Subgroups — #15833218

Order 3328.

672 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13124879	C₂	1	1	yes	maximal, characteristic
2	#13123812	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11718499	C₂	1	1	yes	maximal, characteristic, complemented
4	#13113747	C₂	1	2	yes	maximal, complemented
5	#13113741	C₂	1	2	yes	maximal, complemented
6	#13113676	C₂	1	2	yes	maximal, complemented
7	#13113662	C₂	1	2	yes	maximal, complemented
8	#13113619	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113280	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113123	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1483	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#529	C₂²	1	1	yes	characteristic
13	C₂²×#6094	—	2	1	no	—
14	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₂×#88060	—	2	1	no	—
18	#11718727	C₄	1	2	yes	—
19	#11718718	C₄	1	2	yes	—
20	#11718707	C₄	1	1	yes	characteristic
21	#11718705	C₄	1	1	yes	characteristic
22	#11718697	C₄	1	1	yes	characteristic
23	#11718695	C₄	1	1	yes	characteristic
24	C₄×#6106	C₂²	1	2	yes	—
25	#11718685	C₂²	1	1	yes	characteristic, complemented
26	Q₈×#1055	C₂²	1	1	yes	characteristic, complemented
27	C₄×#6104	C₂²	1	2	yes	—
28	#11718673	C₂²	1	1	yes	characteristic, complemented
29	#11718672	—	2	1	no	—
30	D₄×#1055	—	2	1	no	—
31	D₄×#1055	C₂²	1	1	yes	characteristic, complemented
32	#11718661	—	2	1	no	—
33	#11718658	—	2	1	no	—
34	#11718587	C₂²	1	1	yes	characteristic
35	#11718586	C₂²	1	1	yes	characteristic
36	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
37	#11718499	—	2	1	no	—
38	#11718499	—	2	1	no	—
39	#11718499	C₂²	1	2	yes	—
40	#11718499	C₂²	1	2	yes	—
41	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	complemented
42	C₁₃×D₄⋊C₈	C₂²	1	2	yes	complemented
43	#11718072	C₂²	1	2	yes	complemented
44	#11718071	C₂²	1	2	yes	complemented
45	#11718051	C₂²	1	2	yes	—
46	#11718051	C₂²	1	2	yes	—
47	#11718046	C₂²	1	2	yes	complemented
48	#11718046	C₂²	1	2	yes	complemented
49	C₂²×D₅₂	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₄×D₁₃	—	2	1	no	—
51	C₂×C₁₃×M₁₆	—	2	1	no	—
52	C₂²×C₈×C₁₃	—	2	1	no	—
53	C₁₃×#126	—	2	1	no	—
54	C₁₃×#125	C₂×C₄	1	1	yes	characteristic
55	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
56	C₁₃×#123	—	2	1	no	—
57	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
58	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
59	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₄×D₄×C₁₃	—	2	1	no	—
61	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₁₃×#117	—	2	1	no	—
63	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×#6106	C₂×C₄	1	2	yes	—
65	C₂×#6104	C₂×C₄	1	2	yes	—
66	C₂×#6103	—	2	1	no	—
67	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
68	C₂×#6099	—	2	1	no	—
69	C₂²×#1055	—	2	1	no	—
70	C₂²×#1055	D₄	1	1	yes	characteristic
71	C₂²×#1055	D₄	1	1	yes	characteristic
72	C₂×#6094	—	2	2	no	—
73	C₂×#6094	—	2	2	no	—
74	C₂×#6094	—	4	4	no	—
75	C₄×D₅₂	—	2	1	no	—
76	C₄×D₅₂	—	2	1	no	—
77	C₄×D₅₂	C₂×C₄	1	2	yes	—
78	C₄×D₅₂	C₂³	1	2	yes	—
79	C₁₃×C₄⋊C₈	—	2	1	no	—
80	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
81	C₁₃×#97	—	2	1	no	—
82	C₄×C₈×C₁₃	C₂³	1	2	yes	—
83	#88075	C₂×C₄	1	2	yes	—
84	#88072	C₂×C₄	1	2	yes	—
85	C₂²⋊#1055	—	2	1	no	—
86	C₂²⋊#1055	—	2	1	no	—
87	C₂²⋊#1055	—	2	1	no	—
88	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
89	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
90	#88060	—	2	2	no	—
91	#88060	—	2	2	no	—
92	#88049	C₂×C₄	1	2	yes	—
93	#88049	C₂×C₄	1	2	yes	—
94	#88048	C₂×C₄	1	2	yes	—
95	#88047	C₂×C₄	1	2	yes	—
96	C₄⋊#1055	—	2	1	no	—
97	C₄⋊#1055	—	2	1	no	—
98	C₄⋊#1055	C₂×C₄	1	2	yes	—
99	C₄⋊#1055	C₂³	1	1	yes	characteristic
100	C₄⋊#1055	C₂³	1	1	yes	characteristic
101	#88043	—	2	1	no	—
102	#88043	—	2	1	no	—
103	C₄×#1055	—	2	1	no	—
104	C₄×#1055	D₄	1	1	yes	characteristic
105	C₄×#1055	D₄	1	1	yes	characteristic
106	C₄×#1055	C₂³	1	2	yes	—
107	C₄×#1055	C₂³	1	1	yes	characteristic
108	C₄×#1055	C₂³	1	1	yes	characteristic
109	#17938	—	13	1	no	maximal, Sylow
110	C₂³×D₁₃	—	2	1	no	—
111	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×D₄×C₁₃	—	2	1	no	—
113	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
118	C₂²×Dic₁₃	—	2	1	no	—
119	C₂×D₅₂	—	2	1	no	—
120	C₂×D₅₂	—	4	2	no	—
121	C₂×D₅₂	C₂²×C₄	1	2	yes	—
122	C₂×C₄×D₁₃	—	2	2	no	—
123	C₂×C₄×D₁₃	—	2	2	no	—
124	C₂×C₄×D₁₃	—	4	2	no	—
125	C₂×C₄×D₁₃	—	4	2	no	—
126	C₁₃×M₁₆	—	4	2	no	—
127	C₂×C₈×C₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	—	2	2	no	—
129	C₂×C₈×C₁₃	—	4	2	no	—
130	C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₁₃×C₄⋊C₄	—	2	1	no	—
133	C₁₃×C₄⋊C₄	—	2	1	no	—
134	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
135	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
136	C₁₃×C₂²⋊C₄	—	2	1	no	—
137	C₁₃×C₂²⋊C₄	—	2	1	no	—
138	C₁₃×C₂²⋊C₄	—	2	1	no	—
139	C₁₃×C₂²⋊C₄	—	2	1	no	—
140	C₁₃×C₂²⋊C₄	—	2	1	no	—
141	C₄²×C₁₃	—	2	1	no	—
142	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
143	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₁₃	#41	1	1	yes	characteristic
145	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
146	#6106	—	4	2	no	—
147	#6104	—	4	2	no	—
148	#6103	—	2	2	no	—
149	#6103	—	2	2	no	—
150	C₄⋊Dic₁₃	—	2	1	no	—
151	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
152	#6099	—	4	2	no	—
153	C₂×#1055	—	2	2	no	—
154	C₂×#1055	—	2	1	no	—
155	C₂×#1055	—	2	1	no	—
156	C₂×#1055	—	4	1	no	—
157	C₂×#1055	—	4	2	no	—
158	C₂×#1055	C₂²×C₄	1	2	yes	—
159	C₂×#1055	C₂²×C₄	1	2	yes	—
160	C₂×#1055	C₂×D₄	1	1	yes	characteristic
161	C₂×#1055	C₂×D₄	1	1	yes	characteristic
162	C₂×#1055	C₂×D₄	1	1	yes	characteristic
163	C₂×#1055	C₂×D₄	1	1	yes	characteristic
164	#6094	—	4	4	no	—
165	#6094	—	4	4	no	—
166	#3105	—	13	1	no	—
167	#2966	—	13	1	no	—
168	C₂×#436	—	13	1	no	—
169	#1594	—	13	2	no	—
170	#1592	—	13	2	no	—
171	#1583	—	13	2	no	—
172	#1581	—	13	2	no	—
173	#1573	—	13	1	no	—
174	#1490	—	13	1	no	—
175	#1483	D₁₃	1	1	yes	characteristic, complemented
176	#1451	—	13	1	no	—
177	C₂³×C₁₃	—	2	1	no	—
178	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
179	C₂²×D₁₃	—	2	2	no	—
180	C₂²×D₁₃	—	4	2	no	—
181	C₂²×D₁₃	—	4	2	no	—
182	C₂²×D₁₃	—	4	2	no	—
183	Q₈×C₁₃	—	2	2	no	—
184	D₄×C₁₃	—	2	2	no	—
185	D₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	2	1	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	4	1	no	—
195	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
201	C₂×Dic₁₃	—	2	2	no	—
202	C₂×Dic₁₃	—	4	2	no	—
203	D₅₂	—	2	2	no	—
204	D₅₂	—	2	2	no	—
205	D₅₂	—	4	2	no	—
206	C₄×D₁₃	—	4	4	no	—
207	C₄×D₁₃	—	4	2	no	—
208	C₄×D₁₃	—	4	2	no	—
209	C₈×C₁₃	—	4	2	no	—
210	C₈×C₁₃	—	4	2	no	—
211	#1055	—	2	2	no	—
212	#1055	—	2	2	no	—
213	#1055	—	2	1	no	—
214	#1055	—	2	1	no	—
215	#1055	—	2	1	no	—
216	#1055	—	4	1	no	—
217	#1055	—	4	1	no	—
218	#1055	AGL(1,ℤ/8)	1	2	yes	—
219	C₂²×M₁₆	—	26	1	no	—
220	#529	C₂×D₁₃	1	1	yes	characteristic
221	C₂×C₄×D₄	—	13	1	no	—
222	#484	—	13	1	no	—
223	#481	—	13	1	no	—
224	#478	—	13	2	no	—
225	#463	—	13	2	no	—
226	#450	—	13	1	no	—
227	#447	—	13	1	no	—
228	#446	—	13	1	no	—
229	C₈×Q₈	—	13	1	no	—
230	C₄×SD₁₆	—	13	2	no	—
231	C₄×D₈	—	13	2	no	—
232	#436	—	13	1	no	—
233	#436	—	13	2	no	—
234	#436	—	13	2	no	—
235	#436	—	26	1	no	—
236	#436	—	26	1	no	—
237	#435	—	26	1	no	—
238	C₈×D₄	—	13	1	no	—
239	C₈×D₄	—	26	1	no	—
240	#433	—	26	1	no	—
241	#432	—	13	1	no	—
242	#431	—	13	1	no	—
243	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
244	C₂×C₂²⋊C₈	—	26	1	no	—
245	#405	—	26	1	no	—
246	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
247	C₂×C₄×C₈	—	13	1	no	—
248	#335	—	13	2	no	—
249	#334	—	13	2	no	—
250	Q₈⋊C₈	C₂×D₁₃	1	2	yes	complemented
251	D₄⋊C₈	—	13	2	no	—
252	D₄⋊C₈	—	13	2	no	—
253	D₄⋊C₈	C₂×D₁₃	1	2	yes	complemented
254	#322	—	13	2	no	—
255	#322	—	13	2	no	—
256	C₂²×C₁₃	—	2	1	no	—
257	C₂²×C₁₃	—	2	1	no	—
258	C₂²×C₁₃	—	4	1	no	—
259	C₂²×C₁₃	—	4	1	no	—
260	C₂²×C₁₃	—	4	1	no	—
261	C₂²×C₁₃	#444	1	2	yes	—
262	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
263	C₂×D₁₃	—	4	2	no	—
264	C₂×D₁₃	—	4	2	no	—
265	C₂×D₁₃	—	4	2	no	—
266	C₂×D₁₃	—	8	4	no	—
267	C₄×C₁₃	—	2	1	no	—
268	C₄×C₁₃	—	2	1	no	—
269	C₄×C₁₃	—	2	1	no	—
270	C₄×C₁₃	—	2	1	no	—
271	C₄×C₁₃	—	4	1	no	—
272	C₄×C₁₃	—	4	1	no	—
273	C₄×C₁₃	—	4	1	no	—
274	C₄×C₁₃	#568	1	2	yes	—
275	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
276	C₄×C₁₃	#575	1	1	yes	characteristic
277	Dic₁₃	—	4	2	no	—
278	C₂²×D₄	—	13	1	no	—
279	C₂³×C₄	—	26	1	no	—
280	C₂×SD₁₆	—	13	2	no	—
281	C₂×D₈	—	13	2	no	—
282	C₂×M₁₆	—	2	1	no	—
283	C₂×M₁₆	—	26	2	no	—
284	C₂×M₁₆	—	26	2	no	—
285	C₂×M₁₆	—	26	1	no	—
286	C₂×M₁₆	—	52	4	no	—
287	C₂²×C₈	—	2	1	no	—
288	C₂²×C₈	—	13	1	no	—
289	C₂²×C₈	—	13	1	no	—
290	C₂²×C₈	—	26	1	no	—
291	#126	—	2	1	no	—
292	#125	C₄×D₁₃	1	1	yes	characteristic
293	#124	C₄×D₁₃	1	1	yes	characteristic
294	#123	—	2	1	no	—
295	C₂²⋊Q₈	C₄×D₁₃	1	1	yes	characteristic
296	#121	C₄×D₁₃	1	1	yes	characteristic
297	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	13	2	no	—
300	C₄×D₄	—	13	2	no	—
301	C₄×D₄	—	26	1	no	—
302	C₄×D₄	—	26	1	no	—
303	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
304	#117	—	2	1	no	—
305	C₂×C₄⋊C₄	—	13	1	no	—
306	C₂×C₂²⋊C₄	—	26	1	no	—
307	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
308	#107	—	13	2	no	—
309	#106	—	13	2	no	—
310	C₄⋊C₈	—	2	1	no	—
311	C₄⋊C₈	—	13	2	no	—
312	C₄⋊C₈	—	13	1	no	—
313	C₄⋊C₈	—	13	1	no	—
314	C₄⋊C₈	—	26	1	no	—
315	C₄⋊C₈	—	26	1	no	—
316	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
317	#103	—	13	2	no	—
318	#102	—	13	2	no	—
319	#102	—	13	2	no	—
320	#102	—	13	2	no	—
321	C₂²⋊C₈	—	13	1	no	—
322	C₂²⋊C₈	—	13	1	no	—
323	C₂²⋊C₈	—	26	2	no	—
324	C₂²⋊C₈	—	26	2	no	—
325	C₂²⋊C₈	—	26	1	no	—
326	C₂²⋊C₈	—	26	1	no	—
327	C₂²⋊C₈	—	26	1	no	—
328	#97	—	2	1	no	—
329	#97	—	26	1	no	—
330	#97	—	26	1	no	—
331	C₄×C₈	—	13	1	no	—
332	C₄×C₈	—	13	1	no	—
333	C₄×C₈	—	13	2	no	—
334	C₄×C₈	—	13	1	no	—
335	C₄×C₈	—	13	1	no	—
336	C₄×C₈	—	26	1	no	—
337	C₄×C₈	C₂²×D₁₃	1	2	yes	—
338	C₂×C₁₃	—	2	2	no	—
339	C₂×C₁₃	—	8	1	no	—
340	C₂×C₁₃	#2930	1	1	yes	characteristic
341	C₂×C₁₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
342	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
343	D₁₃	—	8	2	no	—
344	C₂⁴	—	26	1	no	—
345	C₂×Q₈	C₂×C₄×D₁₃	1	1	yes	characteristic
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	13	2	no	—
348	C₂×D₄	—	26	1	no	—
349	C₂×D₄	—	52	2	no	—
350	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	26	1	no	—
353	C₂²×C₄	—	26	2	no	—
354	C₂²×C₄	—	26	2	no	—
355	C₂²×C₄	—	52	2	no	—
356	C₂²×C₄	—	52	2	no	—
357	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
358	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
359	C₂²×C₄	#6129	1	1	yes	characteristic
360	SD₁₆	—	52	2	no	—
361	D₈	—	52	2	no	—
362	M₁₆	—	4	2	no	—
363	M₁₆	—	52	4	no	—
364	M₁₆	—	52	4	no	—
365	M₁₆	—	52	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	4	2	no	—
369	C₂×C₈	—	13	1	no	—
370	C₂×C₈	—	13	2	no	—
371	C₂×C₈	—	13	2	no	—
372	C₂×C₈	—	13	1	no	—
373	C₂×C₈	—	13	1	no	—
374	C₂×C₈	—	13	1	no	—
375	C₂×C₈	—	26	2	no	—
376	C₂×C₈	—	26	1	no	—
377	C₂×C₈	—	26	1	no	—
378	C₂×C₈	—	52	2	no	—
379	C₂×C₈	—	52	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	13	2	no	—
385	C₄⋊C₄	—	26	1	no	—
386	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
387	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
388	C₂²⋊C₄	—	2	1	no	—
389	C₂²⋊C₄	—	2	1	no	—
390	C₂²⋊C₄	—	2	1	no	—
391	C₂²⋊C₄	—	2	1	no	—
392	C₂²⋊C₄	—	2	1	no	—
393	C₂²⋊C₄	—	26	2	no	—
394	C₂²⋊C₄	—	26	2	no	—
395	C₄²	—	2	1	no	—
396	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
397	C₄²	D₄×D₁₃	1	1	yes	characteristic
398	C₄²	#6129	1	1	yes	characteristic
399	C₄²	C₂³×D₁₃	1	1	yes	characteristic
400	C₁₃	#17938	1	1	yes	characteristic, complemented, Sylow
401	C₂³	—	2	1	no	—
402	C₂³	—	26	2	no	—
403	C₂³	—	52	2	no	—
404	C₂³	—	52	2	no	—
405	C₂³	—	52	2	no	—
406	C₂³	#88135	1	1	yes	characteristic
407	Q₈	—	2	2	no	—
408	D₄	—	2	2	no	—
409	D₄	—	4	2	no	—
410	D₄	—	26	2	no	—
411	D₄	—	26	2	no	—
412	D₄	—	52	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	26	2	no	—
423	C₂×C₄	—	52	4	no	—
424	C₂×C₄	—	52	2	no	—
425	C₂×C₄	—	52	2	no	—
426	C₂×C₄	—	52	2	no	—
427	C₂×C₄	#88135	1	1	yes	characteristic
428	C₂×C₄	#88135	1	1	yes	characteristic
429	C₂×C₄	#88135	1	1	yes	characteristic
430	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
431	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
432	C₂×C₄	C₂×#6129	1	1	yes	characteristic
433	C₈	—	4	2	no	—
434	C₈	—	4	2	no	—
435	C₈	—	13	2	no	—
436	C₈	—	26	2	no	—
437	C₈	—	26	2	no	—
438	C₈	—	26	1	no	—
439	C₈	—	26	1	no	—
440	C₈	—	26	1	no	—
441	C₈	—	52	1	no	—
442	C₈	—	52	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	52	2	no	—
449	C₂²	—	52	2	no	—
450	C₂²	—	52	2	no	—
451	C₂²	—	104	4	no	—
452	C₂²	#11718484	1	2	yes	—
453	C₂²	C₂×#88135	1	1	yes	characteristic
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	4	1	no	—
459	C₄	—	4	1	no	—
460	C₄	—	4	1	no	—
461	C₄	—	52	2	no	—
462	C₄	#11719455	1	2	yes	—
463	C₄	D₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
464	C₄	#11719482	1	1	yes	characteristic
465	C₂	—	2	2	no	—
466	C₂	—	8	1	no	—
467	C₂	—	104	2	no	—
468	C₂	#13123542	1	1	yes	characteristic
469	C₂	#13123649	1	1	yes	characteristic
470	C₂	C₂×#11718484	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#1483	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	#11718697	C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1483	D₁₃
hypocenter	C₁₃	#17938
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1483

Complements

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

N	H ≅ G/N	type
2. #13123812	C₂	semidirect
3. C₂×#11718499	C₂	semidirect
4. #13113747	C₂	semidirect
5. #13113741	C₂	semidirect
6. #13113676	C₂	semidirect
7. #13113662	C₂	semidirect
8. #13113619	C₂	semidirect
9. #13113280	C₂	semidirect
10. #13113123	C₂	semidirect
11. C₁₃×#1483	C₂	semidirect
25. #11718685	C₂²	semidirect
26. Q₈×#1055	C₂²	semidirect
28. #11718673	C₂²	semidirect
31. D₄×#1055	C₂²	semidirect
41. C₁₃×Q₈⋊C₈	C₂²	semidirect
42. C₁₃×D₄⋊C₈	C₂²	semidirect
43. #11718072	C₂²	semidirect
44. #11718071	C₂²	semidirect
47. #11718046	C₂²	semidirect
48. #11718046	C₂²	semidirect
175. #1483	D₁₃	semidirect
250. Q₈⋊C₈	C₂×D₁₃	semidirect
253. D₄⋊C₈	C₂×D₁₃	semidirect
400. C₁₃	#17938	semidirect

Maximal subgroups

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

subgroup	index
#13124879	2
#13123812	2
C₂×#11718499	2
#13113747	2
#13113741	2
#13113676	2
#13113662	2
#13113619	2
#13113280	2
#13113123	2
C₁₃×#1483	2
#17938	13