Subgroups — #15834659

Order 3328.

718 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123870	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#6104	C₂	1	1	yes	maximal, characteristic
3	#13113748	C₂	1	2	yes	maximal, complemented
4	#13113665	C₂	1	2	yes	maximal, complemented
5	#13113663	C₂	1	2	yes	maximal, complemented
6	#13113658	C₂	1	2	yes	maximal, complemented
7	#13113597	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113279	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113278	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113126	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2974	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	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
15	C₁₃×#436	C₂²	1	2	yes	complemented
16	C₁₃×#435	—	2	2	no	—
17	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
18	C₁₃×#432	C₂²	1	1	yes	characteristic
19	C₁₃×#431	C₂²	1	1	yes	characteristic
20	C₁₃×#407	—	2	1	no	—
21	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
22	C₂×#88072	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	C₄	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	C₄×#6104	C₂²	1	1	yes	characteristic
31	C₂×#88049	C₄	1	1	yes	characteristic
32	C₂×#88047	C₄	1	1	yes	characteristic
33	#11718587	C₂²	1	1	yes	characteristic
34	C₄×#6099	C₂²	1	1	yes	characteristic
35	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
36	#11718497	—	2	2	no	—
37	#11718387	—	2	1	no	—
38	D₁₃×C₂²⋊C₈	—	2	1	no	—
39	#11718349	C₂²	1	2	yes	complemented
40	C₈×D₅₂	C₂²	1	2	yes	complemented
41	D₄⋊#1055	C₂²	1	2	yes	complemented
42	D₄⋊#1055	C₂²	1	2	yes	complemented
43	#11718075	C₂²	1	2	yes	complemented
44	#11718075	C₂²	1	2	yes	complemented
45	#11718072	C₂²	1	2	yes	complemented
46	#11718071	C₂²	1	2	yes	complemented
47	#11718047	C₂²	1	2	yes	complemented
48	#11718046	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	2	no	—
54	C₂²×C₈×C₁₃	—	2	2	no	—
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	C₂×C₄	1	1	yes	characteristic
59	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
63	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×#6104	—	2	4	no	—
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×#6104	C₂×C₄	1	1	yes	characteristic
69	C₂×#6103	—	2	1	no	—
70	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
71	C₂×#6099	—	2	1	no	—
72	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
73	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
74	C₂×#6094	—	2	2	no	—
75	C₂×C₈×D₁₃	—	2	2	no	—
76	C₄×D₅₂	—	2	1	no	—
77	C₄×D₅₂	—	2	1	no	—
78	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
79	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
80	C₄×D₅₂	C₂³	1	1	yes	characteristic
81	C₄×D₅₂	C₂³	1	1	yes	characteristic
82	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
83	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
84	C₁₃×C₂²⋊C₈	—	2	1	no	—
85	C₁₃×C₂²⋊C₈	—	2	2	no	—
86	C₁₃×C₂²⋊C₈	—	2	2	no	—
87	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
88	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
89	C₁₃×#97	—	2	1	no	—
90	C₄×C₈×C₁₃	C₂³	1	2	yes	—
91	#88072	C₂×C₄	1	1	yes	characteristic
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	C₂²⋊#1055	—	2	1	no	—
96	#88060	—	2	2	no	—
97	#88060	—	2	2	no	—
98	#88049	C₂×C₄	1	1	yes	characteristic
99	#88049	C₂×C₄	1	1	yes	characteristic
100	#88049	C₂×C₄	1	1	yes	characteristic
101	#88049	C₂×C₄	1	1	yes	characteristic
102	#88047	C₂×C₄	1	1	yes	characteristic
103	#88047	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	C₂³	1	2	yes	—
107	#88043	—	2	1	no	—
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	#18064	—	13	1	no	maximal, Sylow
115	C₂⁴×C₁₃	—	2	1	no	—
116	C₂³×D₁₃	—	2	1	no	—
117	C₂×D₄×C₁₃	—	2	2	no	—
118	C₂×D₄×C₁₃	—	2	1	no	—
119	C₂×D₄×C₁₃	—	4	1	no	—
120	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	—	2	1	no	—
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	—	8	2	no	—
128	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
131	C₂²×Dic₁₃	—	2	1	no	—
132	C₂×D₅₂	—	2	2	no	—
133	C₂×D₅₂	—	2	1	no	—
134	C₂×D₅₂	—	4	1	no	—
135	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
136	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₄×D₁₃	—	2	1	no	—
138	C₂×C₄×D₁₃	—	2	1	no	—
139	C₂×C₄×D₁₃	—	2	1	no	—
140	C₂×C₄×D₁₃	—	2	1	no	—
141	C₂×C₄×D₁₃	—	8	2	no	—
142	C₁₃×M₁₆	—	8	2	no	—
143	C₂×C₈×C₁₃	—	2	2	no	—
144	C₂×C₈×C₁₃	—	8	2	no	—
145	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
146	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
147	C₁₃×C₄⋊C₄	—	2	1	no	—
148	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
149	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
150	C₁₃×C₂²⋊C₄	—	2	1	no	—
151	C₁₃×C₂²⋊C₄	—	2	1	no	—
152	C₁₃×C₂²⋊C₄	—	2	1	no	—
153	C₁₃×C₂²⋊C₄	—	2	1	no	—
154	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
155	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₁₃	#41	1	1	yes	characteristic
157	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
158	#6104	—	2	2	no	—
159	#6104	—	2	2	no	—
160	#6104	—	2	2	no	—
161	#6104	M₁₆	1	4	yes	complemented
162	#6103	—	2	1	no	—
163	#6103	—	2	1	no	—
164	#6103	—	2	1	no	—
165	#6103	—	2	1	no	—
166	C₄⋊Dic₁₃	—	2	1	no	—
167	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
168	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
169	#6099	—	4	2	no	—
170	C₂×#1055	—	2	2	no	—
171	C₂×#1055	—	2	2	no	—
172	C₂×#1055	—	2	2	no	—
173	C₂×#1055	—	4	1	no	—
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	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
178	#6094	—	8	2	no	—
179	C₈×D₁₃	—	8	2	no	—
180	#2974	—	13	1	no	—
181	#2974	D₁₃	1	1	yes	characteristic, complemented
182	C₂×C₄×D₈	—	13	1	no	—
183	#1594	—	13	2	no	—
184	#1581	—	13	2	no	—
185	#1581	—	13	2	no	—
186	#1580	—	13	2	no	—
187	#1568	—	13	1	no	—
188	#1490	—	13	1	no	—
189	#1490	—	13	1	no	—
190	#1451	—	13	1	no	—
191	C₂³×C₁₃	—	2	1	no	—
192	C₂³×C₁₃	—	2	1	no	—
193	C₂³×C₁₃	—	4	2	no	—
194	C₂³×C₁₃	—	4	2	no	—
195	C₂³×C₁₃	—	8	1	no	—
196	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
197	C₂²×D₁₃	—	2	1	no	—
198	C₂²×D₁₃	—	2	1	no	—
199	C₂²×D₁₃	—	4	2	no	—
200	C₂²×D₁₃	—	4	2	no	—
201	C₂²×D₁₃	—	8	1	no	—
202	D₄×C₁₃	—	2	1	no	—
203	D₄×C₁₃	—	2	1	no	—
204	D₄×C₁₃	—	2	1	no	—
205	D₄×C₁₃	—	4	2	no	—
206	D₄×C₁₃	C₂×M₁₆	1	2	yes	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	1	no	—
209	C₂×C₄×C₁₃	—	2	1	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	1	no	—
212	C₂×C₄×C₁₃	—	2	1	no	—
213	C₂×C₄×C₁₃	—	4	2	no	—
214	C₂×C₄×C₁₃	—	4	2	no	—
215	C₂×C₄×C₁₃	—	8	1	no	—
216	C₂×C₄×C₁₃	—	8	1	no	—
217	C₂×C₄×C₁₃	—	8	1	no	—
218	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
224	C₂×Dic₁₃	—	2	1	no	—
225	C₂×Dic₁₃	—	2	1	no	—
226	C₂×Dic₁₃	—	8	1	no	—
227	D₅₂	—	2	1	no	—
228	D₅₂	—	2	1	no	—
229	D₅₂	—	2	1	no	—
230	D₅₂	—	4	2	no	—
231	D₅₂	C₂×M₁₆	1	2	yes	—
232	C₄×D₁₃	—	4	2	no	—
233	C₄×D₁₃	—	4	2	no	—
234	C₄×D₁₃	—	8	1	no	—
235	C₄×D₁₃	—	8	1	no	—
236	C₈×C₁₃	—	2	2	no	—
237	C₈×C₁₃	—	2	2	no	—
238	C₈×C₁₃	—	4	2	no	—
239	#1055	—	2	1	no	—
240	#1055	—	2	1	no	—
241	#1055	—	2	1	no	—
242	#1055	—	4	2	no	—
243	#1055	—	4	2	no	—
244	#1055	C₂×M₁₆	1	2	yes	—
245	C₂²×D₈	—	13	1	no	—
246	C₂×C₄×D₄	—	13	1	no	—
247	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
248	C₄×D₈	—	13	1	no	—
249	C₄×D₈	—	13	1	no	—
250	C₄×D₈	—	13	1	no	—
251	C₄×D₈	—	13	1	no	—
252	C₄×D₈	—	13	1	no	—
253	C₄×D₈	—	13	1	no	—
254	C₄×D₈	—	13	1	no	—
255	C₄×D₈	—	13	1	no	—
256	#436	—	13	2	no	—
257	#436	C₂×D₁₃	1	2	yes	complemented
258	#435	—	2	2	no	—
259	#435	—	26	2	no	—
260	C₈×D₄	—	13	2	no	—
261	C₈×D₄	C₂×D₁₃	1	2	yes	complemented
262	#432	—	13	1	no	—
263	#432	C₂×D₁₃	1	1	yes	characteristic
264	#431	C₂×D₁₃	1	1	yes	characteristic
265	C₂×#107	—	13	1	no	—
266	C₂×#102	—	13	1	no	—
267	C₂×#102	—	13	1	no	—
268	#407	—	2	1	no	—
269	#407	—	26	1	no	—
270	C₂×C₂²⋊C₈	—	2	1	no	—
271	C₂×C₂²⋊C₈	—	26	1	no	—
272	C₄×M₁₆	—	13	1	no	—
273	C₂×C₄×C₈	—	13	1	no	—
274	#335	—	13	2	no	—
275	#334	—	13	2	no	—
276	D₄⋊C₈	—	13	2	no	—
277	D₄⋊C₈	—	13	2	no	—
278	D₄⋊C₈	—	13	2	no	—
279	D₄⋊C₈	—	13	2	no	—
280	#322	—	13	2	no	—
281	#322	—	13	2	no	—
282	C₂²×C₁₃	—	2	1	no	—
283	C₂²×C₁₃	—	2	1	no	—
284	C₂²×C₁₃	—	2	2	no	—
285	C₂²×C₁₃	—	4	1	no	—
286	C₂²×C₁₃	—	4	1	no	—
287	C₂²×C₁₃	—	4	1	no	—
288	C₂²×C₁₃	—	4	1	no	—
289	C₂²×C₁₃	—	4	1	no	—
290	C₂²×C₁₃	—	8	4	no	—
291	C₂²×C₁₃	#444	1	2	yes	—
292	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
293	C₂×D₁₃	—	2	2	no	—
294	C₂×D₁₃	—	4	1	no	—
295	C₂×D₁₃	—	4	1	no	—
296	C₂×D₁₃	—	4	1	no	—
297	C₂×D₁₃	—	4	1	no	—
298	C₂×D₁₃	—	4	1	no	—
299	C₂×D₁₃	—	8	4	no	—
300	C₄×C₁₃	—	2	1	no	—
301	C₄×C₁₃	—	2	1	no	—
302	C₄×C₁₃	—	2	1	no	—
303	C₄×C₁₃	—	2	1	no	—
304	C₄×C₁₃	—	4	1	no	—
305	C₄×C₁₃	—	4	1	no	—
306	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
307	C₄×C₁₃	#568	1	1	yes	characteristic
308	C₄×C₁₃	#576	1	2	yes	—
309	Dic₁₃	—	4	1	no	—
310	Dic₁₃	—	4	1	no	—
311	C₂²×D₄	—	13	1	no	—
312	C₂²×D₄	C₄×D₁₃	1	1	yes	characteristic
313	C₂³×C₄	—	2	1	no	—
314	C₂³×C₄	—	26	1	no	—
315	C₂×D₈	—	13	1	no	—
316	C₂×D₈	—	13	1	no	—
317	C₂×D₈	—	13	1	no	—
318	C₂×D₈	—	13	1	no	—
319	C₂×D₈	—	26	4	no	—
320	C₂×M₁₆	—	2	2	no	—
321	C₂×M₁₆	—	26	1	no	—
322	C₂×M₁₆	—	26	2	no	—
323	C₂²×C₈	—	2	2	no	—
324	C₂²×C₈	—	13	1	no	—
325	C₂²×C₈	—	13	1	no	—
326	C₂²×C₈	—	26	2	no	—
327	C₄×D₄	—	2	1	no	—
328	C₄×D₄	—	2	1	no	—
329	C₄×D₄	—	13	1	no	—
330	C₄×D₄	—	13	1	no	—
331	C₄×D₄	—	13	1	no	—
332	C₄×D₄	—	13	1	no	—
333	C₄×D₄	—	26	1	no	—
334	C₄×D₄	—	26	1	no	—
335	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
336	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
337	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
338	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
339	C₂×C₄⋊C₄	—	13	1	no	—
340	C₂×C₄⋊C₄	C₄×D₁₃	1	1	yes	characteristic
341	C₂×C₂²⋊C₄	—	2	1	no	—
342	C₂×C₂²⋊C₄	—	26	1	no	—
343	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
344	#107	—	13	1	no	—
345	#107	—	13	1	no	—
346	#107	—	13	1	no	—
347	#107	—	13	1	no	—
348	C₄⋊C₈	—	13	2	no	—
349	C₄⋊C₈	C₂²⋊D₁₃	1	2	yes	—
350	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
351	#102	—	13	1	no	—
352	#102	—	13	1	no	—
353	#102	—	13	1	no	—
354	#102	—	13	1	no	—
355	#102	—	13	1	no	—
356	#102	—	13	1	no	—
357	#102	—	13	1	no	—
358	#102	—	13	1	no	—
359	C₂²⋊C₈	—	2	1	no	—
360	C₂²⋊C₈	—	2	2	no	—
361	C₂²⋊C₈	—	2	2	no	—
362	C₂²⋊C₈	—	26	1	no	—
363	C₂²⋊C₈	—	26	2	no	—
364	C₂²⋊C₈	—	26	2	no	—
365	C₂²⋊C₈	C₂²⋊D₁₃	1	1	yes	characteristic
366	C₂²⋊C₈	C₂²⋊D₁₃	1	1	yes	characteristic
367	#97	—	2	1	no	—
368	#97	—	26	1	no	—
369	#97	—	26	1	no	—
370	C₄×C₈	—	13	1	no	—
371	C₄×C₈	—	13	1	no	—
372	C₄×C₈	—	13	1	no	—
373	C₄×C₈	—	13	1	no	—
374	C₄×C₈	—	13	2	no	—
375	C₄×C₈	C₂²×D₁₃	1	2	yes	—
376	C₂×C₁₃	—	2	2	no	—
377	C₂×C₁₃	—	4	2	no	—
378	C₂×C₁₃	—	8	1	no	—
379	C₂×C₁₃	D₄×M₁₆	1	1	yes	characteristic
380	C₂×C₁₃	#2948	1	1	yes	characteristic
381	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
382	D₁₃	—	4	2	no	—
383	D₁₃	—	8	1	no	—
384	C₂⁴	—	2	1	no	—
385	C₂⁴	—	26	1	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	4	1	no	—
389	C₂×D₄	—	13	1	no	—
390	C₂×D₄	—	13	1	no	—
391	C₂×D₄	—	26	2	no	—
392	C₂×D₄	—	26	1	no	—
393	C₂×D₄	—	52	1	no	—
394	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
395	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	8	2	no	—
402	C₂²×C₄	—	26	1	no	—
403	C₂²×C₄	—	26	1	no	—
404	C₂²×C₄	—	26	1	no	—
405	C₂²×C₄	—	26	1	no	—
406	C₂²×C₄	—	26	1	no	—
407	C₂²×C₄	—	104	2	no	—
408	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
409	C₂²×C₄	#6127	1	1	yes	characteristic
410	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
411	D₈	—	13	4	no	—
412	D₈	—	26	2	no	—
413	D₈	—	26	2	no	—
414	D₈	—	26	2	no	—
415	M₁₆	—	8	2	no	—
416	M₁₆	—	52	2	no	—
417	M₁₆	—	104	2	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	8	2	no	—
420	C₂×C₈	—	13	1	no	—
421	C₂×C₈	—	13	1	no	—
422	C₂×C₈	—	13	1	no	—
423	C₂×C₈	—	13	1	no	—
424	C₂×C₈	—	26	2	no	—
425	C₂×C₈	—	26	2	no	—
426	C₂×C₈	—	26	2	no	—
427	C₂×C₈	—	52	1	no	—
428	C₂×C₈	—	104	2	no	—
429	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
430	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	13	1	no	—
433	C₄⋊C₄	—	13	1	no	—
434	C₄⋊C₄	—	26	1	no	—
435	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
436	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
437	C₂²⋊C₄	—	2	1	no	—
438	C₂²⋊C₄	—	2	1	no	—
439	C₂²⋊C₄	—	2	1	no	—
440	C₂²⋊C₄	—	2	1	no	—
441	C₂²⋊C₄	—	26	1	no	—
442	C₂²⋊C₄	—	26	1	no	—
443	C₂²⋊C₄	—	26	1	no	—
444	C₂²⋊C₄	—	26	1	no	—
445	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
446	C₄²	#6127	1	1	yes	characteristic
447	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
448	C₄²	C₂³×D₁₃	1	1	yes	characteristic
449	C₁₃	#18064	1	1	yes	characteristic, complemented, Sylow
450	C₂³	—	2	1	no	—
451	C₂³	—	2	1	no	—
452	C₂³	—	4	2	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	8	1	no	—
455	C₂³	—	26	1	no	—
456	C₂³	—	26	1	no	—
457	C₂³	—	52	2	no	—
458	C₂³	—	52	2	no	—
459	C₂³	—	104	1	no	—
460	C₂³	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
461	D₄	—	2	1	no	—
462	D₄	—	2	1	no	—
463	D₄	—	2	1	no	—
464	D₄	—	4	2	no	—
465	D₄	—	13	2	no	—
466	D₄	—	26	1	no	—
467	D₄	—	26	1	no	—
468	D₄	—	26	1	no	—
469	D₄	—	52	2	no	—
470	D₄	M₁₆×D₁₃	1	2	yes	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	8	1	no	—
480	C₂×C₄	—	8	1	no	—
481	C₂×C₄	—	8	1	no	—
482	C₂×C₄	—	26	1	no	—
483	C₂×C₄	—	26	1	no	—
484	C₂×C₄	—	52	2	no	—
485	C₂×C₄	—	52	2	no	—
486	C₂×C₄	—	104	1	no	—
487	C₂×C₄	—	104	1	no	—
488	C₂×C₄	—	104	1	no	—
489	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
490	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
491	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
492	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
493	C₂×C₄	C₂×#6127	1	1	yes	characteristic
494	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
495	C₈	—	2	2	no	—
496	C₈	—	2	2	no	—
497	C₈	—	4	2	no	—
498	C₈	—	13	2	no	—
499	C₈	—	26	1	no	—
500	C₈	—	26	1	no	—
501	C₈	—	26	1	no	—
502	C₈	—	52	2	no	—
503	C₈	—	52	2	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	4	1	no	—
508	C₂²	—	4	1	no	—
509	C₂²	—	4	1	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	1	no	—
512	C₂²	—	8	4	no	—
513	C₂²	—	26	2	no	—
514	C₂²	—	52	1	no	—
515	C₂²	—	52	1	no	—
516	C₂²	—	52	1	no	—
517	C₂²	—	52	1	no	—
518	C₂²	—	52	1	no	—
519	C₂²	—	104	4	no	—
520	C₂²	#11718806	1	2	yes	—
521	C₂²	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
522	C₄	—	2	1	no	—
523	C₄	—	2	1	no	—
524	C₄	—	2	1	no	—
525	C₄	—	2	1	no	—
526	C₄	—	4	1	no	—
527	C₄	—	4	1	no	—
528	C₄	—	52	1	no	—
529	C₄	—	52	1	no	—
530	C₄	C₂×M₁₆×D₁₃	1	1	yes	characteristic
531	C₄	#11719450	1	1	yes	characteristic
532	C₄	#11719540	1	2	yes	—
533	C₂	—	2	2	no	—
534	C₂	—	4	2	no	—
535	C₂	—	8	1	no	—
536	C₂	—	52	2	no	—
537	C₂	—	104	1	no	—
538	C₂	M₁₆×C₂²⋊D₁₃	1	1	yes	characteristic
539	C₂	#13123686	1	1	yes	characteristic
540	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×#2974	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂²×#6104	C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#2974	D₁₃
hypocenter	C₁₃	#18064
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #2974

Complements

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

N	H ≅ G/N	type
1. #13123870	C₂	semidirect
3. #13113748	C₂	semidirect
4. #13113665	C₂	semidirect
5. #13113663	C₂	semidirect
6. #13113658	C₂	semidirect
7. #13113597	C₂	semidirect
8. #13113279	C₂	semidirect
9. #13113278	C₂	semidirect
10. #13113126	C₂	semidirect
11. C₁₃×#2974	C₂	semidirect
15. C₁₃×#436	C₂²	semidirect
17. C₈×D₄×C₁₃	C₂²	semidirect
39. #11718349	C₂²	semidirect
40. C₈×D₅₂	C₂²	semidirect
41. D₄⋊#1055	C₂²	semidirect
42. D₄⋊#1055	C₂²	semidirect
43. #11718075	C₂²	semidirect
44. #11718075	C₂²	semidirect
45. #11718072	C₂²	semidirect
46. #11718071	C₂²	semidirect
47. #11718047	C₂²	semidirect
48. #11718046	C₂²	semidirect
161. #6104	M₁₆	semidirect
181. #2974	D₁₃	semidirect
257. #436	C₂×D₁₃	semidirect
261. C₈×D₄	C₂×D₁₃	semidirect
449. C₁₃	#18064	semidirect

Maximal subgroups

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

subgroup	index
#13123870	2
C₂×C₄×#6104	2
#13113748	2
#13113665	2
#13113663	2
#13113658	2
#13113597	2
#13113279	2
#13113278	2
#13113126	2
C₁₃×#2974	2
#18064	13