Subgroups — #15881361

Order 3328.

858 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718484	C₂	1	2	yes	maximal
2	C₄×#88204	C₂	1	1	yes	maximal, characteristic
3	#13123405	C₂	1	1	yes	maximal, characteristic, complemented
4	#13123404	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115588	C₂	1	2	yes	maximal, complemented
6	#13115112	C₂	1	2	yes	maximal, complemented
7	#13115109	C₂	1	2	yes	maximal, complemented
8	#13115007	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114857	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114705	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1806	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×#88202	C₂²	1	2	yes	—
15	C₂×#88161	C₂²	1	2	yes	—
16	C₄×#6127	C₂²	1	1	yes	characteristic
17	C₁₃×#423	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#104	C₂²	1	2	yes	—
19	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	#11718894	C₂²	1	1	yes	characteristic
21	C₂×#88062	C₂²	1	2	yes	—
22	C₂×#88062	C₂²	1	2	yes	—
23	#11718780	C₂²	1	2	yes	—
24	C₄×#6107	C₄	1	1	yes	characteristic, complemented
25	C₄×#6107	C₄	1	1	yes	characteristic, complemented
26	C₄×#6106	C₄	1	1	yes	characteristic, complemented
27	C₄×#6106	C₄	1	1	yes	characteristic, complemented
28	C₄×#6105	C₄	1	1	yes	characteristic, complemented
29	C₄×#6105	C₄	1	1	yes	characteristic, complemented
30	C₄×#6104	C₄	1	1	yes	characteristic, complemented
31	C₄×#6104	C₄	1	1	yes	characteristic, complemented
32	#11718663	C₂²	1	1	yes	characteristic
33	#11718660	—	2	2	no	—
34	#11718660	C₂²	1	2	yes	—
35	#11718659	C₂²	1	1	yes	characteristic
36	C₂×#88045	C₂²	1	2	yes	—
37	#11718585	—	2	1	no	—
38	#11718585	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊#1055	—	2	1	no	—
40	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
41	C₂×#88043	C₂²	1	2	yes	—
42	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
43	#11718500	—	2	2	no	—
44	#11718498	—	2	1	no	—
45	D₁₃×C₄⋊C₈	—	2	1	no	—
46	#11718484	—	2	8	no	—
47	C₁₃×#339	C₂²	1	2	yes	—
48	#11718116	C₂²	1	2	yes	—
49	#11718115	C₂²	1	2	yes	—
50	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
51	C₂×#6127	C₂³	1	1	yes	characteristic
52	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
53	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
54	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
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	C₁₃×#117	—	2	1	no	—
60	C₁₃×#117	C₂³	1	1	yes	characteristic
61	C₂×C₁₃×C₄⋊C₄	—	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	D₄	1	4	yes	—
66	#88204	Q₈	1	4	yes	—
67	#88202	—	2	4	no	—
68	#88202	—	4	2	no	—
69	C₂×#6107	C₂×C₄	1	1	yes	characteristic
70	C₂×#6106	C₂×C₄	1	1	yes	characteristic
71	C₂×#6105	C₂×C₄	1	1	yes	characteristic
72	C₂×#6104	C₂×C₄	1	1	yes	characteristic
73	C₄×C₂²⋊D₁₃	—	2	1	no	—
74	C₄×C₂²⋊D₁₃	—	2	1	no	—
75	#88180	C₂³	1	1	yes	characteristic
76	C₂×#6099	—	2	2	no	—
77	C₂×#6099	C₂³	1	2	yes	—
78	C₂²×#1055	—	2	2	no	—
79	C₂²×#1055	C₂³	1	1	yes	characteristic
80	C₂²×#1055	C₂³	1	2	yes	—
81	C₂²×#1055	C₂³	1	1	yes	characteristic
82	#88161	—	2	4	no	—
83	#88161	—	4	2	no	—
84	C₂×#6094	—	2	2	no	—
85	C₂×C₈×D₁₃	—	2	2	no	—
86	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
87	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
88	#88126	—	2	1	no	—
89	C₄²×D₁₃	—	2	1	no	—
90	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
91	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
92	C₁₃×C₄⋊C₈	—	2	1	no	—
93	C₁₃×C₄⋊C₈	—	2	1	no	—
94	C₁₃×#104	—	2	4	no	—
95	C₁₃×#95	—	2	1	no	—
96	#88075	C₂×C₄	1	1	yes	characteristic
97	#88075	C₂×C₄	1	1	yes	characteristic
98	#88072	C₂×C₄	1	1	yes	characteristic
99	#88072	C₂×C₄	1	1	yes	characteristic
100	#88062	—	2	4	no	—
101	#88062	—	4	2	no	—
102	#88054	—	2	2	no	—
103	#88054	—	2	2	no	—
104	#88050	C₂×C₄	1	1	yes	characteristic
105	#88050	C₂×C₄	1	1	yes	characteristic
106	#88049	C₂×C₄	1	1	yes	characteristic
107	#88049	C₂×C₄	1	1	yes	characteristic
108	#88048	C₂×C₄	1	1	yes	characteristic
109	#88048	C₂×C₄	1	1	yes	characteristic
110	#88047	C₂×C₄	1	1	yes	characteristic
111	#88047	C₂×C₄	1	1	yes	characteristic
112	#88045	—	2	4	no	—
113	C₄⋊#1055	—	2	1	no	—
114	C₄⋊#1055	—	2	1	no	—
115	C₄⋊#1055	—	2	2	no	—
116	C₄⋊#1055	—	2	2	no	—
117	C₄⋊#1055	D₄	1	2	yes	—
118	C₄⋊#1055	D₄	1	1	yes	characteristic
119	C₄⋊#1055	D₄	1	1	yes	characteristic
120	#88043	—	2	4	no	—
121	C₄×#1055	C₂×C₄	1	1	yes	characteristic
122	C₄×#1055	C₂×C₄	1	1	yes	characteristic
123	C₄×#1055	C₂×C₄	1	1	yes	characteristic
124	C₄×#1055	C₂×C₄	1	1	yes	characteristic
125	#22686	—	13	1	no	maximal, Sylow
126	C₁₃×#41	—	2	1	no	—
127	C₁₃×#41	—	2	1	no	—
128	C₁₃×#41	C₂×D₄	1	2	yes	—
129	C₁₃×#41	C₂×Q₈	1	2	yes	—
130	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₂×D₄×C₁₃	—	2	1	no	—
132	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
140	C₂×C₂²⋊D₁₃	—	2	1	no	—
141	#6127	—	2	1	no	—
142	#6127	—	2	1	no	—
143	#6127	C₂×D₄	1	2	yes	—
144	#6127	C₂×Q₈	1	2	yes	—
145	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₄×D₁₃	—	2	1	no	—
147	C₂×C₄×D₁₃	—	2	1	no	—
148	C₂×C₄×D₁₃	—	2	1	no	—
149	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
150	C₁₃×M₁₆	—	2	2	no	—
151	C₁₃×M₁₆	—	2	2	no	—
152	C₂×C₈×C₁₃	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	2	1	no	—
154	C₁₃×C₄⋊C₄	—	2	1	no	—
155	C₁₃×C₄⋊C₄	—	4	2	no	—
156	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
157	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
158	C₁₃×C₂²⋊C₄	—	2	1	no	—
159	C₁₃×C₂²⋊C₄	—	2	1	no	—
160	C₁₃×C₂²⋊C₄	—	2	1	no	—
161	C₄²×C₁₃	—	2	1	no	—
162	C₄²×C₁₃	—	2	1	no	—
163	C₄²×C₁₃	—	2	1	no	—
164	C₄²×C₁₃	—	2	2	no	—
165	C₄²×C₁₃	—	2	2	no	—
166	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
167	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
168	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂²⋊Dic₁₃	—	2	1	no	—
171	#6107	C₄⋊C₄	1	4	yes	complemented
172	#6106	C₄⋊C₄	1	4	yes	complemented
173	#6105	C₄⋊C₄	1	4	yes	complemented
174	#6104	C₄⋊C₄	1	4	yes	complemented
175	#6103	—	2	1	no	—
176	#6103	—	2	1	no	—
177	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
178	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
179	#6101	—	2	1	no	—
180	#6101	—	2	1	no	—
181	C₄×Dic₁₃	—	2	1	no	—
182	C₄×Dic₁₃	—	2	1	no	—
183	C₄×Dic₁₃	—	2	1	no	—
184	#6099	—	2	2	no	—
185	#6099	—	2	2	no	—
186	#6099	—	4	4	no	—
187	C₂×#1055	—	2	2	no	—
188	C₂×#1055	—	2	2	no	—
189	C₂×#1055	—	2	1	no	—
190	C₂×#1055	—	2	1	no	—
191	C₂×#1055	—	2	2	no	—
192	C₂×#1055	—	4	4	no	—
193	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
194	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
195	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
196	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
197	C₂×#1055	C₂×D₄	1	2	yes	—
198	C₂×#1055	C₂×D₄	1	2	yes	—
199	C₂×#1055	C₂×D₄	1	2	yes	—
200	C₂×#1055	C₂×Q₈	1	2	yes	—
201	#6094	—	4	4	no	—
202	C₈×D₁₃	—	4	4	no	—
203	C₂×#444	—	13	2	no	—
204	C₄×#135	—	13	1	no	—
205	#2906	—	13	1	no	—
206	#2906	—	13	1	no	—
207	#1946	—	13	2	no	—
208	#1866	—	13	2	no	—
209	#1866	—	13	2	no	—
210	#1848	—	13	1	no	—
211	#1806	—	13	1	no	—
212	#1806	D₁₃	1	1	yes	characteristic, complemented
213	#1770	—	13	1	no	—
214	C₂³×C₁₃	—	2	1	no	—
215	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
216	C₂²×D₁₃	—	2	1	no	—
217	Q₈×C₁₃	—	2	1	no	—
218	Q₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
219	D₄×C₁₃	—	2	2	no	—
220	D₄×C₁₃	—	2	2	no	—
221	D₄×C₁₃	—	2	1	no	—
222	D₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
223	C₂×C₄×C₁₃	—	2	1	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	2	1	no	—
229	C₂×C₄×C₁₃	—	4	1	no	—
230	C₂×C₄×C₁₃	—	4	2	no	—
231	C₂×C₄×C₁₃	—	4	2	no	—
232	C₂×C₄×C₁₃	—	4	2	no	—
233	C₂×C₄×C₁₃	—	4	2	no	—
234	C₂×C₄×C₁₃	—	8	1	no	—
235	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
240	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
243	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
244	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
245	C₂²⋊D₁₃	—	2	2	no	—
246	C₂²⋊D₁₃	—	2	2	no	—
247	C₂×Dic₁₃	—	2	1	no	—
248	C₂×Dic₁₃	—	2	1	no	—
249	C₂×Dic₁₃	—	2	1	no	—
250	D₅₂	—	2	1	no	—
251	D₅₂	C₂×C₄⋊C₄	1	2	yes	—
252	C₄×D₁₃	—	2	2	no	—
253	C₄×D₁₃	—	2	2	no	—
254	C₄×D₁₃	—	4	2	no	—
255	C₄×D₁₃	—	8	1	no	—
256	Dic₂₆	—	2	1	no	—
257	Dic₂₆	C₂×C₄⋊C₄	1	2	yes	—
258	C₈×C₁₃	—	4	2	no	—
259	#1055	—	2	1	no	—
260	#1055	—	2	1	no	—
261	#1055	—	2	2	no	—
262	#1055	—	2	2	no	—
263	#1055	—	4	2	no	—
264	#1055	C₂×C₄⋊C₄	1	2	yes	—
265	#1055	C₂×C₄⋊C₄	1	2	yes	—
266	C₂×#135	—	13	1	no	—
267	C₂×#131	—	13	2	no	—
268	C₂×#131	—	13	2	no	—
269	C₄×#41	—	13	1	no	—
270	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
271	#444	—	26	8	no	—
272	C₄×Q₁₆	—	13	1	no	—
273	C₄×Q₁₆	—	13	1	no	—
274	C₄×SD₁₆	—	13	1	no	—
275	C₄×SD₁₆	—	13	1	no	—
276	C₄×SD₁₆	—	13	1	no	—
277	C₄×SD₁₆	—	13	1	no	—
278	C₄×D₈	—	13	1	no	—
279	C₄×D₈	—	13	1	no	—
280	C₂×#108	—	13	2	no	—
281	C₂×#108	—	13	2	no	—
282	#427	—	13	1	no	—
283	#424	—	13	2	no	—
284	#424	—	13	2	no	—
285	#424	—	26	2	no	—
286	#424	—	26	2	no	—
287	#423	—	13	1	no	—
288	#423	—	26	1	no	—
289	#423	—	26	1	no	—
290	#423	C₂×D₁₃	1	1	yes	characteristic
291	C₂×C₄⋊C₈	—	13	1	no	—
292	C₂×C₄⋊C₈	—	26	1	no	—
293	C₂×C₄⋊C₈	—	26	1	no	—
294	C₂×#104	—	13	2	no	—
295	C₂×#104	C₂×D₁₃	1	2	yes	—
296	#416	—	13	1	no	—
297	#416	—	13	1	no	—
298	C₂×#97	—	13	2	no	—
299	C₂×C₄×C₈	—	13	1	no	—
300	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
301	#339	—	13	2	no	—
302	#339	C₂×D₁₃	1	2	yes	—
303	#336	—	13	2	no	—
304	C₂²×C₁₃	—	2	1	no	—
305	C₂²×C₁₃	—	2	1	no	—
306	C₂²×C₁₃	—	2	2	no	—
307	C₂²×C₁₃	—	4	1	no	—
308	C₂²×C₁₃	—	4	1	no	—
309	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
310	C₂²×C₁₃	#547	1	1	yes	characteristic
311	C₂²×C₁₃	#554	1	1	yes	characteristic
312	C₂×D₁₃	—	2	2	no	—
313	C₂×D₁₃	—	4	1	no	—
314	C₂×D₁₃	—	4	1	no	—
315	C₄×C₁₃	—	2	2	no	—
316	C₄×C₁₃	—	2	1	no	—
317	C₄×C₁₃	—	2	1	no	—
318	C₄×C₁₃	—	2	1	no	—
319	C₄×C₁₃	—	4	1	no	—
320	C₄×C₁₃	—	4	1	no	—
321	C₄×C₁₃	—	8	2	no	—
322	C₄×C₁₃	#444	1	2	yes	complemented
323	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
324	C₄×C₁₃	#520	1	1	yes	characteristic
325	C₄×C₁₃	D₄²	1	1	yes	characteristic
326	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
327	Dic₁₃	—	2	2	no	—
328	Dic₁₃	—	4	1	no	—
329	Dic₁₃	—	4	1	no	—
330	C₂×#41	—	13	1	no	—
331	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
332	#135	—	13	4	no	—
333	#135	—	13	4	no	—
334	C₂×Q₁₆	—	13	1	no	—
335	C₂×SD₁₆	—	13	1	no	—
336	C₂×SD₁₆	—	13	1	no	—
337	C₂×D₈	—	13	1	no	—
338	#131	—	26	4	no	—
339	#131	—	26	4	no	—
340	#131	—	52	2	no	—
341	#131	—	52	2	no	—
342	C₂×M₁₆	—	13	2	no	—
343	C₂×M₁₆	—	26	2	no	—
344	C₂×M₁₆	—	26	2	no	—
345	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
346	C₂²×C₈	—	13	1	no	—
347	C₂²×C₈	—	13	2	no	—
348	C₂²×C₈	—	13	1	no	—
349	C₂²×C₈	—	26	2	no	—
350	C₂²×C₈	—	26	2	no	—
351	C₄×Q₈	—	13	1	no	—
352	C₄×Q₈	—	13	1	no	—
353	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
354	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
355	C₄×D₄	—	2	1	no	—
356	C₄×D₄	—	2	1	no	—
357	C₄×D₄	—	13	1	no	—
358	C₄×D₄	—	13	1	no	—
359	C₄×D₄	—	26	1	no	—
360	C₄×D₄	—	26	1	no	—
361	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
362	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
363	#117	—	2	1	no	—
364	#117	—	13	1	no	—
365	#117	—	26	1	no	—
366	#117	C₂²×D₁₃	1	1	yes	characteristic
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄²	—	2	1	no	—
369	C₂×C₄²	—	26	1	no	—
370	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
371	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
372	#108	—	26	4	no	—
373	#108	—	52	2	no	—
374	#107	—	13	1	no	—
375	#107	—	13	1	no	—
376	#106	—	13	1	no	—
377	#106	—	13	1	no	—
378	C₄⋊C₈	—	2	1	no	—
379	C₄⋊C₈	—	2	1	no	—
380	C₄⋊C₈	—	13	1	no	—
381	C₄⋊C₈	—	13	1	no	—
382	C₄⋊C₈	—	13	2	no	—
383	C₄⋊C₈	—	26	2	no	—
384	C₄⋊C₈	—	26	2	no	—
385	C₄⋊C₈	—	26	2	no	—
386	C₄⋊C₈	—	26	2	no	—
387	C₄⋊C₈	—	26	1	no	—
388	C₄⋊C₈	—	26	1	no	—
389	#104	—	2	4	no	—
390	#104	—	26	4	no	—
391	#103	—	13	1	no	—
392	#103	—	13	1	no	—
393	#103	—	13	1	no	—
394	#103	—	13	1	no	—
395	#102	—	13	1	no	—
396	#102	—	13	1	no	—
397	#102	—	13	1	no	—
398	#102	—	13	1	no	—
399	#97	—	26	4	no	—
400	C₄×C₈	—	13	1	no	—
401	C₄×C₈	—	13	1	no	—
402	C₄×C₈	—	13	1	no	—
403	C₄×C₈	—	13	1	no	—
404	#95	—	2	1	no	—
405	C₂×C₁₃	—	2	1	no	—
406	C₂×C₁₃	—	2	1	no	—
407	C₂×C₁₃	—	4	2	no	—
408	C₂×C₁₃	D₄×C₄⋊C₄	1	1	yes	characteristic
409	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
410	C₂×C₁₃	#2957	1	1	yes	characteristic
411	D₁₃	—	4	2	no	—
412	#41	—	2	1	no	—
413	#41	—	2	1	no	—
414	#41	—	13	2	no	—
415	#41	—	13	2	no	—
416	#41	—	26	1	no	—
417	#41	—	26	1	no	—
418	#41	D₄×D₁₃	1	2	yes	—
419	#41	Q₈×D₁₃	1	2	yes	—
420	C₂×Q₈	—	13	1	no	—
421	C₂×Q₈	C₂×C₄×D₁₃	1	1	yes	characteristic
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	—	13	1	no	—
424	C₂×D₄	—	26	1	no	—
425	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	26	1	no	—
431	C₂²×C₄	—	26	1	no	—
432	C₂²×C₄	—	26	1	no	—
433	C₂²×C₄	#6129	1	1	yes	characteristic
434	C₂²×C₄	#6129	1	1	yes	characteristic
435	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
436	Q₁₆	—	13	4	no	—
437	SD₁₆	—	13	4	no	—
438	SD₁₆	—	13	4	no	—
439	D₈	—	13	4	no	—
440	M₁₆	—	2	2	no	—
441	M₁₆	—	2	2	no	—
442	M₁₆	—	26	2	no	—
443	M₁₆	—	26	2	no	—
444	M₁₆	—	52	4	no	—
445	M₁₆	—	52	4	no	—
446	C₂×C₈	—	2	2	no	—
447	C₂×C₈	—	13	1	no	—
448	C₂×C₈	—	13	1	no	—
449	C₂×C₈	—	13	2	no	—
450	C₂×C₈	—	13	2	no	—
451	C₂×C₈	—	13	1	no	—
452	C₂×C₈	—	13	1	no	—
453	C₂×C₈	—	13	2	no	—
454	C₂×C₈	—	13	2	no	—
455	C₂×C₈	—	26	2	no	—
456	C₂×C₈	—	26	1	no	—
457	C₂×C₈	—	26	2	no	—
458	C₂×C₈	—	26	1	no	—
459	C₂×C₈	—	26	2	no	—
460	C₂×C₈	—	52	4	no	—
461	C₂×C₈	—	52	4	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	4	2	no	—
465	C₄⋊C₄	—	13	1	no	—
466	C₄⋊C₄	—	13	1	no	—
467	C₄⋊C₄	—	26	1	no	—
468	C₄⋊C₄	—	26	1	no	—
469	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
470	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	2	1	no	—
474	C₂²⋊C₄	—	26	1	no	—
475	C₂²⋊C₄	—	26	1	no	—
476	C₂²⋊C₄	—	26	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	2	no	—
481	C₄²	—	2	2	no	—
482	C₄²	—	26	1	no	—
483	C₄²	—	26	1	no	—
484	C₄²	—	26	1	no	—
485	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
486	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
487	C₄²	D₄×D₁₃	1	1	yes	characteristic
488	C₄²	D₄×D₁₃	1	1	yes	characteristic
489	C₁₃	#22686	1	1	yes	characteristic, complemented, Sylow
490	C₂³	—	2	1	no	—
491	C₂³	—	26	1	no	—
492	C₂³	C₂×#6129	1	1	yes	characteristic
493	Q₈	—	2	1	no	—
494	Q₈	—	13	2	no	—
495	Q₈	—	26	1	no	—
496	Q₈	C₄⋊C₄×D₁₃	1	2	yes	—
497	D₄	—	2	2	no	—
498	D₄	—	2	2	no	—
499	D₄	—	2	1	no	—
500	D₄	—	13	2	no	—
501	D₄	—	26	2	no	—
502	D₄	—	26	2	no	—
503	D₄	—	26	1	no	—
504	D₄	C₄⋊C₄×D₁₃	1	2	yes	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	8	1	no	—
517	C₂×C₄	—	26	1	no	—
518	C₂×C₄	—	26	2	no	—
519	C₂×C₄	—	26	2	no	—
520	C₂×C₄	—	26	1	no	—
521	C₂×C₄	—	26	1	no	—
522	C₂×C₄	—	52	2	no	—
523	C₂×C₄	—	104	1	no	—
524	C₂×C₄	#88135	1	1	yes	characteristic
525	C₂×C₄	#88135	1	1	yes	characteristic
526	C₂×C₄	#88135	1	1	yes	characteristic
527	C₂×C₄	#88135	1	1	yes	characteristic
528	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
529	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
530	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
531	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
532	C₂×C₄	#88256	1	1	yes	characteristic
533	C₂×C₄	#88257	1	1	yes	characteristic
534	C₈	—	4	2	no	—
535	C₈	—	13	2	no	—
536	C₈	—	13	2	no	—
537	C₈	—	26	1	no	—
538	C₈	—	26	1	no	—
539	C₈	—	26	2	no	—
540	C₈	—	26	2	no	—
541	C₈	—	52	2	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	4	1	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	26	2	no	—
548	C₂²	—	52	1	no	—
549	C₂²	—	52	1	no	—
550	C₂²	C₂×#88135	1	1	yes	characteristic
551	C₂²	#11719316	1	1	yes	characteristic
552	C₂²	#11719340	1	1	yes	characteristic
553	C₄	—	2	2	no	—
554	C₄	—	2	1	no	—
555	C₄	—	2	1	no	—
556	C₄	—	2	1	no	—
557	C₄	—	4	1	no	—
558	C₄	—	4	1	no	—
559	C₄	—	8	2	no	—
560	C₄	—	26	2	no	—
561	C₄	—	52	1	no	—
562	C₄	—	52	1	no	—
563	C₄	#11718484	1	2	yes	complemented
564	C₄	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
565	C₄	#11719228	1	1	yes	characteristic
566	C₄	#11719314	1	1	yes	characteristic
567	C₄	#11719337	1	1	yes	characteristic
568	C₂	—	2	1	no	—
569	C₂	—	2	1	no	—
570	C₂	—	4	2	no	—
571	C₂	—	52	2	no	—
572	C₂	#13117732	1	1	yes	characteristic
573	C₂	C₂×#11718484	1	1	yes	characteristic
574	C₂	#13123749	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#1806	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×#88204	C₂²
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#1806	D₁₃
hypocenter	C₁₃	#22686
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1806

Complements

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

N	H ≅ G/N	type
3. #13123405	C₂	semidirect
4. #13123404	C₂	semidirect
5. #13115588	C₂	semidirect
6. #13115112	C₂	semidirect
7. #13115109	C₂	semidirect
8. #13115007	C₂	semidirect
9. #13114857	C₂	semidirect
10. #13114705	C₂	semidirect
11. C₁₃×#1806	C₂	semidirect
24. C₄×#6107	C₄	semidirect
25. C₄×#6107	C₄	semidirect
26. C₄×#6106	C₄	semidirect
27. C₄×#6106	C₄	semidirect
28. C₄×#6105	C₄	semidirect
29. C₄×#6105	C₄	semidirect
30. C₄×#6104	C₄	semidirect
31. C₄×#6104	C₄	semidirect
171. #6107	C₄⋊C₄	semidirect
172. #6106	C₄⋊C₄	semidirect
173. #6105	C₄⋊C₄	semidirect
174. #6104	C₄⋊C₄	semidirect
212. #1806	D₁₃	semidirect
322. C₄×C₁₃	#444	semidirect
489. C₁₃	#22686	semidirect
563. C₄	#11718484	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718484	2
C₄×#88204	2
#13123405	2
#13123404	2
#13115588	2
#13115112	2
#13115109	2
#13115007	2
#13114857	2
#13114705	2
C₁₃×#1806	2
#22686	13