Subgroups — #15834337

Order 3328.

794 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#6104	C₂	1	1	yes	maximal, characteristic
2	D₄×#6099	C₂	1	1	yes	maximal, characteristic, complemented
3	#13123571	C₂	1	1	yes	maximal, characteristic, complemented
4	#13113718	C₂	1	2	yes	maximal, complemented
5	#13113668	C₂	1	2	yes	maximal, complemented
6	#13113662	C₂	1	2	yes	maximal, complemented
7	#13113628	C₂	1	2	yes	maximal, complemented
8	#13113594	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113262	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113117	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1486	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂²×#6104	C₄	1	1	yes	characteristic
14	C₂²×#6099	—	2	1	no	—
15	C₂×M₁₆×D₁₃	—	2	1	no	—
16	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
17	C₁₃×#431	C₂²	1	1	yes	characteristic
18	C₁₃×#423	C₂²	1	1	yes	characteristic
19	C₂×#88072	C₄	1	1	yes	characteristic
20	#11718868	—	2	1	no	—
21	#11718787	—	2	1	no	—
22	C₄×#6104	C₄	1	1	yes	characteristic
23	C₄×#6104	C₄	1	1	yes	characteristic
24	C₄×#6104	C₄	1	1	yes	characteristic
25	C₄×#6104	C₄	1	1	yes	characteristic
26	C₄×#6104	C₂²	1	1	yes	characteristic
27	C₄×#6104	C₂²	1	1	yes	characteristic
28	C₄×#6104	C₂²	1	1	yes	characteristic
29	C₄×#6104	C₂²	1	1	yes	characteristic
30	#11718673	C₂²	1	2	yes	complemented
31	#11718672	—	2	2	no	—
32	D₄×#1055	C₂²	1	2	yes	complemented
33	C₂×#88049	C₄	1	1	yes	characteristic
34	C₂×#88047	C₄	1	1	yes	characteristic
35	#11718585	C₂²	1	1	yes	characteristic
36	C₄×#6099	C₂²	1	1	yes	characteristic
37	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
38	#11718499	C₂²	1	2	yes	complemented
39	#11718497	—	2	2	no	—
40	#11718495	C₂²	1	2	yes	complemented
41	C₁₃×D₄⋊C₈	C₂²	1	2	yes	complemented
42	C₁₃×D₄⋊C₈	C₂²	1	2	yes	complemented
43	#11718071	C₂²	1	2	yes	complemented
44	#11718071	C₂²	1	2	yes	complemented
45	#11718051	C₂²	1	2	yes	complemented
46	#11718051	C₂²	1	2	yes	complemented
47	#11718046	C₂²	1	2	yes	complemented
48	C₈×#1055	C₂²	1	2	yes	complemented
49	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	—	2	1	no	—
51	C₂²×D₅₂	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₄×D₁₃	—	2	1	no	—
53	C₂×C₁₃×M₁₆	—	2	1	no	—
54	C₄×D₄×C₁₃	—	2	1	no	—
55	C₄×D₄×C₁₃	—	2	1	no	—
56	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
57	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
58	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	C₂×#6104	—	2	4	no	—
64	C₂×#6104	C₂×C₄	1	1	yes	characteristic
65	C₂×#6104	C₂×C₄	1	1	yes	characteristic
66	C₂×#6104	C₂×C₄	1	1	yes	characteristic
67	C₂×#6104	C₂×C₄	1	1	yes	characteristic
68	C₂×#6103	—	2	1	no	—
69	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
70	C₂×#6099	—	2	1	no	—
71	C₂×#6099	—	2	2	no	—
72	C₂×#6099	—	4	4	no	—
73	C₂×#6099	D₄	1	1	yes	characteristic
74	C₂×#6099	D₄	1	1	yes	characteristic
75	C₂²×#1055	—	2	2	no	—
76	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
77	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
78	M₁₆×D₁₃	—	4	4	no	—
79	C₂×#6094	—	2	2	no	—
80	C₂×C₈×D₁₃	—	2	2	no	—
81	C₄×D₅₂	—	2	1	no	—
82	C₄×D₅₂	—	2	1	no	—
83	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
84	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
85	C₄×D₅₂	C₂³	1	1	yes	characteristic
86	C₄×D₅₂	C₂³	1	1	yes	characteristic
87	C₁₃×C₄⋊C₈	—	2	1	no	—
88	C₁₃×C₄⋊C₈	—	2	1	no	—
89	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
90	C₁₃×C₂²⋊C₈	—	2	1	no	—
91	C₄×C₈×C₁₃	C₂³	1	2	yes	—
92	#88072	C₂×C₄	1	1	yes	characteristic
93	#88072	C₂×C₄	1	1	yes	characteristic
94	#88072	C₂×C₄	1	1	yes	characteristic
95	#88072	C₂×C₄	1	1	yes	characteristic
96	C₂²⋊#1055	—	2	2	no	—
97	C₂²⋊#1055	—	2	2	no	—
98	#88060	—	2	2	no	—
99	#88060	—	2	2	no	—
100	#88049	C₂×C₄	1	1	yes	characteristic
101	#88049	C₂×C₄	1	1	yes	characteristic
102	#88049	C₂×C₄	1	1	yes	characteristic
103	#88049	C₂×C₄	1	1	yes	characteristic
104	#88047	C₂×C₄	1	1	yes	characteristic
105	#88047	C₂×C₄	1	1	yes	characteristic
106	#88047	C₂×C₄	1	1	yes	characteristic
107	#88047	C₂×C₄	1	1	yes	characteristic
108	C₄⋊#1055	—	2	1	no	—
109	C₄⋊#1055	C₂³	1	2	yes	—
110	#88043	D₄	1	2	yes	—
111	C₄×#1055	C₂×C₄	1	1	yes	characteristic
112	C₄×#1055	C₂×C₄	1	1	yes	characteristic
113	C₄×#1055	C₂³	1	1	yes	characteristic
114	C₄×#1055	C₂³	1	1	yes	characteristic
115	C₄×#1055	C₂³	1	2	yes	—
116	M₁₆×D₈	—	13	1	no	maximal, Sylow
117	C₂⁴×C₁₃	—	2	1	no	—
118	C₂³×D₁₃	—	2	1	no	—
119	C₂×D₄×C₁₃	—	2	2	no	—
120	C₂×D₄×C₁₃	—	2	1	no	—
121	C₂×D₄×C₁₃	—	4	1	no	—
122	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	—	2	1	no	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₃	—	4	2	no	—
130	C₂²×C₄×C₁₃	—	4	2	no	—
131	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
134	C₂²×Dic₁₃	—	2	1	no	—
135	C₂×D₅₂	—	2	2	no	—
136	C₂×D₅₂	—	2	1	no	—
137	C₂×D₅₂	—	4	1	no	—
138	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
139	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₄×D₁₃	—	2	1	no	—
141	C₂×C₄×D₁₃	—	2	1	no	—
142	C₂×C₄×D₁₃	—	2	1	no	—
143	C₂×C₄×D₁₃	—	2	1	no	—
144	C₂×C₄×D₁₃	—	4	2	no	—
145	C₂×C₄×D₁₃	—	4	2	no	—
146	C₁₃×M₁₆	—	4	2	no	—
147	C₂×C₈×C₁₃	—	2	2	no	—
148	C₂×C₈×C₁₃	—	2	2	no	—
149	C₁₃×C₄⋊C₄	—	2	1	no	—
150	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
151	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
152	C₁₃×C₂²⋊C₄	—	2	1	no	—
153	C₁₃×C₂²⋊C₄	—	2	1	no	—
154	C₁₃×C₂²⋊C₄	—	2	1	no	—
155	C₁₃×C₂²⋊C₄	—	2	1	no	—
156	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
157	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₁₃	#41	1	1	yes	characteristic
159	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
160	#6104	—	2	2	no	—
161	#6104	—	2	2	no	—
162	#6104	—	2	2	no	—
163	#6104	M₁₆	1	4	yes	complemented
164	#6103	—	2	1	no	—
165	#6103	—	2	1	no	—
166	#6103	—	2	1	no	—
167	#6103	—	2	1	no	—
168	C₄⋊Dic₁₃	—	2	1	no	—
169	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
170	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
171	#6099	—	2	2	no	—
172	#6099	—	4	2	no	—
173	#6099	—	4	4	no	—
174	#6099	D₈	1	4	yes	complemented
175	C₂×#1055	—	2	2	no	—
176	C₂×#1055	—	2	2	no	—
177	C₂×#1055	—	4	1	no	—
178	C₂×#1055	—	4	4	no	—
179	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
180	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
181	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
182	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
183	C₂×#1055	C₂×D₄	1	2	yes	—
184	C₂×#1055	C₂×D₄	1	2	yes	—
185	#6094	—	4	4	no	—
186	C₈×D₁₃	—	4	4	no	—
187	C₂×C₄×D₈	—	13	1	no	—
188	D₄×M₁₆	—	13	1	no	—
189	D₄×M₁₆	—	13	1	no	—
190	#1589	—	13	2	no	—
191	#1581	—	13	2	no	—
192	#1581	—	13	2	no	—
193	C₈×D₈	—	13	2	no	—
194	#1567	—	13	1	no	—
195	#1486	—	13	1	no	—
196	#1486	D₁₃	1	1	yes	characteristic, complemented
197	C₈×M₁₆	—	13	1	no	—
198	C₂³×C₁₃	—	2	1	no	—
199	C₂³×C₁₃	—	2	1	no	—
200	C₂³×C₁₃	—	4	2	no	—
201	C₂³×C₁₃	—	4	2	no	—
202	C₂³×C₁₃	—	8	1	no	—
203	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
204	C₂²×D₁₃	—	2	1	no	—
205	C₂²×D₁₃	—	2	1	no	—
206	C₂²×D₁₃	—	4	2	no	—
207	C₂²×D₁₃	—	4	2	no	—
208	C₂²×D₁₃	—	8	1	no	—
209	D₄×C₁₃	—	2	1	no	—
210	D₄×C₁₃	—	2	1	no	—
211	D₄×C₁₃	—	2	1	no	—
212	D₄×C₁₃	—	4	2	no	—
213	D₄×C₁₃	C₂×M₁₆	1	2	yes	complemented
214	C₂×C₄×C₁₃	—	2	1	no	—
215	C₂×C₄×C₁₃	—	2	1	no	—
216	C₂×C₄×C₁₃	—	2	1	no	—
217	C₂×C₄×C₁₃	—	2	1	no	—
218	C₂×C₄×C₁₃	—	4	1	no	—
219	C₂×C₄×C₁₃	—	4	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	—	4	1	no	—
224	C₂×C₄×C₁₃	—	4	2	no	—
225	C₂×C₄×C₁₃	—	4	2	no	—
226	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
230	C₂×C₄×C₁₃	#135	1	2	yes	—
231	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
234	C₂×Dic₁₃	—	2	1	no	—
235	C₂×Dic₁₃	—	2	1	no	—
236	C₂×Dic₁₃	—	4	2	no	—
237	D₅₂	—	2	1	no	—
238	D₅₂	—	2	1	no	—
239	D₅₂	—	2	1	no	—
240	D₅₂	—	4	2	no	—
241	D₅₂	C₂×M₁₆	1	2	yes	complemented
242	C₄×D₁₃	—	4	1	no	—
243	C₄×D₁₃	—	4	1	no	—
244	C₄×D₁₃	—	4	1	no	—
245	C₄×D₁₃	—	4	1	no	—
246	C₄×D₁₃	—	4	2	no	—
247	C₄×D₁₃	—	4	2	no	—
248	C₈×C₁₃	—	4	2	no	—
249	C₈×C₁₃	—	4	2	no	—
250	#1055	—	2	1	no	—
251	#1055	—	2	1	no	—
252	#1055	—	2	1	no	—
253	#1055	—	2	2	no	—
254	#1055	—	4	2	no	—
255	#1055	C₂×M₁₆	1	2	yes	complemented
256	#1055	C₂×D₈	1	4	yes	complemented
257	C₂²×D₈	—	13	1	no	—
258	C₂²×M₁₆	—	26	1	no	—
259	C₂²×M₁₆	—	26	1	no	—
260	C₂×C₄×D₄	—	13	1	no	—
261	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
262	C₄×D₈	—	13	1	no	—
263	C₄×D₈	—	13	1	no	—
264	C₄×D₈	—	13	1	no	—
265	C₄×D₈	—	13	1	no	—
266	C₄×D₈	—	13	1	no	—
267	C₄×D₈	—	13	1	no	—
268	C₄×D₈	—	13	1	no	—
269	C₄×D₈	—	13	1	no	—
270	#436	—	13	2	no	—
271	#436	—	13	2	no	—
272	#435	—	26	2	no	—
273	#435	—	26	2	no	—
274	C₈×D₄	—	13	2	no	—
275	C₈×D₄	—	13	2	no	—
276	#431	C₂×D₁₃	1	1	yes	characteristic
277	C₂×#107	—	13	1	no	—
278	#423	—	13	1	no	—
279	#423	C₂×D₁₃	1	1	yes	characteristic
280	C₂×#102	—	13	1	no	—
281	C₂×#102	—	13	1	no	—
282	#407	—	26	1	no	—
283	#407	—	26	1	no	—
284	C₄×M₁₆	—	13	1	no	—
285	C₂×C₄×C₈	—	13	1	no	—
286	#335	—	13	2	no	—
287	#335	—	13	2	no	—
288	D₄⋊C₈	—	13	2	no	—
289	D₄⋊C₈	—	13	2	no	—
290	D₄⋊C₈	C₂×D₁₃	1	2	yes	complemented
291	D₄⋊C₈	C₂×D₁₃	1	2	yes	complemented
292	#322	—	13	2	no	—
293	C₈²	—	13	2	no	—
294	C₂²×C₁₃	—	2	1	no	—
295	C₂²×C₁₃	—	2	1	no	—
296	C₂²×C₁₃	—	2	2	no	—
297	C₂²×C₁₃	—	4	1	no	—
298	C₂²×C₁₃	—	4	1	no	—
299	C₂²×C₁₃	—	4	1	no	—
300	C₂²×C₁₃	—	4	1	no	—
301	C₂²×C₁₃	—	4	1	no	—
302	C₂²×C₁₃	—	8	4	no	—
303	C₂²×C₁₃	C₄×D₈	1	2	yes	—
304	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
305	C₂×D₁₃	—	2	2	no	—
306	C₂×D₁₃	—	4	1	no	—
307	C₂×D₁₃	—	4	1	no	—
308	C₂×D₁₃	—	4	1	no	—
309	C₂×D₁₃	—	4	1	no	—
310	C₂×D₁₃	—	4	1	no	—
311	C₂×D₁₃	—	8	4	no	—
312	C₄×C₁₃	—	2	1	no	—
313	C₄×C₁₃	—	2	1	no	—
314	C₄×C₁₃	—	2	1	no	—
315	C₄×C₁₃	—	4	1	no	—
316	C₄×C₁₃	—	4	1	no	—
317	C₄×C₁₃	C₄×D₈	1	2	yes	—
318	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
319	C₄×C₁₃	#568	1	1	yes	characteristic
320	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
321	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
322	Dic₁₃	—	4	1	no	—
323	Dic₁₃	—	4	1	no	—
324	C₂²×D₄	—	13	1	no	—
325	C₂²×D₄	C₄×D₁₃	1	1	yes	characteristic
326	C₂³×C₄	—	2	1	no	—
327	C₂³×C₄	—	26	1	no	—
328	C₂×D₈	—	13	1	no	—
329	C₂×D₈	—	13	1	no	—
330	C₂×D₈	—	13	1	no	—
331	C₂×D₈	—	13	1	no	—
332	C₂×D₈	—	26	4	no	—
333	C₂×M₁₆	—	2	1	no	—
334	C₂×M₁₆	—	13	1	no	—
335	C₂×M₁₆	—	13	1	no	—
336	C₂×M₁₆	—	26	2	no	—
337	C₂×M₁₆	—	26	2	no	—
338	C₂×M₁₆	—	26	1	no	—
339	C₂×M₁₆	—	52	4	no	—
340	C₂×M₁₆	—	52	4	no	—
341	C₂²×C₈	—	13	1	no	—
342	C₂²×C₈	—	13	1	no	—
343	C₂²×C₈	—	26	2	no	—
344	C₂²×C₈	—	26	2	no	—
345	C₄×D₄	—	2	1	no	—
346	C₄×D₄	—	2	1	no	—
347	C₄×D₄	—	13	1	no	—
348	C₄×D₄	—	13	1	no	—
349	C₄×D₄	—	13	1	no	—
350	C₄×D₄	—	13	1	no	—
351	C₄×D₄	—	26	1	no	—
352	C₄×D₄	—	26	1	no	—
353	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
354	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
355	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
356	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
357	C₂×C₄⋊C₄	—	13	1	no	—
358	C₂×C₄⋊C₄	C₄×D₁₃	1	1	yes	characteristic
359	C₂×C₂²⋊C₄	—	2	1	no	—
360	C₂×C₂²⋊C₄	—	26	1	no	—
361	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
362	#107	—	13	1	no	—
363	#107	—	13	1	no	—
364	#107	—	13	1	no	—
365	#107	—	13	1	no	—
366	C₄⋊C₈	—	2	1	no	—
367	C₄⋊C₈	—	2	1	no	—
368	C₄⋊C₈	—	13	2	no	—
369	C₄⋊C₈	—	26	1	no	—
370	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
371	#102	—	13	1	no	—
372	#102	—	13	1	no	—
373	#102	—	13	1	no	—
374	#102	—	13	1	no	—
375	#102	—	13	1	no	—
376	#102	—	13	1	no	—
377	#102	—	13	1	no	—
378	#102	—	13	1	no	—
379	C₂²⋊C₈	—	2	1	no	—
380	C₂²⋊C₈	—	26	2	no	—
381	C₂²⋊C₈	—	26	2	no	—
382	C₂²⋊C₈	—	26	2	no	—
383	C₂²⋊C₈	—	26	2	no	—
384	#97	—	13	2	no	—
385	C₄×C₈	—	13	1	no	—
386	C₄×C₈	—	13	1	no	—
387	C₄×C₈	—	13	1	no	—
388	C₄×C₈	—	13	2	no	—
389	C₄×C₈	—	13	1	no	—
390	C₄×C₈	C₂²×D₁₃	1	2	yes	—
391	C₂×C₁₃	—	2	2	no	—
392	C₂×C₁₃	—	4	2	no	—
393	C₂×C₁₃	—	8	1	no	—
394	C₂×C₁₃	D₄×M₁₆	1	1	yes	characteristic
395	C₂×C₁₃	C₂×C₄×D₈	1	1	yes	characteristic
396	C₂×C₁₃	#2957	1	1	yes	characteristic
397	D₁₃	—	4	2	no	—
398	D₁₃	—	8	1	no	—
399	C₂⁴	—	2	1	no	—
400	C₂⁴	—	26	1	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	1	no	—
403	C₂×D₄	—	4	1	no	—
404	C₂×D₄	—	13	1	no	—
405	C₂×D₄	—	13	1	no	—
406	C₂×D₄	—	26	2	no	—
407	C₂×D₄	—	26	1	no	—
408	C₂×D₄	—	52	1	no	—
409	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
410	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	4	2	no	—
417	C₂²×C₄	—	4	2	no	—
418	C₂²×C₄	—	26	1	no	—
419	C₂²×C₄	—	26	1	no	—
420	C₂²×C₄	—	26	1	no	—
421	C₂²×C₄	—	26	1	no	—
422	C₂²×C₄	—	26	1	no	—
423	C₂²×C₄	—	52	2	no	—
424	C₂²×C₄	—	52	2	no	—
425	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
426	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
427	C₂²×C₄	#6129	1	1	yes	characteristic
428	D₈	—	13	4	no	—
429	D₈	—	26	2	no	—
430	D₈	—	26	2	no	—
431	D₈	—	26	2	no	—
432	M₁₆	—	4	2	no	—
433	M₁₆	—	13	4	no	—
434	M₁₆	—	26	2	no	—
435	M₁₆	—	52	4	no	—
436	M₁₆	—	52	4	no	—
437	M₁₆	—	52	2	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	13	1	no	—
441	C₂×C₈	—	13	2	no	—
442	C₂×C₈	—	13	1	no	—
443	C₂×C₈	—	13	1	no	—
444	C₂×C₈	—	13	1	no	—
445	C₂×C₈	—	13	2	no	—
446	C₂×C₈	—	26	2	no	—
447	C₂×C₈	—	26	2	no	—
448	C₂×C₈	—	52	4	no	—
449	C₂×C₈	—	52	4	no	—
450	C₂×C₈	—	52	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	13	1	no	—
453	C₄⋊C₄	—	13	1	no	—
454	C₄⋊C₄	—	26	1	no	—
455	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
456	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
457	C₂²⋊C₄	—	2	1	no	—
458	C₂²⋊C₄	—	2	1	no	—
459	C₂²⋊C₄	—	2	1	no	—
460	C₂²⋊C₄	—	2	1	no	—
461	C₂²⋊C₄	—	26	1	no	—
462	C₂²⋊C₄	—	26	1	no	—
463	C₂²⋊C₄	—	26	1	no	—
464	C₂²⋊C₄	—	26	1	no	—
465	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
466	C₄²	D₄×D₁₃	1	1	yes	characteristic
467	C₄²	#6129	1	1	yes	characteristic
468	C₄²	C₂³×D₁₃	1	1	yes	characteristic
469	C₁₃	M₁₆×D₈	1	1	yes	characteristic, complemented, Sylow
470	C₂³	—	2	1	no	—
471	C₂³	—	2	1	no	—
472	C₂³	—	4	2	no	—
473	C₂³	—	4	2	no	—
474	C₂³	—	8	1	no	—
475	C₂³	—	26	1	no	—
476	C₂³	—	26	1	no	—
477	C₂³	—	52	2	no	—
478	C₂³	—	52	2	no	—
479	C₂³	—	104	1	no	—
480	C₂³	#88135	1	1	yes	characteristic
481	D₄	—	2	1	no	—
482	D₄	—	2	1	no	—
483	D₄	—	2	1	no	—
484	D₄	—	4	2	no	—
485	D₄	—	13	2	no	—
486	D₄	—	26	1	no	—
487	D₄	—	26	1	no	—
488	D₄	—	26	1	no	—
489	D₄	—	52	2	no	—
490	D₄	M₁₆×D₁₃	1	2	yes	complemented
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	26	1	no	—
504	C₂×C₄	—	26	1	no	—
505	C₂×C₄	—	52	2	no	—
506	C₂×C₄	—	52	2	no	—
507	C₂×C₄	—	52	2	no	—
508	C₂×C₄	—	52	1	no	—
509	C₂×C₄	—	52	1	no	—
510	C₂×C₄	—	52	1	no	—
511	C₂×C₄	—	52	1	no	—
512	C₂×C₄	#88135	1	1	yes	characteristic
513	C₂×C₄	#88135	1	1	yes	characteristic
514	C₂×C₄	#88135	1	1	yes	characteristic
515	C₂×C₄	D₈×D₁₃	1	2	yes	—
516	C₂×C₄	#88170	1	2	yes	—
517	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
518	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
519	C₂×C₄	C₂×#6129	1	1	yes	characteristic
520	C₈	—	4	2	no	—
521	C₈	—	4	2	no	—
522	C₈	—	13	2	no	—
523	C₈	—	13	4	no	—
524	C₈	—	26	1	no	—
525	C₈	—	26	1	no	—
526	C₈	—	26	1	no	—
527	C₈	—	26	2	no	—
528	C₈	—	52	2	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	4	1	no	—
536	C₂²	—	4	1	no	—
537	C₂²	—	8	4	no	—
538	C₂²	—	26	2	no	—
539	C₂²	—	52	1	no	—
540	C₂²	—	52	1	no	—
541	C₂²	—	52	1	no	—
542	C₂²	—	52	1	no	—
543	C₂²	—	52	1	no	—
544	C₂²	—	104	4	no	—
545	C₂²	#11718417	1	2	yes	—
546	C₂²	C₂×#88135	1	1	yes	characteristic
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	52	1	no	—
553	C₄	—	52	1	no	—
554	C₄	#11718417	1	2	yes	—
555	C₄	C₂×M₁₆×D₁₃	1	1	yes	characteristic
556	C₄	#11719450	1	1	yes	characteristic
557	C₄	C₂×D₈×D₁₃	1	1	yes	characteristic
558	C₄	C₂×#88170	1	1	yes	characteristic
559	C₂	—	2	2	no	—
560	C₂	—	4	2	no	—
561	C₂	—	8	1	no	—
562	C₂	—	52	2	no	—
563	C₂	—	104	1	no	—
564	C₂	#13123568	1	1	yes	characteristic
565	C₂	C₂×#11718417	1	1	yes	characteristic
566	C₂	#13123749	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#1486	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂²×#6104	C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1486	D₁₃
hypocenter	C₁₃	M₁₆×D₈
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1486

Complements

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

N	H ≅ G/N	type
2. D₄×#6099	C₂	semidirect
3. #13123571	C₂	semidirect
4. #13113718	C₂	semidirect
5. #13113668	C₂	semidirect
6. #13113662	C₂	semidirect
7. #13113628	C₂	semidirect
8. #13113594	C₂	semidirect
9. #13113262	C₂	semidirect
10. #13113117	C₂	semidirect
11. C₁₃×#1486	C₂	semidirect
30. #11718673	C₂²	semidirect
32. D₄×#1055	C₂²	semidirect
38. #11718499	C₂²	semidirect
40. #11718495	C₂²	semidirect
41. C₁₃×D₄⋊C₈	C₂²	semidirect
42. C₁₃×D₄⋊C₈	C₂²	semidirect
43. #11718071	C₂²	semidirect
44. #11718071	C₂²	semidirect
45. #11718051	C₂²	semidirect
46. #11718051	C₂²	semidirect
47. #11718046	C₂²	semidirect
48. C₈×#1055	C₂²	semidirect
163. #6104	M₁₆	semidirect
174. #6099	D₈	semidirect
196. #1486	D₁₃	semidirect
213. D₄×C₁₃	C₂×M₁₆	semidirect
241. D₅₂	C₂×M₁₆	semidirect
255. #1055	C₂×M₁₆	semidirect
256. #1055	C₂×D₈	semidirect
290. D₄⋊C₈	C₂×D₁₃	semidirect
291. D₄⋊C₈	C₂×D₁₃	semidirect
469. C₁₃	M₁₆×D₈	semidirect
490. D₄	M₁₆×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#6104	2
D₄×#6099	2
#13123571	2
#13113718	2
#13113668	2
#13113662	2
#13113628	2
#13113594	2
#13113262	2
#13113117	2
C₁₃×#1486	2
M₁₆×D₈	13