Subgroups — #15833813

Order 3328.

680 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13124840	C₂	1	1	yes	maximal, characteristic
2	M₁₆×D₅₂	C₂	1	1	yes	maximal, characteristic
3	#13113726	C₂	1	2	yes	maximal, complemented
4	#13113679	C₂	1	2	yes	maximal, complemented
5	#13113670	C₂	1	2	yes	maximal, complemented
6	C₈×#6106	C₂	1	2	yes	maximal, complemented
7	#13113606	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113291	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#11718075	C₂	1	1	yes	maximal, characteristic
10	M₁₆×#1055	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#533	C₂²	1	1	yes	characteristic
13	C₂×M₁₆×D₁₃	—	2	1	no	—
14	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
15	C₁₃×#446	—	2	2	no	—
16	C₁₃×#446	C₂²	1	2	yes	complemented
17	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
18	C₁₃×#424	—	2	1	no	—
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₁₃×#405	—	2	1	no	—
21	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
22	#11718787	—	2	1	no	—
23	#11718745	C₄	1	1	yes	characteristic
24	#11718745	C₄	1	1	yes	characteristic
25	#11718744	C₄	1	1	yes	characteristic
26	#11718744	C₄	1	1	yes	characteristic
27	#11718707	C₄	1	2	yes	—
28	#11718704	C₄	1	2	yes	—
29	C₄×#6106	C₂²	1	2	yes	—
30	C₄×#6106	C₂²	1	2	yes	—
31	#11718586	C₂²	1	1	yes	characteristic
32	#11718585	C₂²	1	1	yes	characteristic
33	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
34	#11718367	—	2	2	no	—
35	#11718349	C₂²	1	2	yes	—
36	C₈×D₅₂	C₂²	1	2	yes	—
37	Q₈⋊#1055	C₂²	1	2	yes	complemented
38	Q₈⋊#1055	C₂²	1	2	yes	complemented
39	#11718075	C₂²	1	1	yes	characteristic
40	#11718075	C₂²	1	1	yes	characteristic
41	#11718075	C₂²	1	1	yes	characteristic
42	#11718075	C₂²	1	1	yes	characteristic
43	#11718072	C₂²	1	2	yes	complemented
44	#11718072	C₂²	1	2	yes	complemented
45	#11718047	C₂²	1	2	yes	complemented
46	C₈×#1055	C₂²	1	2	yes	complemented
47	C₂²×D₅₂	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₁₃	—	2	1	no	—
49	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
50	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	—	2	1	no	—
52	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
53	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
54	C₁₃×#125	—	2	1	no	—
55	C₁₃×C₂²⋊Q₈	—	2	1	no	—
56	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
57	C₄×Q₈×C₁₃	—	2	1	no	—
58	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
59	C₁₃×#117	—	2	1	no	—
60	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
61	C₂×#6106	C₂×C₄	1	2	yes	—
62	C₂×#6106	C₂×C₄	1	2	yes	—
63	C₂×#6103	—	2	1	no	—
64	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
65	C₂×#6099	—	2	1	no	—
66	C₂²×#1055	—	2	1	no	—
67	M₁₆×D₁₃	—	4	4	no	—
68	C₂×#6094	—	2	2	no	—
69	C₂×C₈×D₁₃	—	2	2	no	—
70	C₄×D₅₂	—	2	1	no	—
71	C₄×D₅₂	—	2	1	no	—
72	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
73	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
74	C₄×D₅₂	C₂³	1	1	yes	characteristic
75	C₄×D₅₂	C₂³	1	1	yes	characteristic
76	C₁₃×C₄⋊C₈	—	2	2	no	—
77	C₁₃×C₄⋊C₈	—	2	2	no	—
78	C₁₃×C₄⋊C₈	—	2	1	no	—
79	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
80	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
81	C₁₃×#97	—	2	2	no	—
82	C₁₃×#97	D₄	1	2	yes	—
83	C₄×C₈×C₁₃	—	2	2	no	—
84	C₄×C₈×C₁₃	C₂³	1	2	yes	—
85	#88075	C₂×C₄	1	2	yes	—
86	#88075	C₂×C₄	1	2	yes	—
87	C₂²⋊#1055	C₂×C₄	1	2	yes	—
88	#88060	—	2	2	no	—
89	#88060	—	2	2	no	—
90	#88049	C₂×C₄	1	2	yes	—
91	#88049	C₂×C₄	1	2	yes	—
92	#88048	C₂×C₄	1	2	yes	—
93	#88048	C₂×C₄	1	2	yes	—
94	C₄⋊#1055	—	2	1	no	—
95	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
96	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
97	C₄⋊#1055	C₂³	1	2	yes	—
98	C₄×#1055	—	2	1	no	—
99	C₄×#1055	C₂³	1	1	yes	characteristic
100	C₄×#1055	C₂³	1	1	yes	characteristic
101	C₄×#1055	C₂³	1	2	yes	—
102	#17995	—	13	1	no	maximal, Sylow
103	C₂³×D₁₃	—	2	1	no	—
104	C₂×Q₈×C₁₃	—	2	1	no	—
105	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
109	C₂²×Dic₁₃	—	2	1	no	—
110	C₂×D₅₂	—	2	2	no	—
111	C₂×D₅₂	—	2	1	no	—
112	C₂×D₅₂	—	4	1	no	—
113	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
114	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₁₃	—	2	1	no	—
116	C₂×C₄×D₁₃	—	2	1	no	—
117	C₂×C₄×D₁₃	—	2	1	no	—
118	C₂×C₄×D₁₃	—	2	1	no	—
119	C₂×C₄×D₁₃	—	4	2	no	—
120	C₂×C₄×D₁₃	—	4	2	no	—
121	C₁₃×M₁₆	—	2	2	no	—
122	C₁₃×M₁₆	SD₁₆	1	4	yes	complemented
123	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	—	4	2	no	—
126	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
128	C₁₃×C₄⋊C₄	—	2	1	no	—
129	C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
134	C₁₃×C₂²⋊C₄	—	2	2	no	—
135	C₄²×C₁₃	—	2	2	no	—
136	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₁₃	#41	1	1	yes	characteristic
139	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
140	#6106	—	2	4	no	—
141	#6106	—	4	2	no	—
142	#6103	—	2	1	no	—
143	#6103	—	2	1	no	—
144	#6103	—	2	1	no	—
145	#6103	—	2	1	no	—
146	C₄⋊Dic₁₃	—	2	1	no	—
147	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
149	#6099	—	4	2	no	—
150	C₂×#1055	—	2	1	no	—
151	C₂×#1055	—	2	2	no	—
152	C₂×#1055	—	2	1	no	—
153	C₂×#1055	—	4	2	no	—
154	C₂×#1055	C₂²×C₄	1	2	yes	—
155	C₂×#1055	C₂²×C₄	1	2	yes	—
156	#6094	—	4	4	no	—
157	C₈×D₁₃	—	4	4	no	—
158	#3101	—	13	1	no	—
159	#2962	D₁₃	1	1	yes	characteristic, complemented
160	D₄×M₁₆	—	13	1	no	—
161	#1590	—	13	2	no	—
162	#1583	—	13	2	no	—
163	#1582	—	13	2	no	—
164	C₈×SD₁₆	—	13	2	no	—
165	#1570	—	13	1	no	—
166	#1493	—	13	1	no	—
167	C₂×D₄⋊C₈	—	13	1	no	—
168	C₈×M₁₆	—	13	1	no	—
169	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
170	C₂²×D₁₃	—	2	1	no	—
171	C₂²×D₁₃	—	2	1	no	—
172	C₂²×D₁₃	—	4	2	no	—
173	C₂²×D₁₃	—	4	2	no	—
174	C₂²×D₁₃	—	8	1	no	—
175	Q₈×C₁₃	—	2	2	no	—
176	Q₈×C₁₃	—	2	2	no	—
177	Q₈×C₁₃	—	8	1	no	—
178	C₂×C₄×C₁₃	—	2	1	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	—	4	1	no	—
183	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
187	C₂×C₄×C₁₃	#135	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	C₂×#41	1	1	yes	characteristic
191	C₂×Dic₁₃	—	2	1	no	—
192	C₂×Dic₁₃	—	2	1	no	—
193	C₂×Dic₁₃	—	4	2	no	—
194	D₅₂	—	2	1	no	—
195	D₅₂	—	2	1	no	—
196	D₅₂	—	2	1	no	—
197	D₅₂	—	4	2	no	—
198	D₅₂	#131	1	2	yes	—
199	C₄×D₁₃	—	4	1	no	—
200	C₄×D₁₃	—	4	1	no	—
201	C₄×D₁₃	—	4	1	no	—
202	C₄×D₁₃	—	4	1	no	—
203	C₄×D₁₃	—	4	2	no	—
204	C₄×D₁₃	—	4	2	no	—
205	C₈×C₁₃	—	2	2	no	—
206	C₈×C₁₃	—	4	1	no	—
207	C₈×C₁₃	—	4	1	no	—
208	C₈×C₁₃	C₂×SD₁₆	1	4	yes	—
209	#1055	—	2	2	no	—
210	#1055	—	2	2	no	—
211	#1055	—	2	2	no	—
212	#1055	—	4	1	no	—
213	#1055	—	4	2	no	—
214	C₂²×M₁₆	—	26	1	no	—
215	#533	C₂×D₁₃	1	1	yes	characteristic
216	C₂×C₄×D₄	—	13	1	no	—
217	#483	—	13	2	no	—
218	#476	—	13	1	no	—
219	#476	—	13	1	no	—
220	#461	—	13	1	no	—
221	#461	—	13	1	no	—
222	#450	—	13	2	no	—
223	#446	—	2	2	no	—
224	#446	C₂×D₁₃	1	2	yes	complemented
225	C₈×Q₈	C₂×D₁₃	1	2	yes	complemented
226	C₄×SD₁₆	—	13	2	no	—
227	C₄×SD₁₆	—	13	2	no	—
228	#436	—	13	2	no	—
229	#435	—	26	2	no	—
230	C₈×D₄	—	13	2	no	—
231	#431	—	13	1	no	—
232	#424	—	2	1	no	—
233	#423	—	13	1	no	—
234	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
235	#407	—	26	1	no	—
236	#405	—	2	1	no	—
237	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
238	C₂×C₄×C₈	—	13	1	no	—
239	#334	—	13	2	no	—
240	#334	—	13	2	no	—
241	Q₈⋊C₈	—	13	2	no	—
242	Q₈⋊C₈	—	13	2	no	—
243	D₄⋊C₈	—	13	1	no	—
244	D₄⋊C₈	—	13	1	no	—
245	D₄⋊C₈	—	13	1	no	—
246	D₄⋊C₈	—	13	1	no	—
247	#322	—	13	2	no	—
248	C₈²	—	13	2	no	—
249	C₂²×C₁₃	—	2	1	no	—
250	C₂²×C₁₃	—	2	1	no	—
251	C₂²×C₁₃	C₄×SD₁₆	1	2	yes	—
252	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
253	C₂×D₁₃	—	2	2	no	—
254	C₂×D₁₃	—	4	1	no	—
255	C₂×D₁₃	—	4	1	no	—
256	C₂×D₁₃	—	4	1	no	—
257	C₂×D₁₃	—	4	1	no	—
258	C₂×D₁₃	—	4	1	no	—
259	C₂×D₁₃	—	8	4	no	—
260	C₄×C₁₃	—	2	1	no	—
261	C₄×C₁₃	—	2	1	no	—
262	C₄×C₁₃	—	2	1	no	—
263	C₄×C₁₃	—	4	2	no	—
264	C₄×C₁₃	—	4	2	no	—
265	C₄×C₁₃	C₄×SD₁₆	1	2	yes	—
266	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
267	C₄×C₁₃	#568	1	1	yes	characteristic
268	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
269	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
270	Dic₁₃	—	4	1	no	—
271	Dic₁₃	—	4	1	no	—
272	C₂²×D₄	—	13	1	no	—
273	C₂³×C₄	—	26	1	no	—
274	C₂×SD₁₆	—	13	2	no	—
275	C₂×SD₁₆	—	13	2	no	—
276	C₂×M₁₆	—	26	1	no	—
277	C₂×M₁₆	—	26	2	no	—
278	C₂×M₁₆	—	52	4	no	—
279	C₂×M₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
280	C₂×M₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	26	1	no	—
283	C₂²×C₈	—	26	2	no	—
284	C₄⋊Q₈	C₄×D₁₃	1	1	yes	characteristic
285	C₄⋊Q₈	C₄×D₁₃	1	1	yes	characteristic
286	#125	—	2	1	no	—
287	C₂²⋊Q₈	—	2	1	no	—
288	C₂²⋊Q₈	C₄×D₁₃	1	2	yes	—
289	C₄×Q₈	—	2	1	no	—
290	C₄×Q₈	C₂²×D₁₃	1	2	yes	—
291	C₄×D₄	—	13	1	no	—
292	C₄×D₄	—	13	1	no	—
293	C₄×D₄	—	13	1	no	—
294	C₄×D₄	—	13	1	no	—
295	C₄×D₄	—	26	1	no	—
296	C₄×D₄	—	26	1	no	—
297	#117	—	2	1	no	—
298	C₂×C₄⋊C₄	—	13	1	no	—
299	C₂×C₂²⋊C₄	—	26	1	no	—
300	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
301	#106	—	13	2	no	—
302	#106	—	13	2	no	—
303	C₄⋊C₈	—	2	2	no	—
304	C₄⋊C₈	—	2	2	no	—
305	C₄⋊C₈	—	2	1	no	—
306	C₄⋊C₈	—	13	1	no	—
307	C₄⋊C₈	—	13	1	no	—
308	C₄⋊C₈	—	13	2	no	—
309	C₄⋊C₈	—	26	1	no	—
310	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
311	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
312	#103	—	13	2	no	—
313	#103	—	13	2	no	—
314	#102	—	13	2	no	—
315	#102	—	13	2	no	—
316	C₂²⋊C₈	—	13	2	no	—
317	C₂²⋊C₈	—	26	2	no	—
318	C₂²⋊C₈	—	26	2	no	—
319	#97	—	2	2	no	—
320	#97	C₂²⋊D₁₃	1	2	yes	—
321	C₄×C₈	—	2	2	no	—
322	C₄×C₈	—	13	2	no	—
323	C₄×C₈	—	13	1	no	—
324	C₄×C₈	—	13	1	no	—
325	C₄×C₈	—	26	1	no	—
326	C₄×C₈	C₂²×D₁₃	1	2	yes	—
327	C₂×C₁₃	—	2	2	no	—
328	C₂×C₁₃	#2933	1	1	yes	characteristic
329	C₂×C₁₃	C₂×C₄×SD₁₆	1	1	yes	characteristic
330	C₂×C₁₃	#2956	1	1	yes	characteristic
331	D₁₃	—	4	2	no	—
332	D₁₃	—	8	1	no	—
333	C₂⁴	—	26	1	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	C₂×C₄×D₁₃	1	2	yes	—
336	C₂×D₄	—	13	1	no	—
337	C₂×D₄	—	13	1	no	—
338	C₂×D₄	—	26	2	no	—
339	C₂×D₄	—	26	1	no	—
340	C₂×D₄	—	52	1	no	—
341	C₂²×C₄	—	26	1	no	—
342	C₂²×C₄	—	26	1	no	—
343	C₂²×C₄	—	26	1	no	—
344	C₂²×C₄	—	26	1	no	—
345	C₂²×C₄	—	26	1	no	—
346	C₂²×C₄	—	52	2	no	—
347	C₂²×C₄	—	52	2	no	—
348	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
349	C₂²×C₄	#6127	1	1	yes	characteristic
350	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
351	SD₁₆	—	26	4	no	—
352	SD₁₆	—	52	2	no	—
353	M₁₆	—	2	2	no	—
354	M₁₆	—	52	2	no	—
355	M₁₆	—	52	4	no	—
356	M₁₆	#6106	1	4	yes	complemented
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	4	2	no	—
360	C₂×C₈	—	13	2	no	—
361	C₂×C₈	—	13	2	no	—
362	C₂×C₈	—	26	1	no	—
363	C₂×C₈	—	26	1	no	—
364	C₂×C₈	—	26	2	no	—
365	C₂×C₈	—	52	2	no	—
366	C₂×C₈	—	52	4	no	—
367	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
368	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	13	1	no	—
375	C₄⋊C₄	—	13	1	no	—
376	C₄⋊C₄	—	26	1	no	—
377	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	26	1	no	—
380	C₂²⋊C₄	—	26	1	no	—
381	C₂²⋊C₄	—	26	1	no	—
382	C₂²⋊C₄	—	26	1	no	—
383	C₄²	—	2	2	no	—
384	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
385	C₄²	#6127	1	1	yes	characteristic
386	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
387	C₄²	C₂³×D₁₃	1	1	yes	characteristic
388	C₁₃	#17995	1	1	yes	characteristic, complemented, Sylow
389	C₂³	—	26	1	no	—
390	C₂³	—	26	1	no	—
391	C₂³	—	52	2	no	—
392	C₂³	—	52	2	no	—
393	C₂³	—	104	1	no	—
394	C₂³	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
395	Q₈	—	2	2	no	—
396	Q₈	—	2	2	no	—
397	Q₈	—	8	1	no	—
398	D₄	—	13	2	no	—
399	D₄	—	26	1	no	—
400	D₄	—	26	1	no	—
401	D₄	—	26	1	no	—
402	D₄	—	52	2	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	26	1	no	—
409	C₂×C₄	—	26	1	no	—
410	C₂×C₄	—	52	2	no	—
411	C₂×C₄	—	52	2	no	—
412	C₂×C₄	—	52	2	no	—
413	C₂×C₄	—	52	1	no	—
414	C₂×C₄	—	52	1	no	—
415	C₂×C₄	—	52	1	no	—
416	C₂×C₄	—	52	1	no	—
417	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
418	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
419	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
420	C₂×C₄	C₂×#6106	1	2	yes	—
421	C₂×C₄	#88204	1	2	yes	—
422	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
423	C₂×C₄	C₂×#6127	1	1	yes	characteristic
424	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
425	C₈	—	2	2	no	—
426	C₈	—	4	1	no	—
427	C₈	—	4	1	no	—
428	C₈	—	26	2	no	—
429	C₈	—	26	2	no	—
430	C₈	—	26	2	no	—
431	C₈	—	52	1	no	—
432	C₈	—	52	2	no	—
433	C₈	C₂×#6106	1	4	yes	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	26	2	no	—
437	C₂²	—	52	1	no	—
438	C₂²	—	52	1	no	—
439	C₂²	—	52	1	no	—
440	C₂²	—	52	1	no	—
441	C₂²	—	52	1	no	—
442	C₂²	—	104	4	no	—
443	C₂²	C₄×#6106	1	2	yes	—
444	C₂²	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	52	1	no	—
451	C₄	—	52	1	no	—
452	C₄	C₄×#6106	1	2	yes	—
453	C₄	D₁₃×#131	1	1	yes	characteristic
454	C₄	#11719455	1	1	yes	characteristic
455	C₄	C₂²×#6106	1	1	yes	characteristic
456	C₄	C₂×#88204	1	1	yes	characteristic
457	C₂	—	2	2	no	—
458	C₂	—	52	2	no	—
459	C₂	—	104	1	no	—
460	C₂	#13123558	1	1	yes	characteristic
461	C₂	C₂×C₄×#6106	1	1	yes	characteristic
462	C₂	#13123743	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#2962	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂²×D₅₂	C₂×C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#2962	D₁₃
hypocenter	C₁₃	#17995
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ #2962

Complements

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

N	H ≅ G/N	type
3. #13113726	C₂	semidirect
4. #13113679	C₂	semidirect
5. #13113670	C₂	semidirect
6. C₈×#6106	C₂	semidirect
7. #13113606	C₂	semidirect
8. #13113291	C₂	semidirect
10. M₁₆×#1055	C₂	semidirect
11. C₁₃×#2962	C₂	semidirect
16. C₁₃×#446	C₂²	semidirect
17. C₈×Q₈×C₁₃	C₂²	semidirect
37. Q₈⋊#1055	C₂²	semidirect
38. Q₈⋊#1055	C₂²	semidirect
43. #11718072	C₂²	semidirect
44. #11718072	C₂²	semidirect
45. #11718047	C₂²	semidirect
46. C₈×#1055	C₂²	semidirect
122. C₁₃×M₁₆	SD₁₆	semidirect
159. #2962	D₁₃	semidirect
224. #446	C₂×D₁₃	semidirect
225. C₈×Q₈	C₂×D₁₃	semidirect
356. M₁₆	#6106	semidirect
388. C₁₃	#17995	semidirect

Maximal subgroups

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

subgroup	index
#13124840	2
M₁₆×D₅₂	2
#13113726	2
#13113679	2
#13113670	2
C₈×#6106	2
#13113606	2
#13113291	2
C₂×#11718075	2
M₁₆×#1055	2
C₁₃×#2962	2
#17995	13