Subgroups — #15870750

Order 3328.

750 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123771	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#88202	C₂	1	1	yes	maximal, characteristic
3	#13115781	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115612	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115437	C₂	1	2	yes	maximal, complemented
6	#13115113	C₂	1	2	yes	maximal
7	#13114856	C₂	1	1	yes	maximal, characteristic
8	#13114717	C₂	1	2	yes	maximal, complemented
9	#13114701	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114676	C₂	1	2	yes	maximal
11	C₁₃×#3076	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#533	C₂²	1	1	yes	characteristic
13	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
14	C₂×#88202	C₂²	1	1	yes	characteristic
15	C₂×#88202	C₂²	1	1	yes	characteristic
16	C₁₃×#479	C₄	1	2	yes	complemented
17	C₁₃×#478	C₄	1	2	yes	complemented
18	C₁₃×#477	C₄	1	1	yes	characteristic, complemented
19	C₁₃×#476	C₄	1	1	yes	characteristic, complemented
20	C₁₃×#475	C₄	1	1	yes	characteristic, complemented
21	C₁₃×#474	C₄	1	1	yes	characteristic, complemented
22	C₁₃×#427	C₂²	1	2	yes	—
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₁₃×#416	C₂²	1	2	yes	—
25	C₂×#88077	C₂²	1	2	yes	—
26	C₂×#88059	C₂²	1	2	yes	—
27	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
28	#11718685	—	2	1	no	—
29	#11718685	—	2	1	no	—
30	Q₈×#1055	—	2	1	no	—
31	Q₈×#1055	—	2	1	no	—
32	#11718660	C₂²	1	2	yes	—
33	#11718658	—	2	1	no	—
34	#11718658	—	2	1	no	—
35	#11718658	C₂²	1	1	yes	characteristic
36	#11718658	C₂²	1	2	yes	—
37	#11718658	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
39	#11718585	C₂²	1	1	yes	characteristic
40	C₄×#6099	—	2	1	no	—
41	C₄×#6099	C₂²	1	1	yes	characteristic
42	C₂×C₄×#1055	—	2	1	no	—
43	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
44	#11718144	C₂²	1	2	yes	—
45	#11718142	C₂²	1	2	yes	—
46	#11718124	C₂²	1	2	yes	—
47	#11718124	C₂²	1	2	yes	—
48	#11718124	C₂²	1	2	yes	—
49	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
51	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
52	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
53	C₁₃×#125	C₂×C₄	1	2	yes	—
54	C₁₃×C₂²⋊Q₈	—	2	1	no	—
55	C₁₃×C₂²⋊Q₈	—	2	1	no	—
56	C₄×Q₈×C₁₃	—	2	1	no	—
57	C₄×Q₈×C₁₃	—	2	1	no	—
58	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
59	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
60	C₄×D₄×C₁₃	—	2	1	no	—
61	C₄×D₄×C₁₃	—	2	1	no	—
62	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
63	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
64	C₁₃×#117	—	2	1	no	—
65	C₁₃×#117	C₂³	1	1	yes	characteristic
66	C₁₃×#117	C₂³	1	2	yes	—
67	C₂×C₄²×C₁₃	—	2	1	no	—
68	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
69	#88202	—	2	2	no	—
70	#88202	—	2	2	no	—
71	#88202	—	2	2	no	—
72	#88202	Q₈	1	4	yes	complemented
73	C₂×C₄⋊Dic₁₃	—	2	1	no	—
74	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
75	C₂×#6099	—	2	1	no	—
76	C₂×#6099	—	2	1	no	—
77	C₂×#6099	C₂³	1	2	yes	—
78	C₂×#6099	C₂³	1	1	yes	characteristic
79	C₂×#6099	C₂³	1	1	yes	characteristic
80	C₂²×#1055	—	2	1	no	—
81	C₂²×#1055	—	2	1	no	—
82	C₂²×#1055	C₂³	1	1	yes	characteristic
83	C₂²×#1055	C₂³	1	1	yes	characteristic
84	C₁₃×#107	C₂×C₄	1	2	yes	—
85	C₁₃×#107	C₂×C₄	1	2	yes	—
86	C₁₃×#106	C₂×C₄	1	2	yes	—
87	C₁₃×#106	C₂×C₄	1	2	yes	—
88	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
89	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
90	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
91	C₁₃×#103	C₂×C₄	1	2	yes	—
92	C₁₃×#103	C₂×C₄	1	2	yes	—
93	C₁₃×#102	C₂×C₄	1	2	yes	—
94	C₁₃×#102	C₂×C₄	1	2	yes	—
95	#88077	—	2	4	no	—
96	#88071	—	2	1	no	—
97	#88059	—	2	4	no	—
98	C₈×Dic₁₃	—	2	4	no	—
99	C₄⋊#1055	—	2	1	no	—
100	C₄⋊#1055	—	2	1	no	—
101	C₄⋊#1055	—	2	2	no	—
102	C₄⋊#1055	—	2	2	no	—
103	#88043	—	2	1	no	—
104	#88043	—	2	1	no	—
105	#88043	—	2	1	no	—
106	#88043	—	2	2	no	—
107	C₄×#1055	—	2	1	no	—
108	C₄×#1055	—	2	1	no	—
109	C₄×#1055	—	2	1	no	—
110	C₄×#1055	—	2	2	no	—
111	C₄×#1055	D₄	1	1	yes	characteristic
112	C₄×#1055	D₄	1	1	yes	characteristic
113	C₄×#1055	D₄	1	1	yes	characteristic
114	C₄×#1055	D₄	1	1	yes	characteristic
115	#21627	—	13	1	no	maximal, Sylow
116	C₁₃×#41	—	2	1	no	—
117	C₁₃×#41	—	2	1	no	—
118	C₁₃×#41	C₂×Q₈	1	2	yes	—
119	C₁₃×#41	#41	1	2	yes	—
120	C₂×Q₈×C₁₃	—	2	1	no	—
121	C₂×Q₈×C₁₃	—	2	1	no	—
122	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×D₄×C₁₃	—	2	1	no	—
124	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
131	C₂²×Dic₁₃	—	2	2	no	—
132	C₂×C₈×C₁₃	—	2	2	no	—
133	C₂×C₈×C₁₃	—	2	2	no	—
134	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
135	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
136	C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₁₃×C₄⋊C₄	—	2	1	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	2	2	no	—
140	C₁₃×C₄⋊C₄	—	2	1	no	—
141	C₁₃×C₄⋊C₄	—	2	1	no	—
142	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
143	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
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	2	no	—
148	C₁₃×C₂²⋊C₄	—	2	1	no	—
149	C₁₃×C₂²⋊C₄	—	2	1	no	—
150	C₄²×C₁₃	—	2	1	no	—
151	C₄²×C₁₃	—	2	1	no	—
152	C₄²×C₁₃	—	2	1	no	—
153	C₄²×C₁₃	—	2	2	no	—
154	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
155	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
156	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₄⋊Dic₁₃	—	2	4	no	—
159	C₄×Dic₁₃	—	2	2	no	—
160	C₄×Dic₁₃	—	2	2	no	—
161	#6099	—	2	4	no	—
162	#6099	—	2	1	no	—
163	#6099	—	2	1	no	—
164	#6099	—	2	4	no	—
165	#6099	—	2	2	no	—
166	#6099	—	2	2	no	—
167	#6099	C₂×Q₈	1	2	yes	—
168	#6099	#41	1	2	yes	—
169	C₂×#1055	—	2	4	no	—
170	C₂×#1055	—	2	1	no	—
171	C₂×#1055	—	2	1	no	—
172	C₂×#1055	—	2	1	no	—
173	C₂×#1055	—	2	1	no	—
174	C₂×#1055	—	2	4	no	—
175	C₂×#1055	—	2	2	no	—
176	C₂×#1055	C₂×D₄	1	1	yes	characteristic
177	C₂×#1055	C₂×D₄	1	1	yes	characteristic
178	C₂×#1055	C₂×D₄	1	1	yes	characteristic
179	C₂×#1055	C₂×D₄	1	1	yes	characteristic
180	C₂×#1055	C₂×Q₈	1	2	yes	—
181	C₂×#1055	#41	1	2	yes	—
182	#3076	D₁₃	1	1	yes	characteristic
183	#2960	—	13	1	no	—
184	C₄×#131	—	13	1	no	—
185	#1986	—	13	1	no	—
186	#1950	—	13	1	no	—
187	#1922	—	13	2	no	—
188	#1866	—	13	2	no	—
189	#1806	—	13	1	no	—
190	#1772	—	13	2	no	—
191	C₈×C₄⋊C₄	—	13	1	no	—
192	#1764	—	13	2	no	—
193	C₂³×C₁₃	—	2	1	no	—
194	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
195	Q₈×C₁₃	—	2	1	no	—
196	Q₈×C₁₃	—	4	2	no	—
197	Q₈×C₁₃	—	4	2	no	—
198	Q₈×C₁₃	C₄×Q₈	1	2	yes	—
199	D₄×C₁₃	—	2	2	no	—
200	D₄×C₁₃	—	2	2	no	—
201	D₄×C₁₃	—	2	1	no	—
202	D₄×C₁₃	C₄×Q₈	1	2	yes	—
203	C₂×C₄×C₁₃	—	2	1	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	1	no	—
208	C₂×C₄×C₁₃	—	2	1	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	4	1	no	—
212	C₂×C₄×C₁₃	—	4	2	no	—
213	C₂×C₄×C₁₃	—	4	2	no	—
214	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
215	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
216	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
217	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
218	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
224	C₂×Dic₁₃	—	2	4	no	—
225	C₂×Dic₁₃	—	4	2	no	—
226	C₂×Dic₁₃	—	4	2	no	—
227	C₈×C₁₃	—	2	2	no	—
228	C₈×C₁₃	—	2	2	no	—
229	#1055	—	2	2	no	—
230	#1055	—	2	1	no	—
231	#1055	—	2	2	no	—
232	#1055	—	2	1	no	—
233	#1055	—	4	2	no	—
234	#1055	C₂²⋊Q₈	1	2	yes	—
235	#1055	C₂²⋊Q₈	1	2	yes	—
236	C₂×#131	—	13	1	no	—
237	C₂×#131	—	13	1	no	—
238	#533	C₂×D₁₃	1	1	yes	characteristic
239	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
240	#479	Dic₁₃	1	2	yes	complemented
241	#478	Dic₁₃	1	2	yes	complemented
242	#477	Dic₁₃	1	1	yes	characteristic, complemented
243	#476	Dic₁₃	1	1	yes	characteristic, complemented
244	#475	Dic₁₃	1	1	yes	characteristic, complemented
245	#474	Dic₁₃	1	1	yes	characteristic, complemented
246	#446	—	26	1	no	—
247	#446	—	26	1	no	—
248	C₈×Q₈	—	26	1	no	—
249	C₈×Q₈	—	26	1	no	—
250	C₂×#108	—	13	2	no	—
251	#427	C₂×D₁₃	1	2	yes	—
252	#424	—	13	2	no	—
253	#423	—	13	1	no	—
254	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
255	C₂×#104	—	13	2	no	—
256	#416	C₂×D₁₃	1	2	yes	—
257	#405	—	13	1	no	—
258	#405	—	13	1	no	—
259	#405	—	13	2	no	—
260	#405	—	26	1	no	—
261	#405	—	26	1	no	—
262	C₄×M₁₆	—	13	1	no	—
263	C₄×M₁₆	—	26	1	no	—
264	C₂×C₄×C₈	—	13	1	no	—
265	C₂×C₄×C₈	—	13	2	no	—
266	C₂×C₄×C₈	—	26	1	no	—
267	C₄×C₄⋊C₄	—	13	1	no	—
268	#341	—	13	2	no	—
269	#339	—	13	2	no	—
270	#339	—	13	2	no	—
271	#339	—	13	2	no	—
272	#336	—	13	2	no	—
273	C₂²×C₁₃	—	2	1	no	—
274	C₂²×C₁₃	—	2	1	no	—
275	C₂²×C₁₃	—	2	2	no	—
276	C₂²×C₁₃	—	4	1	no	—
277	C₂²×C₁₃	—	4	1	no	—
278	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
279	C₂²×C₁₃	#529	1	1	yes	characteristic
280	C₂²×C₁₃	#533	1	1	yes	characteristic
281	C₄×C₁₃	—	2	1	no	—
282	C₄×C₁₃	—	2	1	no	—
283	C₄×C₁₃	—	2	1	no	—
284	C₄×C₁₃	—	2	2	no	—
285	C₄×C₁₃	—	4	1	no	—
286	C₄×C₁₃	—	4	2	no	—
287	C₄×C₁₃	—	4	1	no	—
288	C₄×C₁₃	—	4	2	no	—
289	C₄×C₁₃	#443	1	2	yes	—
290	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
291	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
292	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
293	C₄×C₁₃	#525	1	1	yes	characteristic
294	Dic₁₃	—	4	4	no	—
295	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
296	#131	—	13	4	no	—
297	#131	—	26	2	no	—
298	#131	—	26	2	no	—
299	#131	—	26	2	no	—
300	C₂×M₁₆	—	13	1	no	—
301	C₂×M₁₆	—	13	1	no	—
302	C₂×M₁₆	—	13	2	no	—
303	C₂×M₁₆	—	26	1	no	—
304	C₂×M₁₆	—	26	1	no	—
305	C₂²×C₈	—	13	1	no	—
306	C₂²×C₈	—	13	1	no	—
307	C₂²×C₈	—	26	1	no	—
308	C₂²×C₈	—	26	1	no	—
309	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
310	C₄⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
311	C₄⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
312	#125	C₂×Dic₁₃	1	2	yes	—
313	C₂²⋊Q₈	—	2	1	no	—
314	C₂²⋊Q₈	—	2	1	no	—
315	C₄×Q₈	—	2	1	no	—
316	C₄×Q₈	—	2	1	no	—
317	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
318	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
319	C₄×D₄	—	2	1	no	—
320	C₄×D₄	—	2	1	no	—
321	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
322	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
323	#117	—	2	1	no	—
324	#117	C₂²×D₁₃	1	1	yes	characteristic
325	#117	C₂²×D₁₃	1	2	yes	—
326	C₂×C₄⋊C₄	—	26	1	no	—
327	C₂×C₄²	—	2	1	no	—
328	C₂×C₄²	—	13	2	no	—
329	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
330	#108	—	26	4	no	—
331	#107	C₂×Dic₁₃	1	2	yes	—
332	#107	C₂×Dic₁₃	1	2	yes	—
333	#106	C₂×Dic₁₃	1	2	yes	—
334	#106	C₂×Dic₁₃	1	2	yes	—
335	C₄⋊C₈	—	26	2	no	—
336	C₄⋊C₈	—	26	2	no	—
337	C₄⋊C₈	—	26	1	no	—
338	C₄⋊C₈	—	26	1	no	—
339	C₄⋊C₈	C₂×Dic₁₃	1	1	yes	characteristic
340	C₄⋊C₈	C₂×Dic₁₃	1	1	yes	characteristic
341	C₄⋊C₈	C₂×Dic₁₃	1	2	yes	—
342	#104	—	26	4	no	—
343	#103	C₂×Dic₁₃	1	2	yes	—
344	#103	C₂×Dic₁₃	1	2	yes	—
345	#102	C₂×Dic₁₃	1	2	yes	—
346	#102	C₂×Dic₁₃	1	2	yes	—
347	#97	—	26	1	no	—
348	#97	—	26	1	no	—
349	#97	—	26	2	no	—
350	#97	—	26	1	no	—
351	C₄×C₈	—	13	1	no	—
352	C₄×C₈	—	13	1	no	—
353	C₄×C₈	—	13	1	no	—
354	C₄×C₈	—	13	1	no	—
355	C₄×C₈	—	26	1	no	—
356	C₄×C₈	—	26	1	no	—
357	C₄×C₈	—	26	2	no	—
358	C₄×C₈	—	26	4	no	—
359	C₄×C₈	—	26	1	no	—
360	#95	—	26	1	no	—
361	C₂×C₁₃	—	2	1	no	—
362	C₂×C₁₃	—	2	1	no	—
363	C₂×C₁₃	—	4	2	no	—
364	C₂×C₁₃	C₄×C₂²⋊Q₈	1	1	yes	characteristic
365	C₂×C₁₃	C₂×#443	1	1	yes	characteristic
366	C₂×C₁₃	#2955	1	1	yes	characteristic
367	#41	—	2	1	no	—
368	#41	—	2	1	no	—
369	#41	Q₈×D₁₃	1	2	yes	—
370	#41	#6131	1	2	yes	—
371	C₂×Q₈	—	2	1	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	C₂²×Dic₁₃	1	1	yes	characteristic
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	26	2	no	—
380	C₂²×C₄	#6129	1	1	yes	characteristic
381	C₂²×C₄	#6129	1	1	yes	characteristic
382	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
383	M₁₆	—	13	2	no	—
384	M₁₆	—	13	2	no	—
385	M₁₆	—	26	4	no	—
386	M₁₆	—	26	4	no	—
387	M₁₆	—	26	1	no	—
388	M₁₆	—	26	1	no	—
389	M₁₆	—	26	2	no	—
390	M₁₆	—	26	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	13	1	no	—
394	C₂×C₈	—	13	1	no	—
395	C₂×C₈	—	13	2	no	—
396	C₂×C₈	—	13	2	no	—
397	C₂×C₈	—	13	1	no	—
398	C₂×C₈	—	13	1	no	—
399	C₂×C₈	—	26	4	no	—
400	C₂×C₈	—	26	4	no	—
401	C₂×C₈	—	26	1	no	—
402	C₂×C₈	—	26	1	no	—
403	C₂×C₈	—	26	1	no	—
404	C₂×C₈	—	26	1	no	—
405	C₂×C₈	—	26	2	no	—
406	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
407	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	26	4	no	—
415	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
416	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
417	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
418	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
419	C₂²⋊C₄	—	2	1	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	1	no	—
422	C₂²⋊C₄	—	2	1	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	1	no	—
425	C₄²	—	2	1	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	26	2	no	—
428	C₄²	—	26	2	no	—
429	C₄²	D₄×D₁₃	1	1	yes	characteristic
430	C₄²	D₄×D₁₃	1	1	yes	characteristic
431	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
432	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
433	C₁₃	#21627	1	1	yes	characteristic, complemented, Sylow
434	C₂³	—	2	1	no	—
435	C₂³	C₂×#6129	1	1	yes	characteristic
436	Q₈	—	2	1	no	—
437	Q₈	—	4	2	no	—
438	Q₈	—	4	2	no	—
439	Q₈	Q₈×Dic₁₃	1	2	yes	—
440	D₄	—	2	2	no	—
441	D₄	—	2	2	no	—
442	D₄	—	2	1	no	—
443	D₄	Q₈×Dic₁₃	1	2	yes	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	26	4	no	—
456	C₂×C₄	—	52	2	no	—
457	C₂×C₄	—	52	2	no	—
458	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
459	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
460	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
461	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
462	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
463	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
464	C₂×C₄	C₂×#6131	1	1	yes	characteristic
465	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
466	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
467	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
468	C₈	—	2	2	no	—
469	C₈	—	2	2	no	—
470	C₈	—	13	2	no	—
471	C₈	—	13	2	no	—
472	C₈	—	26	2	no	—
473	C₈	—	26	1	no	—
474	C₈	—	26	1	no	—
475	C₈	—	26	2	no	—
476	C₈	—	52	2	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	4	1	no	—
481	C₂²	—	4	1	no	—
482	C₂²	#11719327	1	1	yes	characteristic
483	C₂²	#11719329	1	1	yes	characteristic
484	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
485	C₄	—	2	1	no	—
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	2	2	no	—
489	C₄	—	4	1	no	—
490	C₄	—	4	2	no	—
491	C₄	—	4	1	no	—
492	C₄	—	4	2	no	—
493	C₄	—	52	4	no	—
494	C₄	#11718857	1	2	yes	—
495	C₄	D₁₃×C₂²⋊Q₈	1	1	yes	characteristic
496	C₄	#11719332	1	1	yes	characteristic
497	C₄	C₂×Q₈×Dic₁₃	1	1	yes	characteristic
498	C₄	#41×Dic₁₃	1	1	yes	characteristic
499	C₂	—	2	1	no	—
500	C₂	—	2	1	no	—
501	C₂	—	4	2	no	—
502	C₂	C₂²⋊Q₈×Dic₁₃	1	1	yes	characteristic
503	C₂	C₂×#11718857	1	1	yes	characteristic
504	C₂	#13123739	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#3076	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×C₁₃×#41	C₂³
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#3076	D₁₃
hypocenter	C₁₃	#21627
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3076

Complements

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

N	H ≅ G/N	type
1. #13123771	C₂	semidirect
3. #13115781	C₂	semidirect
4. #13115612	C₂	semidirect
5. #13115437	C₂	semidirect
8. #13114717	C₂	semidirect
9. #13114701	C₂	semidirect
16. C₁₃×#479	C₄	semidirect
17. C₁₃×#478	C₄	semidirect
18. C₁₃×#477	C₄	semidirect
19. C₁₃×#476	C₄	semidirect
20. C₁₃×#475	C₄	semidirect
21. C₁₃×#474	C₄	semidirect
72. #88202	Q₈	semidirect
240. #479	Dic₁₃	semidirect
241. #478	Dic₁₃	semidirect
242. #477	Dic₁₃	semidirect
243. #476	Dic₁₃	semidirect
244. #475	Dic₁₃	semidirect
245. #474	Dic₁₃	semidirect
433. C₁₃	#21627	semidirect

Maximal subgroups

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

subgroup	index
#13123771	2
C₄×#88202	2
#13115781	2
#13115612	2
#13115437	2
#13115113	2
#13114856	2
#13114717	2
#13114701	2
#13114676	2
C₁₃×#3076	2
#21627	13