Subgroups — #15866143

Order 3328.

800 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#88204	C₂	1	1	yes	maximal, characteristic
2	#13123478	C₂	1	1	yes	maximal, characteristic, complemented
3	#13115484	C₂	1	2	yes	maximal, complemented
4	#13115435	C₂	1	2	yes	maximal, complemented
5	#13115163	C₂	1	2	yes	maximal
6	#13115111	C₂	1	2	yes	maximal, complemented
7	C₄×#88062	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#88065	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#88077	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114581	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×#131	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#131	C₂²	1	2	yes	—
13	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
14	C₂×#88204	C₂²	1	1	yes	characteristic
15	C₄×#6127	C₂²	1	1	yes	characteristic
16	C₁₃×#405	—	2	2	no	—
17	C₁₃×#405	C₂²	1	2	yes	—
18	C₄×C₁₃×M₁₆	—	2	1	no	—
19	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₈×C₁₃	—	2	1	no	—
21	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×#88077	C₂²	1	2	yes	—
23	#11718894	C₂²	1	1	yes	characteristic
24	C₂×#88065	C₂²	1	2	yes	—
25	C₂×#88062	C₂²	1	2	yes	—
26	#11718771	C₂²	1	2	yes	—
27	#11718763	C₂²	1	2	yes	—
28	C₄×#6107	C₄	1	1	yes	characteristic, complemented
29	C₄×#6107	C₄	1	1	yes	characteristic, complemented
30	C₄×#6106	C₄	1	1	yes	characteristic, complemented
31	C₄×#6106	C₄	1	1	yes	characteristic, complemented
32	C₄×#6105	C₄	1	1	yes	characteristic, complemented
33	C₄×#6105	C₄	1	1	yes	characteristic, complemented
34	C₄×#6104	C₄	1	1	yes	characteristic, complemented
35	C₄×#6104	C₄	1	1	yes	characteristic, complemented
36	#11718663	C₂²	1	1	yes	characteristic
37	#11718659	C₂²	1	1	yes	characteristic
38	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
39	C₄×#6099	C₂²	1	1	yes	characteristic
40	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
41	#11718351	—	2	2	no	—
42	#11718346	—	2	1	no	—
43	#11718346	—	2	1	no	—
44	#11718150	C₂²	1	2	yes	—
45	#11718147	C₂²	1	2	yes	—
46	#11718142	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	C₂×#6127	C₂³	1	1	yes	characteristic
51	C₁₃×#131	—	2	4	no	—
52	C₁₃×#131	—	2	4	no	—
53	C₂×C₁₃×M₁₆	—	2	2	no	—
54	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₃	—	2	2	no	—
56	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
57	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
58	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
59	C₄×D₄×C₁₃	—	2	1	no	—
60	C₄×D₄×C₁₃	—	2	1	no	—
61	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
62	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
63	C₁₃×#117	—	2	1	no	—
64	C₁₃×#117	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₃	—	2	1	no	—
66	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	#88204	—	2	4	no	—
68	C₂×#6107	C₂×C₄	1	1	yes	characteristic
69	C₂×#6106	C₂×C₄	1	1	yes	characteristic
70	C₂×#6105	C₂×C₄	1	1	yes	characteristic
71	C₂×#6104	C₂×C₄	1	1	yes	characteristic
72	C₄×C₂²⋊D₁₃	—	2	1	no	—
73	C₄×C₂²⋊D₁₃	—	2	1	no	—
74	#88180	C₂³	1	1	yes	characteristic
75	C₂×C₄×Dic₁₃	—	2	1	no	—
76	C₂×C₄×Dic₁₃	—	2	1	no	—
77	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
78	C₂×#6099	C₂³	1	2	yes	—
79	C₂²×#1055	C₂³	1	1	yes	characteristic
80	C₂²×#1055	C₂³	1	1	yes	characteristic
81	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
82	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
83	#88126	—	2	1	no	—
84	C₄²×D₁₃	—	2	1	no	—
85	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
86	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
87	C₁₃×#97	—	2	2	no	—
88	C₁₃×#97	—	2	1	no	—
89	C₄×C₈×C₁₃	—	2	2	no	—
90	C₄×C₈×C₁₃	—	2	1	no	—
91	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
92	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
93	C₄×C₈×C₁₃	D₄	1	2	yes	—
94	#88077	—	2	4	no	—
95	#88075	C₂×C₄	1	1	yes	characteristic
96	#88075	C₂×C₄	1	1	yes	characteristic
97	#88072	C₂×C₄	1	1	yes	characteristic
98	#88072	C₂×C₄	1	1	yes	characteristic
99	#88065	—	2	4	no	—
100	#88062	—	2	4	no	—
101	#88060	—	2	2	no	—
102	#88060	—	2	2	no	—
103	#88054	—	2	2	no	—
104	#88054	—	2	2	no	—
105	#88050	C₂×C₄	1	1	yes	characteristic
106	#88050	C₂×C₄	1	1	yes	characteristic
107	#88049	C₂×C₄	1	1	yes	characteristic
108	#88049	C₂×C₄	1	1	yes	characteristic
109	#88048	C₂×C₄	1	1	yes	characteristic
110	#88048	C₂×C₄	1	1	yes	characteristic
111	#88047	C₂×C₄	1	1	yes	characteristic
112	#88047	C₂×C₄	1	1	yes	characteristic
113	#88043	—	2	1	no	—
114	C₄×#1055	—	2	1	no	—
115	C₄×#1055	C₂×C₄	1	1	yes	characteristic
116	C₄×#1055	C₂×C₄	1	1	yes	characteristic
117	C₄×#1055	C₂×C₄	1	1	yes	characteristic
118	C₄×#1055	C₂×C₄	1	1	yes	characteristic
119	#21137	—	13	1	no	maximal, Sylow
120	C₁₃×#41	—	2	2	no	—
121	C₁₃×#41	#41	1	4	yes	—
122	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×D₄×C₁₃	—	2	1	no	—
124	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
131	C₂×C₂²⋊D₁₃	—	2	1	no	—
132	C₂²×Dic₁₃	—	2	2	no	—
133	#6127	—	2	2	no	—
134	#6127	—	2	2	no	—
135	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₄×D₁₃	—	2	1	no	—
137	C₂×C₄×D₁₃	—	2	1	no	—
138	C₂×C₄×D₁₃	—	2	1	no	—
139	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
140	C₁₃×M₁₆	—	2	8	no	—
141	C₁₃×M₁₆	—	2	2	no	—
142	C₁₃×M₁₆	#41	1	4	yes	—
143	C₂×C₈×C₁₃	—	2	8	no	—
144	C₂×C₈×C₁₃	—	2	2	no	—
145	C₂×C₈×C₁₃	—	2	2	no	—
146	C₂×C₈×C₁₃	—	2	2	no	—
147	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
148	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
149	C₁₃×C₄⋊C₄	—	2	1	no	—
150	C₁₃×C₄⋊C₄	—	2	1	no	—
151	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
152	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
153	C₁₃×C₂²⋊C₄	—	2	1	no	—
154	C₁₃×C₂²⋊C₄	—	2	1	no	—
155	C₁₃×C₂²⋊C₄	—	2	1	no	—
156	C₄²×C₁₃	—	2	1	no	—
157	C₄²×C₁₃	—	2	1	no	—
158	C₄²×C₁₃	—	2	1	no	—
159	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
160	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
161	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂²⋊Dic₁₃	—	2	1	no	—
164	#6107	—	2	2	no	—
165	#6106	—	2	2	no	—
166	#6105	—	2	2	no	—
167	#6104	—	2	2	no	—
168	#6103	—	2	1	no	—
169	#6103	—	2	1	no	—
170	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
171	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
172	#6101	—	2	1	no	—
173	#6101	—	2	1	no	—
174	C₄×Dic₁₃	—	2	4	no	—
175	C₄×Dic₁₃	—	2	1	no	—
176	C₄×Dic₁₃	—	2	1	no	—
177	C₄×Dic₁₃	—	2	1	no	—
178	C₄×Dic₁₃	—	2	2	no	—
179	C₄×Dic₁₃	—	2	2	no	—
180	C₄×Dic₁₃	—	4	2	no	—
181	#6099	—	2	2	no	—
182	#6099	—	2	2	no	—
183	C₂×#1055	—	2	2	no	—
184	C₂×#1055	—	2	2	no	—
185	C₂×#1055	—	2	2	no	—
186	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
187	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
188	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
189	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
190	C₄×#135	—	13	1	no	—
191	#2922	—	13	1	no	—
192	C₄×#131	D₁₃	1	1	yes	characteristic, complemented
193	#1929	—	13	2	no	—
194	#1922	—	13	2	no	—
195	#1876	—	13	2	no	—
196	#1866	—	13	2	no	—
197	C₄×#108	—	13	1	no	—
198	C₄×#104	—	13	1	no	—
199	C₄×#104	—	13	1	no	—
200	#1744	—	13	1	no	—
201	C₂³×C₁₃	—	2	1	no	—
202	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
203	C₂²×D₁₃	—	2	1	no	—
204	Q₈×C₁₃	—	2	1	no	—
205	Q₈×C₁₃	#117	1	2	yes	—
206	D₄×C₁₃	—	2	4	no	—
207	D₄×C₁₃	—	2	1	no	—
208	D₄×C₁₃	#117	1	2	yes	—
209	C₂×C₄×C₁₃	—	2	1	no	—
210	C₂×C₄×C₁₃	—	2	4	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	1	no	—
214	C₂×C₄×C₁₃	—	2	1	no	—
215	C₂×C₄×C₁₃	—	4	2	no	—
216	C₂×C₄×C₁₃	—	4	2	no	—
217	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
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	2	yes	—
224	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
225	C₂²⋊D₁₃	—	4	2	no	—
226	C₂×Dic₁₃	—	2	4	no	—
227	C₂×Dic₁₃	—	2	1	no	—
228	C₂×Dic₁₃	—	2	1	no	—
229	C₂×Dic₁₃	—	2	1	no	—
230	C₂×Dic₁₃	—	4	2	no	—
231	C₂×Dic₁₃	—	4	2	no	—
232	D₅₂	—	2	1	no	—
233	D₅₂	—	2	1	no	—
234	C₄×D₁₃	—	4	2	no	—
235	C₄×D₁₃	—	4	2	no	—
236	C₄×D₁₃	—	4	2	no	—
237	Dic₂₆	—	2	1	no	—
238	Dic₂₆	—	2	1	no	—
239	C₈×C₁₃	—	2	2	no	—
240	C₈×C₁₃	—	2	4	no	—
241	C₈×C₁₃	—	2	2	no	—
242	#1055	—	2	1	no	—
243	#1055	—	2	1	no	—
244	#1055	—	2	1	no	—
245	#1055	—	2	1	no	—
246	#1055	—	4	2	no	—
247	C₂×#135	—	13	1	no	—
248	C₂×#131	C₂×D₁₃	1	2	yes	—
249	C₄×#41	—	13	1	no	—
250	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
251	C₄×Q₁₆	—	13	1	no	—
252	C₄×Q₁₆	—	13	1	no	—
253	C₄×SD₁₆	—	13	1	no	—
254	C₄×SD₁₆	—	13	1	no	—
255	C₄×SD₁₆	—	13	1	no	—
256	C₄×SD₁₆	—	13	1	no	—
257	C₄×D₈	—	13	1	no	—
258	C₄×D₈	—	13	1	no	—
259	#433	—	26	2	no	—
260	#431	—	26	1	no	—
261	#431	—	26	1	no	—
262	C₂×#108	—	13	2	no	—
263	#427	—	13	1	no	—
264	#424	—	13	2	no	—
265	C₂×#104	—	13	2	no	—
266	C₂×#104	—	13	2	no	—
267	#416	—	13	1	no	—
268	#416	—	13	1	no	—
269	#408	—	13	2	no	—
270	#405	—	2	2	no	—
271	#405	C₂×D₁₃	1	2	yes	—
272	C₄×M₁₆	—	2	1	no	—
273	C₄×M₁₆	—	13	1	no	—
274	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
275	C₂×C₄×C₈	—	2	1	no	—
276	C₂×C₄×C₈	—	13	1	no	—
277	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
278	C₄³	—	13	1	no	—
279	#341	—	13	2	no	—
280	#339	—	13	2	no	—
281	#339	—	13	2	no	—
282	#336	—	13	2	no	—
283	#336	—	13	2	no	—
284	C₂²×C₁₃	—	2	1	no	—
285	C₂²×C₁₃	—	2	1	no	—
286	C₂²×C₁₃	—	2	2	no	—
287	C₂²×C₁₃	—	4	1	no	—
288	C₂²×C₁₃	—	4	1	no	—
289	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
290	C₂²×C₁₃	#529	1	2	yes	—
291	C₂×D₁₃	—	4	1	no	—
292	C₂×D₁₃	—	4	1	no	—
293	C₂×D₁₃	—	4	1	no	—
294	C₄×C₁₃	—	2	1	no	—
295	C₄×C₁₃	—	2	1	no	—
296	C₄×C₁₃	—	2	2	no	—
297	C₄×C₁₃	—	4	1	no	—
298	C₄×C₁₃	—	4	1	no	—
299	C₄×C₁₃	#443	1	2	yes	—
300	C₄×C₁₃	#444	1	2	yes	—
301	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
302	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
303	C₄×C₁₃	#525	1	2	yes	—
304	Dic₁₃	—	4	4	no	—
305	Dic₁₃	—	4	1	no	—
306	Dic₁₃	—	4	1	no	—
307	Dic₁₃	—	4	1	no	—
308	C₂×#41	—	13	1	no	—
309	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
310	#135	—	26	4	no	—
311	C₂×Q₁₆	—	13	1	no	—
312	C₂×SD₁₆	—	13	1	no	—
313	C₂×SD₁₆	—	13	1	no	—
314	C₂×D₈	—	13	1	no	—
315	#131	—	2	4	no	—
316	#131	—	2	4	no	—
317	C₂×M₁₆	—	2	2	no	—
318	C₂×M₁₆	—	13	2	no	—
319	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
320	C₂²×C₈	—	2	2	no	—
321	C₂²×C₈	—	13	1	no	—
322	C₂²×C₈	—	13	1	no	—
323	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
324	C₄×Q₈	—	13	1	no	—
325	C₄×Q₈	—	13	1	no	—
326	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
327	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
328	C₄×D₄	—	2	1	no	—
329	C₄×D₄	—	2	1	no	—
330	C₄×D₄	—	13	1	no	—
331	C₄×D₄	—	13	1	no	—
332	C₄×D₄	—	26	1	no	—
333	C₄×D₄	—	26	1	no	—
334	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
335	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
336	#117	—	2	1	no	—
337	#117	—	13	1	no	—
338	#117	—	26	1	no	—
339	#117	C₂²×D₁₃	1	1	yes	characteristic
340	C₂×C₄²	—	2	1	no	—
341	C₂×C₄²	—	13	2	no	—
342	C₂×C₄²	—	26	1	no	—
343	C₂×C₄²	—	26	1	no	—
344	C₂×C₄²	—	26	1	no	—
345	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
346	#108	—	26	4	no	—
347	#107	—	13	1	no	—
348	#107	—	13	1	no	—
349	#106	—	13	1	no	—
350	#106	—	13	1	no	—
351	C₄⋊C₈	—	26	2	no	—
352	C₄⋊C₈	—	26	2	no	—
353	#104	—	26	4	no	—
354	#104	—	26	4	no	—
355	#103	—	13	1	no	—
356	#103	—	13	1	no	—
357	#103	—	13	1	no	—
358	#103	—	13	1	no	—
359	#102	—	13	1	no	—
360	#102	—	13	1	no	—
361	#102	—	13	1	no	—
362	#102	—	13	1	no	—
363	C₂²⋊C₈	—	26	2	no	—
364	C₂²⋊C₈	—	26	2	no	—
365	#97	—	2	2	no	—
366	#97	—	2	1	no	—
367	#97	—	26	1	no	—
368	C₄×C₈	—	2	2	no	—
369	C₄×C₈	—	2	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	—	26	1	no	—
375	C₄×C₈	C₂²⋊D₁₃	1	2	yes	—
376	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
377	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
378	C₂×C₁₃	—	2	2	no	—
379	C₂×C₁₃	—	4	2	no	—
380	C₂×C₁₃	#2290	1	1	yes	characteristic
381	C₂×C₁₃	C₂×#443	1	1	yes	characteristic
382	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
383	D₁₃	—	8	1	no	—
384	#41	—	2	2	no	—
385	#41	—	26	2	no	—
386	#41	—	26	2	no	—
387	#41	#6127	1	4	yes	—
388	C₂×Q₈	—	13	1	no	—
389	C₂×Q₈	C₂×C₄×D₁₃	1	1	yes	characteristic
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	13	1	no	—
392	C₂×D₄	—	26	1	no	—
393	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	26	2	no	—
398	C₂²×C₄	—	26	1	no	—
399	C₂²×C₄	—	26	1	no	—
400	C₂²×C₄	—	26	1	no	—
401	C₂²×C₄	#6127	1	1	yes	characteristic
402	C₂²×C₄	#6127	1	1	yes	characteristic
403	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
404	Q₁₆	—	26	2	no	—
405	SD₁₆	—	26	2	no	—
406	SD₁₆	—	26	2	no	—
407	D₈	—	26	2	no	—
408	M₁₆	—	2	8	no	—
409	M₁₆	—	2	2	no	—
410	M₁₆	—	26	2	no	—
411	M₁₆	—	26	2	no	—
412	M₁₆	#6127	1	4	yes	—
413	C₂×C₈	—	2	8	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	13	1	no	—
418	C₂×C₈	—	13	1	no	—
419	C₂×C₈	—	13	1	no	—
420	C₂×C₈	—	13	1	no	—
421	C₂×C₈	—	26	2	no	—
422	C₂×C₈	—	26	2	no	—
423	C₂×C₈	—	26	2	no	—
424	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
425	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	13	1	no	—
429	C₄⋊C₄	—	13	1	no	—
430	C₄⋊C₄	—	26	1	no	—
431	C₄⋊C₄	—	26	1	no	—
432	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
433	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
434	C₂²⋊C₄	—	2	1	no	—
435	C₂²⋊C₄	—	2	1	no	—
436	C₂²⋊C₄	—	2	1	no	—
437	C₂²⋊C₄	—	26	1	no	—
438	C₂²⋊C₄	—	26	1	no	—
439	C₂²⋊C₄	—	26	1	no	—
440	C₄²	—	2	1	no	—
441	C₄²	—	2	1	no	—
442	C₄²	—	2	1	no	—
443	C₄²	—	26	4	no	—
444	C₄²	—	26	1	no	—
445	C₄²	—	26	1	no	—
446	C₄²	—	26	1	no	—
447	C₄²	—	26	2	no	—
448	C₄²	—	26	2	no	—
449	C₄²	—	52	2	no	—
450	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
451	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
452	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
453	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
454	C₁₃	#21137	1	1	yes	characteristic, complemented, Sylow
455	C₂³	—	2	1	no	—
456	C₂³	—	26	1	no	—
457	C₂³	C₂×#6127	1	1	yes	characteristic
458	Q₈	—	2	1	no	—
459	Q₈	—	26	1	no	—
460	Q₈	—	26	1	no	—
461	Q₈	#88126	1	2	yes	—
462	D₄	—	2	4	no	—
463	D₄	—	2	1	no	—
464	D₄	—	26	1	no	—
465	D₄	—	26	1	no	—
466	D₄	—	52	2	no	—
467	D₄	#88126	1	2	yes	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	26	4	no	—
477	C₂×C₄	—	26	1	no	—
478	C₂×C₄	—	26	1	no	—
479	C₂×C₄	—	26	1	no	—
480	C₂×C₄	—	52	2	no	—
481	C₂×C₄	—	52	2	no	—
482	C₂×C₄	—	52	2	no	—
483	C₂×C₄	—	52	2	no	—
484	C₂×C₄	—	52	2	no	—
485	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
486	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
487	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
488	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
489	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
490	C₂×C₄	C₂×#6127	1	2	yes	—
491	C₂×C₄	C₂×#6127	1	2	yes	—
492	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
493	C₈	—	2	2	no	—
494	C₈	—	2	4	no	—
495	C₈	—	2	2	no	—
496	C₈	—	26	1	no	—
497	C₈	—	26	1	no	—
498	C₈	—	26	1	no	—
499	C₈	—	26	1	no	—
500	C₈	—	52	2	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	2	no	—
504	C₂²	—	4	1	no	—
505	C₂²	—	4	1	no	—
506	C₂²	—	52	1	no	—
507	C₂²	—	52	1	no	—
508	C₂²	—	52	1	no	—
509	C₂²	#11719184	1	2	yes	—
510	C₂²	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
511	C₄	—	2	2	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	4	1	no	—
515	C₄	—	4	1	no	—
516	C₄	—	52	4	no	—
517	C₄	—	52	1	no	—
518	C₄	—	52	1	no	—
519	C₄	—	52	1	no	—
520	C₄	#11718805	1	2	yes	—
521	C₄	#11718806	1	2	yes	—
522	C₄	C₂×#88126	1	1	yes	characteristic
523	C₄	C₄×#6127	1	1	yes	characteristic
524	C₄	#11719496	1	2	yes	—
525	C₂	—	2	2	no	—
526	C₂	—	4	2	no	—
527	C₂	—	104	1	no	—
528	C₂	#13117279	1	1	yes	characteristic
529	C₂	C₂×#11718805	1	1	yes	characteristic
530	C₂	C₂×#11718806	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×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×#88204	C₂²
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₄×#131	D₁₃
hypocenter	C₁₃	#21137
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ C₂×C₄×C₈ ◁ C₄×#131

Complements

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

N	H ≅ G/N	type
2. #13123478	C₂	semidirect
3. #13115484	C₂	semidirect
4. #13115435	C₂	semidirect
6. #13115111	C₂	semidirect
7. C₄×#88062	C₂	semidirect
8. C₄×#88065	C₂	semidirect
9. C₄×#88077	C₂	semidirect
10. #13114581	C₂	semidirect
11. C₄×C₁₃×#131	C₂	semidirect
28. C₄×#6107	C₄	semidirect
29. C₄×#6107	C₄	semidirect
30. C₄×#6106	C₄	semidirect
31. C₄×#6106	C₄	semidirect
32. C₄×#6105	C₄	semidirect
33. C₄×#6105	C₄	semidirect
34. C₄×#6104	C₄	semidirect
35. C₄×#6104	C₄	semidirect
192. C₄×#131	D₁₃	semidirect
454. C₁₃	#21137	semidirect

Maximal subgroups

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

subgroup	index
C₄×#88204	2
#13123478	2
#13115484	2
#13115435	2
#13115163	2
#13115111	2
C₄×#88062	2
C₄×#88065	2
C₄×#88077	2
#13114581	2
C₄×C₁₃×#131	2
#21137	13