165	C₂²⋊Dic₁₃	C₄²	1	2	yes	—
166	#6103	C₄²	1	4	yes	—
167	C₄⋊Dic₁₃	C₄²	1	2	yes	—
168	#6101	C₄²	1	4	yes	—
169	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
170	C₄×Dic₁₃	C₂²×C₄	1	4	yes	—
171	#6099	C₄²	1	4	yes	complemented
172	C₂×#1055	C₄²	1	4	yes	complemented
173	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
174	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
175	C₂×#1055	C₂²×C₄	1	2	yes	—
176	#6094	C₄²	1	8	yes	complemented
177	C₈×D₁₃	C₄²	1	4	yes	complemented
178	C₈×D₁₃	C₄²	1	4	yes	complemented
179	C₈×D₁₃	C₂²×C₄	1	4	yes	—
180	C₈×D₁₃	C₂²×C₄	1	2	yes	—
181	C₈×D₁₃	C₂²×C₄	1	4	yes	—
182	C₈×D₁₃	C₂²×C₄	1	2	yes	—
183	C₈×D₁₃	C₂²×C₄	1	2	yes	—
184	C₈×D₁₃	C₂²×C₄	1	2	yes	—
185	C₂×#405	—	13	1	no	—
186	C₂×#405	—	13	1	no	—
187	C₂×#405	—	13	1	no	—
188	C₂×#405	—	13	1	no	—
189	C₂×C₄×M₁₆	—	13	1	no	—
190	C₂²×#97	—	13	1	no	—
191	C₄×#117	—	13	1	no	—
192	#1726	—	13	2	no	—
193	#1726	—	13	2	no	—
194	C₄×#97	—	13	2	no	—
195	C₄×#97	—	13	2	no	—
196	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
197	C₂²×D₁₃	—	2	4	no	—
198	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
199	C₂²×D₁₃	C₂×C₄²	1	2	yes	—
200	C₂²×D₁₃	C₂×C₄²	1	2	yes	—
201	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
202	C₂×#261	—	2	4	no	—
203	C₂×#261	—	2	8	no	—
204	C₂×#261	—	2	4	no	—
205	C₂×#261	—	4	8	no	—
206	C₂×#261	C₂×C₄²	1	4	yes	—
207	C₂×#261	C₂×C₄²	1	4	yes	—
208	C₂×#261	C₂×C₄²	1	8	yes	—
209	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
210	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
212	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
213	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
214	C₂×Dic₁₃	C₂×C₄²	1	4	yes	—
215	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
216	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
217	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
218	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
219	C₄×D₁₃	—	2	8	no	—
220	C₄×D₁₃	C₂×C₄²	1	2	yes	—
221	C₄×D₁₃	C₂×C₄²	1	2	yes	—
222	C₄×D₁₃	C₂×C₄²	1	2	yes	—
223	C₄×D₁₃	C₂×C₄²	1	2	yes	—
224	C₄×D₁₃	C₂×C₄²	1	2	yes	—
225	C₄×D₁₃	C₂×C₄²	1	2	yes	—
226	C₄×D₁₃	C₂³×C₄	1	1	yes	characteristic
227	C₄×D₁₃	C₂³×C₄	1	1	yes	characteristic
228	C₄×D₁₃	C₂³×C₄	1	1	yes	characteristic
229	C₄×D₁₃	C₂³×C₄	1	1	yes	characteristic
230	#1057	C₂×C₄²	1	4	yes	—
231	#1057	C₂×C₄²	1	4	yes	—
232	#1057	C₂×C₄²	1	8	yes	—
233	C₈×C₁₃	C₂×C₄²	1	2	yes	—
234	C₈×C₁₃	C₂×C₄²	1	2	yes	—
235	C₈×C₁₃	C₂×C₄²	1	4	yes	—
236	#1055	C₂×C₄²	1	2	yes	—
237	#1055	C₂×C₄²	1	2	yes	—
238	#1055	C₂×C₄²	1	4	yes	—
239	C₂²×M₁₆	—	13	1	no	—
240	C₂²×M₁₆	—	13	1	no	—
241	C₂³×C₈	—	13	1	no	—
242	C₂³×C₈	—	13	1	no	—
243	C₂×#117	—	13	1	no	—
244	C₂×#117	—	13	1	no	—
245	C₂²×C₄²	—	13	1	no	—
246	#405	—	13	4	no	—
247	#405	—	13	4	no	—
248	#405	—	13	8	no	—
249	#405	—	13	8	no	—
250	#405	—	13	1	no	—
251	#405	—	13	1	no	—
252	#405	—	13	1	no	—
253	#405	—	13	2	no	—
254	#405	—	13	2	no	—
255	#405	#261	1	1	yes	characteristic, complemented
256	C₄×M₁₆	—	13	8	no	—
257	C₂×#97	—	13	8	no	—
258	C₂×#97	—	13	1	no	—
259	C₂×#97	—	13	1	no	—
260	C₂×#97	—	13	1	no	—
261	C₂×#97	—	13	1	no	—
262	C₂×#97	—	13	2	no	—
263	C₂×#97	—	13	2	no	—
264	C₂×#97	—	13	2	no	—
265	C₂×#97	—	13	2	no	—
266	C₂×#97	—	13	2	no	—
267	C₂×C₄×C₈	—	13	2	no	—
268	C₂×C₄×C₈	—	13	2	no	—
269	C₂×C₄×C₈	—	13	2	no	—
270	C₂×C₄×C₈	—	13	2	no	—
271	C₂×C₄×C₈	—	13	2	no	—
272	C₄×C₄⋊C₄	—	13	4	no	—
273	C₄×C₂²⋊C₄	—	13	4	no	—
274	#376	—	13	2	no	—
275	C₄³	—	13	2	no	—
276	C₂²×C₁₃	—	2	2	no	—
277	C₂²×C₁₃	C₄³	1	2	yes	—
278	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
279	C₂×D₁₃	—	2	2	no	—
280	C₂×D₁₃	—	2	4	no	—
281	C₂×D₁₃	—	2	4	no	—
282	C₂×D₁₃	C₄³	1	2	yes	—
283	C₂×D₁₃	C₂²×C₄²	1	1	yes	characteristic
284	C₂×D₁₃	C₂²×C₄²	1	1	yes	characteristic
285	C₂×D₁₃	#568	1	4	yes	—
286	#261	—	2	4	no	—
287	#261	—	2	4	no	—
288	#261	—	2	8	no	—
289	C₄×C₁₃	—	2	4	no	—
290	C₄×C₁₃	C₄³	1	2	yes	—
291	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
292	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
293	Dic₁₃	—	2	4	no	—
294	Dic₁₃	C₄³	1	2	yes	—
295	Dic₁₃	C₂²×C₄²	1	1	yes	characteristic
296	Dic₁₃	C₂²×C₄²	1	1	yes	characteristic
297	C₂³×C₄	—	13	1	no	—
298	C₂³×C₄	—	13	2	no	—
299	C₂×M₁₆	—	13	4	no	—
300	C₂×M₁₆	—	13	2	no	—
301	C₂×M₁₆	—	13	4	no	—
302	C₂×M₁₆	—	13	2	no	—
303	C₂×M₁₆	—	13	1	no	—
304	C₂×M₁₆	—	13	4	no	—
305	C₂×M₁₆	—	13	4	no	—
306	C₂×M₁₆	—	13	2	no	—
307	C₂×M₁₆	C₂×#261	1	1	yes	characteristic
308	C₂²×C₈	—	13	1	no	—
309	C₂²×C₈	—	13	1	no	—
310	C₂²×C₈	—	13	4	no	—
311	C₂²×C₈	—	13	4	no	—
312	C₂²×C₈	—	13	2	no	—
313	C₂²×C₈	—	13	2	no	—
314	C₂²×C₈	—	13	2	no	—
315	C₂²×C₈	—	13	1	no	—
316	C₂²×C₈	—	13	4	no	—
317	C₂²×C₈	—	13	4	no	—
318	C₂²×C₈	—	13	1	no	—
319	C₂²×C₈	—	13	1	no	—
320	C₂²×C₈	—	13	1	no	—
321	C₂²×C₈	—	13	1	no	—
322	C₂²×C₈	—	13	2	no	—
323	C₂²×C₈	C₂×#261	1	1	yes	characteristic
324	#117	—	13	4	no	—
325	#117	—	13	4	no	—
326	#117	—	13	1	no	—
327	#117	—	13	2	no	—
328	#117	—	13	2	no	—
329	#117	—	13	2	no	—
330	#117	C₂×#261	1	1	yes	characteristic
331	C₂×C₄⋊C₄	—	13	2	no	—
332	C₂×C₄⋊C₄	—	13	2	no	—
333	C₂×C₂²⋊C₄	—	13	2	no	—
334	C₂×C₂²⋊C₄	—	13	2	no	—
335	C₂×C₄²	—	13	2	no	—
336	C₂×C₄²	—	13	1	no	—
337	C₂×C₄²	—	13	1	no	—
338	C₂×C₄²	—	13	2	no	—
339	C₂×C₄²	—	13	4	no	—
340	C₂×C₄²	—	13	4	no	—
341	C₂×C₄²	—	13	2	no	—
342	C₂×C₄²	—	13	8	no	—
343	#97	—	13	4	no	—
344	#97	—	13	4	no	—
345	#97	—	13	4	no	—
346	#97	—	13	4	no	—
347	#97	—	13	8	no	—
348	#97	—	13	8	no	—
349	#97	—	13	8	no	—
350	#97	—	13	8	no	—
351	#97	—	13	2	no	—
352	#97	—	13	2	no	—
353	#97	—	13	2	no	—
354	#97	C₂×#261	1	2	yes	complemented
355	C₄×C₈	—	13	8	no	—
356	C₄×C₈	—	13	8	no	—
357	C₄×C₈	—	13	8	no	—
358	C₄×C₈	—	13	8	no	—
359	C₄×C₈	—	13	2	no	—
360	C₄×C₈	—	13	2	no	—
361	C₄×C₈	—	13	2	no	—
362	C₄×C₈	C₂×#261	1	2	yes	complemented
363	#95	—	13	8	no	—
364	C₂×C₁₃	—	2	2	no	—
365	C₂×C₁₃	C₂×C₄³	1	1	yes	characteristic
366	C₂×C₁₃	#2875	1	2	yes	—
367	D₁₃	—	2	2	no	—
368	D₁₃	#2873	1	2	yes	—
369	D₁₃	#2875	1	2	yes	—
370	C₂⁴	—	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	—	13	1	no	—
378	C₂²×C₄	—	13	1	no	—
379	C₂²×C₄	—	13	1	no	—
380	C₂²×C₄	—	13	2	no	—
381	C₂²×C₄	—	13	4	no	—
382	C₂²×C₄	—	13	2	no	—
383	C₂²×C₄	—	13	8	no	—
384	C₂²×C₄	—	13	4	no	—
385	C₂²×C₄	—	52	4	no	—
386	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
387	M₁₆	—	13	8	no	—
388	M₁₆	—	13	8	no	—
389	M₁₆	—	13	4	no	—
390	M₁₆	—	13	8	no	—
391	M₁₆	C₄×#261	1	4	yes	complemented
392	C₂×C₈	—	13	2	no	—
393	C₂×C₈	—	13	2	no	—
394	C₂×C₈	—	13	4	no	—
395	C₂×C₈	—	13	4	no	—
396	C₂×C₈	—	13	4	no	—
397	C₂×C₈	—	13	2	no	—
398	C₂×C₈	—	13	2	no	—
399	C₂×C₈	—	13	2	no	—
400	C₂×C₈	—	13	2	no	—
401	C₂×C₈	—	13	8	no	—
402	C₂×C₈	—	13	8	no	—
403	C₂×C₈	—	13	4	no	—
404	C₂×C₈	—	13	1	no	—
405	C₂×C₈	—	13	2	no	—
406	C₂×C₈	—	13	1	no	—
407	C₂×C₈	—	13	2	no	—
408	C₂×C₈	—	13	4	no	—
409	C₂×C₈	—	13	4	no	—
410	C₂×C₈	—	13	2	no	—
411	C₂×C₈	—	13	2	no	—
412	C₂×C₈	—	13	2	no	—
413	C₂×C₈	—	13	4	no	—
414	C₂×C₈	—	13	4	no	—
415	C₂×C₈	C₄×#261	1	4	yes	complemented
416	C₂×C₈	C₂²×#261	1	1	yes	characteristic
417	C₂×C₈	C₂²×#261	1	2	yes	—
418	C₂×C₈	C₂²×#261	1	1	yes	characteristic
419	C₄⋊C₄	—	13	8	no	—
420	C₄⋊C₄	—	13	4	no	—
421	C₄⋊C₄	—	13	2	no	—
422	C₄⋊C₄	C₄×#261	1	2	yes	—
423	C₂²⋊C₄	—	13	8	no	—
424	C₂²⋊C₄	—	13	2	no	—
425	C₂²⋊C₄	—	13	4	no	—
426	C₂²⋊C₄	C₄×#261	1	2	yes	—
427	C₄²	—	13	2	no	—
428	C₄²	—	13	4	no	—
429	C₄²	—	13	4	no	—
430	C₄²	—	13	2	no	—
431	C₄²	—	13	2	no	—
432	C₄²	—	13	2	no	—
433	C₄²	—	13	8	no	—
434	C₄²	—	13	4	no	—
435	C₄²	—	13	2	no	—
436	C₄²	—	52	8	no	—
437	C₄²	C₂²×#261	1	2	yes	—
438	C₁₃	#20331	1	1	yes	characteristic, complemented, Sylow
439	C₂³	—	13	1	no	—
440	C₂³	—	13	2	no	—
441	C₂³	—	13	2	no	—
442	C₂³	—	13	1	no	—
443	C₂³	—	26	4	no	—
444	C₂³	C₂×C₄×#261	1	1	yes	characteristic
445	C₂×C₄	—	13	2	no	—
446	C₂×C₄	—	13	2	no	—
447	C₂×C₄	—	13	1	no	—
448	C₂×C₄	—	13	1	no	—
449	C₂×C₄	—	13	2	no	—
450	C₂×C₄	—	13	2	no	—
451	C₂×C₄	—	13	2	no	—
452	C₂×C₄	—	13	2	no	—
453	C₂×C₄	—	13	1	no	—
454	C₂×C₄	—	13	1	no	—
455	C₂×C₄	—	13	1	no	—
456	C₂×C₄	—	13	1	no	—
457	C₂×C₄	—	13	2	no	—
458	C₂×C₄	—	13	2	no	—
459	C₂×C₄	—	13	4	no	—
460	C₂×C₄	—	13	4	no	—
461	C₂×C₄	—	13	8	no	—
462	C₂×C₄	—	13	4	no	—
463	C₂×C₄	—	26	8	no	—
464	C₂×C₄	—	26	4	no	—
465	C₂×C₄	—	26	8	no	—
466	C₂×C₄	—	26	4	no	—
467	C₂×C₄	—	52	8	no	—
468	C₂×C₄	C₂×C₄×#261	1	4	yes	—
469	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
470	C₂×C₄	C₂×C₄×#261	1	2	yes	—
471	C₂×C₄	C₂×C₄×#261	1	2	yes	—
472	C₂×C₄	C₂³×#261	1	1	yes	characteristic
473	C₈	—	13	4	no	—
474	C₈	—	13	4	no	—
475	C₈	—	13	8	no	—
476	C₈	—	13	2	no	—
477	C₈	—	13	2	no	—
478	C₈	—	13	4	no	—
479	C₈	C₂×C₄×#261	1	2	yes	—
480	C₈	C₂×C₄×#261	1	2	yes	—
481	C₈	C₂×C₄×#261	1	4	yes	—
482	C₂²	—	2	2	no	—
483	C₂²	—	13	4	no	—
484	C₂²	—	13	1	no	—
485	C₂²	—	13	1	no	—
486	C₂²	—	13	2	no	—
487	C₂²	—	26	4	no	—
488	C₂²	—	26	4	no	—
489	C₂²	—	26	2	no	—
490	C₂²	C₄²×#261	1	2	yes	—
491	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
492	C₄	—	2	4	no	—
493	C₄	—	13	2	no	—
494	C₄	—	13	1	no	—
495	C₄	—	13	1	no	—
496	C₄	—	26	8	no	—
497	C₄	—	26	4	no	—
498	C₄	—	26	4	no	—
499	C₄	—	26	4	no	—
500	C₄	C₄²×#261	1	2	yes	—
501	C₄	C₂²×C₄×#261	1	1	yes	characteristic
502	C₄	C₂²×C₄×#261	1	1	yes	characteristic
503	C₂	—	2	2	no	—
504	C₂	—	13	2	no	—
505	C₂	—	13	2	no	—
506	C₂	—	26	2	no	—
507	C₂	C₂×C₄²×#261	1	1	yes	characteristic
508	C₂	#13131406	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator	C₂×C₁₃	C₂×C₄³
Fitting	C₁₃×#405	C₄
socle	C₂²×C₁₃	C₂²×C₄²
prime radical	C₂³×D₁₃	C₂²×C₄
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	#405	#261
hypocenter	C₁₃	#20331
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #405

Complements

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

N	H ≅ G/N	type
7. #13130494	C₂	semidirect
8. #13130492	C₂	semidirect
9. C₄×#88100	C₂	semidirect
10. #97×#261	C₂	semidirect
19. #11719099	C₄	semidirect
20. M₁₆×#261	C₄	semidirect
21. #11719089	C₄	semidirect
22. C₂×#88100	C₄	semidirect
34. #11719072	C₄	semidirect
36. #11719062	C₄	semidirect
41. C₁₃×#405	C₄	semidirect
42. #11718783	C₄	semidirect
43. #11718762	C₄	semidirect
44. #11718658	C₄	semidirect
45. #11718369	C₄	semidirect
47. #11718350	C₄	semidirect
96. #88110	C₂×C₄	semidirect
97. C₄×#1057	C₂×C₄	semidirect
103. #88100	C₂×C₄	semidirect
104. #88100	C₂×C₄	semidirect
106. C₈×#261	C₂×C₄	semidirect
107. C₈×#261	C₂×C₄	semidirect
108. C₁₃×#97	C₂×C₄	semidirect
109. C₄×C₈×C₁₃	C₂×C₄	semidirect
110. #88055	C₂×C₄	semidirect
111. #88055	C₂×C₄	semidirect
112. C₈×Dic₁₃	C₂×C₄	semidirect
113. C₈×Dic₁₃	C₂×C₄	semidirect
114. #88043	C₂×C₄	semidirect
115. C₄×#1055	C₂×C₄	semidirect
135. #6122	C₄²	semidirect
136. C₂×#1057	C₄²	semidirect
149. #6118	C₄²	semidirect
150. D₁₃⋊C₈	C₄²	semidirect
157. C₁₃×M₁₆	C₄²	semidirect
158. C₂×C₈×C₁₃	C₄²	semidirect
171. #6099	C₄²	semidirect
172. C₂×#1055	C₄²	semidirect
176. #6094	C₄²	semidirect
177. C₈×D₁₃	C₄²	semidirect
178. C₈×D₁₃	C₄²	semidirect
255. #405	#261	semidirect
354. #97	C₂×#261	semidirect
362. C₄×C₈	C₂×#261	semidirect
391. M₁₆	C₄×#261	semidirect
415. C₂×C₈	C₄×#261	semidirect
438. C₁₃	#20331	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11719099	2
#13131396	2
C₂×#11719089	2
C₂×M₁₆×#261	2
C₂²×#88100	2
#117×#261	2
#13130494	2
#13130492	2
C₄×#88100	2
#97×#261	2
D₁₃×#405	2
#20331	13