Subgroups — #15834651

Order 3328.

648 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	#13123965	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#88204	C₂	1	1	yes	maximal, characteristic
3	#13113748	C₂	1	2	yes	maximal, complemented
4	#13113679	C₂	1	2	yes	maximal, complemented
5	#13113677	C₂	1	2	yes	maximal, complemented
6	#13113653	C₂	1	2	yes	maximal, complemented
7	#13113591	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113275	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113273	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113126	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2991	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₂×#88204	C₄	1	1	yes	characteristic
14	C₄×#6127	C₂²	1	1	yes	characteristic
15	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
16	C₁₃×#436	—	2	2	no	—
17	C₁₃×#436	C₂²	1	2	yes	—
18	C₁₃×#431	—	2	1	no	—
19	C₁₃×#431	C₂²	1	1	yes	characteristic
20	C₁₃×#423	—	2	1	no	—
21	C₁₃×#423	C₂²	1	1	yes	characteristic
22	#11718894	C₄	1	1	yes	characteristic
23	C₄×#6107	C₄	1	1	yes	characteristic
24	C₄×#6107	C₂²	1	1	yes	characteristic
25	C₄×#6106	C₄	1	1	yes	characteristic
26	C₄×#6106	C₂²	1	1	yes	characteristic
27	C₄×#6105	C₄	1	1	yes	characteristic
28	C₄×#6105	C₂²	1	1	yes	characteristic
29	C₄×#6104	C₄	1	1	yes	characteristic
30	C₄×#6104	C₂²	1	1	yes	characteristic
31	#11718663	C₄	1	1	yes	characteristic
32	#11718659	C₄	1	1	yes	characteristic
33	#11718585	C₂²	1	1	yes	characteristic
34	C₄×#6099	C₂²	1	1	yes	characteristic
35	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
36	#11718498	—	2	1	no	—
37	#11718494	—	2	1	no	—
38	#11718390	—	2	2	no	—
39	#11718349	C₂²	1	2	yes	—
40	C₈×Dic₂₆	C₂²	1	2	yes	—
41	Q₈⋊#1055	C₂²	1	2	yes	—
42	D₄⋊#1055	C₂²	1	2	yes	—
43	#11718076	C₂²	1	2	yes	—
44	#11718075	C₂²	1	2	yes	—
45	#11718072	C₂²	1	2	yes	—
46	#11718072	C₂²	1	2	yes	—
47	#11718047	C₂²	1	2	yes	—
48	#11718046	C₂²	1	2	yes	—
49	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
50	C₂×#6127	C₂×C₄	1	1	yes	characteristic
51	C₂×C₁₃×M₁₆	—	2	1	no	—
52	C₂×C₁₃×M₁₆	—	2	2	no	—
53	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
54	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₄×D₄×C₁₃	—	2	1	no	—
56	C₄×D₄×C₁₃	—	2	1	no	—
57	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
58	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₁₃×#117	—	2	1	no	—
60	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	—	2	1	no	—
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	#88204	—	2	4	no	—
64	C₂×#6107	C₂×C₄	1	1	yes	characteristic
65	C₂×#6106	C₂×C₄	1	1	yes	characteristic
66	C₂×#6105	C₂×C₄	1	1	yes	characteristic
67	C₂×#6104	C₂×C₄	1	1	yes	characteristic
68	C₄×C₂²⋊D₁₃	—	2	1	no	—
69	C₄×C₂²⋊D₁₃	—	2	1	no	—
70	#88180	C₂×C₄	1	1	yes	characteristic
71	C₂×#6099	—	2	1	no	—
72	C₂×#6099	—	2	1	no	—
73	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
74	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
75	C₂×#6094	—	2	2	no	—
76	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
77	C₄×D₅₂	C₂³	1	1	yes	characteristic
78	#88126	—	2	1	no	—
79	C₄²×D₁₃	—	2	1	no	—
80	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
81	C₄×Dic₂₆	C₂³	1	1	yes	characteristic
82	C₁₃×C₄⋊C₈	—	2	2	no	—
83	C₁₃×C₄⋊C₈	—	2	1	no	—
84	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
85	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
86	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
87	C₁₃×C₂²⋊C₈	—	2	2	no	—
88	C₁₃×C₂²⋊C₈	D₄	1	2	yes	—
89	C₄×C₈×C₁₃	—	2	2	no	—
90	C₄×C₈×C₁₃	C₂³	1	2	yes	—
91	#88075	C₂×C₄	1	1	yes	characteristic
92	#88075	C₂×C₄	1	1	yes	characteristic
93	#88072	C₂×C₄	1	1	yes	characteristic
94	#88072	C₂×C₄	1	1	yes	characteristic
95	#88060	—	2	2	no	—
96	#88054	—	2	2	no	—
97	C₈×Dic₁₃	—	2	2	no	—
98	#88050	C₂×C₄	1	1	yes	characteristic
99	#88050	C₂×C₄	1	1	yes	characteristic
100	#88049	C₂×C₄	1	1	yes	characteristic
101	#88049	C₂×C₄	1	1	yes	characteristic
102	#88048	C₂×C₄	1	1	yes	characteristic
103	#88048	C₂×C₄	1	1	yes	characteristic
104	#88047	C₂×C₄	1	1	yes	characteristic
105	#88047	C₂×C₄	1	1	yes	characteristic
106	C₄⋊#1055	—	2	1	no	—
107	C₄⋊#1055	C₂³	1	2	yes	—
108	#88043	—	2	1	no	—
109	C₄×#1055	C₂×C₄	1	1	yes	characteristic
110	C₄×#1055	C₂×C₄	1	1	yes	characteristic
111	C₄×#1055	C₂³	1	2	yes	—
112	C₄×#1055	C₂³	1	1	yes	characteristic
113	C₄×#1055	C₂³	1	1	yes	characteristic
114	#18063	—	13	1	no	maximal, Sylow
115	C₁₃×#41	—	2	2	no	—
116	C₁₃×#41	—	4	1	no	—
117	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×D₄×C₁₃	—	2	1	no	—
119	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	1	no	—
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
126	C₂×C₂²⋊D₁₃	—	2	1	no	—
127	#6127	—	2	2	no	—
128	#6127	—	4	1	no	—
129	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₄×D₁₃	—	2	1	no	—
131	C₂×C₄×D₁₃	—	2	1	no	—
132	C₂×C₄×D₁₃	—	2	1	no	—
133	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
134	C₁₃×M₁₆	—	8	2	no	—
135	C₁₃×M₁₆	—	8	1	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
138	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
139	C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₁₃×C₄⋊C₄	—	2	1	no	—
141	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
142	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
143	C₁₃×C₂²⋊C₄	—	2	1	no	—
144	C₁₃×C₂²⋊C₄	—	2	1	no	—
145	C₁₃×C₂²⋊C₄	—	2	1	no	—
146	C₄²×C₁₃	—	2	1	no	—
147	C₄²×C₁₃	—	2	1	no	—
148	C₄²×C₁₃	—	2	1	no	—
149	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
150	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₁₃	#41	1	1	yes	characteristic
152	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
153	C₂²⋊Dic₁₃	—	2	1	no	—
154	#6107	M₁₆	1	4	yes	complemented
155	#6106	—	2	2	no	—
156	#6105	—	2	2	no	—
157	#6104	—	2	2	no	—
158	#6103	—	2	1	no	—
159	#6103	—	2	1	no	—
160	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
161	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
162	#6101	—	2	1	no	—
163	#6101	—	2	1	no	—
164	C₄×Dic₁₃	—	2	1	no	—
165	C₄×Dic₁₃	—	2	1	no	—
166	C₄×Dic₁₃	—	2	1	no	—
167	#6099	—	4	2	no	—
168	#6099	—	8	1	no	—
169	C₂×#1055	—	2	2	no	—
170	C₂×#1055	—	2	2	no	—
171	C₂×#1055	—	2	2	no	—
172	C₂×#1055	—	4	1	no	—
173	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
174	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
175	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
176	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
177	#6094	—	8	2	no	—
178	#2991	—	13	1	no	—
179	#2991	D₁₃	1	1	yes	characteristic, complemented
180	C₄×#135	—	13	1	no	—
181	#1594	—	13	2	no	—
182	#1583	—	13	2	no	—
183	#1583	—	13	2	no	—
184	#1579	—	13	2	no	—
185	#1566	—	13	1	no	—
186	#1489	—	13	1	no	—
187	#1489	—	13	1	no	—
188	#1451	—	13	1	no	—
189	C₂³×C₁₃	—	2	1	no	—
190	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
191	C₂²×D₁₃	—	2	1	no	—
192	Q₈×C₁₃	—	2	1	no	—
193	Q₈×C₁₃	C₂×M₁₆	1	2	yes	—
194	D₄×C₁₃	—	2	1	no	—
195	D₄×C₁₃	—	2	1	no	—
196	D₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	2	1	no	—
198	C₂×C₄×C₁₃	—	2	1	no	—
199	C₂×C₄×C₁₃	—	2	1	no	—
200	C₂×C₄×C₁₃	—	2	1	no	—
201	C₂×C₄×C₁₃	—	2	1	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	1	no	—
204	C₂×C₄×C₁₃	—	2	1	no	—
205	C₂×C₄×C₁₃	—	4	2	no	—
206	C₂×C₄×C₁₃	—	4	1	no	—
207	C₂×C₄×C₁₃	—	4	1	no	—
208	C₂×C₄×C₁₃	—	4	2	no	—
209	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
213	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
215	C₂²⋊D₁₃	—	4	2	no	—
216	C₂×Dic₁₃	—	2	1	no	—
217	C₂×Dic₁₃	—	2	1	no	—
218	C₂×Dic₁₃	—	2	1	no	—
219	D₅₂	—	2	1	no	—
220	D₅₂	—	2	1	no	—
221	C₄×D₁₃	—	4	2	no	—
222	C₄×D₁₃	—	4	1	no	—
223	C₄×D₁₃	—	4	1	no	—
224	C₄×D₁₃	—	4	2	no	—
225	Dic₂₆	—	2	1	no	—
226	Dic₂₆	C₂×M₁₆	1	2	yes	—
227	C₈×C₁₃	—	2	2	no	—
228	C₈×C₁₃	—	2	2	no	—
229	C₈×C₁₃	—	4	2	no	—
230	#1055	—	2	1	no	—
231	#1055	—	2	1	no	—
232	#1055	—	2	1	no	—
233	#1055	—	4	2	no	—
234	#1055	—	4	2	no	—
235	#1055	C₂×M₁₆	1	2	yes	—
236	C₂×#135	—	13	1	no	—
237	C₄×#41	—	13	1	no	—
238	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
239	C₈×Q₈	—	13	2	no	—
240	C₈×Q₈	C₂×D₁₃	1	2	yes	—
241	C₄×Q₁₆	—	13	1	no	—
242	C₄×Q₁₆	—	13	1	no	—
243	C₄×SD₁₆	—	13	1	no	—
244	C₄×SD₁₆	—	13	1	no	—
245	C₄×SD₁₆	—	13	1	no	—
246	C₄×SD₁₆	—	13	1	no	—
247	C₄×D₈	—	13	1	no	—
248	C₄×D₈	—	13	1	no	—
249	#436	—	2	2	no	—
250	#436	—	13	2	no	—
251	#436	—	26	2	no	—
252	#436	C₂×D₁₃	1	2	yes	—
253	#431	—	2	1	no	—
254	#431	—	26	1	no	—
255	#431	C₂×D₁₃	1	1	yes	characteristic
256	#427	—	13	1	no	—
257	#423	—	2	1	no	—
258	#423	—	13	1	no	—
259	#423	—	26	1	no	—
260	#423	C₂×D₁₃	1	1	yes	characteristic
261	#416	—	13	1	no	—
262	#416	—	13	1	no	—
263	C₄×M₁₆	—	13	1	no	—
264	C₂×C₄×C₈	—	13	1	no	—
265	#334	—	13	2	no	—
266	#334	—	13	2	no	—
267	Q₈⋊C₈	—	13	2	no	—
268	Q₈⋊C₈	—	13	2	no	—
269	D₄⋊C₈	—	13	2	no	—
270	D₄⋊C₈	—	13	2	no	—
271	#322	—	13	2	no	—
272	#322	—	13	2	no	—
273	C₂²×C₁₃	—	2	1	no	—
274	C₂²×C₁₃	—	2	1	no	—
275	C₂²×C₁₃	—	2	1	no	—
276	C₂²×C₁₃	—	4	1	no	—
277	C₂²×C₁₃	—	4	1	no	—
278	C₂²×C₁₃	—	4	1	no	—
279	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
280	C₂×D₁₃	—	4	1	no	—
281	C₂×D₁₃	—	4	1	no	—
282	C₂×D₁₃	—	4	1	no	—
283	C₄×C₁₃	—	2	1	no	—
284	C₄×C₁₃	—	2	2	no	—
285	C₄×C₁₃	—	2	1	no	—
286	C₄×C₁₃	—	2	1	no	—
287	C₄×C₁₃	—	4	1	no	—
288	C₄×C₁₃	—	4	1	no	—
289	C₄×C₁₃	#444	1	2	yes	—
290	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
291	C₄×C₁₃	#568	1	1	yes	characteristic
292	C₄×C₁₃	#577	1	1	yes	characteristic
293	C₄×C₁₃	#577	1	1	yes	characteristic
294	Dic₁₃	—	2	2	no	—
295	Dic₁₃	—	4	1	no	—
296	Dic₁₃	—	4	1	no	—
297	C₂×#41	—	13	1	no	—
298	C₂×#41	C₄×D₁₃	1	1	yes	characteristic
299	#135	—	26	4	no	—
300	C₂×Q₁₆	—	13	1	no	—
301	C₂×SD₁₆	—	13	1	no	—
302	C₂×SD₁₆	—	13	1	no	—
303	C₂×D₈	—	13	1	no	—
304	C₂×M₁₆	—	2	1	no	—
305	C₂×M₁₆	—	2	2	no	—
306	C₂×M₁₆	—	26	1	no	—
307	C₂×M₁₆	—	26	1	no	—
308	C₂×M₁₆	—	26	2	no	—
309	C₂²×C₈	—	13	1	no	—
310	C₂²×C₈	—	13	1	no	—
311	C₄×Q₈	—	13	1	no	—
312	C₄×Q₈	—	13	1	no	—
313	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
314	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	—	13	1	no	—
318	C₄×D₄	—	13	1	no	—
319	C₄×D₄	—	26	1	no	—
320	C₄×D₄	—	26	1	no	—
321	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
322	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
323	#117	—	2	1	no	—
324	#117	—	13	1	no	—
325	#117	—	26	1	no	—
326	#117	C₄×D₁₃	1	1	yes	characteristic
327	C₂×C₄²	—	2	1	no	—
328	C₂×C₄²	—	26	1	no	—
329	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
330	#107	—	13	1	no	—
331	#107	—	13	1	no	—
332	#106	—	13	1	no	—
333	#106	—	13	1	no	—
334	C₄⋊C₈	—	2	2	no	—
335	C₄⋊C₈	—	2	1	no	—
336	C₄⋊C₈	—	13	2	no	—
337	C₄⋊C₈	—	26	2	no	—
338	C₄⋊C₈	—	26	1	no	—
339	C₄⋊C₈	C₂²⋊D₁₃	1	1	yes	characteristic
340	C₄⋊C₈	C₂²⋊D₁₃	1	1	yes	characteristic
341	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
342	#103	—	13	1	no	—
343	#103	—	13	1	no	—
344	#103	—	13	1	no	—
345	#103	—	13	1	no	—
346	#102	—	13	1	no	—
347	#102	—	13	1	no	—
348	#102	—	13	1	no	—
349	#102	—	13	1	no	—
350	C₂²⋊C₈	—	2	2	no	—
351	C₂²⋊C₈	—	26	2	no	—
352	C₂²⋊C₈	C₂²⋊D₁₃	1	2	yes	—
353	#97	—	26	1	no	—
354	C₄×C₈	—	2	2	no	—
355	C₄×C₈	—	13	1	no	—
356	C₄×C₈	—	13	1	no	—
357	C₄×C₈	—	13	1	no	—
358	C₄×C₈	—	13	1	no	—
359	C₄×C₈	—	13	2	no	—
360	C₄×C₈	—	26	2	no	—
361	C₄×C₈	C₂²×D₁₃	1	2	yes	—
362	C₂×C₁₃	—	4	1	no	—
363	C₂×C₁₃	—	8	1	no	—
364	C₂×C₁₃	D₄×M₁₆	1	1	yes	characteristic
365	C₂×C₁₃	#2952	1	1	yes	characteristic
366	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
367	D₁₃	—	8	1	no	—
368	#41	—	2	2	no	—
369	#41	—	4	1	no	—
370	#41	—	26	2	no	—
371	#41	—	52	1	no	—
372	C₂×Q₈	—	13	1	no	—
373	C₂×Q₈	C₂×C₄×D₁₃	1	1	yes	characteristic
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	13	1	no	—
376	C₂×D₄	—	26	1	no	—
377	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	26	1	no	—
382	C₂²×C₄	—	26	1	no	—
383	C₂²×C₄	—	26	1	no	—
384	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
385	C₂²×C₄	#6127	1	1	yes	characteristic
386	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
387	Q₁₆	—	13	4	no	—
388	SD₁₆	—	26	2	no	—
389	SD₁₆	—	26	2	no	—
390	D₈	—	26	2	no	—
391	M₁₆	—	8	2	no	—
392	M₁₆	—	8	1	no	—
393	M₁₆	—	52	2	no	—
394	M₁₆	—	104	2	no	—
395	M₁₆	—	104	1	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	13	1	no	—
398	C₂×C₈	—	13	1	no	—
399	C₂×C₈	—	13	1	no	—
400	C₂×C₈	—	13	1	no	—
401	C₂×C₈	—	26	2	no	—
402	C₂×C₈	—	26	2	no	—
403	C₂×C₈	—	26	2	no	—
404	C₂×C₈	—	52	1	no	—
405	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
406	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	13	1	no	—
410	C₄⋊C₄	—	13	1	no	—
411	C₄⋊C₄	—	26	1	no	—
412	C₄⋊C₄	—	26	1	no	—
413	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
414	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
415	C₂²⋊C₄	—	2	1	no	—
416	C₂²⋊C₄	—	2	1	no	—
417	C₂²⋊C₄	—	2	1	no	—
418	C₂²⋊C₄	—	26	1	no	—
419	C₂²⋊C₄	—	26	1	no	—
420	C₂²⋊C₄	—	26	1	no	—
421	C₄²	—	2	1	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	26	1	no	—
425	C₄²	—	26	1	no	—
426	C₄²	—	26	1	no	—
427	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
428	C₄²	#6127	1	1	yes	characteristic
429	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
430	C₄²	C₂³×D₁₃	1	1	yes	characteristic
431	C₁₃	#18063	1	1	yes	characteristic, complemented, Sylow
432	C₂³	—	2	1	no	—
433	C₂³	—	26	1	no	—
434	C₂³	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
435	Q₈	—	2	1	no	—
436	Q₈	—	13	2	no	—
437	Q₈	—	26	1	no	—
438	Q₈	M₁₆×D₁₃	1	2	yes	—
439	D₄	—	2	1	no	—
440	D₄	—	2	1	no	—
441	D₄	—	4	2	no	—
442	D₄	—	26	1	no	—
443	D₄	—	26	1	no	—
444	D₄	—	52	2	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	26	1	no	—
458	C₂×C₄	—	26	1	no	—
459	C₂×C₄	—	26	1	no	—
460	C₂×C₄	—	52	2	no	—
461	C₂×C₄	—	52	1	no	—
462	C₂×C₄	—	52	1	no	—
463	C₂×C₄	—	52	2	no	—
464	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
465	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
466	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
467	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
468	C₂×C₄	C₂×#6127	1	1	yes	characteristic
469	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
470	C₈	—	2	2	no	—
471	C₈	—	2	2	no	—
472	C₈	—	4	2	no	—
473	C₈	—	13	2	no	—
474	C₈	—	26	1	no	—
475	C₈	—	26	1	no	—
476	C₈	—	26	1	no	—
477	C₈	—	52	2	no	—
478	C₈	—	52	2	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	4	1	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	52	1	no	—
486	C₂²	—	52	1	no	—
487	C₂²	—	52	1	no	—
488	C₂²	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	2	no	—
493	C₄	—	4	1	no	—
494	C₄	—	4	1	no	—
495	C₄	—	26	2	no	—
496	C₄	—	52	1	no	—
497	C₄	—	52	1	no	—
498	C₄	#11718806	1	2	yes	—
499	C₄	C₂×M₁₆×D₁₃	1	1	yes	characteristic
500	C₄	#11719450	1	1	yes	characteristic
501	C₄	#11719541	1	1	yes	characteristic
502	C₄	#11719542	1	1	yes	characteristic
503	C₂	—	4	1	no	—
504	C₂	—	8	1	no	—
505	C₂	—	104	1	no	—
506	C₂	M₁₆×C₂²⋊D₁₃	1	1	yes	characteristic
507	C₂	#13123717	1	1	yes	characteristic
508	C₂	C₂×#11718806	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#2991	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×#88204	C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#2991	D₁₃
hypocenter	C₁₃	#18063
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #2991

Complements

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

N	H ≅ G/N	type
1. #13123965	C₂	semidirect
3. #13113748	C₂	semidirect
4. #13113679	C₂	semidirect
5. #13113677	C₂	semidirect
6. #13113653	C₂	semidirect
7. #13113591	C₂	semidirect
8. #13113275	C₂	semidirect
9. #13113273	C₂	semidirect
10. #13113126	C₂	semidirect
11. C₁₃×#2991	C₂	semidirect
154. #6107	M₁₆	semidirect
179. #2991	D₁₃	semidirect
431. C₁₃	#18063	semidirect

Maximal subgroups

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

subgroup	index
#13123965	2
C₄×#88204	2
#13113748	2
#13113679	2
#13113677	2
#13113653	2
#13113591	2
#13113275	2
#13113273	2
#13113126	2
C₁₃×#2991	2
#18063	13