Subgroups — #15875226

Order 3328.

648 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13124624	C₂	1	1	yes	maximal, characteristic
2	#13123770	C₂	1	1	yes	maximal, characteristic, complemented
3	#13115780	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115611	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115581	C₂	1	2	yes	maximal, complemented
6	#13115543	C₂	1	2	yes	maximal
7	#13115481	C₂	1	2	yes	maximal
8	#13115432	C₂	1	2	yes	maximal, complemented
9	#13114856	C₂	1	1	yes	maximal, characteristic
10	C₈×C₄⋊Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2922	C₂	1	1	yes	maximal, characteristic
12	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
13	#11719175	C₂²	1	1	yes	characteristic
14	C₁₃×#433	—	2	1	no	—
15	C₁₃×#433	—	2	1	no	—
16	C₁₃×#431	—	2	1	no	—
17	C₁₃×#431	—	2	1	no	—
18	C₁₃×#424	C₂²	1	1	yes	characteristic
19	C₁₃×#424	C₂²	1	1	yes	characteristic
20	C₁₃×#408	C₂²	1	1	yes	characteristic
21	C₁₃×#408	C₂²	1	1	yes	characteristic
22	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×#88077	C₂²	1	2	yes	—
25	#11718894	C₂²	1	2	yes	—
26	C₂×#88062	C₂²	1	2	yes	—
27	#11718763	C₂²	1	2	yes	—
28	#11718762	C₂²	1	2	yes	—
29	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
30	#11718683	C₄	1	2	yes	complemented
31	#11718682	C₄	1	1	yes	characteristic, complemented
32	#11718681	C₄	1	1	yes	characteristic, complemented
33	#11718670	C₄	1	2	yes	complemented
34	#11718669	C₄	1	1	yes	characteristic, complemented
35	#11718668	C₄	1	1	yes	characteristic, complemented
36	#11718659	C₂²	1	2	yes	—
37	C₄×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
38	#11718585	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
40	#11718340	—	2	1	no	—
41	#11718340	—	2	1	no	—
42	C₈×Dic₂₆	—	2	1	no	—
43	C₈×Dic₂₆	—	2	1	no	—
44	#11718150	C₂²	1	2	yes	—
45	#11718147	C₂²	1	2	yes	—
46	#11718147	C₂²	1	2	yes	—
47	#11718142	C₂²	1	2	yes	—
48	#11718124	C₂²	1	2	yes	—
49	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
50	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
51	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
55	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
56	C₄×D₄×C₁₃	—	2	1	no	—
57	C₄×D₄×C₁₃	—	2	1	no	—
58	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
59	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
60	C₁₃×#117	—	2	1	no	—
61	C₁₃×#117	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₃	—	2	1	no	—
63	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
64	#88180	C₂³	1	2	yes	—
65	C₂×C₄⋊Dic₁₃	—	2	1	no	—
66	#88178	—	2	1	no	—
67	#88178	—	2	1	no	—
68	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
69	C₂×#6099	C₂³	1	2	yes	—
70	C₂²×#1055	C₂³	1	2	yes	—
71	#88124	C₂×C₄	1	2	yes	—
72	#88123	C₂×C₄	1	1	yes	characteristic
73	#88123	C₂×C₄	1	1	yes	characteristic
74	C₄×Dic₂₆	—	2	1	no	—
75	C₄×Dic₂₆	—	2	1	no	—
76	C₁₃×C₄⋊C₈	—	2	1	no	—
77	C₁₃×C₄⋊C₈	—	2	1	no	—
78	C₁₃×C₄⋊C₈	—	2	1	no	—
79	C₁₃×C₄⋊C₈	—	2	1	no	—
80	C₁₃×C₂²⋊C₈	—	2	1	no	—
81	C₁₃×C₂²⋊C₈	—	2	1	no	—
82	C₁₃×C₂²⋊C₈	—	2	1	no	—
83	C₁₃×C₂²⋊C₈	—	2	1	no	—
84	C₁₃×#97	—	2	1	no	—
85	C₄×C₈×C₁₃	—	2	1	no	—
86	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
87	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
88	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
89	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
90	#88077	—	4	2	no	—
91	#88075	C₂×C₄	1	2	yes	—
92	#88075	C₂×C₄	1	2	yes	—
93	#88072	C₂×C₄	1	2	yes	—
94	#88072	C₂×C₄	1	2	yes	—
95	#88071	—	2	1	no	—
96	#88062	—	4	2	no	—
97	#88055	—	2	2	no	—
98	#88054	—	2	2	no	—
99	#88054	—	2	2	no	—
100	C₈×Dic₁₃	—	2	2	no	—
101	C₈×Dic₁₃	—	4	2	no	—
102	#88048	C₂×C₄	1	2	yes	—
103	#88048	C₂×C₄	1	2	yes	—
104	#88047	C₂×C₄	1	2	yes	—
105	#88047	C₂×C₄	1	2	yes	—
106	C₄⋊#1055	—	2	1	no	—
107	C₄⋊#1055	—	2	1	no	—
108	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
109	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
110	C₄⋊#1055	C₂×C₄	1	2	yes	—
111	#22130	—	13	1	no	maximal, Sylow
112	C₁₃×#41	—	2	1	no	—
113	C₁₃×#41	—	2	1	no	—
114	C₁₃×#41	—	2	1	no	—
115	C₁₃×#41	—	2	1	no	—
116	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×D₄×C₁₃	—	2	1	no	—
118	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	1	no	—
122	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
125	C₂²×Dic₁₃	—	2	2	no	—
126	C₂×Dic₂₆	—	2	1	no	—
127	C₂×Dic₂₆	—	2	1	no	—
128	C₁₃×M₁₆	—	2	1	no	—
129	C₁₃×M₁₆	—	2	1	no	—
130	C₁₃×M₁₆	—	2	1	no	—
131	C₁₃×M₁₆	—	2	1	no	—
132	C₂×C₈×C₁₃	—	2	1	no	—
133	C₂×C₈×C₁₃	—	2	1	no	—
134	C₂×C₈×C₁₃	—	2	1	no	—
135	C₂×C₈×C₁₃	—	2	1	no	—
136	C₂×C₈×C₁₃	—	2	1	no	—
137	C₂×C₈×C₁₃	—	2	1	no	—
138	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₁₃×C₄⋊C₄	—	2	1	no	—
143	C₁₃×C₄⋊C₄	—	2	1	no	—
144	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
145	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
146	C₁₃×C₂²⋊C₄	—	2	1	no	—
147	C₁₃×C₂²⋊C₄	—	2	1	no	—
148	C₁₃×C₂²⋊C₄	—	2	1	no	—
149	C₄²×C₁₃	—	2	1	no	—
150	C₄²×C₁₃	—	2	1	no	—
151	C₄²×C₁₃	—	2	1	no	—
152	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
153	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
154	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂²⋊Dic₁₃	—	2	2	no	—
157	C₄⋊Dic₁₃	—	2	4	no	—
158	C₄⋊Dic₁₃	—	2	1	no	—
159	C₄⋊Dic₁₃	—	2	1	no	—
160	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
161	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
162	#6101	—	2	2	no	—
163	#6101	—	2	2	no	—
164	C₄×Dic₁₃	—	2	2	no	—
165	C₄×Dic₁₃	—	2	2	no	—
166	C₄×Dic₁₃	—	2	2	no	—
167	#6099	—	2	2	no	—
168	#6099	—	2	2	no	—
169	C₂×#1055	—	2	2	no	—
170	C₂×#1055	—	2	2	no	—
171	C₂×#1055	—	2	2	no	—
172	C₂×#1055	C₂²×C₄	1	2	yes	—
173	C₂×#1055	C₂²×C₄	1	2	yes	—
174	#3076	—	13	1	no	—
175	#2960	—	13	1	no	—
176	#2922	D₁₃	1	1	yes	characteristic
177	#1986	—	13	1	no	—
178	#1950	—	13	1	no	—
179	#1945	—	13	2	no	—
180	#1937	—	13	2	no	—
181	#1929	—	13	2	no	—
182	#1922	—	13	2	no	—
183	#1806	—	13	1	no	—
184	C₈×C₄⋊C₄	—	13	1	no	—
185	C₂³×C₁₃	—	2	1	no	—
186	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
187	Q₈×C₁₃	—	2	1	no	—
188	Q₈×C₁₃	—	2	1	no	—
189	D₄×C₁₃	—	2	1	no	—
190	D₄×C₁₃	—	2	1	no	—
191	D₄×C₁₃	—	4	1	no	—
192	D₄×C₁₃	—	4	1	no	—
193	C₂×C₄×C₁₃	—	2	2	no	—
194	C₂×C₄×C₁₃	—	2	1	no	—
195	C₂×C₄×C₁₃	—	2	1	no	—
196	C₂×C₄×C₁₃	—	2	1	no	—
197	C₂×C₄×C₁₃	—	4	1	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	4	1	no	—
200	C₂×C₄×C₁₃	—	4	1	no	—
201	C₂×C₄×C₁₃	—	4	2	no	—
202	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
209	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
210	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
211	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
212	C₂×Dic₁₃	—	2	4	no	—
213	C₂×Dic₁₃	—	2	2	no	—
214	C₂×Dic₁₃	—	2	2	no	—
215	C₂×Dic₁₃	—	4	2	no	—
216	C₂×Dic₁₃	—	4	2	no	—
217	Dic₂₆	—	4	2	no	—
218	Dic₂₆	—	4	2	no	—
219	C₈×C₁₃	—	2	1	no	—
220	C₈×C₁₃	—	2	1	no	—
221	C₈×C₁₃	—	2	1	no	—
222	C₈×C₁₃	—	2	1	no	—
223	C₈×C₁₃	—	4	1	no	—
224	C₈×C₁₃	—	4	1	no	—
225	#1055	—	2	2	no	—
226	#1055	—	2	2	no	—
227	#1055	—	4	2	no	—
228	#533	—	13	1	no	—
229	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
230	#479	—	13	2	no	—
231	#478	—	13	2	no	—
232	#477	—	13	1	no	—
233	#476	—	13	1	no	—
234	#475	—	13	1	no	—
235	#474	—	13	1	no	—
236	#446	—	26	1	no	—
237	#446	—	26	1	no	—
238	C₈×Q₈	—	26	1	no	—
239	C₈×Q₈	—	26	1	no	—
240	#433	—	2	1	no	—
241	#433	—	2	1	no	—
242	#431	—	2	1	no	—
243	#431	—	2	1	no	—
244	C₂×#108	—	13	2	no	—
245	#427	—	13	2	no	—
246	#424	—	13	2	no	—
247	#424	C₂×D₁₃	1	1	yes	characteristic
248	#424	C₂×D₁₃	1	1	yes	characteristic
249	#423	—	13	1	no	—
250	C₂×C₄⋊C₈	—	13	1	no	—
251	C₂×#104	—	13	2	no	—
252	#416	—	13	2	no	—
253	#408	C₂×D₁₃	1	1	yes	characteristic
254	#408	C₂×D₁₃	1	1	yes	characteristic
255	#405	—	13	2	no	—
256	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
257	C₂×C₄×C₈	—	13	2	no	—
258	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
259	C₄×C₄⋊C₄	—	13	1	no	—
260	#341	—	13	2	no	—
261	#339	—	13	2	no	—
262	#339	—	13	2	no	—
263	#339	—	13	2	no	—
264	#336	—	13	2	no	—
265	C₂²×C₁₃	—	2	1	no	—
266	C₂²×C₁₃	—	2	1	no	—
267	C₂²×C₁₃	—	4	1	no	—
268	C₂²×C₁₃	—	4	1	no	—
269	C₂²×C₁₃	—	4	1	no	—
270	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
271	C₂²×C₁₃	#541	1	1	yes	characteristic
272	C₂²×C₁₃	#542	1	1	yes	characteristic
273	C₄×C₁₃	—	2	1	no	—
274	C₄×C₁₃	—	2	1	no	—
275	C₄×C₁₃	—	2	1	no	—
276	C₄×C₁₃	—	4	1	no	—
277	C₄×C₁₃	—	4	1	no	—
278	C₄×C₁₃	—	4	1	no	—
279	C₄×C₁₃	#443	1	2	yes	—
280	C₄×C₁₃	#519	1	1	yes	characteristic
281	C₄×C₁₃	#520	1	1	yes	characteristic
282	C₄×C₁₃	#536	1	1	yes	characteristic
283	C₄×C₁₃	#537	1	1	yes	characteristic
284	Dic₁₃	—	4	4	no	—
285	Dic₁₃	—	4	2	no	—
286	Dic₁₃	—	4	2	no	—
287	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
288	C₂×M₁₆	—	13	2	no	—
289	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
290	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
291	C₂²×C₈	—	13	2	no	—
292	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
293	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
294	C₄⋊Q₈	—	13	1	no	—
295	C₄⋊Q₈	—	13	1	no	—
296	#125	—	13	2	no	—
297	C₂²⋊Q₈	—	26	1	no	—
298	C₂²⋊Q₈	—	26	1	no	—
299	C₄×Q₈	—	26	1	no	—
300	C₄×Q₈	—	26	1	no	—
301	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
302	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
303	C₄×D₄	—	2	1	no	—
304	C₄×D₄	—	2	1	no	—
305	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
306	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
307	#117	—	2	1	no	—
308	#117	—	13	2	no	—
309	#117	C₂²×D₁₃	1	1	yes	characteristic
310	C₂×C₄⋊C₄	—	26	1	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	—	13	2	no	—
313	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
314	#108	—	52	2	no	—
315	#107	—	13	2	no	—
316	#107	—	13	2	no	—
317	#106	—	13	2	no	—
318	#106	—	13	2	no	—
319	C₄⋊C₈	—	2	1	no	—
320	C₄⋊C₈	—	2	1	no	—
321	C₄⋊C₈	—	2	1	no	—
322	C₄⋊C₈	—	2	1	no	—
323	C₄⋊C₈	—	13	1	no	—
324	C₄⋊C₈	—	13	1	no	—
325	C₄⋊C₈	—	13	2	no	—
326	C₄⋊C₈	—	26	2	no	—
327	C₄⋊C₈	—	26	2	no	—
328	C₄⋊C₈	—	26	1	no	—
329	C₄⋊C₈	—	26	1	no	—
330	#104	—	52	2	no	—
331	#103	—	13	2	no	—
332	#103	—	13	2	no	—
333	#102	—	13	2	no	—
334	#102	—	13	2	no	—
335	C₂²⋊C₈	—	2	1	no	—
336	C₂²⋊C₈	—	2	1	no	—
337	C₂²⋊C₈	—	2	1	no	—
338	C₂²⋊C₈	—	2	1	no	—
339	#97	—	2	1	no	—
340	#97	—	26	2	no	—
341	C₄×C₈	—	2	1	no	—
342	C₄×C₈	—	26	2	no	—
343	C₄×C₈	—	52	2	no	—
344	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
345	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
346	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
347	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
348	#95	—	26	1	no	—
349	C₂×C₁₃	—	2	1	no	—
350	C₂×C₁₃	—	2	1	no	—
351	C₂×C₁₃	—	8	1	no	—
352	C₂×C₁₃	#2323	1	1	yes	characteristic
353	C₂×C₁₃	C₂×#443	1	1	yes	characteristic
354	C₂×C₁₃	#2955	1	1	yes	characteristic
355	#41	—	2	1	no	—
356	#41	—	2	1	no	—
357	#41	—	2	1	no	—
358	#41	—	2	1	no	—
359	C₂×Q₈	—	26	1	no	—
360	C₂×Q₈	—	26	1	no	—
361	C₂×Q₈	C₂×C₄×D₁₃	1	1	yes	characteristic
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	26	2	no	—
368	C₂²×C₄	#6127	1	1	yes	characteristic
369	C₂²×C₄	#6127	1	1	yes	characteristic
370	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
371	M₁₆	—	2	1	no	—
372	M₁₆	—	2	1	no	—
373	M₁₆	—	2	1	no	—
374	M₁₆	—	2	1	no	—
375	M₁₆	—	26	2	no	—
376	M₁₆	—	26	2	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	13	2	no	—
384	C₂×C₈	—	13	2	no	—
385	C₂×C₈	—	26	2	no	—
386	C₂×C₈	—	26	2	no	—
387	C₂×C₈	—	26	2	no	—
388	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
389	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
390	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
391	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	13	2	no	—
395	C₄⋊C₄	—	13	2	no	—
396	C₄⋊C₄	—	26	4	no	—
397	C₄⋊C₄	—	26	2	no	—
398	C₄⋊C₄	—	26	2	no	—
399	C₄⋊C₄	—	26	1	no	—
400	C₄⋊C₄	—	26	1	no	—
401	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
402	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
403	C₂²⋊C₄	—	2	1	no	—
404	C₂²⋊C₄	—	2	1	no	—
405	C₂²⋊C₄	—	2	1	no	—
406	C₂²⋊C₄	—	26	2	no	—
407	C₄²	—	2	1	no	—
408	C₄²	—	2	1	no	—
409	C₄²	—	2	1	no	—
410	C₄²	—	26	2	no	—
411	C₄²	—	26	2	no	—
412	C₄²	—	26	2	no	—
413	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
414	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
415	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
416	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
417	C₁₃	#22130	1	1	yes	characteristic, complemented, Sylow
418	C₂³	—	2	1	no	—
419	C₂³	C₂×#6127	1	1	yes	characteristic
420	Q₈	—	2	1	no	—
421	Q₈	—	2	1	no	—
422	Q₈	—	52	2	no	—
423	Q₈	—	52	2	no	—
424	D₄	—	2	1	no	—
425	D₄	—	2	1	no	—
426	D₄	—	4	1	no	—
427	D₄	—	4	1	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	26	4	no	—
438	C₂×C₄	—	26	2	no	—
439	C₂×C₄	—	26	2	no	—
440	C₂×C₄	—	52	2	no	—
441	C₂×C₄	—	52	2	no	—
442	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
443	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
444	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
445	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
446	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
447	C₂×C₄	#88256	1	1	yes	characteristic
448	C₂×C₄	#88257	1	1	yes	characteristic
449	C₂×C₄	#88257	1	1	yes	characteristic
450	C₂×C₄	#88257	1	1	yes	characteristic
451	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
452	C₈	—	2	1	no	—
453	C₈	—	2	1	no	—
454	C₈	—	2	1	no	—
455	C₈	—	2	1	no	—
456	C₈	—	4	1	no	—
457	C₈	—	4	1	no	—
458	C₈	—	26	2	no	—
459	C₈	—	26	2	no	—
460	C₈	—	52	2	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	—	4	1	no	—
466	C₂²	#11719223	1	1	yes	characteristic
467	C₂²	#11719239	1	1	yes	characteristic
468	C₂²	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	4	1	no	—
473	C₄	—	4	1	no	—
474	C₄	—	4	1	no	—
475	C₄	—	52	4	no	—
476	C₄	—	52	2	no	—
477	C₄	—	52	2	no	—
478	C₄	#11718805	1	2	yes	—
479	C₄	#11719221	1	1	yes	characteristic
480	C₄	#11719228	1	1	yes	characteristic
481	C₄	#11719530	1	1	yes	characteristic
482	C₄	#11719538	1	1	yes	characteristic
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	8	1	no	—
486	C₂	#13117518	1	1	yes	characteristic
487	C₂	C₂×#11718805	1	1	yes	characteristic
488	C₂	#13123737	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#2922	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×C₁₃×#41	C₂³
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#2922	D₁₃
hypocenter	C₁₃	#22130
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2922

Complements

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

N	H ≅ G/N	type
2. #13123770	C₂	semidirect
3. #13115780	C₂	semidirect
4. #13115611	C₂	semidirect
5. #13115581	C₂	semidirect
8. #13115432	C₂	semidirect
10. C₈×C₄⋊Dic₁₃	C₂	semidirect
30. #11718683	C₄	semidirect
31. #11718682	C₄	semidirect
32. #11718681	C₄	semidirect
33. #11718670	C₄	semidirect
34. #11718669	C₄	semidirect
35. #11718668	C₄	semidirect
417. C₁₃	#22130	semidirect

Maximal subgroups

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

subgroup	index
#13124624	2
#13123770	2
#13115780	2
#13115611	2
#13115581	2
#13115543	2
#13115481	2
#13115432	2
#13114856	2
C₈×C₄⋊Dic₁₃	2
C₁₃×#2922	2
#22130	13