Subgroups — #15865509

Order 3328.

1000 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718786	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11718666	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718666	C₂	1	1	yes	maximal, characteristic
4	C₂×#11718793	C₂	1	1	yes	maximal, characteristic
5	#13123255	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115506	C₂	1	8	yes	maximal, complemented
7	C₂×#11718125	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1733	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#6127	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
13	C₂²×#6099	C₂²	1	1	yes	characteristic
14	C₂²×#6099	C₂²	1	1	yes	characteristic
15	C₂²×#6099	C₂²	1	1	yes	characteristic
16	C₂×#88064	C₄	1	2	yes	complemented
17	#11718793	C₄	1	4	yes	complemented
18	#11718793	C₂²	1	4	yes	—
19	C₂×#88063	C₄	1	2	yes	complemented
20	#11718786	—	2	2	no	—
21	#11718786	C₂²	1	4	yes	complemented
22	C₂×#88059	—	2	2	no	—
23	#11718666	—	2	2	no	—
24	#11718666	—	2	2	no	—
25	#11718666	—	2	2	no	—
26	#11718666	C₂²	1	4	yes	—
27	#11718658	—	2	2	no	—
28	#11718658	—	2	2	no	—
29	C₂×#88045	—	2	2	no	—
30	C₂×#88045	C₂²	1	4	yes	—
31	C₄×#6099	C₂²	1	4	yes	complemented
32	C₁₃×#339	C₂²	1	4	yes	complemented
33	#11718125	C₂²	1	4	yes	complemented
34	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
35	C₂²×C₂²⋊D₁₃	—	2	1	no	—
36	C₂×#6127	—	2	1	no	—
37	C₂×#6127	—	2	1	no	—
38	C₂×#6127	—	2	1	no	—
39	C₂×#6127	—	2	1	no	—
40	C₂×#6127	—	2	1	no	—
41	C₂×#6127	—	2	1	no	—
42	C₂×#6127	—	2	1	no	—
43	C₂×#6127	—	2	1	no	—
44	C₂×#6127	—	2	1	no	—
45	C₂×#6127	—	2	1	no	—
46	C₂×#6127	C₂×C₄	1	2	yes	—
47	C₂×#6127	C₂³	1	2	yes	—
48	C₂²×D₅₂	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₄×D₁₃	—	2	1	no	—
50	C₂²×Dic₂₆	C₂×C₄	1	1	yes	characteristic
51	C₂×C₁₃×M₁₆	—	2	1	no	—
52	C₂×C₁₃×M₁₆	—	2	1	no	—
53	C₂×C₁₃×M₁₆	—	2	1	no	—
54	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
55	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
56	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
57	C₂²×C₈×C₁₃	—	2	1	no	—
58	C₁₃×#117	—	2	1	no	—
59	C₁₃×#117	—	2	1	no	—
60	C₁₃×#117	—	2	1	no	—
61	C₁₃×#117	—	2	1	no	—
62	C₁₃×#117	—	2	1	no	—
63	C₁₃×#117	D₄	1	2	yes	—
64	C₁₃×#117	D₄	1	2	yes	—
65	C₁₃×#117	C₂³	1	2	yes	—
66	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
70	C₂×C₄²×C₁₃	—	2	1	no	—
71	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
72	C₂×#6099	—	2	1	no	—
73	C₂×#6099	—	2	1	no	—
74	C₂×#6099	—	2	1	no	—
75	C₂×#6099	—	2	1	no	—
76	C₂×#6099	—	2	1	no	—
77	C₂×#6099	—	2	1	no	—
78	C₂×#6099	—	2	1	no	—
79	C₂×#6099	—	2	1	no	—
80	C₂×#6099	—	2	1	no	—
81	C₂×#6099	—	2	1	no	—
82	C₂×#6099	—	2	1	no	—
83	C₂×#6099	C₂×C₄	1	2	yes	—
84	C₂×#6099	C₂×C₄	1	2	yes	—
85	C₂×#6099	D₄	1	2	yes	—
86	C₂×#6099	D₄	1	2	yes	—
87	C₂×#6099	C₂³	1	2	yes	—
88	C₂×#6099	C₂³	1	2	yes	—
89	C₂×#6099	C₂³	1	2	yes	—
90	C₂²×#1055	—	2	1	no	—
91	C₂²×#1055	—	2	1	no	—
92	C₂²×#1055	—	2	1	no	—
93	#88064	C₂×C₄	1	8	yes	complemented
94	#88063	C₂×C₄	1	8	yes	complemented
95	#88059	—	2	8	no	—
96	#88045	—	2	8	no	—
97	#88045	—	2	8	no	—
98	#88043	—	2	4	no	—
99	C₄×#1055	—	2	4	no	—
100	#21080	—	13	1	no	maximal, Sylow
101	C₂⁴×C₁₃	#41	1	1	yes	characteristic
102	C₂³×D₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	4	1	no	—
105	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
119	C₂×C₂²⋊D₁₃	—	2	2	no	—
120	C₂×C₂²⋊D₁₃	—	2	2	no	—
121	C₂×C₂²⋊D₁₃	—	4	1	no	—
122	C₂×C₂²⋊D₁₃	—	4	1	no	—
123	C₂×C₂²⋊D₁₃	—	4	1	no	—
124	C₂×C₂²⋊D₁₃	—	4	1	no	—
125	C₂²×Dic₁₃	—	2	1	no	—
126	#6127	—	2	2	no	—
127	#6127	—	2	2	no	—
128	#6127	—	2	2	no	—
129	#6127	—	2	2	no	—
130	#6127	—	2	2	no	—
131	#6127	—	2	2	no	—
132	#6127	—	2	2	no	—
133	#6127	—	2	2	no	—
134	#6127	—	4	1	no	—
135	#6127	—	4	1	no	—
136	#6127	—	4	1	no	—
137	#6127	—	4	1	no	—
138	#6127	—	4	1	no	—
139	#6127	—	4	1	no	—
140	#6127	—	4	1	no	—
141	#6127	—	4	1	no	—
142	C₂×D₅₂	—	2	1	no	—
143	C₂×D₅₂	—	2	1	no	—
144	C₂×D₅₂	—	2	1	no	—
145	C₂×D₅₂	—	2	1	no	—
146	C₂×D₅₂	—	2	1	no	—
147	C₂×D₅₂	C₂²×C₄	1	2	yes	—
148	C₂×C₄×D₁₃	—	2	2	no	—
149	C₂×C₄×D₁₃	—	2	2	no	—
150	C₂×C₄×D₁₃	—	4	1	no	—
151	C₂×C₄×D₁₃	—	4	1	no	—
152	C₂×C₄×D₁₃	—	4	1	no	—
153	C₂×C₄×D₁₃	—	4	1	no	—
154	C₂×Dic₂₆	—	2	1	no	—
155	C₂×Dic₂₆	—	2	1	no	—
156	C₂×Dic₂₆	—	2	1	no	—
157	C₂×Dic₂₆	—	2	1	no	—
158	C₂×Dic₂₆	—	2	1	no	—
159	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
160	C₁₃×M₁₆	—	2	2	no	—
161	C₁₃×M₁₆	—	2	2	no	—
162	C₁₃×M₁₆	—	2	2	no	—
163	C₁₃×M₁₆	C₂²×C₄	1	4	yes	—
164	C₂×C₈×C₁₃	—	2	2	no	—
165	C₂×C₈×C₁₃	—	2	2	no	—
166	C₂×C₈×C₁₃	—	2	2	no	—
167	C₁₃×C₄⋊C₄	—	2	2	no	—
168	C₁₃×C₄⋊C₄	—	2	2	no	—
169	C₁₃×C₄⋊C₄	—	2	2	no	—
170	C₁₃×C₄⋊C₄	—	4	1	no	—
171	C₁₃×C₂²⋊C₄	—	2	2	no	—
172	C₁₃×C₂²⋊C₄	—	2	2	no	—
173	C₁₃×C₂²⋊C₄	—	2	2	no	—
174	C₁₃×C₂²⋊C₄	—	4	1	no	—
175	C₄²×C₁₃	—	2	2	no	—
176	C₄²×C₁₃	—	2	2	no	—
177	C₄²×C₁₃	—	4	1	no	—
178	C₄²×C₁₃	C₂×D₄	1	4	yes	—
179	#6099	—	2	2	no	—
180	#6099	—	2	2	no	—
181	#6099	—	2	2	no	—
182	#6099	—	2	2	no	—
183	#6099	—	2	2	no	—
184	#6099	—	2	2	no	—
185	#6099	—	2	2	no	—
186	#6099	—	2	2	no	—
187	#6099	—	4	1	no	—
188	#6099	—	4	1	no	—
189	#6099	C₂²×C₄	1	4	yes	—
190	#6099	C₂×D₄	1	4	yes	—
191	C₂×#1055	—	2	2	no	—
192	C₂×#1055	—	2	2	no	—
193	C₂×#1055	—	2	2	no	—
194	C₂×#1055	—	2	2	no	—
195	C₂×#1055	—	2	2	no	—
196	C₂×#1055	—	2	2	no	—
197	C₂×#1055	—	2	2	no	—
198	C₂×#1055	—	4	1	no	—
199	C₂×#1055	—	4	1	no	—
200	C₂×#430	—	13	1	no	—
201	C₂×#421	—	13	1	no	—
202	C₂×#421	—	13	1	no	—
203	C₂×#413	—	13	1	no	—
204	#2873	—	13	1	no	—
205	#1932	—	13	8	no	—
206	C₂×#344	—	13	1	no	—
207	#1733	D₁₃	1	1	yes	characteristic, complemented
208	C₂³×C₁₃	—	8	1	no	—
209	C₂³×C₁₃	#117	1	1	yes	characteristic
210	C₂³×C₁₃	#117	1	1	yes	characteristic
211	C₂³×C₁₃	#123	1	1	yes	characteristic
212	C₂³×C₁₃	#123	1	1	yes	characteristic
213	C₂³×C₁₃	#124	1	1	yes	characteristic
214	C₂³×C₁₃	#124	1	1	yes	characteristic
215	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
216	C₂²×D₁₃	—	2	2	no	—
217	C₂²×D₁₃	—	4	1	no	—
218	C₂²×D₁₃	—	4	1	no	—
219	C₂²×D₁₃	—	8	2	no	—
220	C₂×C₄×C₁₃	—	2	4	no	—
221	C₂×C₄×C₁₃	—	4	2	no	—
222	C₂×C₄×C₁₃	—	8	2	no	—
223	C₂×C₄×C₁₃	—	8	2	no	—
224	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
225	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
235	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
236	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
237	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
238	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
239	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
240	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
241	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
242	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
243	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
244	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
245	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
247	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
250	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
251	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
252	C₂²⋊D₁₃	—	4	2	no	—
253	C₂²⋊D₁₃	—	4	2	no	—
254	C₂²⋊D₁₃	—	4	2	no	—
255	C₂²⋊D₁₃	—	4	2	no	—
256	C₂×Dic₁₃	—	2	2	no	—
257	C₂×Dic₁₃	—	4	1	no	—
258	C₂×Dic₁₃	—	4	1	no	—
259	D₅₂	—	2	2	no	—
260	D₅₂	—	2	2	no	—
261	D₅₂	—	4	1	no	—
262	D₅₂	—	4	1	no	—
263	C₄×D₁₃	—	4	2	no	—
264	C₄×D₁₃	—	4	2	no	—
265	C₄×D₁₃	—	4	2	no	—
266	C₄×D₁₃	—	4	2	no	—
267	Dic₂₆	—	2	2	no	—
268	Dic₂₆	—	2	2	no	—
269	Dic₂₆	—	4	1	no	—
270	Dic₂₆	—	4	1	no	—
271	C₈×C₁₃	—	2	4	no	—
272	#1055	—	2	4	no	—
273	#1055	—	2	4	no	—
274	#1055	—	4	2	no	—
275	C₂²×#41	—	13	1	no	—
276	C₂²×M₁₆	—	13	1	no	—
277	C₂²×M₁₆	—	13	1	no	—
278	C₂²×M₁₆	—	13	1	no	—
279	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
280	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
281	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
282	#430	—	13	4	no	—
283	#430	—	26	2	no	—
284	C₂×#108	—	26	2	no	—
285	#421	—	13	4	no	—
286	#421	—	26	2	no	—
287	#421	—	26	2	no	—
288	#421	—	26	2	no	—
289	C₂×#104	—	13	4	no	—
290	C₂×#104	—	26	2	no	—
291	#413	—	13	4	no	—
292	#413	—	13	4	no	—
293	C₂×#101	—	13	2	no	—
294	C₂×#100	—	13	2	no	—
295	#405	—	26	2	no	—
296	#405	—	26	2	no	—
297	C₄×M₁₆	—	13	4	no	—
298	#344	—	13	4	no	—
299	#339	C₂×D₁₃	1	4	yes	complemented
300	C₂²×C₁₃	—	4	1	no	—
301	C₂²×C₁₃	—	4	1	no	—
302	C₂²×C₁₃	—	4	1	no	—
303	C₂²×C₁₃	—	4	1	no	—
304	C₂²×C₁₃	—	4	1	no	—
305	C₂²×C₁₃	—	4	1	no	—
306	C₂²×C₁₃	—	4	1	no	—
307	C₂²×C₁₃	#388	1	1	yes	characteristic
308	C₂²×C₁₃	#388	1	1	yes	characteristic
309	C₂²×C₁₃	#388	1	1	yes	characteristic
310	C₂²×C₁₃	#388	1	1	yes	characteristic
311	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
312	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
313	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
314	C₂×D₁₃	—	4	2	no	—
315	C₂×D₁₃	—	8	2	no	—
316	C₂×D₁₃	—	8	2	no	—
317	C₂×D₁₃	—	8	2	no	—
318	C₄×C₁₃	—	4	4	no	—
319	C₄×C₁₃	—	8	2	no	—
320	C₄×C₁₃	#388	1	1	yes	characteristic
321	C₄×C₁₃	#388	1	1	yes	characteristic
322	C₄×C₁₃	#388	1	1	yes	characteristic
323	C₄×C₁₃	#388	1	1	yes	characteristic
324	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
325	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
326	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
327	C₄×C₁₃	C₂×#126	1	1	yes	characteristic
328	Dic₁₃	—	4	2	no	—
329	C₂×#41	—	13	2	no	—
330	C₂×#41	—	13	2	no	—
331	C₂×#41	—	26	1	no	—
332	C₂×#41	—	26	1	no	—
333	C₂×#41	—	26	1	no	—
334	C₂×#41	—	26	1	no	—
335	C₂×#41	—	26	1	no	—
336	C₂×#41	—	26	1	no	—
337	C₂×#41	—	26	1	no	—
338	C₂×#41	—	26	1	no	—
339	C₂×#41	—	26	1	no	—
340	C₂×#41	—	26	1	no	—
341	C₂²×Q₈	—	13	1	no	—
342	C₂²×D₄	—	13	1	no	—
343	C₂²×D₄	—	26	1	no	—
344	C₂³×C₄	—	26	1	no	—
345	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
346	C₂×M₁₆	—	2	1	no	—
347	C₂×M₁₆	—	2	1	no	—
348	C₂×M₁₆	—	2	1	no	—
349	C₂×M₁₆	—	13	2	no	—
350	C₂×M₁₆	—	13	2	no	—
351	C₂×M₁₆	—	13	2	no	—
352	C₂×M₁₆	—	13	2	no	—
353	C₂×M₁₆	—	13	2	no	—
354	C₂×M₁₆	—	13	2	no	—
355	C₂×M₁₆	—	13	2	no	—
356	C₂×M₁₆	—	26	1	no	—
357	C₂×M₁₆	—	26	1	no	—
358	C₂×M₁₆	—	26	1	no	—
359	C₂×M₁₆	—	26	1	no	—
360	C₂×M₁₆	—	26	1	no	—
361	C₂×M₁₆	—	26	1	no	—
362	C₂×M₁₆	—	26	1	no	—
363	C₂×M₁₆	—	26	1	no	—
364	C₂×M₁₆	—	26	1	no	—
365	C₂×M₁₆	—	26	1	no	—
366	C₂×M₁₆	—	26	1	no	—
367	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
368	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
369	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
370	C₂²×C₈	—	2	1	no	—
371	C₂²×C₈	—	26	1	no	—
372	C₂²×C₈	—	26	1	no	—
373	C₂²×C₈	—	26	1	no	—
374	#117	—	2	1	no	—
375	#117	—	2	1	no	—
376	#117	—	2	1	no	—
377	#117	—	2	1	no	—
378	#117	—	2	1	no	—
379	#117	D₅₂	1	2	yes	—
380	#117	D₅₂	1	2	yes	—
381	#117	C₂²×D₁₃	1	2	yes	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₂²⋊C₄	—	2	1	no	—
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₄²	—	2	1	no	—
387	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
388	#108	—	26	8	no	—
389	#104	—	26	8	no	—
390	#104	—	26	8	no	—
391	#101	—	13	8	no	—
392	#100	—	13	8	no	—
393	#97	—	26	4	no	—
394	C₄×C₈	—	26	4	no	—
395	C₂×C₁₃	—	2	1	no	—
396	C₂×C₁₃	—	2	1	no	—
397	C₂×C₁₃	—	2	1	no	—
398	C₂×C₁₃	—	2	1	no	—
399	C₂×C₁₃	—	2	1	no	—
400	C₂×C₁₃	—	2	1	no	—
401	C₂×C₁₃	—	2	1	no	—
402	C₂×C₁₃	C₂×#388	1	1	yes	characteristic
403	D₁₃	—	8	2	no	—
404	C₂⁴	—	26	1	no	—
405	C₂⁴	#6129	1	1	yes	characteristic
406	#41	—	26	2	no	—
407	#41	—	26	2	no	—
408	#41	—	26	2	no	—
409	#41	—	26	2	no	—
410	#41	—	26	2	no	—
411	#41	—	26	2	no	—
412	#41	—	26	2	no	—
413	#41	—	26	2	no	—
414	#41	—	52	1	no	—
415	#41	—	52	1	no	—
416	#41	—	52	1	no	—
417	#41	—	52	1	no	—
418	#41	—	52	1	no	—
419	#41	—	52	1	no	—
420	#41	—	52	1	no	—
421	#41	—	52	1	no	—
422	C₂×Q₈	—	13	2	no	—
423	C₂×Q₈	—	26	1	no	—
424	C₂×Q₈	—	26	1	no	—
425	C₂×Q₈	—	26	1	no	—
426	C₂×Q₈	—	26	1	no	—
427	C₂×Q₈	—	26	1	no	—
428	C₂×D₄	—	13	2	no	—
429	C₂×D₄	—	26	2	no	—
430	C₂×D₄	—	26	2	no	—
431	C₂×D₄	—	26	1	no	—
432	C₂×D₄	—	26	1	no	—
433	C₂×D₄	—	26	1	no	—
434	C₂×D₄	—	26	1	no	—
435	C₂×D₄	—	26	1	no	—
436	C₂×D₄	—	52	1	no	—
437	C₂×D₄	—	52	1	no	—
438	C₂×D₄	—	52	1	no	—
439	C₂×D₄	—	52	1	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	4	1	no	—
442	C₂²×C₄	—	26	1	no	—
443	C₂²×C₄	—	26	2	no	—
444	C₂²×C₄	—	26	2	no	—
445	C₂²×C₄	—	52	1	no	—
446	C₂²×C₄	—	52	1	no	—
447	C₂²×C₄	—	52	1	no	—
448	C₂²×C₄	—	52	1	no	—
449	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
450	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
453	C₂²×C₄	#6127	1	1	yes	characteristic
454	C₂²×C₄	#6127	1	1	yes	characteristic
455	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
456	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
457	C₂²×C₄	#6129	1	1	yes	characteristic
458	C₂²×C₄	#6129	1	1	yes	characteristic
459	C₂²×C₄	#6129	1	1	yes	characteristic
460	C₂²×C₄	#6131	1	1	yes	characteristic
461	C₂²×C₄	#6131	1	1	yes	characteristic
462	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
463	M₁₆	—	2	2	no	—
464	M₁₆	—	2	2	no	—
465	M₁₆	—	2	2	no	—
466	M₁₆	—	13	4	no	—
467	M₁₆	—	13	4	no	—
468	M₁₆	—	26	2	no	—
469	M₁₆	—	26	2	no	—
470	M₁₆	—	26	2	no	—
471	M₁₆	—	26	2	no	—
472	M₁₆	—	26	2	no	—
473	M₁₆	—	26	2	no	—
474	M₁₆	—	26	2	no	—
475	M₁₆	—	26	2	no	—
476	M₁₆	—	52	1	no	—
477	M₁₆	—	52	1	no	—
478	M₁₆	C₂×C₄×D₁₃	1	4	yes	—
479	C₂×C₈	—	2	2	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	26	2	no	—
483	C₂×C₈	—	26	2	no	—
484	C₂×C₈	—	26	2	no	—
485	C₂×C₈	—	26	2	no	—
486	C₂×C₈	—	26	2	no	—
487	C₂×C₈	—	26	2	no	—
488	C₂×C₈	—	26	2	no	—
489	C₂×C₈	—	52	1	no	—
490	C₂×C₈	—	52	1	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	4	1	no	—
495	C₂²⋊C₄	—	2	2	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	4	1	no	—
499	C₄²	—	2	2	no	—
500	C₄²	—	2	2	no	—
501	C₄²	—	4	1	no	—
502	C₄²	C₂×D₅₂	1	4	yes	—
503	C₁₃	#21080	1	1	yes	characteristic, complemented, Sylow
504	C₂³	—	8	1	no	—
505	C₂³	—	26	2	no	—
506	C₂³	—	52	1	no	—
507	C₂³	—	52	1	no	—
508	C₂³	—	104	2	no	—
509	C₂³	#88139	1	1	yes	characteristic
510	C₂³	#88139	1	1	yes	characteristic
511	C₂³	#88140	1	1	yes	characteristic
512	C₂³	#88140	1	1	yes	characteristic
513	C₂³	#88146	1	1	yes	characteristic
514	C₂³	#88146	1	1	yes	characteristic
515	C₂³	C₂×#6129	1	1	yes	characteristic
516	Q₈	—	26	2	no	—
517	Q₈	—	26	2	no	—
518	Q₈	—	52	1	no	—
519	Q₈	—	52	1	no	—
520	D₄	—	26	2	no	—
521	D₄	—	26	2	no	—
522	D₄	—	52	2	no	—
523	D₄	—	52	2	no	—
524	D₄	—	52	2	no	—
525	D₄	—	52	2	no	—
526	D₄	—	52	1	no	—
527	D₄	—	52	1	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	8	2	no	—
531	C₂×C₄	—	8	2	no	—
532	C₂×C₄	—	26	2	no	—
533	C₂×C₄	—	52	1	no	—
534	C₂×C₄	—	52	1	no	—
535	C₂×C₄	—	52	2	no	—
536	C₂×C₄	—	52	2	no	—
537	C₂×C₄	—	52	2	no	—
538	C₂×C₄	—	52	2	no	—
539	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
540	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
541	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
542	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
543	C₂×C₄	#88135	1	1	yes	characteristic
544	C₂×C₄	#88135	1	1	yes	characteristic
545	C₂×C₄	#88135	1	1	yes	characteristic
546	C₂×C₄	#88135	1	1	yes	characteristic
547	C₂×C₄	#88139	1	1	yes	characteristic
548	C₂×C₄	#88139	1	1	yes	characteristic
549	C₂×C₄	#88140	1	1	yes	characteristic
550	C₂×C₄	#88140	1	1	yes	characteristic
551	C₂×C₄	#88146	1	1	yes	characteristic
552	C₂×C₄	#88146	1	1	yes	characteristic
553	C₂×C₄	#88149	1	1	yes	characteristic
554	C₂×C₄	#88149	1	1	yes	characteristic
555	C₂×C₄	#88149	1	1	yes	characteristic
556	C₂×C₄	#88149	1	1	yes	characteristic
557	C₂×C₄	#88152	1	1	yes	characteristic
558	C₂×C₄	#88152	1	1	yes	characteristic
559	C₂×C₄	#88152	1	1	yes	characteristic
560	C₂×C₄	#88152	1	1	yes	characteristic
561	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
562	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
563	C₂×C₄	C₂×#6127	1	1	yes	characteristic
564	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
565	C₂×C₄	C₂×#6129	1	1	yes	characteristic
566	C₂×C₄	C₂×#6131	1	1	yes	characteristic
567	C₈	—	2	4	no	—
568	C₈	—	26	4	no	—
569	C₈	—	26	4	no	—
570	C₈	—	52	2	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	52	2	no	—
579	C₂²	—	104	2	no	—
580	C₂²	—	104	2	no	—
581	C₂²	—	104	2	no	—
582	C₂²	#11718331	1	1	yes	characteristic
583	C₂²	#11718331	1	1	yes	characteristic
584	C₂²	#11718331	1	1	yes	characteristic
585	C₂²	#11718331	1	1	yes	characteristic
586	C₂²	C₂×#88139	1	1	yes	characteristic
587	C₂²	C₂×#88140	1	1	yes	characteristic
588	C₂²	C₂×#88146	1	1	yes	characteristic
589	C₄	—	4	4	no	—
590	C₄	—	8	2	no	—
591	C₄	—	52	2	no	—
592	C₄	#11718331	1	1	yes	characteristic
593	C₄	#11718331	1	1	yes	characteristic
594	C₄	#11718331	1	1	yes	characteristic
595	C₄	#11718331	1	1	yes	characteristic
596	C₄	C₂×C₄×D₅₂	1	1	yes	characteristic
597	C₄	C₂×#88135	1	1	yes	characteristic
598	C₄	C₂×#88149	1	1	yes	characteristic
599	C₄	C₂×#88152	1	1	yes	characteristic
600	C₂	—	2	1	no	—
601	C₂	—	2	1	no	—
602	C₂	—	2	1	no	—
603	C₂	—	2	1	no	—
604	C₂	—	2	1	no	—
605	C₂	—	2	1	no	—
606	C₂	—	2	1	no	—
607	C₂	—	104	2	no	—
608	C₂	C₂×#11718331	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#88149
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#1733	C₂
socle	C₂×C₁₃	C₂×#388
prime radical	C₂²×#6127	C₂²
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#1733	D₁₃
hypocenter	C₁₃	#21080
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ #1733

Complements

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

N	H ≅ G/N	type
1. C₂×#11718786	C₂	semidirect
5. #13123255	C₂	semidirect
6. #13115506	C₂	semidirect
7. C₂×#11718125	C₂	semidirect
8. C₁₃×#1733	C₂	semidirect
16. C₂×#88064	C₄	semidirect
17. #11718793	C₄	semidirect
19. C₂×#88063	C₄	semidirect
21. #11718786	C₂²	semidirect
31. C₄×#6099	C₂²	semidirect
32. C₁₃×#339	C₂²	semidirect
33. #11718125	C₂²	semidirect
93. #88064	C₂×C₄	semidirect
94. #88063	C₂×C₄	semidirect
207. #1733	D₁₃	semidirect
299. #339	C₂×D₁₃	semidirect
503. C₁₃	#21080	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718786	2
C₂×#11718666	2
C₂×#11718793	2
#13123255	2
#13115506	2
C₂×#11718125	2
C₁₃×#1733	2
#21080	13