Subgroups — #15870760

Order 3328.

738 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13124624	C₂	1	1	yes	maximal, characteristic
2	#13123770	C₂	1	1	yes	maximal, characteristic, complemented
3	#13115780	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115611	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115435	C₂	1	2	yes	maximal, complemented
6	#13115111	C₂	1	2	yes	maximal
7	#13114856	C₂	1	1	yes	maximal, characteristic
8	#13114721	C₂	1	2	yes	maximal, complemented
9	#13114703	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114678	C₂	1	2	yes	maximal
11	C₄×C₁₃×#131	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
14	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
15	#11719175	C₂²	1	1	yes	characteristic
16	C₁₃×#405	—	2	1	no	—
17	C₁₃×#405	—	2	1	no	—
18	C₁₃×#405	C₂²	1	1	yes	characteristic
19	C₁₃×#405	C₂²	1	1	yes	characteristic
20	C₄×C₁₃×M₁₆	—	2	1	no	—
21	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₁₃	—	2	1	no	—
23	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×#88077	C₂²	1	2	yes	—
25	#11718894	C₂²	1	2	yes	—
26	C₂×#88062	C₂²	1	2	yes	—
27	#11718763	C₂²	1	2	yes	—
28	#11718762	C₂²	1	2	yes	—
29	C₂×#88055	C₂²	1	2	yes	—
30	#11718683	C₄	1	2	yes	complemented
31	#11718682	C₄	1	1	yes	characteristic, complemented
32	#11718681	C₄	1	1	yes	characteristic, complemented
33	#11718670	C₄	1	2	yes	complemented
34	#11718669	C₄	1	1	yes	characteristic, complemented
35	#11718668	C₄	1	1	yes	characteristic, complemented
36	#11718659	C₂²	1	2	yes	—
37	C₄×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
38	#11718585	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
40	#11718340	—	2	1	no	—
41	#11718340	—	2	1	no	—
42	C₈×Dic₂₆	—	2	1	no	—
43	C₈×Dic₂₆	—	2	1	no	—
44	#11718150	C₂²	1	2	yes	—
45	#11718147	C₂²	1	2	yes	—
46	#11718147	C₂²	1	2	yes	—
47	#11718142	C₂²	1	2	yes	—
48	#11718124	C₂²	1	2	yes	—
49	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
50	C₁₃×#131	—	2	2	no	—
51	C₁₃×#131	—	2	2	no	—
52	C₁₃×#131	—	2	2	no	—
53	C₁₃×#131	Q₈	1	4	yes	complemented
54	C₂×C₁₃×M₁₆	—	2	1	no	—
55	C₂×C₁₃×M₁₆	—	2	1	no	—
56	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
57	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₃	—	2	1	no	—
59	C₂²×C₈×C₁₃	—	2	1	no	—
60	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
63	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
64	C₄×D₄×C₁₃	—	2	1	no	—
65	C₄×D₄×C₁₃	—	2	1	no	—
66	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
67	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
68	C₁₃×#117	—	2	1	no	—
69	C₁₃×#117	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	—	2	1	no	—
71	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
72	#88180	C₂³	1	2	yes	—
73	C₂×C₄⋊Dic₁₃	—	2	1	no	—
74	#88178	—	2	1	no	—
75	#88178	—	2	1	no	—
76	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
77	C₂×#6099	C₂³	1	2	yes	—
78	C₂²×#1055	C₂³	1	2	yes	—
79	#88124	C₂×C₄	1	2	yes	—
80	#88123	C₂×C₄	1	1	yes	characteristic
81	#88123	C₂×C₄	1	1	yes	characteristic
82	C₄×Dic₂₆	—	2	1	no	—
83	C₄×Dic₂₆	—	2	1	no	—
84	C₁₃×#97	—	2	1	no	—
85	C₁₃×#97	—	2	1	no	—
86	C₁₃×#97	—	2	1	no	—
87	C₄×C₈×C₁₃	—	2	1	no	—
88	C₄×C₈×C₁₃	—	2	1	no	—
89	C₄×C₈×C₁₃	—	2	1	no	—
90	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
91	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
92	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
93	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
94	#88077	—	2	4	no	—
95	#88075	C₂×C₄	1	2	yes	—
96	#88075	C₂×C₄	1	2	yes	—
97	#88072	C₂×C₄	1	2	yes	—
98	#88072	C₂×C₄	1	2	yes	—
99	#88071	—	2	1	no	—
100	#88062	—	2	4	no	—
101	#88055	—	2	2	no	—
102	#88055	—	2	4	no	—
103	#88054	—	2	2	no	—
104	#88054	—	2	2	no	—
105	C₈×Dic₁₃	—	2	2	no	—
106	#88048	C₂×C₄	1	2	yes	—
107	#88048	C₂×C₄	1	2	yes	—
108	#88047	C₂×C₄	1	2	yes	—
109	#88047	C₂×C₄	1	2	yes	—
110	C₄⋊#1055	—	2	1	no	—
111	C₄⋊#1055	—	2	1	no	—
112	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
113	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
114	C₄⋊#1055	C₂×C₄	1	2	yes	—
115	#21628	—	13	1	no	maximal, Sylow
116	C₁₃×#41	—	2	1	no	—
117	C₁₃×#41	—	2	1	no	—
118	C₁₃×#41	C₂×Q₈	1	2	yes	—
119	C₁₃×#41	#41	1	2	yes	—
120	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×D₄×C₁₃	—	2	1	no	—
122	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
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	#41	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
129	C₂²×Dic₁₃	—	2	2	no	—
130	C₂×Dic₂₆	—	2	1	no	—
131	C₂×Dic₂₆	—	2	1	no	—
132	C₁₃×M₁₆	—	2	4	no	—
133	C₁₃×M₁₆	—	2	1	no	—
134	C₁₃×M₁₆	—	2	1	no	—
135	C₁₃×M₁₆	—	2	4	no	—
136	C₁₃×M₁₆	C₂×Q₈	1	2	yes	—
137	C₁₃×M₁₆	#41	1	2	yes	—
138	C₂×C₈×C₁₃	—	2	4	no	—
139	C₂×C₈×C₁₃	—	2	1	no	—
140	C₂×C₈×C₁₃	—	2	1	no	—
141	C₂×C₈×C₁₃	—	2	1	no	—
142	C₂×C₈×C₁₃	—	2	1	no	—
143	C₂×C₈×C₁₃	—	2	4	no	—
144	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
149	C₂×C₈×C₁₃	#41	1	2	yes	—
150	C₁₃×C₄⋊C₄	—	2	1	no	—
151	C₁₃×C₄⋊C₄	—	2	1	no	—
152	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
153	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
154	C₁₃×C₂²⋊C₄	—	2	1	no	—
155	C₁₃×C₂²⋊C₄	—	2	1	no	—
156	C₁₃×C₂²⋊C₄	—	2	1	no	—
157	C₄²×C₁₃	—	2	1	no	—
158	C₄²×C₁₃	—	2	1	no	—
159	C₄²×C₁₃	—	2	1	no	—
160	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
161	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
162	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂²⋊Dic₁₃	—	2	2	no	—
165	C₄⋊Dic₁₃	—	2	1	no	—
166	C₄⋊Dic₁₃	—	2	1	no	—
167	C₄⋊Dic₁₃	—	4	2	no	—
168	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
169	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
170	#6101	—	2	2	no	—
171	#6101	—	2	2	no	—
172	C₄×Dic₁₃	—	2	2	no	—
173	C₄×Dic₁₃	—	2	2	no	—
174	C₄×Dic₁₃	—	2	2	no	—
175	#6099	—	2	2	no	—
176	#6099	—	2	2	no	—
177	C₂×#1055	—	2	2	no	—
178	C₂×#1055	—	2	2	no	—
179	C₂×#1055	—	2	2	no	—
180	C₂×#1055	C₂²×C₄	1	2	yes	—
181	C₂×#1055	C₂²×C₄	1	2	yes	—
182	#3076	—	13	1	no	—
183	#2960	—	13	1	no	—
184	C₄×#131	D₁₃	1	1	yes	characteristic
185	#1986	—	13	1	no	—
186	#1950	—	13	1	no	—
187	#1922	—	13	2	no	—
188	#1866	—	13	2	no	—
189	#1806	—	13	1	no	—
190	#1773	—	13	2	no	—
191	#1770	—	13	1	no	—
192	#1765	—	13	2	no	—
193	C₂³×C₁₃	—	2	1	no	—
194	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
195	Q₈×C₁₃	—	2	1	no	—
196	Q₈×C₁₃	C₄×Q₈	1	2	yes	—
197	D₄×C₁₃	—	2	2	no	—
198	D₄×C₁₃	—	2	2	no	—
199	D₄×C₁₃	—	2	1	no	—
200	D₄×C₁₃	C₄×Q₈	1	2	yes	—
201	C₂×C₄×C₁₃	—	2	1	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	1	no	—
206	C₂×C₄×C₁₃	—	2	1	no	—
207	C₂×C₄×C₁₃	—	4	1	no	—
208	C₂×C₄×C₁₃	—	4	2	no	—
209	C₂×C₄×C₁₃	—	4	2	no	—
210	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
215	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
217	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
218	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
220	C₂×Dic₁₃	—	2	2	no	—
221	C₂×Dic₁₃	—	2	2	no	—
222	C₂×Dic₁₃	—	4	2	no	—
223	C₂×Dic₁₃	—	4	2	no	—
224	C₂×Dic₁₃	—	4	2	no	—
225	Dic₂₆	—	4	2	no	—
226	Dic₂₆	—	4	2	no	—
227	C₈×C₁₃	—	2	2	no	—
228	C₈×C₁₃	—	2	1	no	—
229	C₈×C₁₃	—	2	2	no	—
230	C₈×C₁₃	—	2	1	no	—
231	C₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
232	C₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
233	#1055	—	2	2	no	—
234	#1055	—	2	2	no	—
235	#1055	—	4	2	no	—
236	C₂×#131	C₂×D₁₃	1	1	yes	characteristic
237	C₂×#131	C₂×D₁₃	1	1	yes	characteristic
238	#533	—	13	1	no	—
239	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
240	#479	—	13	2	no	—
241	#478	—	13	2	no	—
242	#477	—	13	1	no	—
243	#476	—	13	1	no	—
244	#475	—	13	1	no	—
245	#474	—	13	1	no	—
246	#446	—	26	1	no	—
247	#446	—	26	1	no	—
248	C₈×Q₈	—	26	1	no	—
249	C₈×Q₈	—	26	1	no	—
250	C₂×#108	—	13	2	no	—
251	#427	—	13	2	no	—
252	#424	—	13	2	no	—
253	#423	—	13	1	no	—
254	C₂×C₄⋊C₈	—	13	1	no	—
255	C₂×#104	—	13	2	no	—
256	#416	—	13	2	no	—
257	#405	—	2	1	no	—
258	#405	—	2	1	no	—
259	#405	—	13	2	no	—
260	#405	C₂×D₁₃	1	1	yes	characteristic
261	#405	C₂×D₁₃	1	1	yes	characteristic
262	C₄×M₁₆	—	2	1	no	—
263	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
264	C₂×#97	—	13	2	no	—
265	C₂×C₄×C₈	—	2	1	no	—
266	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
267	C₄×C₄⋊C₄	—	13	1	no	—
268	#341	—	13	2	no	—
269	#339	—	13	2	no	—
270	#339	—	13	2	no	—
271	#339	—	13	2	no	—
272	#336	—	13	2	no	—
273	C₂²×C₁₃	—	2	1	no	—
274	C₂²×C₁₃	—	2	1	no	—
275	C₂²×C₁₃	—	2	2	no	—
276	C₂²×C₁₃	—	4	1	no	—
277	C₂²×C₁₃	—	4	1	no	—
278	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
279	C₂²×C₁₃	#529	1	1	yes	characteristic
280	C₂²×C₁₃	#533	1	1	yes	characteristic
281	C₄×C₁₃	—	2	1	no	—
282	C₄×C₁₃	—	2	1	no	—
283	C₄×C₁₃	—	2	1	no	—
284	C₄×C₁₃	—	2	2	no	—
285	C₄×C₁₃	—	4	1	no	—
286	C₄×C₁₃	—	4	1	no	—
287	C₄×C₁₃	#444	1	2	yes	—
288	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
289	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
290	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
291	C₄×C₁₃	#525	1	1	yes	characteristic
292	Dic₁₃	—	4	2	no	—
293	Dic₁₃	—	4	2	no	—
294	Dic₁₃	—	8	2	no	—
295	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
296	#131	—	2	2	no	—
297	#131	—	2	2	no	—
298	#131	—	2	2	no	—
299	#131	Dic₂₆	1	4	yes	complemented
300	C₂×M₁₆	—	2	1	no	—
301	C₂×M₁₆	—	2	1	no	—
302	C₂×M₁₆	—	13	2	no	—
303	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
304	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
305	C₂²×C₈	—	2	1	no	—
306	C₂²×C₈	—	2	1	no	—
307	C₂²×C₈	—	13	2	no	—
308	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
309	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
310	C₄⋊Q₈	—	13	1	no	—
311	C₄⋊Q₈	—	13	1	no	—
312	#125	—	13	2	no	—
313	C₂²⋊Q₈	—	26	1	no	—
314	C₂²⋊Q₈	—	26	1	no	—
315	C₄×Q₈	—	26	1	no	—
316	C₄×Q₈	—	26	1	no	—
317	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
318	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
319	C₄×D₄	—	2	1	no	—
320	C₄×D₄	—	2	1	no	—
321	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
322	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
323	#117	—	2	1	no	—
324	#117	—	13	2	no	—
325	#117	C₂²×D₁₃	1	1	yes	characteristic
326	C₂×C₄⋊C₄	—	26	1	no	—
327	C₂×C₄²	—	2	1	no	—
328	C₂×C₄²	—	13	2	no	—
329	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
330	#108	—	26	4	no	—
331	#107	—	13	2	no	—
332	#107	—	13	2	no	—
333	#106	—	13	2	no	—
334	#106	—	13	2	no	—
335	C₄⋊C₈	—	13	1	no	—
336	C₄⋊C₈	—	13	1	no	—
337	C₄⋊C₈	—	13	2	no	—
338	C₄⋊C₈	—	26	2	no	—
339	C₄⋊C₈	—	26	2	no	—
340	C₄⋊C₈	—	26	1	no	—
341	C₄⋊C₈	—	26	1	no	—
342	#104	—	26	4	no	—
343	#103	—	13	2	no	—
344	#103	—	13	2	no	—
345	#102	—	13	2	no	—
346	#102	—	13	2	no	—
347	#97	—	2	1	no	—
348	#97	—	2	1	no	—
349	#97	—	2	1	no	—
350	#97	—	26	4	no	—
351	#97	—	26	2	no	—
352	C₄×C₈	—	2	1	no	—
353	C₄×C₈	—	2	1	no	—
354	C₄×C₈	—	2	1	no	—
355	C₄×C₈	—	26	2	no	—
356	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
357	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
358	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
359	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
360	#95	—	26	1	no	—
361	C₂×C₁₃	—	2	1	no	—
362	C₂×C₁₃	—	2	1	no	—
363	C₂×C₁₃	—	4	2	no	—
364	C₂×C₁₃	C₄×C₂²⋊Q₈	1	1	yes	characteristic
365	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
366	C₂×C₁₃	#2955	1	1	yes	characteristic
367	#41	—	2	1	no	—
368	#41	—	2	1	no	—
369	#41	C₂×Dic₂₆	1	2	yes	—
370	#41	#6127	1	2	yes	—
371	C₂×Q₈	—	26	1	no	—
372	C₂×Q₈	—	26	1	no	—
373	C₂×Q₈	C₂×C₄×D₁₃	1	1	yes	characteristic
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	26	2	no	—
380	C₂²×C₄	#6127	1	1	yes	characteristic
381	C₂²×C₄	#6127	1	1	yes	characteristic
382	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
383	M₁₆	—	2	4	no	—
384	M₁₆	—	2	1	no	—
385	M₁₆	—	2	1	no	—
386	M₁₆	—	2	4	no	—
387	M₁₆	—	26	2	no	—
388	M₁₆	—	26	2	no	—
389	M₁₆	C₂×Dic₂₆	1	2	yes	—
390	M₁₆	#6127	1	2	yes	—
391	C₂×C₈	—	2	4	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	4	no	—
397	C₂×C₈	—	13	2	no	—
398	C₂×C₈	—	13	2	no	—
399	C₂×C₈	—	26	2	no	—
400	C₂×C₈	—	26	2	no	—
401	C₂×C₈	—	26	2	no	—
402	C₂×C₈	C₂×Dic₂₆	1	2	yes	—
403	C₂×C₈	#6127	1	2	yes	—
404	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
405	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
406	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
407	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	13	2	no	—
411	C₄⋊C₄	—	13	2	no	—
412	C₄⋊C₄	—	26	2	no	—
413	C₄⋊C₄	—	26	2	no	—
414	C₄⋊C₄	—	26	1	no	—
415	C₄⋊C₄	—	26	1	no	—
416	C₄⋊C₄	—	52	2	no	—
417	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
418	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
419	C₂²⋊C₄	—	2	1	no	—
420	C₂²⋊C₄	—	2	1	no	—
421	C₂²⋊C₄	—	2	1	no	—
422	C₂²⋊C₄	—	26	2	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	1	no	—
425	C₄²	—	2	1	no	—
426	C₄²	—	26	2	no	—
427	C₄²	—	26	2	no	—
428	C₄²	—	26	2	no	—
429	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
430	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
431	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
432	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
433	C₁₃	#21628	1	1	yes	characteristic, complemented, Sylow
434	C₂³	—	2	1	no	—
435	C₂³	C₂×#6127	1	1	yes	characteristic
436	Q₈	—	2	1	no	—
437	Q₈	—	52	2	no	—
438	Q₈	—	52	2	no	—
439	Q₈	C₄×Dic₂₆	1	2	yes	—
440	D₄	—	2	2	no	—
441	D₄	—	2	2	no	—
442	D₄	—	2	1	no	—
443	D₄	C₄×Dic₂₆	1	2	yes	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	26	2	no	—
454	C₂×C₄	—	26	2	no	—
455	C₂×C₄	—	52	2	no	—
456	C₂×C₄	—	52	2	no	—
457	C₂×C₄	—	52	2	no	—
458	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
459	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
460	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
461	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
462	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
463	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
464	C₂×C₄	C₂×#6127	1	1	yes	characteristic
465	C₂×C₄	C₂×#6127	1	1	yes	characteristic
466	C₂×C₄	C₂×#6127	1	1	yes	characteristic
467	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
468	C₈	—	2	2	no	—
469	C₈	—	2	1	no	—
470	C₈	—	2	2	no	—
471	C₈	—	2	1	no	—
472	C₈	—	26	2	no	—
473	C₈	—	26	2	no	—
474	C₈	—	52	2	no	—
475	C₈	#88178	1	2	yes	—
476	C₈	#88178	1	2	yes	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	4	1	no	—
481	C₂²	—	4	1	no	—
482	C₂²	#11719175	1	1	yes	characteristic
483	C₂²	#11719184	1	1	yes	characteristic
484	C₂²	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
485	C₄	—	2	1	no	—
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	2	2	no	—
489	C₄	—	4	1	no	—
490	C₄	—	4	1	no	—
491	C₄	—	52	2	no	—
492	C₄	—	52	2	no	—
493	C₄	—	104	2	no	—
494	C₄	#11718806	1	2	yes	—
495	C₄	C₂×C₄×Dic₂₆	1	1	yes	characteristic
496	C₄	C₄×#6127	1	1	yes	characteristic
497	C₄	C₂×#88178	1	1	yes	characteristic
498	C₄	#11719496	1	1	yes	characteristic
499	C₂	—	2	1	no	—
500	C₂	—	2	1	no	—
501	C₂	—	4	2	no	—
502	C₂	C₄×#88178	1	1	yes	characteristic
503	C₂	C₂×#11718806	1	1	yes	characteristic
504	C₂	#13123737	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₄×C₁₃×#131	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×C₁₃×#41	C₂³
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₄×#131	D₁₃
hypocenter	C₁₃	#21628
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ C₄×#131

Complements

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

N	H ≅ G/N	type
2. #13123770	C₂	semidirect
3. #13115780	C₂	semidirect
4. #13115611	C₂	semidirect
5. #13115435	C₂	semidirect
8. #13114721	C₂	semidirect
9. #13114703	C₂	semidirect
30. #11718683	C₄	semidirect
31. #11718682	C₄	semidirect
32. #11718681	C₄	semidirect
33. #11718670	C₄	semidirect
34. #11718669	C₄	semidirect
35. #11718668	C₄	semidirect
53. C₁₃×#131	Q₈	semidirect
299. #131	Dic₂₆	semidirect
433. C₁₃	#21628	semidirect

Maximal subgroups

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

subgroup	index
#13124624	2
#13123770	2
#13115780	2
#13115611	2
#13115435	2
#13115111	2
#13114856	2
#13114721	2
#13114703	2
#13114678	2
C₄×C₁₃×#131	2
#21628	13