Subgroups — #15869696

Order 3328.

998 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13124417	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718361	C₂	1	1	yes	maximal, characteristic, complemented
3	#13123530	C₂	1	2	yes	maximal, complemented
4	#13115724	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115584	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115540	C₂	1	2	yes	maximal, complemented
7	#13115279	C₂	1	2	yes	maximal, complemented
8	#13114874	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114715	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114673	C₂	1	2	yes	maximal, complemented
11	C₂²×C₄×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
15	#11719496	C₂²	1	2	yes	—
16	C₂×#88158	C₂²	1	1	yes	characteristic
17	C₂×#88155	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₁₃	—	2	4	no	—
19	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	#11718868	C₂²	1	2	yes	—
24	#11718777	C₄	1	2	yes	complemented
25	#11718776	C₄	1	2	yes	complemented
26	#11718775	C₄	1	4	yes	complemented
27	#11718774	C₂²	1	2	yes	—
28	#11718772	—	2	4	no	—
29	#11718771	C₂²	1	2	yes	—
30	C₈×C₂²⋊D₁₃	—	2	4	no	—
31	C₂×#88059	C₂²	1	1	yes	characteristic
32	C₂×#88059	C₂²	1	1	yes	characteristic
33	#11718767	C₂²	1	1	yes	characteristic
34	#11718763	C₂²	1	2	yes	—
35	#11718762	C₂²	1	2	yes	—
36	C₂×#88045	C₂²	1	2	yes	—
37	C₂×#88045	C₂²	1	2	yes	—
38	#11718361	—	2	4	no	—
39	#11718144	C₂²	1	2	yes	—
40	#11718115	C₂²	1	2	yes	—
41	#11718115	C₂²	1	2	yes	—
42	C₂³×C₄×C₁₃	—	2	1	no	—
43	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₂×#6127	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃	—	2	2	no	—
46	C₂²×C₈×C₁₃	—	2	2	no	—
47	C₂²×C₈×C₁₃	—	2	2	no	—
48	C₂²×C₈×C₁₃	—	2	2	no	—
49	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
50	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
51	C₂²×C₈×C₁₃	D₄	1	2	yes	—
52	C₂²×C₈×C₁₃	D₄	1	2	yes	—
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₁₃	—	2	1	no	—
58	C₂×C₄²×C₁₃	—	2	2	no	—
59	C₂×C₄²×C₁₃	—	2	2	no	—
60	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
62	#88207	—	2	2	no	—
63	#88184	C₂×C₄	1	4	yes	—
64	#88183	—	2	2	no	—
65	C₄×C₂²⋊D₁₃	—	2	4	no	—
66	#88180	C₂³	1	2	yes	—
67	#88178	C₂×C₄	1	4	yes	—
68	C₂×#6099	C₂³	1	2	yes	—
69	C₂×#6099	C₂³	1	2	yes	—
70	C₂×Dic₅₂	C₂×C₄	1	1	yes	characteristic, complemented
71	#88158	—	2	2	no	—
72	#88158	—	2	2	no	—
73	C₂×D₁₀₄	C₂×C₄	1	1	yes	characteristic, complemented
74	C₂×#6095	C₂×C₄	1	2	yes	complemented
75	#88155	—	2	4	no	—
76	#88155	—	2	4	no	—
77	C₂×#6094	—	2	2	no	—
78	C₂×C₈×D₁₃	—	2	2	no	—
79	C₄×C₈×C₁₃	—	2	2	no	—
80	C₄×C₈×C₁₃	—	2	2	no	—
81	C₄×C₈×C₁₃	—	2	2	no	—
82	C₄×C₈×C₁₃	D₄	1	4	yes	complemented
83	C₂²⋊#1055	—	2	4	no	—
84	#88061	C₂×C₄	1	4	yes	complemented
85	#88060	—	2	4	no	—
86	#88059	—	2	2	no	—
87	#88059	—	2	2	no	—
88	#88058	C₂×C₄	1	2	yes	complemented
89	#88057	C₂×C₄	1	2	yes	complemented
90	#88056	C₂×C₄	1	4	yes	complemented
91	#88055	—	2	2	no	—
92	#88054	—	2	4	no	—
93	C₈×Dic₁₃	—	2	2	no	—
94	#88045	—	2	4	no	—
95	#88045	—	2	4	no	—
96	#21544	—	13	1	no	maximal, Sylow
97	C₂⁴×C₁₃	#41	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	—	2	4	no	—
99	C₂²×C₄×C₁₃	—	2	8	no	—
100	C₂²×C₄×C₁₃	—	2	1	no	—
101	C₂²×C₄×C₁₃	—	2	1	no	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
110	C₂×C₂²⋊D₁₃	—	2	4	no	—
111	C₂×C₂²⋊D₁₃	—	2	2	no	—
112	#6127	—	2	2	no	—
113	#6127	—	2	2	no	—
114	#6127	—	2	2	no	—
115	#6127	—	2	2	no	—
116	C₂×D₅₂	C₂²×C₄	1	2	yes	—
117	C₂×C₄×D₁₃	—	2	2	no	—
118	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₁₃	—	2	1	no	—
120	C₂×C₈×C₁₃	—	2	1	no	—
121	C₂×C₈×C₁₃	—	2	1	no	—
122	C₂×C₈×C₁₃	—	2	1	no	—
123	C₂×C₈×C₁₃	—	2	4	no	—
124	C₂×C₈×C₁₃	—	2	4	no	—
125	C₂×C₈×C₁₃	—	2	4	no	—
126	C₂×C₈×C₁₃	—	2	4	no	—
127	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
128	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
132	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₁₃	#41	1	2	yes	—
136	C₂×C₈×C₁₃	#41	1	2	yes	—
137	C₄²×C₁₃	—	2	4	no	—
138	C₄²×C₁₃	—	2	1	no	—
139	C₄²×C₁₃	—	2	1	no	—
140	C₄²×C₁₃	C₂×D₄	1	2	yes	—
141	C₄²×C₁₃	#41	1	2	yes	—
142	C₂²⋊Dic₁₃	—	2	4	no	—
143	C₂²⋊Dic₁₃	—	2	2	no	—
144	#6103	—	2	4	no	—
145	C₄⋊Dic₁₃	C₂²×C₄	1	4	yes	—
146	#6101	—	2	4	no	—
147	C₄×Dic₁₃	—	2	2	no	—
148	#6099	—	2	2	no	—
149	#6099	—	2	2	no	—
150	#6099	—	2	2	no	—
151	#6099	—	2	2	no	—
152	C₂×#1055	—	2	2	no	—
153	C₂×#1055	—	2	2	no	—
154	Dic₅₂	—	2	2	no	—
155	D₁₀₄	—	2	2	no	—
156	#6095	—	2	4	no	—
157	#6094	—	4	4	no	—
158	C₈×D₁₃	—	4	4	no	—
159	#3050	—	13	1	no	—
160	C₂×#443	—	13	1	no	—
161	#2929	—	13	2	no	—
162	C₂²×C₄×C₈	D₁₃	1	1	yes	characteristic, complemented
163	#1974	—	13	1	no	—
164	#1945	—	13	1	no	—
165	#1937	—	13	2	no	—
166	#1896	—	13	2	no	—
167	#1810	—	13	1	no	—
168	#1772	—	13	1	no	—
169	#1764	—	13	2	no	—
170	C₂³×C₁₃	—	2	1	no	—
171	C₂³×C₁₃	—	2	1	no	—
172	C₂³×C₁₃	—	2	4	no	—
173	C₂³×C₁₃	C₄×D₄	1	2	yes	—
174	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
175	C₂²×D₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	16	no	—
177	C₂×C₄×C₁₃	—	2	4	no	—
178	C₂×C₄×C₁₃	—	2	4	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
188	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
194	C₂²⋊D₁₃	—	4	2	no	—
195	C₂²⋊D₁₃	—	4	2	no	—
196	C₂²⋊D₁₃	—	4	8	no	—
197	C₂×Dic₁₃	—	2	4	no	—
198	C₂×Dic₁₃	—	2	2	no	—
199	D₅₂	—	2	2	no	—
200	D₅₂	—	2	2	no	—
201	C₄×D₁₃	—	4	2	no	—
202	C₄×D₁₃	—	4	2	no	—
203	Dic₂₆	—	2	2	no	—
204	Dic₂₆	—	2	2	no	—
205	C₈×C₁₃	—	2	2	no	—
206	C₈×C₁₃	—	2	2	no	—
207	C₈×C₁₃	C₄×D₄	1	2	yes	—
208	C₈×C₁₃	C₄×D₄	1	2	yes	—
209	C₈×C₁₃	#121	1	2	yes	—
210	C₈×C₁₃	#121	1	2	yes	—
211	#1055	—	4	2	no	—
212	#1055	—	4	2	no	—
213	C₂×#135	—	13	1	no	—
214	C₂×#131	—	13	2	no	—
215	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
216	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
217	#525	—	13	2	no	—
218	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
219	#467	—	13	2	no	—
220	#466	—	13	2	no	—
221	#465	—	13	4	no	—
222	#443	—	26	4	no	—
223	#435	—	26	4	no	—
224	C₈×D₄	—	26	4	no	—
225	C₂×#108	—	13	1	no	—
226	C₂×#108	—	13	1	no	—
227	#427	—	13	1	no	—
228	#424	—	13	2	no	—
229	C₂×#104	—	13	2	no	—
230	C₂×#104	—	13	2	no	—
231	#416	—	13	2	no	—
232	#408	—	13	2	no	—
233	#407	—	13	2	no	—
234	#405	—	13	2	no	—
235	C₂×C₄×C₈	—	2	4	no	—
236	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
237	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
238	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
239	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
240	#341	—	13	2	no	—
241	#339	—	13	2	no	—
242	#339	—	13	2	no	—
243	C₂²×C₁₃	—	2	4	no	—
244	C₂²×C₁₃	—	2	4	no	—
245	C₂²×C₁₃	—	2	2	no	—
246	C₂²×C₁₃	—	2	2	no	—
247	C₂²×C₁₃	—	2	2	no	—
248	C₂²×C₁₃	#443	1	4	yes	complemented
249	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
250	C₂²×C₁₃	#525	1	1	yes	characteristic
251	C₂²×C₁₃	#529	1	1	yes	characteristic
252	C₂×D₁₃	—	4	4	no	—
253	C₂×D₁₃	—	4	2	no	—
254	C₄×C₁₃	—	2	4	no	—
255	C₄×C₁₃	—	2	4	no	—
256	C₄×C₁₃	—	2	2	no	—
257	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
258	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
259	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
260	C₄×C₁₃	#532	1	1	yes	characteristic
261	Dic₁₃	—	4	4	no	—
262	Dic₁₃	—	4	2	no	—
263	C₂×#41	—	13	2	no	—
264	C₂³×C₄	—	2	1	no	—
265	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
266	#135	—	26	2	no	—
267	#135	—	26	2	no	—
268	C₂×Q₁₆	—	13	1	no	—
269	C₂×SD₁₆	—	13	2	no	—
270	C₂×D₈	—	13	1	no	—
271	#131	—	26	4	no	—
272	#131	—	26	4	no	—
273	C₂×M₁₆	—	13	2	no	—
274	C₂×M₁₆	—	13	2	no	—
275	C₂×M₁₆	—	26	2	no	—
276	C₂²×C₈	—	2	2	no	—
277	C₂²×C₈	—	2	2	no	—
278	C₂²×C₈	—	2	2	no	—
279	C₂²×C₈	—	2	2	no	—
280	C₂²×C₈	—	26	2	no	—
281	C₂²×C₈	C₄×D₁₃	1	2	yes	—
282	C₂²×C₈	C₄×D₁₃	1	2	yes	—
283	C₂²×C₈	D₅₂	1	2	yes	—
284	C₂²×C₈	D₅₂	1	2	yes	—
285	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
286	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
287	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
288	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
289	#123	—	26	2	no	—
290	C₂²⋊Q₈	—	13	4	no	—
291	#121	—	13	4	no	—
292	#120	—	26	2	no	—
293	C₄×D₄	—	26	4	no	—
294	#117	—	13	2	no	—
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	—	2	2	no	—
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
299	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
300	#108	—	26	2	no	—
301	#108	—	26	2	no	—
302	#107	—	13	2	no	—
303	#106	—	13	2	no	—
304	C₄⋊C₈	—	26	4	no	—
305	#104	—	26	4	no	—
306	#104	—	26	4	no	—
307	#103	—	13	4	no	—
308	#102	—	13	4	no	—
309	C₂²⋊C₈	—	26	4	no	—
310	C₂²⋊C₈	—	26	4	no	—
311	#97	—	26	2	no	—
312	C₄×C₈	—	2	2	no	—
313	C₄×C₈	—	2	2	no	—
314	C₄×C₈	—	2	2	no	—
315	C₄×C₈	—	26	2	no	—
316	C₄×C₈	C₂²⋊D₁₃	1	4	yes	complemented
317	C₂×C₁₃	—	2	1	no	—
318	C₂×C₁₃	—	2	1	no	—
319	C₂×C₁₃	—	2	4	no	—
320	C₂×C₁₃	C₄×#121	1	1	yes	characteristic
321	C₂×C₁₃	C₂×#443	1	2	yes	—
322	D₁₃	—	8	2	no	—
323	C₂⁴	#6127	1	1	yes	characteristic
324	#41	—	26	2	no	—
325	#41	—	26	2	no	—
326	#41	—	26	2	no	—
327	#41	—	26	2	no	—
328	C₂×Q₈	—	13	2	no	—
329	C₂×D₄	—	13	2	no	—
330	C₂×D₄	—	26	4	no	—
331	C₂×D₄	—	26	2	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	8	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	26	2	no	—
341	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
342	C₂²×C₄	C₂×D₅₂	1	2	yes	—
343	C₂²×C₄	#6127	1	1	yes	characteristic
344	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
345	Q₁₆	—	26	2	no	—
346	SD₁₆	—	26	4	no	—
347	D₈	—	26	2	no	—
348	M₁₆	—	26	2	no	—
349	M₁₆	—	26	2	no	—
350	M₁₆	—	26	2	no	—
351	M₁₆	—	26	2	no	—
352	M₁₆	—	52	4	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	4	no	—
358	C₂×C₈	—	2	4	no	—
359	C₂×C₈	—	2	4	no	—
360	C₂×C₈	—	2	4	no	—
361	C₂×C₈	—	26	2	no	—
362	C₂×C₈	—	26	2	no	—
363	C₂×C₈	—	52	4	no	—
364	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
365	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
366	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
367	C₂×C₈	C₂×D₅₂	1	2	yes	—
368	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
369	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
370	C₂×C₈	#6127	1	2	yes	—
371	C₂×C₈	#6127	1	2	yes	—
372	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
373	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
374	C₄⋊C₄	—	13	4	no	—
375	C₄⋊C₄	—	26	4	no	—
376	C₂²⋊C₄	—	26	4	no	—
377	C₂²⋊C₄	—	26	2	no	—
378	C₂²⋊C₄	—	26	4	no	—
379	C₄²	—	2	4	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	26	2	no	—
383	C₄²	#6127	1	2	yes	—
384	C₄²	C₂×C₂²⋊D₁₃	1	2	yes	—
385	C₁₃	#21544	1	1	yes	characteristic, complemented, Sylow
386	C₂³	—	2	1	no	—
387	C₂³	—	2	1	no	—
388	C₂³	—	2	4	no	—
389	C₂³	—	26	2	no	—
390	C₂³	C₄×D₅₂	1	2	yes	—
391	C₂³	C₂×#6127	1	1	yes	characteristic
392	Q₈	—	26	2	no	—
393	Q₈	—	26	2	no	—
394	D₄	—	26	2	no	—
395	D₄	—	26	2	no	—
396	D₄	—	52	2	no	—
397	D₄	—	52	2	no	—
398	D₄	—	52	8	no	—
399	C₂×C₄	—	2	16	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	26	4	no	—
411	C₂×C₄	—	26	2	no	—
412	C₂×C₄	—	52	2	no	—
413	C₂×C₄	—	52	2	no	—
414	C₂×C₄	C₄×D₅₂	1	2	yes	—
415	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
417	C₂×C₄	C₂×#6127	1	1	yes	characteristic
418	C₂×C₄	C₂×#6127	1	1	yes	characteristic
419	C₂×C₄	C₂×#6127	1	1	yes	characteristic
420	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
421	C₈	—	2	2	no	—
422	C₈	—	2	2	no	—
423	C₈	—	52	2	no	—
424	C₈	—	52	2	no	—
425	C₈	C₄×C₂²⋊D₁₃	1	2	yes	—
426	C₈	C₄×C₂²⋊D₁₃	1	2	yes	—
427	C₈	#88184	1	2	yes	—
428	C₈	#88184	1	2	yes	—
429	C₂²	—	2	4	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	52	4	no	—
435	C₂²	—	52	2	no	—
436	C₂²	#11718361	1	4	yes	complemented
437	C₂²	C₂×C₄×D₅₂	1	1	yes	characteristic
438	C₂²	#11719184	1	1	yes	characteristic
439	C₂²	#11719496	1	1	yes	characteristic
440	C₄	—	2	4	no	—
441	C₄	—	2	4	no	—
442	C₄	—	2	2	no	—
443	C₄	—	52	4	no	—
444	C₄	—	52	2	no	—
445	C₄	C₄×#6127	1	1	yes	characteristic
446	C₄	#11719182	1	1	yes	characteristic
447	C₄	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
448	C₄	C₂×#88184	1	1	yes	characteristic
449	C₂	—	2	1	no	—
450	C₂	—	2	1	no	—
451	C₂	—	2	4	no	—
452	C₂	—	104	2	no	—
453	C₂	C₄×#88184	1	1	yes	characteristic
454	C₂	C₂×#11718361	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂×D₅₂
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂²×C₄×C₈×C₁₃	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	#13124417	C₂
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂²×C₄×C₈	D₁₃
hypocenter	C₁₃	#21544
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂³×C₈ ◁ C₂²×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×#11718361	C₂	semidirect
3. #13123530	C₂	semidirect
4. #13115724	C₂	semidirect
5. #13115584	C₂	semidirect
6. #13115540	C₂	semidirect
7. #13115279	C₂	semidirect
8. #13114874	C₂	semidirect
9. #13114715	C₂	semidirect
10. #13114673	C₂	semidirect
11. C₂²×C₄×C₈×C₁₃	C₂	semidirect
24. #11718777	C₄	semidirect
25. #11718776	C₄	semidirect
26. #11718775	C₄	semidirect
70. C₂×Dic₅₂	C₂×C₄	semidirect
73. C₂×D₁₀₄	C₂×C₄	semidirect
74. C₂×#6095	C₂×C₄	semidirect
82. C₄×C₈×C₁₃	D₄	semidirect
84. #88061	C₂×C₄	semidirect
88. #88058	C₂×C₄	semidirect
89. #88057	C₂×C₄	semidirect
90. #88056	C₂×C₄	semidirect
162. C₂²×C₄×C₈	D₁₃	semidirect
248. C₂²×C₁₃	#443	semidirect
316. C₄×C₈	C₂²⋊D₁₃	semidirect
385. C₁₃	#21544	semidirect
436. C₂²	#11718361	semidirect

Maximal subgroups

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

subgroup	index
#13124417	2
C₂×#11718361	2
#13123530	2
#13115724	2
#13115584	2
#13115540	2
#13115279	2
#13114874	2
#13114715	2
#13114673	2
C₂²×C₄×C₈×C₁₃	2
#21544	13