Subgroups — #15832443

Order 3328.

688 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123799	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈×#6129	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#88166	C₂	1	1	yes	maximal, characteristic
4	#13113688	C₂	1	1	yes	maximal, characteristic, complemented
5	#13113685	C₂	1	1	yes	maximal, characteristic, complemented
6	#13113682	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113677	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113672	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113669	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113666	C₂	1	1	yes	maximal, characteristic, complemented
11	#13113583	C₂	1	1	yes	maximal, characteristic, complemented
12	#13113215	C₂	1	1	yes	maximal, characteristic, complemented
13	#13113215	C₂	1	1	yes	maximal, characteristic, complemented
14	D₁₃×#322	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1581	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#88166	C₄	1	1	yes	characteristic
17	C₄×#6129	C₂²	1	1	yes	characteristic
18	C₄×#6129	C₂²	1	1	yes	characteristic
19	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
20	C₁₃×#436	C₂²	1	1	yes	characteristic
21	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	D₈×Dic₁₃	C₄	1	1	yes	characteristic
23	#11718788	—	2	1	no	—
24	M₁₆×Dic₁₃	—	2	1	no	—
25	C₈×C₂²⋊D₁₃	—	2	1	no	—
26	C₂×C₈×Dic₁₃	—	2	1	no	—
27	C₄×#6105	C₂²	1	1	yes	characteristic
28	C₄×#6105	C₂²	1	1	yes	characteristic
29	#11718673	C₂²	1	1	yes	characteristic
30	D₄×#1055	C₂²	1	1	yes	characteristic
31	#11718541	C₄	1	1	yes	characteristic
32	#11718534	C₄	1	1	yes	characteristic
33	#11718494	C₂²	1	1	yes	characteristic
34	#11718494	C₂²	1	1	yes	characteristic
35	#11718492	C₂²	1	1	yes	characteristic
36	#11718491	C₂²	1	1	yes	characteristic
37	#11718433	C₄	1	1	yes	characteristic
38	#11718433	C₄	1	1	yes	characteristic
39	#11718419	C₄	1	1	yes	characteristic
40	#11718419	C₄	1	1	yes	characteristic
41	#11718389	—	2	1	no	—
42	#11718386	—	2	1	no	—
43	#11718379	—	2	1	no	—
44	#11718379	—	2	1	no	—
45	C₄×Dic₅₂	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
48	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
49	#11718340	C₂²	1	1	yes	characteristic
50	C₈×Dic₂₆	C₂²	1	1	yes	characteristic
51	C₁₃×#335	C₂²	1	1	yes	characteristic
52	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
53	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
54	C₁₃×#322	C₂²	1	1	yes	characteristic
55	D₄⋊#1055	C₂²	1	1	yes	characteristic
56	D₄⋊#1055	C₂²	1	1	yes	characteristic
57	#11718076	C₂²	1	1	yes	characteristic
58	#11718076	C₂²	1	1	yes	characteristic
59	#11718072	C₂²	1	1	yes	characteristic
60	#11718072	C₂²	1	1	yes	characteristic
61	#11718050	C₂²	1	1	yes	characteristic
62	#11718048	C₂²	1	1	yes	characteristic
63	#11718048	C₂²	1	1	yes	characteristic
64	#11718047	C₂²	1	1	yes	characteristic
65	#11718046	C₂²	1	1	yes	characteristic
66	#11718046	C₂²	1	1	yes	characteristic
67	C₂×#6129	C₂×C₄	1	1	yes	characteristic
68	C₂×#6129	C₂×C₄	1	1	yes	characteristic
69	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
70	C₂×C₁₃×M₁₆	—	2	1	no	—
71	C₂²×C₈×C₁₃	—	2	1	no	—
72	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
74	D₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
75	D₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
76	C₂×#6105	C₂×C₄	1	1	yes	characteristic
77	C₂×#6105	C₂×C₄	1	1	yes	characteristic
78	C₄×C₂²⋊D₁₃	—	2	1	no	—
79	C₄×C₂²⋊D₁₃	—	2	1	no	—
80	C₂×C₄×Dic₁₃	—	2	1	no	—
81	C₂×C₄×Dic₁₃	—	2	1	no	—
82	C₂×#6099	—	2	1	no	—
83	C₂²×#1055	—	2	1	no	—
84	#88166	—	2	4	no	—
85	C₂×Dic₅₂	C₂×C₄	1	1	yes	characteristic
86	C₂×C₈×D₁₃	—	2	1	no	—
87	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
88	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
89	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
90	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
91	#88146	C₂×C₄	1	1	yes	characteristic
92	#88146	C₂×C₄	1	1	yes	characteristic
93	#88141	C₂×C₄	1	1	yes	characteristic
94	#88141	C₂×C₄	1	1	yes	characteristic
95	#88135	—	2	1	no	—
96	#88135	—	2	1	no	—
97	#88131	—	2	1	no	—
98	#88131	—	2	1	no	—
99	C₄²×D₁₃	C₂³	1	1	yes	characteristic
100	C₄×Dic₂₆	C₂³	1	1	yes	characteristic
101	C₄×Dic₂₆	C₂³	1	1	yes	characteristic
102	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
103	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
104	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
105	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
106	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
107	C₁₃×C₂²⋊C₈	—	2	1	no	—
108	C₁₃×C₂²⋊C₈	—	2	1	no	—
109	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
110	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
111	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
112	#88072	C₂×C₄	1	1	yes	characteristic
113	#88072	C₂×C₄	1	1	yes	characteristic
114	C₂²⋊#1055	—	2	1	no	—
115	C₂²⋊#1055	—	2	1	no	—
116	#88060	—	2	1	no	—
117	#88060	—	2	1	no	—
118	#88058	C₂×C₄	1	1	yes	characteristic
119	#88056	C₂×C₄	1	1	yes	characteristic
120	#88056	C₂×C₄	1	1	yes	characteristic
121	#88055	—	2	1	no	—
122	#88055	—	2	1	no	—
123	#88054	—	2	1	no	—
124	#88054	—	2	1	no	—
125	#88054	—	2	1	no	—
126	#88054	—	2	1	no	—
127	C₈×Dic₁₃	—	2	1	no	—
128	C₈×Dic₁₃	—	2	1	no	—
129	C₈×Dic₁₃	—	2	1	no	—
130	C₈×Dic₁₃	—	2	1	no	—
131	C₈×Dic₁₃	—	2	1	no	—
132	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
133	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
134	C₈×Dic₁₃	D₄	1	1	yes	characteristic
135	C₈×Dic₁₃	D₄	1	1	yes	characteristic
136	#88050	C₂×C₄	1	1	yes	characteristic
137	#88050	C₂×C₄	1	1	yes	characteristic
138	#88048	C₂×C₄	1	1	yes	characteristic
139	#88048	C₂×C₄	1	1	yes	characteristic
140	C₄⋊#1055	C₂³	1	1	yes	characteristic
141	C₄⋊#1055	C₂³	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	#17863	—	13	1	no	maximal, Sylow
146	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	—	2	1	no	—
149	C₂²×C₄×C₁₃	—	2	1	no	—
150	C₂×C₂²⋊D₁₃	—	2	1	no	—
151	C₂×C₂²⋊D₁₃	—	2	1	no	—
152	C₂²×Dic₁₃	—	2	1	no	—
153	C₂²×Dic₁₃	—	2	1	no	—
154	C₂²×Dic₁₃	—	2	1	no	—
155	C₂²×Dic₁₃	—	2	1	no	—
156	#6129	—	2	2	no	—
157	#6129	—	2	2	no	—
158	#6129	—	2	2	no	—
159	#6129	M₁₆	1	4	yes	complemented
160	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
163	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
164	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
165	C₁₃×D₈	—	2	2	no	—
166	C₁₃×M₁₆	—	4	2	no	—
167	C₂×C₈×C₁₃	—	2	1	no	—
168	C₂×C₈×C₁₃	—	2	1	no	—
169	C₂×C₈×C₁₃	—	2	1	no	—
170	C₂×C₈×C₁₃	—	4	2	no	—
171	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
176	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
177	C₁₃×C₂²⋊C₄	—	2	1	no	—
178	C₁₃×C₂²⋊C₄	—	2	1	no	—
179	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
180	C₂²⋊Dic₁₃	—	2	1	no	—
181	C₂²⋊Dic₁₃	—	2	1	no	—
182	#6105	—	2	2	no	—
183	#6105	—	2	2	no	—
184	#6103	—	2	1	no	—
185	#6103	—	2	1	no	—
186	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
187	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
188	#6101	—	2	1	no	—
189	#6101	—	2	1	no	—
190	#6101	—	2	1	no	—
191	#6101	—	2	1	no	—
192	C₄×Dic₁₃	—	2	1	no	—
193	C₄×Dic₁₃	—	2	1	no	—
194	C₄×Dic₁₃	—	2	1	no	—
195	C₄×Dic₁₃	—	2	1	no	—
196	C₄×Dic₁₃	—	2	1	no	—
197	C₄×Dic₁₃	—	2	1	no	—
198	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
199	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
200	C₄×Dic₁₃	#41	1	1	yes	characteristic
201	#6099	—	4	2	no	—
202	C₂×#1055	—	2	1	no	—
203	C₂×#1055	—	2	1	no	—
204	C₂×#1055	—	2	1	no	—
205	C₂×#1055	—	4	2	no	—
206	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
207	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
208	C₂×#1055	C₂×D₄	1	1	yes	characteristic
209	C₂×#1055	C₂×D₄	1	1	yes	characteristic
210	Dic₅₂	—	2	2	no	—
211	C₈×D₁₃	—	2	2	no	—
212	C₈×D₁₃	—	2	2	no	—
213	C₈×D₁₃	—	2	2	no	—
214	C₈×D₁₃	—	2	2	no	—
215	C₈×D₁₃	—	4	2	no	—
216	#2965	—	13	1	no	—
217	C₈×#41	—	13	1	no	—
218	C₄×#135	—	13	1	no	—
219	#1584	—	13	1	no	—
220	#1584	—	13	1	no	—
221	#1583	—	13	1	no	—
222	#1583	—	13	1	no	—
223	#1582	—	13	1	no	—
224	#1582	—	13	1	no	—
225	#1581	—	13	1	no	—
226	#1581	D₁₃	1	1	yes	characteristic, complemented
227	#1564	—	13	1	no	—
228	#1476	—	13	1	no	—
229	#1476	—	13	1	no	—
230	C₂×#322	—	13	1	no	—
231	C₂³×C₁₃	—	2	1	no	—
232	C₂³×C₁₃	—	2	1	no	—
233	C₂²×D₁₃	C₄×D₄	1	1	yes	characteristic
234	D₄×C₁₃	—	2	1	no	—
235	D₄×C₁₃	—	2	1	no	—
236	D₄×C₁₃	—	2	1	no	—
237	D₄×C₁₃	C₂×M₁₆	1	2	yes	—
238	C₂×C₄×C₁₃	—	2	1	no	—
239	C₂×C₄×C₁₃	—	2	1	no	—
240	C₂×C₄×C₁₃	—	4	1	no	—
241	C₂×C₄×C₁₃	—	4	1	no	—
242	C₂×C₄×C₁₃	—	4	1	no	—
243	C₂×C₄×C₁₃	—	4	1	no	—
244	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
245	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
247	C₂²⋊D₁₃	—	2	4	no	—
248	C₂²⋊D₁₃	—	4	2	no	—
249	C₂×Dic₁₃	—	2	1	no	—
250	C₂×Dic₁₃	—	2	4	no	—
251	C₂×Dic₁₃	—	2	1	no	—
252	C₂×Dic₁₃	—	2	1	no	—
253	C₂×Dic₁₃	—	2	1	no	—
254	C₂×Dic₁₃	—	4	2	no	—
255	C₂×Dic₁₃	—	4	2	no	—
256	C₂×Dic₁₃	—	4	2	no	—
257	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
258	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
259	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
260	C₄×D₁₃	—	2	1	no	—
261	C₄×D₁₃	—	2	1	no	—
262	C₄×D₁₃	—	2	2	no	—
263	C₄×D₁₃	C₂×M₁₆	1	2	yes	—
264	C₄×D₁₃	#131	1	2	yes	—
265	Dic₂₆	—	2	1	no	—
266	Dic₂₆	—	2	1	no	—
267	Dic₂₆	—	2	1	no	—
268	Dic₂₆	C₂×M₁₆	1	2	yes	—
269	C₈×C₁₃	—	2	1	no	—
270	C₈×C₁₃	—	2	1	no	—
271	C₈×C₁₃	—	2	1	no	—
272	C₈×C₁₃	—	4	1	no	—
273	C₈×C₁₃	—	4	1	no	—
274	C₈×C₁₃	—	4	1	no	—
275	C₈×C₁₃	#135	1	2	yes	complemented
276	#1055	—	2	1	no	—
277	#1055	—	2	1	no	—
278	#1055	—	2	1	no	—
279	#1055	—	4	1	no	—
280	#1055	—	4	1	no	—
281	#1055	—	4	1	no	—
282	#1055	#135	1	2	yes	complemented
283	C₂×#135	—	13	1	no	—
284	C₄×#41	—	13	1	no	—
285	C₄×#41	—	13	1	no	—
286	#446	—	13	1	no	—
287	#446	—	13	1	no	—
288	C₈×Q₈	—	13	1	no	—
289	C₈×Q₈	—	13	1	no	—
290	C₄×Q₁₆	—	13	1	no	—
291	C₄×Q₁₆	—	13	1	no	—
292	C₄×SD₁₆	—	13	1	no	—
293	C₄×SD₁₆	—	13	1	no	—
294	C₄×SD₁₆	—	13	1	no	—
295	C₄×SD₁₆	—	13	1	no	—
296	C₄×D₈	—	13	1	no	—
297	C₄×D₈	C₂×D₁₃	1	1	yes	characteristic
298	#436	—	13	1	no	—
299	#436	C₂×D₁₃	1	1	yes	characteristic
300	#435	—	26	1	no	—
301	#435	—	26	1	no	—
302	C₈×D₄	—	13	1	no	—
303	C₈×D₄	—	26	1	no	—
304	C₈×D₄	—	26	1	no	—
305	C₈×D₄	C₂×D₁₃	1	1	yes	characteristic
306	#431	—	13	1	no	—
307	#431	—	13	1	no	—
308	#431	—	26	1	no	—
309	#431	—	26	1	no	—
310	#427	—	13	1	no	—
311	#416	—	13	1	no	—
312	#416	—	13	1	no	—
313	C₄×M₁₆	—	26	1	no	—
314	C₂×C₄×C₈	—	13	1	no	—
315	C₂×C₄×C₈	—	13	1	no	—
316	C₂×C₄×C₈	—	13	1	no	—
317	C₂×C₄×C₈	—	26	1	no	—
318	#335	—	13	1	no	—
319	#335	C₂×D₁₃	1	1	yes	characteristic
320	#334	—	13	1	no	—
321	#334	—	13	1	no	—
322	Q₈⋊C₈	—	13	1	no	—
323	Q₈⋊C₈	—	13	1	no	—
324	Q₈⋊C₈	—	13	1	no	—
325	Q₈⋊C₈	—	13	1	no	—
326	D₄⋊C₈	—	13	1	no	—
327	D₄⋊C₈	—	13	1	no	—
328	D₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
329	D₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
330	#322	—	13	1	no	—
331	#322	—	13	1	no	—
332	#322	—	13	1	no	—
333	#322	C₂×D₁₃	1	1	yes	characteristic
334	C₂²×C₁₃	—	2	2	no	—
335	C₂²×C₁₃	—	4	1	no	—
336	C₂²×C₁₃	—	4	1	no	—
337	C₂²×C₁₃	—	4	1	no	—
338	C₂²×C₁₃	—	4	1	no	—
339	C₂²×C₁₃	—	4	1	no	—
340	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
341	C₂×D₁₃	—	2	1	no	—
342	C₂×D₁₃	—	2	1	no	—
343	C₂×D₁₃	#435	1	2	yes	—
344	C₄×C₁₃	—	2	1	no	—
345	C₄×C₁₃	—	4	1	no	—
346	C₄×C₁₃	—	4	1	no	—
347	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
348	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
349	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
350	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
351	Dic₁₃	—	2	2	no	—
352	Dic₁₃	—	2	1	no	—
353	Dic₁₃	—	4	1	no	—
354	Dic₁₃	—	4	1	no	—
355	Dic₁₃	—	4	1	no	—
356	Dic₁₃	#435	1	2	yes	—
357	Dic₁₃	#444	1	2	yes	—
358	C₂×#41	—	13	1	no	—
359	C₂×#41	—	13	1	no	—
360	#135	—	26	4	no	—
361	C₂×Q₁₆	—	13	1	no	—
362	C₂×SD₁₆	—	13	1	no	—
363	C₂×SD₁₆	—	13	1	no	—
364	C₂×D₈	C₄×D₁₃	1	1	yes	characteristic
365	C₂×M₁₆	—	2	1	no	—
366	C₂×M₁₆	—	26	1	no	—
367	C₂²×C₈	—	2	1	no	—
368	C₂²×C₈	—	13	1	no	—
369	C₂²×C₈	—	13	1	no	—
370	C₂²×C₈	—	13	1	no	—
371	C₂²×C₈	—	13	1	no	—
372	C₂²×C₈	—	26	1	no	—
373	C₂²×C₈	—	26	1	no	—
374	C₄×Q₈	—	13	1	no	—
375	C₄×Q₈	—	13	1	no	—
376	C₄×Q₈	—	13	1	no	—
377	C₄×Q₈	—	13	1	no	—
378	C₄×D₄	—	13	1	no	—
379	C₄×D₄	—	13	1	no	—
380	C₄×D₄	—	26	1	no	—
381	C₄×D₄	—	26	1	no	—
382	C₄×D₄	—	26	1	no	—
383	C₄×D₄	—	26	1	no	—
384	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
385	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
386	#117	—	13	1	no	—
387	#117	—	13	1	no	—
388	#117	—	26	1	no	—
389	#117	—	26	1	no	—
390	C₂×C₄²	—	13	1	no	—
391	C₂×C₄²	—	26	1	no	—
392	C₂×C₄²	—	26	1	no	—
393	#107	—	13	1	no	—
394	#107	C₄×D₁₃	1	1	yes	characteristic
395	#106	—	13	1	no	—
396	#106	—	13	1	no	—
397	C₄⋊C₈	—	13	1	no	—
398	C₄⋊C₈	—	13	1	no	—
399	C₄⋊C₈	—	26	1	no	—
400	C₄⋊C₈	—	26	1	no	—
401	C₄⋊C₈	—	26	1	no	—
402	C₄⋊C₈	—	26	1	no	—
403	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
404	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
405	#103	—	13	1	no	—
406	#103	—	13	1	no	—
407	#103	—	13	1	no	—
408	#103	—	13	1	no	—
409	#102	—	13	1	no	—
410	#102	—	13	1	no	—
411	#102	C₄×D₁₃	1	1	yes	characteristic
412	#102	C₄×D₁₃	1	1	yes	characteristic
413	C₂²⋊C₈	—	2	1	no	—
414	C₂²⋊C₈	—	2	1	no	—
415	C₂²⋊C₈	—	26	1	no	—
416	C₂²⋊C₈	—	26	1	no	—
417	C₂²⋊C₈	—	26	1	no	—
418	C₂²⋊C₈	—	26	1	no	—
419	#97	—	26	1	no	—
420	#97	—	26	1	no	—
421	C₄×C₈	—	13	1	no	—
422	C₄×C₈	—	13	1	no	—
423	C₄×C₈	—	13	1	no	—
424	C₄×C₈	—	13	1	no	—
425	C₄×C₈	—	13	1	no	—
426	C₄×C₈	—	13	1	no	—
427	C₄×C₈	—	13	1	no	—
428	C₄×C₈	—	26	1	no	—
429	C₄×C₈	—	26	1	no	—
430	C₄×C₈	—	26	1	no	—
431	C₄×C₈	—	26	1	no	—
432	C₄×C₈	—	26	1	no	—
433	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
434	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
435	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
436	C₂×C₁₃	—	4	2	no	—
437	C₂×C₁₃	—	8	1	no	—
438	C₂×C₁₃	C₂×#435	1	1	yes	characteristic
439	C₂×C₁₃	C₄×#135	1	1	yes	characteristic
440	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
441	D₁₃	—	2	2	no	—
442	#41	—	13	4	no	—
443	#41	—	26	2	no	—
444	#41	—	26	2	no	—
445	#41	—	26	2	no	—
446	C₂×Q₈	—	13	1	no	—
447	C₂×Q₈	—	13	1	no	—
448	C₂×D₄	—	26	1	no	—
449	C₂×D₄	—	26	1	no	—
450	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
451	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	13	1	no	—
455	C₂²×C₄	—	13	1	no	—
456	C₂²×C₄	—	13	1	no	—
457	C₂²×C₄	—	26	1	no	—
458	C₂²×C₄	—	26	1	no	—
459	C₂²×C₄	—	26	1	no	—
460	C₂²×C₄	—	26	1	no	—
461	Q₁₆	—	26	2	no	—
462	SD₁₆	—	26	2	no	—
463	SD₁₆	—	26	2	no	—
464	D₈	—	2	2	no	—
465	M₁₆	—	4	2	no	—
466	M₁₆	—	52	2	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	4	2	no	—
471	C₂×C₈	—	13	1	no	—
472	C₂×C₈	—	13	1	no	—
473	C₂×C₈	—	13	1	no	—
474	C₂×C₈	—	13	1	no	—
475	C₂×C₈	—	26	2	no	—
476	C₂×C₈	—	26	2	no	—
477	C₂×C₈	—	26	2	no	—
478	C₂×C₈	—	26	2	no	—
479	C₂×C₈	—	26	1	no	—
480	C₂×C₈	—	26	1	no	—
481	C₂×C₈	—	26	1	no	—
482	C₂×C₈	—	52	2	no	—
483	C₂×C₈	—	52	2	no	—
484	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
485	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
486	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
487	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
488	C₄⋊C₄	—	13	1	no	—
489	C₄⋊C₄	—	13	1	no	—
490	C₄⋊C₄	—	26	1	no	—
491	C₄⋊C₄	—	26	1	no	—
492	C₄⋊C₄	—	26	1	no	—
493	C₄⋊C₄	—	26	1	no	—
494	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
495	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
496	C₂²⋊C₄	—	2	1	no	—
497	C₂²⋊C₄	—	2	1	no	—
498	C₂²⋊C₄	—	26	1	no	—
499	C₂²⋊C₄	—	26	1	no	—
500	C₂²⋊C₄	—	26	1	no	—
501	C₂²⋊C₄	—	26	1	no	—
502	C₄²	—	13	1	no	—
503	C₄²	—	13	1	no	—
504	C₄²	—	13	1	no	—
505	C₄²	—	26	1	no	—
506	C₄²	—	26	1	no	—
507	C₄²	—	26	1	no	—
508	C₄²	—	26	1	no	—
509	C₄²	—	26	1	no	—
510	C₄²	—	26	1	no	—
511	C₄²	C₂³×D₁₃	1	1	yes	characteristic
512	C₁₃	#17863	1	1	yes	characteristic, complemented, Sylow
513	C₂³	—	2	1	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	13	1	no	—
516	Q₈	—	13	2	no	—
517	Q₈	—	26	1	no	—
518	Q₈	—	26	1	no	—
519	Q₈	—	26	1	no	—
520	D₄	—	2	1	no	—
521	D₄	—	2	1	no	—
522	D₄	—	2	1	no	—
523	D₄	—	26	4	no	—
524	D₄	—	52	2	no	—
525	D₄	M₁₆×D₁₃	1	2	yes	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	13	1	no	—
533	C₂×C₄	—	13	1	no	—
534	C₂×C₄	—	13	2	no	—
535	C₂×C₄	—	13	2	no	—
536	C₂×C₄	—	13	1	no	—
537	C₂×C₄	—	26	2	no	—
538	C₂×C₄	—	26	4	no	—
539	C₂×C₄	—	26	1	no	—
540	C₂×C₄	—	26	1	no	—
541	C₂×C₄	—	26	1	no	—
542	C₂×C₄	—	26	1	no	—
543	C₂×C₄	—	26	1	no	—
544	C₂×C₄	—	26	1	no	—
545	C₂×C₄	—	52	2	no	—
546	C₂×C₄	—	52	2	no	—
547	C₂×C₄	—	52	2	no	—
548	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
549	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
550	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
551	C₈	—	2	1	no	—
552	C₈	—	2	1	no	—
553	C₈	—	2	1	no	—
554	C₈	—	4	1	no	—
555	C₈	—	4	1	no	—
556	C₈	—	4	1	no	—
557	C₈	—	13	2	no	—
558	C₈	—	26	1	no	—
559	C₈	—	26	1	no	—
560	C₈	—	26	1	no	—
561	C₈	—	52	1	no	—
562	C₈	—	52	1	no	—
563	C₈	—	52	1	no	—
564	C₈	#88166	1	2	yes	complemented
565	C₂²	—	2	2	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	1	no	—
570	C₂²	—	4	1	no	—
571	C₂²	—	13	2	no	—
572	C₂²	—	26	1	no	—
573	C₂²	—	26	1	no	—
574	C₂²	C₄×D₄×D₁₃	1	1	yes	characteristic
575	C₄	—	2	1	no	—
576	C₄	—	4	1	no	—
577	C₄	—	4	1	no	—
578	C₄	—	13	2	no	—
579	C₄	—	13	2	no	—
580	C₄	—	26	1	no	—
581	C₄	—	26	2	no	—
582	C₄	—	52	1	no	—
583	C₄	—	52	1	no	—
584	C₄	—	52	1	no	—
585	C₄	C₂×M₁₆×D₁₃	1	1	yes	characteristic
586	C₄	D₁₃×#131	1	1	yes	characteristic
587	C₄	C₂×#88166	1	1	yes	characteristic
588	C₄	D₁₃×#135	1	1	yes	characteristic
589	C₂	—	4	2	no	—
590	C₂	—	8	1	no	—
591	C₂	—	26	2	no	—
592	C₂	D₁₃×#435	1	1	yes	characteristic
593	C₂	C₄×#88166	1	1	yes	characteristic
594	C₂	D₁₃×#444	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×#88166	C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1581	D₁₃
hypocenter	C₁₃	#17863
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
1. #13123799	C₂	semidirect
2. C₈×#6129	C₂	semidirect
4. #13113688	C₂	semidirect
5. #13113685	C₂	semidirect
6. #13113682	C₂	semidirect
7. #13113677	C₂	semidirect
8. #13113672	C₂	semidirect
9. #13113669	C₂	semidirect
10. #13113666	C₂	semidirect
11. #13113583	C₂	semidirect
12. #13113215	C₂	semidirect
13. #13113215	C₂	semidirect
14. D₁₃×#322	C₂	semidirect
15. C₁₃×#1581	C₂	semidirect
159. #6129	M₁₆	semidirect
226. #1581	D₁₃	semidirect
275. C₈×C₁₃	#135	semidirect
282. #1055	#135	semidirect
512. C₁₃	#17863	semidirect
564. C₈	#88166	semidirect

Maximal subgroups

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

subgroup	index
#13123799	2
C₈×#6129	2
C₄×#88166	2
#13113688	2
#13113685	2
#13113682	2
#13113677	2
#13113672	2
#13113669	2
#13113666	2
#13113583	2
#13113215	2
D₁₃×#322	2
C₁₃×#1581	2
#17863	13