Subgroups — #15834338

Order 3328.

794 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₈×D₁₃	C₂	1	1	yes	maximal, characteristic
2	#13123572	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×#6094	C₂	1	1	yes	maximal, characteristic, complemented
4	#13113719	C₂	1	1	yes	maximal, characteristic, complemented
5	#13113718	C₂	1	1	yes	maximal, characteristic, complemented
6	#13113667	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113666	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113664	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×#6104	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113628	C₂	1	1	yes	maximal, characteristic, complemented
11	#13113593	C₂	1	1	yes	maximal, characteristic, complemented
12	#13113259	C₂	1	1	yes	maximal, characteristic, complemented
13	#13113259	C₂	1	1	yes	maximal, characteristic, complemented
14	#13113115	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1581	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₈×D₁₃	C₄	1	1	yes	characteristic
17	C₂×M₁₆×D₁₃	—	2	1	no	—
18	C₂²×#6094	—	2	1	no	—
19	C₄×D₄×D₁₃	C₂²	1	1	yes	characteristic
20	C₄×D₄×D₁₃	C₂²	1	1	yes	characteristic
21	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
22	C₁₃×#436	C₂²	1	1	yes	characteristic, complemented
23	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
24	D₈×Dic₁₃	C₄	1	1	yes	characteristic
25	#11718788	—	2	1	no	—
26	#11718772	—	2	1	no	—
27	C₄×#6104	C₂²	1	1	yes	characteristic
28	C₄×#6104	C₂²	1	1	yes	characteristic
29	#11718673	C₂²	1	1	yes	characteristic, complemented
30	D₄×#1055	C₂²	1	1	yes	characteristic, complemented
31	D₁₃×#107	C₄	1	1	yes	characteristic
32	#11718533	C₄	1	1	yes	characteristic
33	#11718499	C₂²	1	1	yes	characteristic, complemented
34	#11718498	C₂²	1	1	yes	characteristic
35	#11718498	C₂²	1	1	yes	characteristic
36	#11718495	C₂²	1	1	yes	characteristic, complemented
37	D₁₃×#102	C₄	1	1	yes	characteristic
38	D₁₃×#102	C₄	1	1	yes	characteristic
39	#11718417	C₄	1	1	yes	characteristic
40	#11718417	C₄	1	1	yes	characteristic
41	#11718391	—	2	1	no	—
42	#11718389	—	2	1	no	—
43	#11718387	—	2	1	no	—
44	#11718387	—	2	1	no	—
45	C₄×D₁₀₄	C₂²	1	1	yes	characteristic
46	#11718349	C₂²	1	1	yes	characteristic, complemented
47	C₄×#6094	C₂²	1	1	yes	characteristic
48	C₈×D₅₂	C₂²	1	1	yes	characteristic, complemented
49	#11718346	C₂²	1	1	yes	characteristic
50	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
51	C₁₃×#335	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#322	C₂²	1	1	yes	characteristic, complemented
55	D₄⋊#1055	C₂²	1	1	yes	characteristic, complemented
56	D₄⋊#1055	C₂²	1	1	yes	characteristic, complemented
57	#11718075	C₂²	1	1	yes	characteristic, complemented
58	#11718075	C₂²	1	1	yes	characteristic, complemented
59	#11718071	C₂²	1	1	yes	characteristic, complemented
60	#11718071	C₂²	1	1	yes	characteristic, complemented
61	#11718051	C₂²	1	1	yes	characteristic, complemented
62	#11718051	C₂²	1	1	yes	characteristic, complemented
63	#11718050	C₂²	1	1	yes	characteristic, complemented
64	#11718046	C₂²	1	1	yes	characteristic, complemented
65	C₈×#1055	C₂²	1	1	yes	characteristic, complemented
66	C₈×#1055	C₂²	1	1	yes	characteristic, complemented
67	C₂×D₄×D₁₃	C₂×C₄	1	1	yes	characteristic
68	C₂×D₄×D₁₃	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₄×D₁₃	—	2	1	no	—
70	C₂²×C₄×D₁₃	—	2	1	no	—
71	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
72	C₂×C₁₃×M₁₆	—	2	1	no	—
73	C₂²×C₈×C₁₃	—	2	1	no	—
74	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
76	D₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
77	D₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
78	C₂×#6104	C₂×C₄	1	1	yes	characteristic
79	C₂×#6104	C₂×C₄	1	1	yes	characteristic
80	C₄×C₂²⋊D₁₃	—	2	1	no	—
81	C₄×C₂²⋊D₁₃	—	2	1	no	—
82	C₂×#6099	—	2	1	no	—
83	C₂²×#1055	—	2	1	no	—
84	D₈×D₁₃	—	2	4	no	—
85	M₁₆×D₁₃	—	4	4	no	—
86	C₂×D₁₀₄	C₂×C₄	1	1	yes	characteristic
87	C₂×#6094	—	2	1	no	—
88	C₂×#6094	—	2	1	no	—
89	C₂×#6094	—	2	1	no	—
90	C₂×#6094	—	2	1	no	—
91	C₂×#6094	—	4	4	no	—
92	C₂×#6094	D₄	1	1	yes	characteristic
93	C₂×#6094	D₄	1	1	yes	characteristic
94	C₂×C₈×D₁₃	—	2	1	no	—
95	C₂×C₈×D₁₃	—	2	1	no	—
96	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
97	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
98	#88147	C₂×C₄	1	1	yes	characteristic
99	#88147	C₂×C₄	1	1	yes	characteristic
100	C₄⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
101	C₄⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
102	#88135	—	2	1	no	—
103	#88135	—	2	1	no	—
104	C₂²⋊C₄×D₁₃	—	2	1	no	—
105	C₂²⋊C₄×D₁₃	—	2	1	no	—
106	C₄×D₅₂	C₂³	1	1	yes	characteristic
107	C₄×D₅₂	C₂³	1	1	yes	characteristic
108	C₄²×D₁₃	C₂³	1	1	yes	characteristic
109	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
110	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
111	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
112	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
113	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
114	C₁₃×C₂²⋊C₈	—	2	1	no	—
115	C₁₃×C₂²⋊C₈	—	2	1	no	—
116	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
117	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
118	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
119	#88072	C₂×C₄	1	1	yes	characteristic
120	#88072	C₂×C₄	1	1	yes	characteristic
121	C₂²⋊#1055	—	2	1	no	—
122	C₂²⋊#1055	—	2	1	no	—
123	#88061	C₂×C₄	1	1	yes	characteristic
124	#88061	C₂×C₄	1	1	yes	characteristic
125	#88060	—	2	1	no	—
126	#88060	—	2	1	no	—
127	#88060	—	2	1	no	—
128	#88060	—	2	1	no	—
129	#88060	—	2	1	no	—
130	#88058	C₂×C₄	1	1	yes	characteristic
131	#88055	D₄	1	1	yes	characteristic
132	#88055	D₄	1	1	yes	characteristic
133	#88054	—	2	1	no	—
134	#88054	—	2	1	no	—
135	#88054	—	2	1	no	—
136	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
137	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
138	#88049	C₂×C₄	1	1	yes	characteristic
139	#88049	C₂×C₄	1	1	yes	characteristic
140	#88047	C₂×C₄	1	1	yes	characteristic
141	#88047	C₂×C₄	1	1	yes	characteristic
142	C₄⋊#1055	C₂³	1	1	yes	characteristic
143	C₄⋊#1055	C₂³	1	1	yes	characteristic
144	C₄×#1055	C₂³	1	1	yes	characteristic
145	C₄×#1055	C₂³	1	1	yes	characteristic
146	C₄×#1055	C₂³	1	1	yes	characteristic
147	M₁₆×D₈	—	13	1	no	maximal, Sylow
148	C₂³×D₁₃	—	2	1	no	—
149	C₂³×D₁₃	—	2	1	no	—
150	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
151	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	—	2	1	no	—
153	C₂²×C₄×C₁₃	—	2	1	no	—
154	C₂×C₂²⋊D₁₃	—	2	1	no	—
155	C₂×C₂²⋊D₁₃	—	2	1	no	—
156	C₂²×Dic₁₃	—	2	1	no	—
157	C₂²×Dic₁₃	—	2	1	no	—
158	D₄×D₁₃	—	2	2	no	—
159	D₄×D₁₃	—	2	2	no	—
160	D₄×D₁₃	—	4	1	no	—
161	D₄×D₁₃	—	4	1	no	—
162	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
163	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₄×D₁₃	—	2	1	no	—
165	C₂×C₄×D₁₃	—	2	1	no	—
166	C₂×C₄×D₁₃	—	2	1	no	—
167	C₂×C₄×D₁₃	—	2	1	no	—
168	C₂×C₄×D₁₃	—	2	1	no	—
169	C₂×C₄×D₁₃	—	2	1	no	—
170	C₂×C₄×D₁₃	—	4	2	no	—
171	C₂×C₄×D₁₃	—	4	2	no	—
172	C₂×C₄×D₁₃	—	4	2	no	—
173	C₂×C₄×D₁₃	—	4	2	no	—
174	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
176	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
177	C₁₃×D₈	—	2	2	no	—
178	C₁₃×M₁₆	—	4	2	no	—
179	C₂×C₈×C₁₃	—	2	1	no	—
180	C₂×C₈×C₁₃	—	2	1	no	—
181	C₂×C₈×C₁₃	—	2	1	no	—
182	C₂×C₈×C₁₃	—	4	2	no	—
183	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
188	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
189	C₁₃×C₂²⋊C₄	—	2	1	no	—
190	C₁₃×C₂²⋊C₄	—	2	1	no	—
191	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
192	C₂²⋊Dic₁₃	—	2	1	no	—
193	C₂²⋊Dic₁₃	—	2	1	no	—
194	#6104	—	2	2	no	—
195	#6104	M₁₆	1	4	yes	complemented
196	#6103	—	2	1	no	—
197	#6103	—	2	1	no	—
198	#6103	—	2	1	no	—
199	#6103	—	2	1	no	—
200	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
201	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
202	#6101	—	2	1	no	—
203	#6101	—	2	1	no	—
204	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
205	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
206	C₄×Dic₁₃	#41	1	1	yes	characteristic
207	#6099	—	4	2	no	—
208	C₂×#1055	—	2	1	no	—
209	C₂×#1055	—	2	1	no	—
210	C₂×#1055	—	2	1	no	—
211	C₂×#1055	—	4	2	no	—
212	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
213	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
214	C₂×#1055	C₂×D₄	1	1	yes	characteristic
215	C₂×#1055	C₂×D₄	1	1	yes	characteristic
216	D₁₀₄	—	2	2	no	—
217	#6094	—	2	2	no	—
218	#6094	—	4	2	no	—
219	#6094	—	4	2	no	—
220	#6094	—	4	2	no	—
221	#6094	—	4	2	no	—
222	#6094	D₈	1	4	yes	complemented
223	C₈×D₁₃	—	2	2	no	—
224	C₈×D₁₃	—	4	1	no	—
225	C₈×D₁₃	—	4	2	no	—
226	C₈×D₁₃	—	4	2	no	—
227	C₂×C₄×D₈	—	13	1	no	—
228	D₄×M₁₆	—	13	1	no	—
229	D₄×M₁₆	—	13	1	no	—
230	#1589	—	13	1	no	—
231	#1589	—	13	1	no	—
232	#1581	—	13	1	no	—
233	#1581	—	13	1	no	—
234	#1581	—	13	1	no	—
235	#1581	D₁₃	1	1	yes	characteristic, complemented
236	C₈×D₈	—	13	1	no	—
237	C₈×D₈	—	13	1	no	—
238	#1567	—	13	1	no	—
239	#1486	—	13	1	no	—
240	#1486	—	13	1	no	—
241	C₈×M₁₆	—	13	1	no	—
242	C₂³×C₁₃	—	2	1	no	—
243	C₂³×C₁₃	—	2	1	no	—
244	C₂²×D₁₃	—	2	1	no	—
245	C₂²×D₁₃	—	2	1	no	—
246	C₂²×D₁₃	—	4	2	no	—
247	C₂²×D₁₃	—	4	2	no	—
248	C₂²×D₁₃	—	4	2	no	—
249	C₂²×D₁₃	—	4	2	no	—
250	C₂²×D₁₃	—	8	1	no	—
251	C₂²×D₁₃	—	8	1	no	—
252	C₂²×D₁₃	C₄×D₄	1	1	yes	characteristic
253	D₄×C₁₃	—	2	1	no	—
254	D₄×C₁₃	—	2	1	no	—
255	D₄×C₁₃	—	2	1	no	—
256	D₄×C₁₃	C₂×M₁₆	1	2	yes	complemented
257	C₂×C₄×C₁₃	—	2	1	no	—
258	C₂×C₄×C₁₃	—	2	1	no	—
259	C₂×C₄×C₁₃	—	4	1	no	—
260	C₂×C₄×C₁₃	—	4	1	no	—
261	C₂×C₄×C₁₃	—	4	1	no	—
262	C₂×C₄×C₁₃	—	4	1	no	—
263	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
264	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
266	C₂²⋊D₁₃	—	4	2	no	—
267	C₂²⋊D₁₃	—	4	2	no	—
268	C₂×Dic₁₃	—	2	1	no	—
269	C₂×Dic₁₃	—	2	1	no	—
270	C₂×Dic₁₃	—	4	2	no	—
271	C₂×Dic₁₃	—	4	2	no	—
272	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
273	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
274	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
275	D₅₂	—	2	1	no	—
276	D₅₂	—	2	1	no	—
277	D₅₂	—	2	1	no	—
278	D₅₂	C₂×M₁₆	1	2	yes	complemented
279	C₄×D₁₃	—	2	1	no	—
280	C₄×D₁₃	—	2	1	no	—
281	C₄×D₁₃	—	4	1	no	—
282	C₄×D₁₃	—	4	2	no	—
283	C₄×D₁₃	—	4	2	no	—
284	C₄×D₁₃	—	4	1	no	—
285	C₄×D₁₃	—	4	1	no	—
286	C₄×D₁₃	—	4	1	no	—
287	C₄×D₁₃	—	4	1	no	—
288	C₄×D₁₃	—	4	2	no	—
289	C₄×D₁₃	—	4	2	no	—
290	C₄×D₁₃	C₂×D₈	1	2	yes	—
291	C₄×D₁₃	#135	1	2	yes	—
292	C₈×C₁₃	—	2	1	no	—
293	C₈×C₁₃	—	2	1	no	—
294	C₈×C₁₃	—	2	1	no	—
295	C₈×C₁₃	—	4	1	no	—
296	C₈×C₁₃	—	4	1	no	—
297	C₈×C₁₃	—	4	1	no	—
298	C₈×C₁₃	C₂×D₈	1	2	yes	complemented
299	#1055	—	2	1	no	—
300	#1055	—	2	1	no	—
301	#1055	—	4	1	no	—
302	#1055	—	4	1	no	—
303	#1055	—	4	1	no	—
304	#1055	C₂×M₁₆	1	2	yes	complemented
305	#1055	C₂×D₈	1	2	yes	complemented
306	C₂²×D₈	—	13	1	no	—
307	C₂²×M₁₆	—	26	1	no	—
308	C₂²×M₁₆	—	26	1	no	—
309	C₂×C₄×D₄	—	13	1	no	—
310	C₂×C₄×D₄	—	13	1	no	—
311	C₄×D₈	—	13	1	no	—
312	C₄×D₈	—	13	1	no	—
313	C₄×D₈	—	13	1	no	—
314	C₄×D₈	—	13	1	no	—
315	C₄×D₈	—	13	1	no	—
316	C₄×D₈	—	13	1	no	—
317	C₄×D₈	—	13	1	no	—
318	C₄×D₈	C₂×D₁₃	1	1	yes	characteristic
319	#436	—	13	1	no	—
320	#436	—	13	1	no	—
321	#436	—	13	1	no	—
322	#436	C₂×D₁₃	1	1	yes	characteristic, complemented
323	#435	—	26	1	no	—
324	#435	—	26	1	no	—
325	#435	—	26	1	no	—
326	#435	—	26	1	no	—
327	C₈×D₄	—	13	1	no	—
328	C₈×D₄	—	13	1	no	—
329	C₈×D₄	—	13	1	no	—
330	C₈×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
331	#431	—	13	1	no	—
332	C₂×#107	—	13	1	no	—
333	#423	—	13	1	no	—
334	#423	—	13	1	no	—
335	C₂×#102	—	13	1	no	—
336	C₂×#102	—	13	1	no	—
337	#407	—	26	1	no	—
338	#407	—	26	1	no	—
339	C₄×M₁₆	—	13	1	no	—
340	C₂×C₄×C₈	—	13	1	no	—
341	#335	—	13	1	no	—
342	#335	—	13	1	no	—
343	#335	—	13	1	no	—
344	#335	C₂×D₁₃	1	1	yes	characteristic, complemented
345	D₄⋊C₈	—	13	1	no	—
346	D₄⋊C₈	—	13	1	no	—
347	D₄⋊C₈	—	13	1	no	—
348	D₄⋊C₈	—	13	1	no	—
349	D₄⋊C₈	—	13	1	no	—
350	D₄⋊C₈	—	13	1	no	—
351	D₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic, complemented
352	D₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic, complemented
353	#322	—	13	1	no	—
354	#322	C₂×D₁₃	1	1	yes	characteristic, complemented
355	C₈²	—	13	1	no	—
356	C₈²	—	13	1	no	—
357	C₂²×C₁₃	—	2	2	no	—
358	C₂²×C₁₃	—	4	1	no	—
359	C₂²×C₁₃	—	4	1	no	—
360	C₂²×C₁₃	—	4	1	no	—
361	C₂²×C₁₃	—	4	1	no	—
362	C₂²×C₁₃	—	4	1	no	—
363	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
364	C₂×D₁₃	—	2	1	no	—
365	C₂×D₁₃	—	2	1	no	—
366	C₂×D₁₃	—	2	2	no	—
367	C₂×D₁₃	—	4	1	no	—
368	C₂×D₁₃	—	4	1	no	—
369	C₂×D₁₃	—	4	1	no	—
370	C₂×D₁₃	—	4	1	no	—
371	C₂×D₁₃	—	4	1	no	—
372	C₂×D₁₃	—	8	4	no	—
373	C₂×D₁₃	—	8	4	no	—
374	C₂×D₁₃	C₄×D₈	1	2	yes	—
375	C₄×C₁₃	—	2	1	no	—
376	C₄×C₁₃	—	4	1	no	—
377	C₄×C₁₃	—	4	1	no	—
378	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
379	C₄×C₁₃	#568	1	1	yes	characteristic
380	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
381	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
382	Dic₁₃	—	2	1	no	—
383	Dic₁₃	—	2	1	no	—
384	Dic₁₃	—	4	1	no	—
385	Dic₁₃	—	4	1	no	—
386	Dic₁₃	C₄×D₈	1	2	yes	—
387	C₂²×D₄	—	13	1	no	—
388	C₂²×D₄	—	13	1	no	—
389	C₂³×C₄	—	26	1	no	—
390	C₂³×C₄	—	26	1	no	—
391	C₂×D₈	—	13	1	no	—
392	C₂×D₈	—	13	1	no	—
393	C₂×D₈	—	13	1	no	—
394	C₂×D₈	—	26	4	no	—
395	C₂×D₈	C₄×D₁₃	1	1	yes	characteristic
396	C₂×M₁₆	—	2	1	no	—
397	C₂×M₁₆	—	13	1	no	—
398	C₂×M₁₆	—	13	1	no	—
399	C₂×M₁₆	—	26	1	no	—
400	C₂×M₁₆	—	26	1	no	—
401	C₂×M₁₆	—	26	1	no	—
402	C₂×M₁₆	—	26	1	no	—
403	C₂×M₁₆	—	26	1	no	—
404	C₂×M₁₆	—	52	4	no	—
405	C₂×M₁₆	—	52	4	no	—
406	C₂²×C₈	—	2	1	no	—
407	C₂²×C₈	—	13	1	no	—
408	C₂²×C₈	—	13	1	no	—
409	C₂²×C₈	—	26	1	no	—
410	C₂²×C₈	—	26	1	no	—
411	C₂²×C₈	—	26	1	no	—
412	C₄×D₄	—	13	1	no	—
413	C₄×D₄	—	13	1	no	—
414	C₄×D₄	—	13	1	no	—
415	C₄×D₄	—	13	1	no	—
416	C₄×D₄	—	13	1	no	—
417	C₄×D₄	—	13	1	no	—
418	C₄×D₄	—	26	1	no	—
419	C₄×D₄	—	26	1	no	—
420	C₄×D₄	—	26	1	no	—
421	C₄×D₄	—	26	1	no	—
422	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
423	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
424	C₂×C₄⋊C₄	—	13	1	no	—
425	C₂×C₄⋊C₄	—	13	1	no	—
426	C₂×C₂²⋊C₄	—	26	1	no	—
427	C₂×C₂²⋊C₄	—	26	1	no	—
428	C₂×C₄²	—	13	1	no	—
429	#107	—	13	1	no	—
430	#107	—	13	1	no	—
431	#107	—	13	1	no	—
432	#107	C₄×D₁₃	1	1	yes	characteristic
433	C₄⋊C₈	—	13	1	no	—
434	C₄⋊C₈	—	13	1	no	—
435	C₄⋊C₈	—	26	1	no	—
436	C₄⋊C₈	—	26	1	no	—
437	C₄⋊C₈	—	26	1	no	—
438	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
439	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
440	#102	—	13	1	no	—
441	#102	—	13	1	no	—
442	#102	—	13	1	no	—
443	#102	—	13	1	no	—
444	#102	—	13	1	no	—
445	#102	—	13	1	no	—
446	#102	C₄×D₁₃	1	1	yes	characteristic
447	#102	C₄×D₁₃	1	1	yes	characteristic
448	C₂²⋊C₈	—	2	1	no	—
449	C₂²⋊C₈	—	2	1	no	—
450	C₂²⋊C₈	—	26	1	no	—
451	C₂²⋊C₈	—	26	1	no	—
452	C₂²⋊C₈	—	26	1	no	—
453	C₂²⋊C₈	—	26	1	no	—
454	C₂²⋊C₈	—	26	1	no	—
455	C₂²⋊C₈	—	26	1	no	—
456	C₂²⋊C₈	—	26	1	no	—
457	#97	—	13	1	no	—
458	#97	—	13	1	no	—
459	C₄×C₈	—	13	1	no	—
460	C₄×C₈	—	13	1	no	—
461	C₄×C₈	—	13	1	no	—
462	C₄×C₈	—	13	1	no	—
463	C₄×C₈	—	13	1	no	—
464	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
465	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
466	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
467	C₂×C₁₃	—	4	2	no	—
468	C₂×C₁₃	—	8	1	no	—
469	C₂×C₁₃	D₄×M₁₆	1	1	yes	characteristic
470	C₂×C₁₃	C₂×C₄×D₈	1	1	yes	characteristic
471	C₂×C₁₃	#2957	1	1	yes	characteristic
472	D₁₃	—	2	2	no	—
473	D₁₃	—	4	2	no	—
474	D₁₃	—	8	1	no	—
475	C₂⁴	—	26	1	no	—
476	C₂⁴	—	26	1	no	—
477	C₂×D₄	—	13	1	no	—
478	C₂×D₄	—	13	1	no	—
479	C₂×D₄	—	26	1	no	—
480	C₂×D₄	—	26	1	no	—
481	C₂×D₄	—	26	2	no	—
482	C₂×D₄	—	26	2	no	—
483	C₂×D₄	—	52	1	no	—
484	C₂×D₄	—	52	1	no	—
485	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
486	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	13	1	no	—
490	C₂²×C₄	—	13	1	no	—
491	C₂²×C₄	—	13	1	no	—
492	C₂²×C₄	—	26	1	no	—
493	C₂²×C₄	—	26	1	no	—
494	C₂²×C₄	—	26	1	no	—
495	C₂²×C₄	—	26	1	no	—
496	C₂²×C₄	—	26	1	no	—
497	C₂²×C₄	—	26	1	no	—
498	C₂²×C₄	—	26	1	no	—
499	C₂²×C₄	—	26	1	no	—
500	C₂²×C₄	—	52	2	no	—
501	C₂²×C₄	—	52	2	no	—
502	C₂²×C₄	—	52	2	no	—
503	C₂²×C₄	—	52	2	no	—
504	D₈	—	2	2	no	—
505	D₈	—	13	4	no	—
506	D₈	—	26	2	no	—
507	D₈	—	26	2	no	—
508	M₁₆	—	4	2	no	—
509	M₁₆	—	13	4	no	—
510	M₁₆	—	26	2	no	—
511	M₁₆	—	52	2	no	—
512	M₁₆	—	52	2	no	—
513	M₁₆	—	52	2	no	—
514	M₁₆	—	52	2	no	—
515	M₁₆	—	52	2	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	4	2	no	—
520	C₂×C₈	—	13	1	no	—
521	C₂×C₈	—	13	1	no	—
522	C₂×C₈	—	13	1	no	—
523	C₂×C₈	—	13	1	no	—
524	C₂×C₈	—	26	2	no	—
525	C₂×C₈	—	26	1	no	—
526	C₂×C₈	—	26	1	no	—
527	C₂×C₈	—	26	1	no	—
528	C₂×C₈	—	52	1	no	—
529	C₂×C₈	—	52	2	no	—
530	C₂×C₈	—	52	2	no	—
531	C₂×C₈	—	52	2	no	—
532	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
533	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
534	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
535	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
536	C₄⋊C₄	—	13	1	no	—
537	C₄⋊C₄	—	13	1	no	—
538	C₄⋊C₄	—	26	1	no	—
539	C₄⋊C₄	—	26	1	no	—
540	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
541	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
542	C₂²⋊C₄	—	2	1	no	—
543	C₂²⋊C₄	—	2	1	no	—
544	C₂²⋊C₄	—	26	1	no	—
545	C₂²⋊C₄	—	26	1	no	—
546	C₂²⋊C₄	—	26	1	no	—
547	C₂²⋊C₄	—	26	1	no	—
548	C₂²⋊C₄	—	26	1	no	—
549	C₂²⋊C₄	—	26	1	no	—
550	C₄²	—	13	1	no	—
551	C₄²	—	13	1	no	—
552	C₄²	—	13	1	no	—
553	C₄²	C₂³×D₁₃	1	1	yes	characteristic
554	C₁₃	M₁₆×D₈	1	1	yes	characteristic, complemented, Sylow
555	C₂³	—	2	1	no	—
556	C₂³	—	2	1	no	—
557	C₂³	—	13	1	no	—
558	C₂³	—	26	1	no	—
559	C₂³	—	26	1	no	—
560	C₂³	—	52	2	no	—
561	C₂³	—	52	2	no	—
562	C₂³	—	52	2	no	—
563	C₂³	—	52	2	no	—
564	C₂³	—	104	1	no	—
565	C₂³	—	104	1	no	—
566	D₄	—	2	1	no	—
567	D₄	—	2	1	no	—
568	D₄	—	2	1	no	—
569	D₄	—	13	2	no	—
570	D₄	—	26	1	no	—
571	D₄	—	26	1	no	—
572	D₄	—	26	1	no	—
573	D₄	—	52	2	no	—
574	D₄	—	52	2	no	—
575	D₄	M₁₆×D₁₃	1	2	yes	complemented
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	13	1	no	—
583	C₂×C₄	—	13	2	no	—
584	C₂×C₄	—	13	2	no	—
585	C₂×C₄	—	13	1	no	—
586	C₂×C₄	—	13	1	no	—
587	C₂×C₄	—	26	1	no	—
588	C₂×C₄	—	26	1	no	—
589	C₂×C₄	—	26	1	no	—
590	C₂×C₄	—	26	1	no	—
591	C₂×C₄	—	52	1	no	—
592	C₂×C₄	—	52	2	no	—
593	C₂×C₄	—	52	2	no	—
594	C₂×C₄	—	52	2	no	—
595	C₂×C₄	—	52	2	no	—
596	C₂×C₄	—	52	2	no	—
597	C₂×C₄	—	52	2	no	—
598	C₂×C₄	—	52	1	no	—
599	C₂×C₄	—	52	1	no	—
600	C₂×C₄	—	52	1	no	—
601	C₂×C₄	—	52	1	no	—
602	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
603	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
604	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
605	C₈	—	2	1	no	—
606	C₈	—	2	1	no	—
607	C₈	—	2	1	no	—
608	C₈	—	4	1	no	—
609	C₈	—	4	1	no	—
610	C₈	—	4	1	no	—
611	C₈	—	13	2	no	—
612	C₈	—	13	2	no	—
613	C₈	—	26	1	no	—
614	C₈	—	26	1	no	—
615	C₈	—	52	1	no	—
616	C₈	—	52	1	no	—
617	C₈	—	52	1	no	—
618	C₈	D₈×D₁₃	1	2	yes	complemented
619	C₂²	—	2	2	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	1	no	—
624	C₂²	—	4	1	no	—
625	C₂²	—	13	2	no	—
626	C₂²	—	26	1	no	—
627	C₂²	—	26	1	no	—
628	C₂²	—	26	2	no	—
629	C₂²	—	52	1	no	—
630	C₂²	—	52	1	no	—
631	C₂²	—	52	1	no	—
632	C₂²	—	52	1	no	—
633	C₂²	—	52	1	no	—
634	C₂²	—	104	4	no	—
635	C₂²	—	104	4	no	—
636	C₂²	C₄×D₄×D₁₃	1	1	yes	characteristic
637	C₄	—	2	1	no	—
638	C₄	—	4	1	no	—
639	C₄	—	4	1	no	—
640	C₄	—	13	2	no	—
641	C₄	—	26	1	no	—
642	C₄	—	26	1	no	—
643	C₄	—	52	1	no	—
644	C₄	—	52	1	no	—
645	C₄	C₂×M₁₆×D₁₃	1	1	yes	characteristic
646	C₄	#11719455	1	1	yes	characteristic
647	C₄	C₂×D₈×D₁₃	1	1	yes	characteristic
648	C₄	D₁₃×#135	1	1	yes	characteristic
649	C₂	—	4	2	no	—
650	C₂	—	8	1	no	—
651	C₂	—	26	2	no	—
652	C₂	—	52	2	no	—
653	C₂	—	104	1	no	—
654	C₂	#13123569	1	1	yes	characteristic
655	C₂	C₄×D₈×D₁₃	1	1	yes	characteristic
656	C₂	#13123750	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×#1581	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×D₈×D₁₃	C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1581	D₁₃
hypocenter	C₁₃	M₁₆×D₈
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1581

Complements

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

N	H ≅ G/N	type
2. #13123572	C₂	semidirect
3. D₄×#6094	C₂	semidirect
4. #13113719	C₂	semidirect
5. #13113718	C₂	semidirect
6. #13113667	C₂	semidirect
7. #13113666	C₂	semidirect
8. #13113664	C₂	semidirect
9. C₈×#6104	C₂	semidirect
10. #13113628	C₂	semidirect
11. #13113593	C₂	semidirect
12. #13113259	C₂	semidirect
13. #13113259	C₂	semidirect
14. #13113115	C₂	semidirect
15. C₁₃×#1581	C₂	semidirect
22. C₁₃×#436	C₂²	semidirect
23. C₈×D₄×C₁₃	C₂²	semidirect
29. #11718673	C₂²	semidirect
30. D₄×#1055	C₂²	semidirect
33. #11718499	C₂²	semidirect
36. #11718495	C₂²	semidirect
46. #11718349	C₂²	semidirect
48. C₈×D₅₂	C₂²	semidirect
51. C₁₃×#335	C₂²	semidirect
52. C₁₃×D₄⋊C₈	C₂²	semidirect
53. C₁₃×D₄⋊C₈	C₂²	semidirect
54. C₁₃×#322	C₂²	semidirect
55. D₄⋊#1055	C₂²	semidirect
56. D₄⋊#1055	C₂²	semidirect
57. #11718075	C₂²	semidirect
58. #11718075	C₂²	semidirect
59. #11718071	C₂²	semidirect
60. #11718071	C₂²	semidirect
61. #11718051	C₂²	semidirect
62. #11718051	C₂²	semidirect
63. #11718050	C₂²	semidirect
64. #11718046	C₂²	semidirect
65. C₈×#1055	C₂²	semidirect
66. C₈×#1055	C₂²	semidirect
195. #6104	M₁₆	semidirect
222. #6094	D₈	semidirect
235. #1581	D₁₃	semidirect
256. D₄×C₁₃	C₂×M₁₆	semidirect
278. D₅₂	C₂×M₁₆	semidirect
298. C₈×C₁₃	C₂×D₈	semidirect
304. #1055	C₂×M₁₆	semidirect
305. #1055	C₂×D₈	semidirect
322. #436	C₂×D₁₃	semidirect
330. C₈×D₄	C₂×D₁₃	semidirect
344. #335	C₂×D₁₃	semidirect
351. D₄⋊C₈	C₂×D₁₃	semidirect
352. D₄⋊C₈	C₂×D₁₃	semidirect
354. #322	C₂×D₁₃	semidirect
554. C₁₃	M₁₆×D₈	semidirect
575. D₄	M₁₆×D₁₃	semidirect
618. C₈	D₈×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₈×D₁₃	2
#13123572	2
D₄×#6094	2
#13113719	2
#13113718	2
#13113667	2
#13113666	2
#13113664	2
C₈×#6104	2
#13113628	2
#13113593	2
#13113259	2
#13113115	2
C₁₃×#1581	2
M₁₆×D₈	13