Subgroups — #15869745

Order 3328.

938 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13124441	C₂	1	1	yes	maximal, characteristic
2	#13123537	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×#6094	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115730	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115587	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115537	C₂	1	2	yes	maximal, complemented
7	#13115276	C₂	1	2	yes	maximal, complemented
8	#13114875	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114715	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114678	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#443	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#131	C₂²	1	2	yes	—
14	#11719533	C₂²	1	2	yes	—
15	C₂²×#6094	C₂²	1	1	yes	characteristic
16	C₂²×#6094	C₂²	1	1	yes	characteristic
17	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#443	—	2	4	no	—
19	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#104	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×#88077	C₂²	1	2	yes	—
23	#11718895	C₂²	1	2	yes	—
24	#11718894	C₂²	1	2	yes	—
25	#11718850	C₄	1	2	yes	complemented
26	#11718835	C₄	1	4	yes	complemented
27	#11718820	C₄	1	2	yes	complemented
28	#11718789	—	2	4	no	—
29	#11718787	C₂²	1	2	yes	—
30	#11718780	C₂²	1	2	yes	—
31	#11718772	—	2	4	no	—
32	C₂×#88059	C₂²	1	1	yes	characteristic
33	#11718767	C₂²	1	1	yes	characteristic
34	#11718762	C₂²	1	2	yes	—
35	C₂×#88055	C₂²	1	1	yes	characteristic
36	C₂×#88055	C₂²	1	1	yes	characteristic
37	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
38	C₄×#6094	—	2	4	no	—
39	#11718150	C₂²	1	2	yes	—
40	#11718147	C₂²	1	2	yes	—
41	#11718115	C₂²	1	2	yes	—
42	C₂×C₁₃×#41	C₂³	1	2	yes	—
43	C₂²×C₄×D₁₃	—	2	1	no	—
44	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
45	C₁₃×#135	—	2	2	no	—
46	C₁₃×#135	—	2	2	no	—
47	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
48	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	complemented
49	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic, complemented
50	C₁₃×#131	—	2	4	no	—
51	C₁₃×#131	—	2	4	no	—
52	C₂×C₁₃×M₁₆	—	2	2	no	—
53	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
54	C₂²×C₈×C₁₃	—	2	2	no	—
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
58	#88200	C₂×C₄	1	4	yes	—
59	#88192	C₂×C₄	1	4	yes	—
60	#88191	—	2	2	no	—
61	#88189	—	2	2	no	—
62	C₄×C₂²⋊D₁₃	—	2	4	no	—
63	#88180	C₂³	1	2	yes	—
64	C₂×C₄×Dic₁₃	—	2	1	no	—
65	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
66	C₂×#6099	C₂³	1	2	yes	—
67	C₂²×#1055	C₂³	1	1	yes	characteristic
68	C₂²×#1055	C₂³	1	1	yes	characteristic
69	C₂×#6094	—	2	2	no	—
70	C₂×#6094	—	2	2	no	—
71	C₂×#6094	—	2	2	no	—
72	C₂×#6094	—	2	2	no	—
73	C₂×#6094	C₂×C₄	1	2	yes	—
74	C₂×#6094	C₂×C₄	1	2	yes	—
75	C₂×#6094	D₄	1	2	yes	—
76	C₂×#6094	D₄	1	2	yes	—
77	C₄²×D₁₃	—	2	2	no	—
78	C₄²×D₁₃	—	2	2	no	—
79	C₁₃×#108	—	2	2	no	—
80	C₁₃×#104	—	2	4	no	—
81	C₄×C₈×C₁₃	D₄	1	4	yes	complemented
82	#88077	—	2	4	no	—
83	#88075	C₂×C₄	1	4	yes	complemented
84	#88072	C₂×C₄	1	4	yes	complemented
85	C₂²⋊#1055	—	2	4	no	—
86	#88060	—	2	4	no	—
87	#88059	—	2	2	no	—
88	#88058	C₂×C₄	1	2	yes	complemented
89	#88057	C₂×C₄	1	2	yes	complemented
90	#88055	—	2	2	no	—
91	#88055	—	2	2	no	—
92	#88055	—	2	2	no	—
93	#88054	—	2	4	no	—
94	C₈×Dic₁₃	—	2	2	no	—
95	C₄×#1055	—	2	2	no	—
96	#21549	—	13	1	no	maximal, Sylow
97	C₂³×D₁₃	#41	1	1	yes	characteristic
98	C₁₃×#41	—	2	2	no	—
99	C₁₃×#41	—	2	2	no	—
100	C₁₃×#41	—	2	2	no	—
101	C₁₃×#41	—	2	2	no	—
102	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
103	C₂×D₄×C₁₃	—	2	2	no	—
104	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
108	C₂×C₂²⋊D₁₃	—	2	4	no	—
109	C₂²×Dic₁₃	—	2	1	no	—
110	C₂²×Dic₁₃	#41	1	1	yes	characteristic
111	C₂×C₄×D₁₃	—	2	1	no	—
112	C₂×C₄×D₁₃	—	2	1	no	—
113	C₂×C₄×D₁₃	—	2	1	no	—
114	C₂×C₄×D₁₃	—	2	1	no	—
115	C₂×C₄×D₁₃	—	2	4	no	—
116	C₂×C₄×D₁₃	—	4	4	no	—
117	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
118	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
119	C₁₃×Q₁₆	—	2	2	no	—
120	C₁₃×SD₁₆	—	2	4	no	—
121	C₁₃×D₈	—	2	2	no	—
122	C₁₃×M₁₆	—	2	2	no	—
123	C₁₃×M₁₆	—	2	2	no	—
124	C₁₃×M₁₆	—	4	4	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	4	4	no	—
127	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
133	C₂×C₈×C₁₃	#41	1	2	yes	—
134	C₂×C₈×C₁₃	#41	1	2	yes	—
135	C₄²×C₁₃	—	2	1	no	—
136	C₄²×C₁₃	C₂×D₄	1	2	yes	—
137	C₂²⋊Dic₁₃	—	2	2	no	—
138	C₂²⋊Dic₁₃	—	2	4	no	—
139	#6103	—	2	4	no	—
140	C₄⋊Dic₁₃	C₂²×C₄	1	4	yes	—
141	#6101	—	2	4	no	—
142	C₄×Dic₁₃	—	2	4	no	—
143	C₄×Dic₁₃	—	2	1	no	—
144	C₄×Dic₁₃	—	2	2	no	—
145	C₄×Dic₁₃	#41	1	2	yes	—
146	#6099	—	2	2	no	—
147	#6099	—	2	2	no	—
148	C₂×#1055	—	2	1	no	—
149	C₂×#1055	—	2	1	no	—
150	C₂×#1055	—	2	1	no	—
151	C₂×#1055	—	2	1	no	—
152	C₂×#1055	—	2	2	no	—
153	C₂×#1055	C₂²×C₄	1	2	yes	—
154	C₂×#1055	C₂×D₄	1	2	yes	—
155	#6094	—	2	4	no	—
156	#6094	—	2	4	no	—
157	#6094	—	2	4	no	—
158	#6094	—	2	4	no	—
159	#3054	—	13	1	no	—
160	C₂×#443	D₁₃	1	1	yes	characteristic, complemented
161	#2930	—	13	2	no	—
162	C₂×C₄×M₁₆	—	13	1	no	—
163	#1975	—	13	1	no	—
164	#1946	—	13	1	no	—
165	#1937	—	13	2	no	—
166	#1896	—	13	2	no	—
167	#1811	—	13	1	no	—
168	#1772	—	13	1	no	—
169	#1765	—	13	2	no	—
170	C₂³×C₁₃	—	2	2	no	—
171	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
172	C₂²×D₁₃	—	2	1	no	—
173	C₂²×D₁₃	—	2	1	no	—
174	C₂²×D₁₃	—	4	2	no	—
175	C₂²×D₁₃	C₄×D₄	1	2	yes	—
176	Q₈×C₁₃	—	2	2	no	—
177	Q₈×C₁₃	—	2	2	no	—
178	D₄×C₁₃	—	2	2	no	—
179	D₄×C₁₃	—	2	2	no	—
180	D₄×C₁₃	—	4	2	no	—
181	D₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	2	4	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂×#41	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	C₂²⋊D₁₃	—	8	4	no	—
194	C₂×Dic₁₃	—	2	1	no	—
195	C₂×Dic₁₃	—	2	1	no	—
196	C₂×Dic₁₃	—	2	4	no	—
197	C₂×Dic₁₃	—	2	2	no	—
198	C₂×Dic₁₃	—	4	2	no	—
199	C₂×Dic₁₃	C₄×D₄	1	2	yes	—
200	C₄×D₁₃	—	2	2	no	—
201	C₄×D₁₃	—	2	2	no	—
202	C₄×D₁₃	—	2	2	no	—
203	C₄×D₁₃	—	2	2	no	—
204	C₄×D₁₃	—	4	8	no	—
205	C₈×C₁₃	—	4	2	no	—
206	C₈×C₁₃	C₄×D₄	1	2	yes	—
207	C₈×C₁₃	C₄×D₄	1	2	yes	—
208	C₈×C₁₃	#121	1	2	yes	—
209	C₈×C₁₃	#121	1	2	yes	—
210	#1055	—	2	2	no	—
211	#1055	—	2	2	no	—
212	#1055	—	4	2	no	—
213	C₂×#135	C₂×D₁₃	1	1	yes	characteristic
214	C₂×#131	C₂×D₁₃	1	2	yes	—
215	C₂²×M₁₆	—	13	1	no	—
216	C₂²×M₁₆	—	13	1	no	—
217	#525	—	13	2	no	—
218	C₂²×C₄²	—	13	1	no	—
219	#470	—	13	2	no	—
220	#469	—	13	2	no	—
221	#468	—	13	4	no	—
222	#443	—	2	4	no	—
223	#436	—	26	4	no	—
224	#435	—	26	4	no	—
225	C₂×#108	—	13	1	no	—
226	C₂×#108	C₂×D₁₃	1	1	yes	characteristic
227	#427	—	13	1	no	—
228	#424	—	13	2	no	—
229	C₂×#104	—	13	2	no	—
230	C₂×#104	C₂×D₁₃	1	2	yes	—
231	#416	—	13	2	no	—
232	#408	—	13	2	no	—
233	#407	—	13	2	no	—
234	#405	—	13	2	no	—
235	C₄×M₁₆	—	26	4	no	—
236	C₂×#97	—	13	1	no	—
237	C₂×#97	—	13	1	no	—
238	C₂×C₄×C₈	—	13	1	no	—
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	2	no	—
244	C₂²×C₁₃	—	4	4	no	—
245	C₂²×C₁₃	—	4	2	no	—
246	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
247	C₂²×C₁₃	#525	1	1	yes	characteristic
248	C₂²×C₁₃	#529	1	1	yes	characteristic
249	C₂×D₁₃	—	2	4	no	—
250	C₂×D₁₃	—	2	2	no	—
251	C₂×D₁₃	—	4	2	no	—
252	C₂×D₁₃	—	4	2	no	—
253	C₄×C₁₃	—	2	4	no	—
254	C₄×C₁₃	—	4	2	no	—
255	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
256	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
257	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
258	C₄×C₁₃	#532	1	1	yes	characteristic
259	Dic₁₃	—	2	2	no	—
260	Dic₁₃	—	4	2	no	—
261	Dic₁₃	—	4	4	no	—
262	C₂×#41	C₂²×D₁₃	1	2	yes	—
263	C₂³×C₄	—	13	1	no	—
264	C₂³×C₄	—	26	1	no	—
265	#135	—	2	2	no	—
266	#135	—	2	2	no	—
267	C₂×Q₁₆	C₄×D₁₃	1	1	yes	characteristic, complemented
268	C₂×SD₁₆	C₄×D₁₃	1	2	yes	complemented
269	C₂×D₈	C₄×D₁₃	1	1	yes	characteristic, complemented
270	#131	—	2	4	no	—
271	#131	—	2	4	no	—
272	C₂×M₁₆	—	2	2	no	—
273	C₂×M₁₆	—	13	2	no	—
274	C₂×M₁₆	—	13	2	no	—
275	C₂×M₁₆	—	13	2	no	—
276	C₂×M₁₆	—	13	2	no	—
277	C₂×M₁₆	—	13	2	no	—
278	C₂×M₁₆	—	26	2	no	—
279	C₂×M₁₆	—	26	2	no	—
280	C₂×M₁₆	—	26	2	no	—
281	C₂×M₁₆	—	26	2	no	—
282	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
283	C₂²×C₈	—	2	2	no	—
284	C₂²×C₈	—	13	1	no	—
285	C₂²×C₈	—	13	1	no	—
286	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
287	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
288	#123	—	26	2	no	—
289	C₂²⋊Q₈	—	13	4	no	—
290	#121	—	13	4	no	—
291	#120	—	26	2	no	—
292	C₄×D₄	—	26	4	no	—
293	#117	—	13	2	no	—
294	C₂×C₄²	—	13	1	no	—
295	C₂×C₄²	—	26	2	no	—
296	C₂×C₄²	—	26	1	no	—
297	C₂×C₄²	—	26	2	no	—
298	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
299	#108	—	2	2	no	—
300	#108	—	26	2	no	—
301	#107	—	13	2	no	—
302	#106	—	13	2	no	—
303	C₄⋊C₈	—	26	4	no	—
304	#104	—	2	4	no	—
305	#104	—	26	4	no	—
306	#103	—	13	4	no	—
307	#102	—	13	4	no	—
308	C₂²⋊C₈	—	26	4	no	—
309	C₂²⋊C₈	—	26	4	no	—
310	#97	—	26	2	no	—
311	#97	—	26	2	no	—
312	#97	—	26	2	no	—
313	C₄×C₈	—	26	2	no	—
314	C₄×C₈	—	26	2	no	—
315	C₄×C₈	C₂²⋊D₁₃	1	4	yes	complemented
316	C₂×C₁₃	—	2	1	no	—
317	C₂×C₁₃	—	2	1	no	—
318	C₂×C₁₃	—	8	2	no	—
319	C₂×C₁₃	C₄×#121	1	1	yes	characteristic
320	C₂×C₁₃	#2956	1	2	yes	—
321	D₁₃	—	4	2	no	—
322	C₂⁴	—	13	1	no	—
323	#41	—	2	2	no	—
324	#41	—	2	2	no	—
325	#41	—	2	2	no	—
326	#41	—	2	2	no	—
327	C₂×Q₈	C₂×C₄×D₁₃	1	2	yes	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	26	4	no	—
330	C₂×D₄	C₂×C₄×D₁₃	1	2	yes	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	13	1	no	—
334	C₂²×C₄	—	13	2	no	—
335	C₂²×C₄	—	13	2	no	—
336	C₂²×C₄	—	26	4	no	—
337	C₂²×C₄	—	26	1	no	—
338	C₂²×C₄	—	26	1	no	—
339	C₂²×C₄	—	26	1	no	—
340	C₂²×C₄	—	26	1	no	—
341	C₂²×C₄	—	26	1	no	—
342	C₂²×C₄	—	52	4	no	—
343	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
344	Q₁₆	—	2	2	no	—
345	SD₁₆	—	2	4	no	—
346	D₈	—	2	2	no	—
347	M₁₆	—	2	2	no	—
348	M₁₆	—	2	2	no	—
349	M₁₆	—	4	4	no	—
350	M₁₆	—	26	4	no	—
351	M₁₆	—	26	4	no	—
352	M₁₆	—	26	4	no	—
353	M₁₆	—	26	4	no	—
354	M₁₆	—	26	2	no	—
355	M₁₆	—	26	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	4	4	no	—
358	C₂×C₈	—	13	2	no	—
359	C₂×C₈	—	13	2	no	—
360	C₂×C₈	—	26	1	no	—
361	C₂×C₈	—	26	1	no	—
362	C₂×C₈	—	26	1	no	—
363	C₂×C₈	—	26	1	no	—
364	C₂×C₈	—	26	2	no	—
365	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
366	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
367	C₂×C₈	#6127	1	2	yes	—
368	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
369	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
370	C₂×C₈	#6129	1	2	yes	—
371	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
372	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
373	C₄⋊C₄	—	13	4	no	—
374	C₄⋊C₄	—	26	4	no	—
375	C₂²⋊C₄	—	26	4	no	—
376	C₂²⋊C₄	—	26	4	no	—
377	C₂²⋊C₄	—	26	2	no	—
378	C₄²	—	2	1	no	—
379	C₄²	—	13	2	no	—
380	C₄²	—	26	4	no	—
381	C₄²	—	26	2	no	—
382	C₄²	—	26	1	no	—
383	C₄²	C₂×C₂²⋊D₁₃	1	2	yes	—
384	C₁₃	#21549	1	1	yes	characteristic, complemented, Sylow
385	C₂³	—	2	2	no	—
386	C₂³	—	13	2	no	—
387	C₂³	—	26	1	no	—
388	C₂³	—	26	1	no	—
389	C₂³	—	52	2	no	—
390	C₂³	#41×D₁₃	1	1	yes	characteristic
391	Q₈	—	2	2	no	—
392	Q₈	—	2	2	no	—
393	D₄	—	2	2	no	—
394	D₄	—	2	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	104	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	13	2	no	—
404	C₂×C₄	—	26	1	no	—
405	C₂×C₄	—	26	1	no	—
406	C₂×C₄	—	26	2	no	—
407	C₂×C₄	—	26	2	no	—
408	C₂×C₄	—	26	2	no	—
409	C₂×C₄	—	26	2	no	—
410	C₂×C₄	—	26	4	no	—
411	C₂×C₄	—	26	2	no	—
412	C₂×C₄	—	52	8	no	—
413	C₂×C₄	—	52	2	no	—
414	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
415	C₂×C₄	C₂×#6127	1	1	yes	characteristic
416	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
417	C₂×C₄	C₂×#6129	1	1	yes	characteristic
418	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
419	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
420	C₈	—	4	2	no	—
421	C₈	—	26	2	no	—
422	C₈	—	26	2	no	—
423	C₈	—	52	2	no	—
424	C₈	C₄×C₂²⋊D₁₃	1	2	yes	—
425	C₈	C₄×C₂²⋊D₁₃	1	2	yes	—
426	C₈	#88192	1	2	yes	—
427	C₈	#88192	1	2	yes	—
428	C₂²	—	2	2	no	—
429	C₂²	—	4	4	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	26	4	no	—
432	C₂²	—	26	2	no	—
433	C₂²	—	52	2	no	—
434	C₂²	—	52	2	no	—
435	C₂²	C₄×D₄×D₁₃	1	1	yes	characteristic
436	C₂²	#11719262	1	1	yes	characteristic
437	C₂²	#11719533	1	1	yes	characteristic
438	C₄	—	2	4	no	—
439	C₄	—	4	2	no	—
440	C₄	—	26	2	no	—
441	C₄	—	52	2	no	—
442	C₄	—	52	4	no	—
443	C₄	C₄×#6129	1	1	yes	characteristic
444	C₄	#11719253	1	1	yes	characteristic
445	C₄	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
446	C₄	C₂×#88192	1	1	yes	characteristic
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	8	2	no	—
450	C₂	—	52	2	no	—
451	C₂	C₄×#88192	1	1	yes	characteristic
452	C₂	#13123741	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂×C₁₃×#443	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	#13124441	C₂
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×#443	D₁₃
hypocenter	C₁₃	#21549
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×#443

Complements

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

N	H ≅ G/N	type
2. #13123537	C₂	semidirect
3. C₂×C₄×#6094	C₂	semidirect
4. #13115730	C₂	semidirect
5. #13115587	C₂	semidirect
6. #13115537	C₂	semidirect
7. #13115276	C₂	semidirect
8. #13114875	C₂	semidirect
9. #13114715	C₂	semidirect
10. #13114678	C₂	semidirect
11. C₂×C₁₃×#443	C₂	semidirect
25. #11718850	C₄	semidirect
26. #11718835	C₄	semidirect
27. #11718820	C₄	semidirect
47. C₂×C₁₃×Q₁₆	C₂×C₄	semidirect
48. C₂×C₁₃×SD₁₆	C₂×C₄	semidirect
49. C₂×C₁₃×D₈	C₂×C₄	semidirect
81. C₄×C₈×C₁₃	D₄	semidirect
83. #88075	C₂×C₄	semidirect
84. #88072	C₂×C₄	semidirect
88. #88058	C₂×C₄	semidirect
89. #88057	C₂×C₄	semidirect
160. C₂×#443	D₁₃	semidirect
267. C₂×Q₁₆	C₄×D₁₃	semidirect
268. C₂×SD₁₆	C₄×D₁₃	semidirect
269. C₂×D₈	C₄×D₁₃	semidirect
315. C₄×C₈	C₂²⋊D₁₃	semidirect
384. C₁₃	#21549	semidirect

Maximal subgroups

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

subgroup	index
#13124441	2
#13123537	2
C₂×C₄×#6094	2
#13115730	2
#13115587	2
#13115537	2
#13115276	2
#13114875	2
#13114715	2
#13114678	2
C₂×C₁₃×#443	2
#21549	13