Subgroups — #15866146

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	#13123480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#88161	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115487	C₂	1	2	yes	maximal, complemented
5	#13115438	C₂	1	2	yes	maximal, complemented
6	#13115160	C₂	1	2	yes	maximal
7	#13115112	C₂	1	2	yes	maximal, complemented
8	C₄×#88062	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#88045	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114582	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×#104	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₂×#88204	C₂²	1	1	yes	characteristic
14	C₂×#88161	C₂²	1	2	yes	—
15	C₄×#6127	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#104	C₂²	1	2	yes	—
17	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
18	C₄³×C₁₃	C₂²	1	1	yes	characteristic
19	#11718895	C₂²	1	2	yes	—
20	#11718894	C₂²	1	1	yes	characteristic
21	C₂×#88062	C₂²	1	2	yes	—
22	#11718783	C₂²	1	2	yes	—
23	C₄×#6107	C₄	1	1	yes	characteristic, complemented
24	C₄×#6107	C₄	1	1	yes	characteristic, complemented
25	C₄×#6106	C₄	1	1	yes	characteristic, complemented
26	C₄×#6106	C₄	1	1	yes	characteristic, complemented
27	C₄×#6105	C₄	1	1	yes	characteristic, complemented
28	C₄×#6105	C₄	1	1	yes	characteristic, complemented
29	C₄×#6104	C₄	1	1	yes	characteristic, complemented
30	C₄×#6104	C₄	1	1	yes	characteristic, complemented
31	#11718663	C₂²	1	1	yes	characteristic
32	#11718661	—	2	2	no	—
33	#11718660	C₂²	1	2	yes	—
34	#11718659	C₂²	1	1	yes	characteristic
35	C₂×#88045	C₂²	1	2	yes	—
36	#11718586	—	2	1	no	—
37	#11718586	—	2	1	no	—
38	C₄×#6099	C₂²	1	1	yes	characteristic
39	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
40	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
41	#11718369	—	2	2	no	—
42	C₄×#6094	—	2	1	no	—
43	C₄×C₈×D₁₃	—	2	1	no	—
44	C₁₃×#339	C₂²	1	2	yes	—
45	#11718150	C₂²	1	2	yes	—
46	#11718116	C₂²	1	2	yes	—
47	#11718116	C₂²	1	2	yes	—
48	#11718115	C₂²	1	2	yes	—
49	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
50	C₂×#6127	C₂³	1	1	yes	characteristic
51	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
52	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
53	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
54	C₄×D₄×C₁₃	—	2	1	no	—
55	C₄×D₄×C₁₃	—	2	1	no	—
56	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
57	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
58	C₁₃×#117	—	2	1	no	—
59	C₁₃×#117	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₁₃	—	2	1	no	—
61	C₂×C₄²×C₁₃	—	2	1	no	—
62	C₂×C₄²×C₁₃	—	2	1	no	—
63	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
64	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
65	#88204	—	2	4	no	—
66	C₂×#6107	C₂×C₄	1	1	yes	characteristic
67	C₂×#6106	C₂×C₄	1	1	yes	characteristic
68	C₂×#6105	C₂×C₄	1	1	yes	characteristic
69	C₂×#6104	C₂×C₄	1	1	yes	characteristic
70	C₄×C₂²⋊D₁₃	—	2	1	no	—
71	C₄×C₂²⋊D₁₃	—	2	1	no	—
72	#88180	C₂³	1	1	yes	characteristic
73	C₂×#6099	C₂³	1	2	yes	—
74	C₂²×#1055	C₂³	1	1	yes	characteristic
75	C₂²×#1055	C₂³	1	1	yes	characteristic
76	C₂²×#1055	C₂³	1	2	yes	—
77	#88161	—	2	4	no	—
78	#88161	—	2	4	no	—
79	C₂×#6094	—	2	2	no	—
80	C₂×C₈×D₁₃	—	2	2	no	—
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×#104	—	2	4	no	—
88	C₁₃×#97	—	2	1	no	—
89	C₄×C₈×C₁₃	—	2	1	no	—
90	#88075	C₂×C₄	1	1	yes	characteristic
91	#88075	C₂×C₄	1	1	yes	characteristic
92	#88072	C₂×C₄	1	1	yes	characteristic
93	#88072	C₂×C₄	1	1	yes	characteristic
94	C₂²⋊#1055	—	2	2	no	—
95	C₂²⋊#1055	—	2	2	no	—
96	#88062	—	2	4	no	—
97	#88055	—	2	2	no	—
98	C₈×Dic₁₃	—	2	2	no	—
99	#88050	C₂×C₄	1	1	yes	characteristic
100	#88050	C₂×C₄	1	1	yes	characteristic
101	#88049	C₂×C₄	1	1	yes	characteristic
102	#88049	C₂×C₄	1	1	yes	characteristic
103	#88048	C₂×C₄	1	1	yes	characteristic
104	#88048	C₂×C₄	1	1	yes	characteristic
105	#88047	C₂×C₄	1	1	yes	characteristic
106	#88047	C₂×C₄	1	1	yes	characteristic
107	#88045	—	2	4	no	—
108	C₄⋊#1055	—	2	2	no	—
109	C₄⋊#1055	—	2	2	no	—
110	#88043	—	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	1	yes	characteristic
115	C₄×#1055	C₂×C₄	1	1	yes	characteristic
116	C₄×#1055	D₄	1	2	yes	—
117	C₄×#1055	D₄	1	1	yes	characteristic
118	C₄×#1055	D₄	1	1	yes	characteristic
119	#21137	—	13	1	no	maximal, Sylow
120	C₁₃×#41	—	2	2	no	—
121	C₁₃×#41	—	2	2	no	—
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	2	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
132	C₂×C₂²⋊D₁₃	—	2	1	no	—
133	#6127	—	2	2	no	—
134	#6127	#41	1	4	yes	—
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	2	no	—
141	C₁₃×M₁₆	#41	1	4	yes	—
142	C₂×C₈×C₁₃	—	2	2	no	—
143	C₁₃×C₄⋊C₄	—	2	1	no	—
144	C₁₃×C₄⋊C₄	—	2	1	no	—
145	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
146	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
147	C₁₃×C₂²⋊C₄	—	2	1	no	—
148	C₁₃×C₂²⋊C₄	—	2	1	no	—
149	C₁₃×C₂²⋊C₄	—	2	1	no	—
150	C₄²×C₁₃	—	2	4	no	—
151	C₄²×C₁₃	—	2	1	no	—
152	C₄²×C₁₃	—	2	1	no	—
153	C₄²×C₁₃	—	2	1	no	—
154	C₄²×C₁₃	—	2	2	no	—
155	C₄²×C₁₃	—	2	2	no	—
156	C₄²×C₁₃	—	4	2	no	—
157	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
158	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
159	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂²⋊Dic₁₃	—	2	1	no	—
162	#6107	—	2	2	no	—
163	#6106	—	2	2	no	—
164	#6105	—	2	2	no	—
165	#6104	—	2	2	no	—
166	#6103	—	2	1	no	—
167	#6103	—	2	1	no	—
168	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
169	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
170	#6101	—	2	1	no	—
171	#6101	—	2	1	no	—
172	C₄×Dic₁₃	—	2	1	no	—
173	C₄×Dic₁₃	—	2	1	no	—
174	C₄×Dic₁₃	—	2	1	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	—	2	2	no	—
181	C₂×#1055	—	2	2	no	—
182	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
183	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
184	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
185	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
186	C₂×#1055	C₂×D₄	1	2	yes	—
187	C₂×#1055	C₂×D₄	1	2	yes	—
188	#6094	—	2	8	no	—
189	C₈×D₁₃	—	2	8	no	—
190	C₄×#135	—	13	1	no	—
191	#2922	—	13	1	no	—
192	C₄×#131	—	13	1	no	—
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	D₁₃	1	1	yes	characteristic, complemented
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	—	2	1	no	—
206	D₄×C₁₃	—	2	1	no	—
207	D₄×C₁₃	—	2	1	no	—
208	D₄×C₁₃	—	4	2	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	4	no	—
212	C₂×C₄×C₁₃	—	2	1	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	—	4	2	no	—
218	C₂×C₄×C₁₃	—	4	2	no	—
219	C₂×C₄×C₁₃	—	4	2	no	—
220	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
227	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
228	C₂²⋊D₁₃	—	2	4	no	—
229	C₂×Dic₁₃	—	2	1	no	—
230	C₂×Dic₁₃	—	2	1	no	—
231	C₂×Dic₁₃	—	2	1	no	—
232	D₅₂	—	2	1	no	—
233	D₅₂	#117	1	2	yes	—
234	C₄×D₁₃	—	2	4	no	—
235	C₄×D₁₃	—	4	2	no	—
236	C₄×D₁₃	—	4	2	no	—
237	Dic₂₆	—	2	1	no	—
238	Dic₂₆	#117	1	2	yes	—
239	C₈×C₁₃	—	2	4	no	—
240	#1055	—	2	1	no	—
241	#1055	—	2	1	no	—
242	#1055	—	2	1	no	—
243	#1055	—	2	1	no	—
244	#1055	—	2	2	no	—
245	#1055	—	2	2	no	—
246	#1055	—	4	2	no	—
247	C₂×#135	—	13	1	no	—
248	C₂×#131	—	13	2	no	—
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	C₂×D₁₃	1	2	yes	—
267	#416	—	13	1	no	—
268	#416	—	13	1	no	—
269	#408	—	13	2	no	—
270	#405	—	13	2	no	—
271	#405	—	26	2	no	—
272	C₄×M₁₆	—	13	1	no	—
273	C₄×M₁₆	—	26	1	no	—
274	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
275	C₂×C₄×C₈	—	13	1	no	—
276	C₂×C₄×C₈	—	13	1	no	—
277	C₂×C₄×C₈	—	26	1	no	—
278	C₄³	C₂×D₁₃	1	1	yes	characteristic
279	#341	—	13	2	no	—
280	#339	—	13	2	no	—
281	#339	C₂×D₁₃	1	2	yes	—
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	—	4	1	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	—	2	2	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	—	4	4	no	—
297	C₄×C₁₃	—	4	1	no	—
298	C₄×C₁₃	—	4	1	no	—
299	C₄×C₁₃	—	4	1	no	—
300	C₄×C₁₃	#443	1	2	yes	—
301	C₄×C₁₃	#444	1	2	yes	—
302	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
303	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
304	C₄×C₁₃	#525	1	2	yes	—
305	Dic₁₃	—	2	2	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	—	26	4	no	—
316	#131	—	26	4	no	—
317	C₂×M₁₆	—	13	2	no	—
318	C₂×M₁₆	—	26	2	no	—
319	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
320	C₂²×C₈	—	13	2	no	—
321	C₂²×C₈	—	13	1	no	—
322	C₂²×C₈	—	13	1	no	—
323	C₂²×C₈	—	26	2	no	—
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	—	2	1	no	—
342	C₂×C₄²	—	2	1	no	—
343	C₂×C₄²	—	26	1	no	—
344	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
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	—	2	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	1	no	—
366	#97	—	26	2	no	—
367	#97	—	26	1	no	—
368	C₄×C₈	—	2	1	no	—
369	C₄×C₈	—	13	1	no	—
370	C₄×C₈	—	13	1	no	—
371	C₄×C₈	—	13	1	no	—
372	C₄×C₈	—	13	1	no	—
373	C₄×C₈	—	13	2	no	—
374	C₄×C₈	—	13	1	no	—
375	C₄×C₈	—	13	1	no	—
376	C₄×C₈	—	26	2	no	—
377	C₄×C₈	—	26	1	no	—
378	C₂×C₁₃	—	2	2	no	—
379	C₂×C₁₃	—	8	1	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	—	4	2	no	—
384	#41	—	2	2	no	—
385	#41	—	2	2	no	—
386	#41	—	13	4	no	—
387	#41	—	26	2	no	—
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	2	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	26	1	no	—
399	C₂²×C₄	—	26	1	no	—
400	C₂²×C₄	—	26	1	no	—
401	C₂²×C₄	#6129	1	1	yes	characteristic
402	C₂²×C₄	#6129	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	2	no	—
409	M₁₆	—	26	8	no	—
410	M₁₆	—	26	2	no	—
411	M₁₆	—	26	2	no	—
412	M₁₆	#6127	1	4	yes	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	13	1	no	—
415	C₂×C₈	—	13	1	no	—
416	C₂×C₈	—	13	1	no	—
417	C₂×C₈	—	13	1	no	—
418	C₂×C₈	—	13	2	no	—
419	C₂×C₈	—	13	2	no	—
420	C₂×C₈	—	26	8	no	—
421	C₂×C₈	—	26	2	no	—
422	C₂×C₈	—	26	2	no	—
423	C₂×C₈	—	26	2	no	—
424	C₂×C₈	—	26	2	no	—
425	C₂×C₈	—	26	2	no	—
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	4	no	—
441	C₄²	—	2	1	no	—
442	C₄²	—	2	1	no	—
443	C₄²	—	2	1	no	—
444	C₄²	—	2	2	no	—
445	C₄²	—	2	2	no	—
446	C₄²	—	4	2	no	—
447	C₄²	—	26	1	no	—
448	C₄²	—	26	1	no	—
449	C₄²	—	26	1	no	—
450	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
451	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
452	C₄²	D₄×D₁₃	1	1	yes	characteristic
453	C₄²	D₄×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×#6129	1	1	yes	characteristic
458	Q₈	—	2	1	no	—
459	Q₈	—	2	1	no	—
460	Q₈	—	13	2	no	—
461	Q₈	—	26	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	4	no	—
467	D₄	—	26	1	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	1	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	—	4	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	26	1	no	—
480	C₂×C₄	—	26	4	no	—
481	C₂×C₄	—	26	1	no	—
482	C₂×C₄	—	26	1	no	—
483	C₂×C₄	—	52	2	no	—
484	C₂×C₄	—	52	2	no	—
485	C₂×C₄	#88135	1	1	yes	characteristic
486	C₂×C₄	#88135	1	1	yes	characteristic
487	C₂×C₄	#88135	1	1	yes	characteristic
488	C₂×C₄	#88135	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×D₄×D₁₃	1	1	yes	characteristic
492	C₂×C₄	#41×D₁₃	1	2	yes	—
493	C₈	—	2	4	no	—
494	C₈	—	26	1	no	—
495	C₈	—	26	1	no	—
496	C₈	—	26	1	no	—
497	C₈	—	26	1	no	—
498	C₈	—	26	2	no	—
499	C₈	—	26	2	no	—
500	C₈	—	52	2	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	4	1	no	—
505	C₂²	—	4	1	no	—
506	C₂²	—	26	2	no	—
507	C₂²	—	52	1	no	—
508	C₂²	—	52	1	no	—
509	C₂²	C₂×#88135	1	1	yes	characteristic
510	C₂²	#11719262	1	2	yes	—
511	C₄	—	2	1	no	—
512	C₄	—	2	1	no	—
513	C₄	—	4	4	no	—
514	C₄	—	4	1	no	—
515	C₄	—	4	1	no	—
516	C₄	—	4	1	no	—
517	C₄	—	26	2	no	—
518	C₄	—	52	1	no	—
519	C₄	—	52	1	no	—
520	C₄	#11718484	1	2	yes	—
521	C₄	#11718485	1	2	yes	—
522	C₄	C₄×#6127	1	1	yes	characteristic
523	C₄	D₁₃×#117	1	1	yes	characteristic
524	C₄	#11719252	1	2	yes	—
525	C₂	—	2	2	no	—
526	C₂	—	8	1	no	—
527	C₂	—	52	2	no	—
528	C₂	#13117282	1	1	yes	characteristic
529	C₂	C₂×#11718485	1	1	yes	characteristic
530	C₂	C₂×#11718484	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₄×C₁₃×#104	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×#88204	C₂²
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₄×#104	D₁₃
hypocenter	C₁₃	#21137
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ C₄×#104

Complements

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

N	H ≅ G/N	type
2. #13123480	C₂	semidirect
3. C₄×#88161	C₂	semidirect
4. #13115487	C₂	semidirect
5. #13115438	C₂	semidirect
7. #13115112	C₂	semidirect
8. C₄×#88062	C₂	semidirect
9. C₄×#88045	C₂	semidirect
10. #13114582	C₂	semidirect
11. C₄×C₁₃×#104	C₂	semidirect
23. C₄×#6107	C₄	semidirect
24. C₄×#6107	C₄	semidirect
25. C₄×#6106	C₄	semidirect
26. C₄×#6106	C₄	semidirect
27. C₄×#6105	C₄	semidirect
28. C₄×#6105	C₄	semidirect
29. C₄×#6104	C₄	semidirect
30. C₄×#6104	C₄	semidirect
199. C₄×#104	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
#13123480	2
C₄×#88161	2
#13115487	2
#13115438	2
#13115160	2
#13115112	2
C₄×#88062	2
C₄×#88045	2
#13114582	2
C₄×C₁₃×#104	2
#21137	13