Subgroups — #16807344

Order 3328.

564 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131222	C₂	1	1	yes	maximal, characteristic, complemented
2	#13131221	C₂	1	1	yes	maximal, characteristic, complemented
3	#13131221	C₂	1	1	yes	maximal, characteristic, complemented
4	#13131220	C₂	1	1	yes	maximal, characteristic, complemented
5	#13131219	C₂	1	1	yes	maximal, characteristic, complemented
6	#13131218	C₂	1	1	yes	maximal, characteristic, complemented
7	#13131217	C₂	1	1	yes	maximal, characteristic, complemented
8	#13131216	C₂	1	1	yes	maximal, characteristic, complemented
9	#13131204	C₂	1	1	yes	maximal, characteristic, complemented
10	#13131203	C₂	1	1	yes	maximal, characteristic, complemented
11	#13131068	C₂	1	1	yes	maximal, characteristic, complemented
12	#13131067	C₂	1	1	yes	maximal, characteristic, complemented
13	#13131065	C₂	1	1	yes	maximal, characteristic, complemented
14	#13131064	C₂	1	1	yes	maximal, characteristic, complemented
15	#13123527	C₂	1	1	yes	maximal, characteristic
16	C₂×#88161	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
18	#11719252	C₄	1	1	yes	characteristic
19	C₂×#88106	C₂²	1	1	yes	characteristic
20	C₂×#88106	C₂²	1	1	yes	characteristic
21	C₂×#88106	C₂²	1	1	yes	characteristic, complemented
22	C₂²×#6092	C₂²	1	1	yes	characteristic, complemented
23	C₂×#88098	C₂²	1	1	yes	characteristic
24	C₂×#88098	C₂²	1	1	yes	characteristic
25	C₂×#88098	C₂²	1	1	yes	characteristic, complemented
26	C₂×D₁₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
27	C₁₃×#435	C₄	1	1	yes	characteristic
28	#11718788	C₄	1	1	yes	characteristic
29	#11718772	C₄	1	1	yes	characteristic
30	D₄×#1055	C₂²	1	1	yes	characteristic
31	#11718500	C₄	1	1	yes	characteristic
32	#11718495	C₂²	1	1	yes	characteristic
33	#11718388	C₄	1	1	yes	characteristic
34	#11718387	C₄	1	1	yes	characteristic
35	#11718386	C₂²	1	1	yes	characteristic
36	#11718386	C₂²	1	1	yes	characteristic
37	#11718369	C₂²	1	1	yes	characteristic
38	#11718367	C₄	1	1	yes	characteristic
39	C₂²⋊#6092	C₂²	1	1	yes	characteristic
40	C₂²⋊#6092	C₂²	1	1	yes	characteristic
41	C₂²⋊#6092	C₂²	1	1	yes	characteristic, complemented
42	C₂²⋊#6092	C₂²	1	1	yes	characteristic, complemented
43	#11718260	C₂²	1	1	yes	characteristic, complemented
44	#11718260	C₂²	1	1	yes	characteristic, complemented
45	#11718259	C₂²	1	1	yes	characteristic
46	#11718259	C₂²	1	1	yes	characteristic
47	#11718259	C₂²	1	1	yes	characteristic
48	#11718259	C₂²	1	1	yes	characteristic
49	#11718259	C₂²	1	1	yes	characteristic
50	#11718259	C₂²	1	1	yes	characteristic
51	#11718259	C₂²	1	1	yes	characteristic, complemented
52	#11718259	C₂²	1	1	yes	characteristic, complemented
53	#11718258	C₂²	1	1	yes	characteristic, complemented
54	#11718257	C₂²	1	1	yes	characteristic, complemented
55	#11718231	C₂²	1	1	yes	characteristic, complemented
56	C₄⋊#6092	C₂²	1	1	yes	characteristic, complemented
57	C₄⋊#6092	C₂²	1	1	yes	characteristic, complemented
58	C₄×#6092	C₂²	1	1	yes	characteristic, complemented
59	C₂×#6127	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
63	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
64	#88193	C₈	1	1	yes	characteristic
65	#88191	C₈	1	1	yes	characteristic
66	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
67	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
68	C₂²×#1055	C₂³	1	1	yes	characteristic
69	C₂²×#1055	C₂³	1	1	yes	characteristic
70	#88161	—	4	1	no	—
71	#88161	—	4	1	no	—
72	C₂×#6094	C₂×C₄	1	1	yes	characteristic
73	C₂×#6094	C₂×C₄	1	1	yes	characteristic
74	C₂×#6094	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₁₃	—	4	1	no	—
76	C₂×C₈×D₁₃	—	4	1	no	—
77	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
80	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
81	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
82	#88150	C₈	1	1	yes	characteristic
83	#88148	C₈	1	1	yes	characteristic
84	#88138	C₈	1	1	yes	characteristic
85	#88137	C₈	1	1	yes	characteristic
86	#88136	C₈	1	1	yes	characteristic
87	#88132	C₈	1	1	yes	characteristic
88	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
89	#88126	C₂×C₄	1	1	yes	characteristic
90	#88106	—	4	1	no	—
91	#88106	—	4	1	no	—
92	#88106	—	4	1	no	—
93	C₂×#6092	—	4	1	no	—
94	C₂×#6092	C₂³	1	1	yes	characteristic
95	C₂×#6092	C₂³	1	1	yes	characteristic
96	C₂×#6092	C₂³	1	1	yes	characteristic
97	C₂×#6092	C₂³	1	1	yes	characteristic
98	C₂×#6092	C₂³	1	1	yes	characteristic
99	C₂×#6092	C₂³	1	1	yes	characteristic
100	C₂×#6092	C₂³	1	1	yes	characteristic
101	C₂×#6092	C₂³	1	1	yes	characteristic
102	#88098	—	4	1	no	—
103	#88098	—	4	1	no	—
104	#88098	—	4	1	no	—
105	D₁₃⋊C₁₆	—	4	1	no	—
106	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
107	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
108	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
109	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
110	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
111	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
112	#88060	C₂×C₄	1	1	yes	characteristic
113	#88060	C₂×C₄	1	1	yes	characteristic
114	#88060	C₂×C₄	1	1	yes	characteristic
115	#88060	C₂×C₄	1	1	yes	characteristic
116	#88055	C₂×C₄	1	1	yes	characteristic
117	#88054	C₂×C₄	1	1	yes	characteristic
118	#88054	C₂×C₄	1	1	yes	characteristic
119	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
120	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
121	C₄×#1055	C₂³	1	1	yes	characteristic
122	#33492	—	13	1	no	maximal, Sylow
123	C₂³×D₁₃	C₂×C₈	1	1	yes	characteristic
124	C₂×D₄×C₁₃	C₂×C₈	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
128	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
129	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
130	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
131	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
132	#6127	—	4	1	no	—
133	#6127	—	4	1	no	—
134	C₂×D₅₂	C₂×C₈	1	1	yes	characteristic
135	C₂×D₅₂	C₂×C₈	1	1	yes	characteristic
136	C₂×C₄×D₁₃	—	4	1	no	—
137	C₂×C₄×D₁₃	—	4	1	no	—
138	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
139	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
140	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
143	C₂×Dic₂₆	C₂×C₈	1	1	yes	characteristic
144	C₁₃×M₁₆	—	4	1	no	—
145	C₂×C₈×C₁₃	—	4	1	no	—
146	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
150	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
151	C₁₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
152	C₁₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
153	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
154	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
155	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
156	#6103	C₂×C₈	1	1	yes	characteristic
157	#6103	C₂×C₈	1	1	yes	characteristic
158	#6103	C₂×C₈	1	1	yes	characteristic
159	#6103	C₂×C₈	1	1	yes	characteristic
160	#6103	C₂×C₈	1	1	yes	characteristic
161	#6103	C₂×C₈	1	1	yes	characteristic
162	C₄⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
163	#6101	C₂×C₈	1	1	yes	characteristic
164	#6101	C₂×C₈	1	1	yes	characteristic
165	#6101	C₂×C₈	1	1	yes	characteristic
166	#6101	C₂×C₈	1	1	yes	characteristic
167	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
168	C₂×#1055	—	2	1	no	—
169	C₂×#1055	—	2	1	no	—
170	C₂×#1055	—	2	1	no	—
171	C₂×#1055	—	2	1	no	—
172	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
173	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
174	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
175	C₂×#1055	C₂⁴	1	1	yes	characteristic
176	#6094	—	4	1	no	—
177	#6094	—	4	1	no	—
178	#6094	—	4	1	no	—
179	C₈×D₁₃	—	2	1	no	—
180	C₈×D₁₃	—	2	1	no	—
181	C₈×D₁₃	—	2	1	no	—
182	C₈×D₁₃	—	2	1	no	—
183	C₈×D₁₃	—	2	1	no	—
184	C₈×D₁₃	—	2	1	no	—
185	C₈×D₁₃	—	4	1	no	—
186	C₈×D₁₃	—	4	1	no	—
187	#6092	—	2	1	no	—
188	#6092	—	2	1	no	—
189	#6092	—	2	1	no	—
190	#6092	—	2	1	no	—
191	#6092	—	2	1	no	—
192	#6092	—	2	1	no	—
193	#6092	—	2	1	no	—
194	#6092	—	2	1	no	—
195	#2929	—	13	1	no	—
196	#2169	—	13	1	no	—
197	#2169	—	13	1	no	—
198	#2169	—	13	1	no	—
199	#2169	—	13	1	no	—
200	#2168	—	13	1	no	—
201	#2168	—	13	1	no	—
202	#2168	—	13	1	no	—
203	#2168	—	13	1	no	—
204	#2164	—	13	1	no	—
205	#2164	—	13	1	no	—
206	#2113	—	13	1	no	—
207	#2113	—	13	1	no	—
208	#2112	—	13	1	no	—
209	#2112	—	13	1	no	—
210	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
211	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
212	C₂²×D₁₃	—	4	1	no	—
213	C₂²×D₁₃	—	4	1	no	—
214	C₂²×D₁₃	—	4	1	no	—
215	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
216	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
217	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
218	D₄×C₁₃	—	4	1	no	—
219	C₂×C₄×C₁₃	—	2	1	no	—
220	C₂×C₄×C₁₃	—	2	1	no	—
221	C₂×C₄×C₁₃	—	2	1	no	—
222	C₂×C₄×C₁₃	—	2	1	no	—
223	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
228	C₂²⋊D₁₃	—	4	1	no	—
229	C₂²⋊D₁₃	—	4	1	no	—
230	C₂²⋊D₁₃	—	4	1	no	—
231	C₂²⋊D₁₃	—	4	1	no	—
232	C₂×Dic₁₃	—	4	1	no	—
233	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
234	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
235	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
236	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
237	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
238	D₅₂	—	4	1	no	—
239	D₅₂	—	4	1	no	—
240	C₄×D₁₃	—	2	1	no	—
241	C₄×D₁₃	—	2	1	no	—
242	C₄×D₁₃	—	2	1	no	—
243	C₄×D₁₃	—	2	1	no	—
244	C₄×D₁₃	—	2	1	no	—
245	C₄×D₁₃	—	2	1	no	—
246	C₄×D₁₃	—	4	1	no	—
247	C₄×D₁₃	—	4	1	no	—
248	Dic₂₆	—	4	1	no	—
249	C₈×C₁₃	—	2	1	no	—
250	C₈×C₁₃	—	2	1	no	—
251	C₈×C₁₃	—	2	1	no	—
252	C₈×C₁₃	—	2	1	no	—
253	#1055	—	2	1	no	—
254	#1055	—	2	1	no	—
255	#1055	—	2	1	no	—
256	#1055	H(5,𝔽₂)	1	1	yes	characteristic
257	#1055	H(5,𝔽₂)	1	1	yes	characteristic
258	C₂×#131	—	13	1	no	—
259	C₂³×C₈	—	13	1	no	—
260	#525	—	13	1	no	—
261	C₂×M₃₂	—	13	1	no	—
262	C₂×M₃₂	—	13	1	no	—
263	C₂×M₃₂	—	13	1	no	—
264	C₂×M₃₂	—	13	1	no	—
265	C₂×M₃₂	—	13	1	no	—
266	C₂×M₃₂	—	13	1	no	—
267	C₂²×C₁₆	—	13	1	no	—
268	C₂²×C₁₆	—	13	1	no	—
269	#435	—	13	1	no	—
270	#435	—	13	1	no	—
271	#435	—	13	1	no	—
272	#435	#261	1	1	yes	characteristic
273	C₈×D₄	—	13	1	no	—
274	C₈×D₄	—	13	1	no	—
275	C₈×D₄	—	13	1	no	—
276	C₈×D₄	—	13	1	no	—
277	#424	—	13	1	no	—
278	#408	—	13	1	no	—
279	#407	—	13	1	no	—
280	#405	—	13	1	no	—
281	C₄⋊C₁₆	—	13	1	no	—
282	C₄⋊C₁₆	—	13	1	no	—
283	C₄⋊C₁₆	—	13	1	no	—
284	C₄⋊C₁₆	—	13	1	no	—
285	C₂²⋊C₁₆	—	13	1	no	—
286	C₂²⋊C₁₆	—	13	1	no	—
287	C₂²⋊C₁₆	—	13	1	no	—
288	C₂²⋊C₁₆	—	13	1	no	—
289	C₂²⋊C₁₆	—	13	1	no	—
290	C₂²⋊C₁₆	—	13	1	no	—
291	C₂²⋊C₁₆	—	13	1	no	—
292	C₂²⋊C₁₆	—	13	1	no	—
293	C₂²⋊C₁₆	—	13	1	no	—
294	C₂²⋊C₁₆	—	13	1	no	—
295	C₂²⋊C₁₆	—	13	1	no	—
296	C₂²⋊C₁₆	—	13	1	no	—
297	#346	—	13	1	no	—
298	#346	—	13	1	no	—
299	C₄×C₁₆	—	13	1	no	—
300	C₄×C₁₆	—	13	1	no	—
301	C₂²×C₁₃	—	2	1	no	—
302	C₂²×C₁₃	—	2	1	no	—
303	C₂²×C₁₃	—	2	1	no	—
304	C₂²×C₁₃	—	2	1	no	—
305	C₂²×C₁₃	—	2	1	no	—
306	C₂²×C₁₃	—	2	1	no	—
307	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
308	C₂×D₁₃	—	2	1	no	—
309	C₂×D₁₃	—	2	1	no	—
310	C₂×D₁₃	—	2	1	no	—
311	C₂×D₁₃	—	2	1	no	—
312	C₂×D₁₃	—	2	1	no	—
313	C₂×D₁₃	—	2	1	no	—
314	C₂×D₁₃	—	2	1	no	—
315	C₂×D₁₃	—	2	1	no	—
316	C₂×D₁₃	—	2	1	no	—
317	C₂×D₁₃	—	4	4	no	—
318	C₄×C₁₃	—	2	1	no	—
319	C₄×C₁₃	—	2	1	no	—
320	C₄×C₁₃	—	2	1	no	—
321	C₄×C₁₃	—	2	1	no	—
322	C₄×C₁₃	#518	1	1	yes	characteristic
323	C₄×C₁₃	#568	1	1	yes	characteristic
324	Dic₁₃	—	2	1	no	—
325	Dic₁₃	—	2	1	no	—
326	Dic₁₃	—	2	1	no	—
327	Dic₁₃	—	2	1	no	—
328	Dic₁₃	—	2	1	no	—
329	C₂×#41	—	13	1	no	—
330	C₂³×C₄	—	13	1	no	—
331	#131	—	52	1	no	—
332	#131	—	52	1	no	—
333	C₂×M₁₆	—	13	1	no	—
334	C₂×M₁₆	—	13	1	no	—
335	C₂×M₁₆	—	13	1	no	—
336	C₂×M₁₆	C₂×#261	1	1	yes	characteristic
337	C₂²×C₈	—	13	1	no	—
338	C₂²×C₈	—	13	1	no	—
339	C₂²×C₈	—	13	1	no	—
340	C₂²×C₈	—	13	1	no	—
341	C₂²×C₈	—	13	1	no	—
342	C₂²×C₈	—	13	1	no	—
343	C₂²×C₈	—	13	1	no	—
344	C₂²×C₈	—	52	1	no	—
345	C₂²×C₈	—	52	1	no	—
346	C₂²×C₈	C₂×#261	1	1	yes	characteristic
347	#123	—	13	1	no	—
348	#123	—	13	1	no	—
349	C₂²⋊Q₈	—	13	1	no	—
350	C₂²⋊Q₈	—	13	1	no	—
351	#121	—	13	1	no	—
352	#121	—	13	1	no	—
353	#120	—	13	1	no	—
354	#120	—	13	1	no	—
355	C₄×D₄	—	13	1	no	—
356	C₄×D₄	—	13	1	no	—
357	C₄×D₄	—	13	1	no	—
358	C₄×D₄	C₂×#261	1	1	yes	characteristic
359	#117	—	13	1	no	—
360	M₃₂	—	52	1	no	—
361	M₃₂	—	52	1	no	—
362	M₃₂	—	52	1	no	—
363	M₃₂	—	52	1	no	—
364	M₃₂	—	52	1	no	—
365	M₃₂	—	52	1	no	—
366	C₂×C₁₆	—	13	1	no	—
367	C₂×C₁₆	—	13	1	no	—
368	C₂×C₁₆	—	13	1	no	—
369	C₂×C₁₆	—	13	1	no	—
370	C₂×C₁₆	—	13	1	no	—
371	C₂×C₁₆	—	13	1	no	—
372	C₂×C₁₆	—	13	1	no	—
373	C₂×C₁₆	—	13	1	no	—
374	C₂×C₁₆	—	52	1	no	—
375	C₂×C₁₆	—	52	1	no	—
376	C₄⋊C₈	—	13	1	no	—
377	C₄⋊C₈	—	13	1	no	—
378	C₄⋊C₈	—	13	1	no	—
379	C₄⋊C₈	C₂×#261	1	1	yes	characteristic
380	C₂²⋊C₈	—	13	1	no	—
381	C₂²⋊C₈	—	13	1	no	—
382	C₂²⋊C₈	—	13	1	no	—
383	C₂²⋊C₈	—	13	1	no	—
384	C₂²⋊C₈	—	13	1	no	—
385	C₂²⋊C₈	—	13	1	no	—
386	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
387	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
388	#97	—	13	1	no	—
389	#97	C₂×#261	1	1	yes	characteristic
390	C₄×C₈	—	13	1	no	—
391	C₄×C₈	—	13	1	no	—
392	C₂×C₁₃	—	4	1	no	—
393	C₂×C₁₃	—	4	1	no	—
394	C₂×C₁₃	#2972	1	1	yes	characteristic
395	C₂×C₁₃	#3407	1	1	yes	characteristic
396	C₂×C₁₃	#3407	1	1	yes	characteristic
397	D₁₃	—	4	1	no	—
398	D₁₃	—	4	1	no	—
399	D₁₃	—	4	1	no	—
400	C₂⁴	—	13	1	no	—
401	#41	—	52	1	no	—
402	#41	—	52	1	no	—
403	C₂×Q₈	—	13	1	no	—
404	C₂×D₄	—	13	1	no	—
405	C₂×D₄	—	13	1	no	—
406	C₂×D₄	—	13	1	no	—
407	C₂×D₄	—	13	1	no	—
408	C₂×D₄	—	13	1	no	—
409	C₂×D₄	—	13	1	no	—
410	C₂×D₄	D₁₃⋊C₈	1	1	yes	characteristic
411	C₂²×C₄	—	13	1	no	—
412	C₂²×C₄	—	13	1	no	—
413	C₂²×C₄	—	13	1	no	—
414	C₂²×C₄	—	13	1	no	—
415	C₂²×C₄	—	13	1	no	—
416	C₂²×C₄	—	13	1	no	—
417	C₂²×C₄	—	52	1	no	—
418	C₂²×C₄	—	52	1	no	—
419	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
420	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
421	M₁₆	—	4	1	no	—
422	M₁₆	—	52	1	no	—
423	M₁₆	—	52	1	no	—
424	M₁₆	—	52	1	no	—
425	C₂×C₈	—	4	1	no	—
426	C₂×C₈	—	13	1	no	—
427	C₂×C₈	—	13	1	no	—
428	C₂×C₈	—	13	1	no	—
429	C₂×C₈	—	13	1	no	—
430	C₂×C₈	—	26	1	no	—
431	C₂×C₈	—	26	1	no	—
432	C₂×C₈	—	26	1	no	—
433	C₂×C₈	—	26	1	no	—
434	C₂×C₈	—	26	1	no	—
435	C₂×C₈	—	26	1	no	—
436	C₂×C₈	—	26	1	no	—
437	C₂×C₈	—	26	1	no	—
438	C₂×C₈	—	26	1	no	—
439	C₂×C₈	—	26	1	no	—
440	C₂×C₈	—	52	1	no	—
441	C₂×C₈	—	52	1	no	—
442	C₂×C₈	C₂²×#261	1	1	yes	characteristic
443	C₂×C₈	C₂²×#261	1	1	yes	characteristic
444	C₂×C₈	C₂²×#261	1	1	yes	characteristic
445	C₂×C₈	C₂²×#261	1	1	yes	characteristic
446	C₄⋊C₄	—	13	1	no	—
447	C₄⋊C₄	—	13	1	no	—
448	C₄⋊C₄	—	13	1	no	—
449	C₄⋊C₄	—	13	1	no	—
450	C₄⋊C₄	—	13	1	no	—
451	C₄⋊C₄	D₁₃⋊C₈	1	1	yes	characteristic
452	C₂²⋊C₄	—	13	1	no	—
453	C₂²⋊C₄	—	13	1	no	—
454	C₂²⋊C₄	—	13	1	no	—
455	C₂²⋊C₄	—	13	1	no	—
456	C₂²⋊C₄	—	13	1	no	—
457	C₂²⋊C₄	—	13	1	no	—
458	C₂²⋊C₄	—	13	1	no	—
459	C₂²⋊C₄	—	13	1	no	—
460	C₂²⋊C₄	D₁₃⋊C₈	1	1	yes	characteristic
461	C₂²⋊C₄	D₁₃⋊C₈	1	1	yes	characteristic
462	C₄²	—	13	1	no	—
463	C₄²	C₂²×#261	1	1	yes	characteristic
464	C₁₆	—	26	1	no	—
465	C₁₆	—	26	1	no	—
466	C₁₆	—	26	1	no	—
467	C₁₆	—	26	1	no	—
468	C₁₆	—	26	1	no	—
469	C₁₆	—	26	1	no	—
470	C₁₆	—	26	1	no	—
471	C₁₆	—	26	1	no	—
472	C₁₃	#33492	1	1	yes	characteristic, complemented, Sylow
473	C₂³	—	13	1	no	—
474	C₂³	—	13	1	no	—
475	C₂³	—	13	1	no	—
476	C₂³	—	52	1	no	—
477	C₂³	—	52	1	no	—
478	C₂³	—	52	1	no	—
479	C₂³	C₂×D₁₃⋊C₈	1	1	yes	characteristic
480	C₂³	C₂×D₁₃⋊C₈	1	1	yes	characteristic
481	Q₈	—	52	1	no	—
482	D₄	—	4	1	no	—
483	D₄	—	52	1	no	—
484	D₄	—	52	1	no	—
485	D₄	—	52	1	no	—
486	D₄	—	52	1	no	—
487	D₄	—	52	1	no	—
488	D₄	—	52	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	13	1	no	—
494	C₂×C₄	—	13	1	no	—
495	C₂×C₄	—	13	1	no	—
496	C₂×C₄	—	13	1	no	—
497	C₂×C₄	—	13	1	no	—
498	C₂×C₄	—	26	1	no	—
499	C₂×C₄	—	26	1	no	—
500	C₂×C₄	—	26	1	no	—
501	C₂×C₄	—	26	1	no	—
502	C₂×C₄	—	26	1	no	—
503	C₂×C₄	—	26	1	no	—
504	C₂×C₄	—	52	1	no	—
505	C₂×C₄	—	52	1	no	—
506	C₂×C₄	—	52	1	no	—
507	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
508	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
509	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
510	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
511	C₂×C₄	C₂³×#261	1	1	yes	characteristic
512	C₈	—	2	1	no	—
513	C₈	—	2	1	no	—
514	C₈	—	2	1	no	—
515	C₈	—	2	1	no	—
516	C₈	—	13	1	no	—
517	C₈	—	13	1	no	—
518	C₈	—	26	1	no	—
519	C₈	—	26	1	no	—
520	C₈	—	26	1	no	—
521	C₂²	—	2	1	no	—
522	C₂²	—	2	1	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	2	1	no	—
527	C₂²	—	26	1	no	—
528	C₂²	—	26	1	no	—
529	C₂²	—	26	1	no	—
530	C₂²	—	26	1	no	—
531	C₂²	—	26	1	no	—
532	C₂²	—	26	1	no	—
533	C₂²	—	26	1	no	—
534	C₂²	—	26	1	no	—
535	C₂²	—	26	1	no	—
536	C₂²	—	52	4	no	—
537	C₂²	C₂²×D₁₃⋊C₈	1	1	yes	characteristic
538	C₄	—	2	1	no	—
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	2	1	no	—
542	C₄	—	26	1	no	—
543	C₄	—	26	1	no	—
544	C₄	—	26	1	no	—
545	C₄	—	26	1	no	—
546	C₄	—	26	1	no	—
547	C₄	#11719623	1	1	yes	characteristic
548	C₄	#11719629	1	1	yes	characteristic
549	C₂	—	4	1	no	—
550	C₂	—	4	1	no	—
551	C₂	—	52	1	no	—
552	C₂	—	52	1	no	—
553	C₂	—	52	1	no	—
554	C₂	#13131684	1	1	yes	characteristic
555	C₂	#13131804	1	1	yes	characteristic
556	C₂	#13131805	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂³×C₈
Fitting	C₁₃×#435	C₄
prime radical	#11719252	C₄
cosocle	C₂×#1055	C₂⁴
hypercenter	#435	#261
hypocenter	C₁₃	#33492
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
1. #13131222	C₂	semidirect
2. #13131221	C₂	semidirect
3. #13131221	C₂	semidirect
4. #13131220	C₂	semidirect
5. #13131219	C₂	semidirect
6. #13131218	C₂	semidirect
7. #13131217	C₂	semidirect
8. #13131216	C₂	semidirect
9. #13131204	C₂	semidirect
10. #13131203	C₂	semidirect
11. #13131068	C₂	semidirect
12. #13131067	C₂	semidirect
13. #13131065	C₂	semidirect
14. #13131064	C₂	semidirect
21. C₂×#88106	C₂²	semidirect
22. C₂²×#6092	C₂²	semidirect
25. C₂×#88098	C₂²	semidirect
26. C₂×D₁₃⋊C₁₆	C₂²	semidirect
41. C₂²⋊#6092	C₂²	semidirect
42. C₂²⋊#6092	C₂²	semidirect
43. #11718260	C₂²	semidirect
44. #11718260	C₂²	semidirect
51. #11718259	C₂²	semidirect
52. #11718259	C₂²	semidirect
53. #11718258	C₂²	semidirect
54. #11718257	C₂²	semidirect
55. #11718231	C₂²	semidirect
56. C₄⋊#6092	C₂²	semidirect
57. C₄⋊#6092	C₂²	semidirect
58. C₄×#6092	C₂²	semidirect
472. C₁₃	#33492	semidirect

Maximal subgroups

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

subgroup	index
#13131222	2
#13131221	2
#13131220	2
#13131219	2
#13131218	2
#13131217	2
#13131216	2
#13131204	2
#13131203	2
#13131068	2
#13131067	2
#13131065	2
#13131064	2
#13123527	2
#33492	13