Subgroups — #15770748

Order 3328.

886 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88045	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718663	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718790	C₂	1	1	yes	maximal, characteristic
4	C₂×#11718150	C₂	1	1	yes	maximal, characteristic, complemented
5	#13114533	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11718116	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#339	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#6127	C₂²	1	1	yes	characteristic
9	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
11	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
12	C₂²×#6099	C₂²	1	1	yes	characteristic
13	C₂³×#1055	C₂²	1	1	yes	characteristic
14	C₂³×#1055	C₂²	1	1	yes	characteristic
15	#11718790	—	2	2	no	—
16	#11718790	—	2	2	no	—
17	C₂×#88060	—	2	2	no	—
18	#11718663	—	2	2	no	—
19	#11718663	—	2	2	no	—
20	C₂×#88050	C₄	1	2	yes	complemented
21	C₂×#88049	C₄	1	2	yes	complemented
22	C₂×#88045	—	2	2	no	—
23	C₂×#88045	—	2	2	no	—
24	C₂×#88045	—	2	2	no	—
25	C₁₃×#339	—	2	2	no	—
26	#11718150	—	2	2	no	—
27	#11718116	—	2	2	no	—
28	#11718116	—	2	2	no	—
29	C₂³×C₄×C₁₃	—	2	1	no	—
30	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
31	C₂²×C₂²⋊D₁₃	—	2	1	no	—
32	C₂×#6127	—	2	1	no	—
33	C₂×#6127	—	2	1	no	—
34	C₂×#6127	—	2	1	no	—
35	C₂×#6127	—	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	D₄	1	2	yes	—
43	C₂×#6127	D₄	1	2	yes	—
44	C₂²×D₅₂	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₄×D₁₃	—	2	1	no	—
46	C₂²×Dic₂₆	C₂×C₄	1	1	yes	characteristic
47	C₂×C₁₃×M₁₆	—	2	1	no	—
48	C₂×C₁₃×M₁₆	—	2	1	no	—
49	C₂×C₁₃×M₁₆	—	2	1	no	—
50	C₂×C₁₃×M₁₆	—	2	1	no	—
51	C₂×C₁₃×M₁₆	—	2	1	no	—
52	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
53	C₂²×C₈×C₁₃	—	2	1	no	—
54	C₁₃×#117	—	2	1	no	—
55	C₁₃×#117	—	2	1	no	—
56	C₁₃×#117	—	2	1	no	—
57	C₁₃×#117	—	2	1	no	—
58	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
59	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
60	C₂×C₄²×C₁₃	—	2	1	no	—
61	C₂×C₄²×C₁₃	—	2	1	no	—
62	C₂×C₄²×C₁₃	—	2	1	no	—
63	C₂×C₄²×C₁₃	—	2	1	no	—
64	C₂×C₄²×C₁₃	—	2	1	no	—
65	C₂×C₄²×C₁₃	—	2	1	no	—
66	C₂×C₄²×C₁₃	D₄	1	2	yes	—
67	C₂×#6099	—	2	1	no	—
68	C₂×#6099	—	2	1	no	—
69	C₂×#6099	—	2	1	no	—
70	C₂×#6099	—	2	1	no	—
71	C₂×#6099	—	2	1	no	—
72	C₂×#6099	D₄	1	2	yes	—
73	C₂²×#1055	—	2	1	no	—
74	C₂²×#1055	—	2	1	no	—
75	C₂²×#1055	—	2	1	no	—
76	C₂²×#1055	—	2	1	no	—
77	C₂²×#1055	—	2	1	no	—
78	C₂²×#1055	—	2	1	no	—
79	C₂²×#1055	—	2	1	no	—
80	C₂²×#1055	—	2	1	no	—
81	C₂²×#1055	—	2	1	no	—
82	C₂²×#1055	—	2	1	no	—
83	C₂²×#1055	—	2	1	no	—
84	C₂²×#1055	—	2	1	no	—
85	C₂²×#1055	—	2	1	no	—
86	C₂²×#1055	C₂×C₄	1	2	yes	—
87	C₂²×#1055	D₄	1	2	yes	—
88	#88060	—	2	8	no	—
89	#88050	—	2	4	no	—
90	#88049	—	2	4	no	—
91	#88045	—	2	8	no	—
92	#11191	—	13	1	no	maximal, Sylow
93	C₂⁴×C₁₃	#41	1	1	yes	characteristic
94	C₂³×D₁₃	—	2	1	no	—
95	C₂²×C₄×C₁₃	—	2	4	no	—
96	C₂²×C₄×C₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₃	—	4	2	no	—
99	C₂²×C₄×C₁₃	—	4	1	no	—
100	C₂²×C₄×C₁₃	—	4	1	no	—
101	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂×D₄	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×C₄×C₁₃	#41	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	#41	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	C₂×C₂²⋊D₁₃	—	2	2	no	—
116	C₂×C₂²⋊D₁₃	—	2	2	no	—
117	C₂×C₂²⋊D₁₃	—	4	1	no	—
118	C₂×C₂²⋊D₁₃	—	4	1	no	—
119	C₂×C₂²⋊D₁₃	—	4	1	no	—
120	C₂×C₂²⋊D₁₃	—	4	1	no	—
121	C₂²×Dic₁₃	—	2	1	no	—
122	#6127	—	2	2	no	—
123	#6127	—	2	2	no	—
124	#6127	—	2	2	no	—
125	#6127	—	2	2	no	—
126	#6127	—	2	2	no	—
127	#6127	—	2	2	no	—
128	#6127	—	2	2	no	—
129	#6127	—	2	2	no	—
130	#6127	—	4	1	no	—
131	#6127	—	4	1	no	—
132	#6127	—	4	1	no	—
133	#6127	—	4	1	no	—
134	#6127	—	4	1	no	—
135	#6127	—	4	1	no	—
136	#6127	—	4	1	no	—
137	#6127	—	4	1	no	—
138	C₂×D₅₂	—	2	1	no	—
139	C₂×D₅₂	—	2	1	no	—
140	C₂×D₅₂	—	2	1	no	—
141	C₂×D₅₂	—	2	1	no	—
142	C₂×D₅₂	—	2	1	no	—
143	C₂×D₅₂	C₂²⋊C₄	1	2	yes	—
144	C₂×C₄×D₁₃	—	2	2	no	—
145	C₂×C₄×D₁₃	—	2	2	no	—
146	C₂×C₄×D₁₃	—	4	1	no	—
147	C₂×C₄×D₁₃	—	4	1	no	—
148	C₂×C₄×D₁₃	—	4	1	no	—
149	C₂×C₄×D₁₃	—	4	1	no	—
150	C₂×Dic₂₆	—	2	1	no	—
151	C₂×Dic₂₆	—	2	1	no	—
152	C₂×Dic₂₆	—	2	1	no	—
153	C₂×Dic₂₆	—	2	1	no	—
154	C₂×Dic₂₆	—	2	1	no	—
155	C₂×Dic₂₆	C₂²⋊C₄	1	2	yes	—
156	C₁₃×M₁₆	—	2	2	no	—
157	C₁₃×M₁₆	—	2	2	no	—
158	C₁₃×M₁₆	—	4	1	no	—
159	C₁₃×M₁₆	—	4	1	no	—
160	C₂×C₈×C₁₃	—	2	2	no	—
161	C₂×C₈×C₁₃	—	4	1	no	—
162	C₂×C₈×C₁₃	—	4	1	no	—
163	C₁₃×C₄⋊C₄	—	2	2	no	—
164	C₁₃×C₄⋊C₄	—	2	2	no	—
165	C₁₃×C₂²⋊C₄	—	4	1	no	—
166	C₁₃×C₂²⋊C₄	—	4	1	no	—
167	C₄²×C₁₃	—	2	2	no	—
168	C₄²×C₁₃	—	2	2	no	—
169	C₄²×C₁₃	—	4	1	no	—
170	C₄²×C₁₃	—	4	1	no	—
171	C₄²×C₁₃	—	4	1	no	—
172	C₄²×C₁₃	—	4	1	no	—
173	#6099	—	2	2	no	—
174	#6099	—	2	2	no	—
175	#6099	—	4	1	no	—
176	#6099	—	4	1	no	—
177	C₂×#1055	—	2	2	no	—
178	C₂×#1055	—	2	2	no	—
179	C₂×#1055	—	2	2	no	—
180	C₂×#1055	—	2	2	no	—
181	C₂×#1055	—	2	2	no	—
182	C₂×#1055	—	2	2	no	—
183	C₂×#1055	—	2	2	no	—
184	C₂×#1055	—	4	1	no	—
185	C₂×#1055	—	4	1	no	—
186	C₂×#1055	—	4	1	no	—
187	C₂×#1055	—	4	1	no	—
188	C₂×#1055	—	4	1	no	—
189	C₂×#1055	—	4	1	no	—
190	C₂×#1055	—	4	1	no	—
191	C₂×#1055	—	4	1	no	—
192	C₂×#1055	—	4	1	no	—
193	C₂×#1055	—	4	1	no	—
194	C₂²×#104	—	13	1	no	—
195	C₂×#416	—	13	1	no	—
196	C₂×#408	—	13	1	no	—
197	C₂×#341	—	13	1	no	—
198	C₂×#339	D₁₃	1	1	yes	characteristic, complemented
199	#1729	—	13	1	no	—
200	C₂×#336	—	13	1	no	—
201	C₂³×C₁₃	—	2	2	no	—
202	C₂³×C₁₃	—	2	2	no	—
203	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
204	C₂³×C₁₃	#121	1	1	yes	characteristic
205	C₂³×C₁₃	#123	1	1	yes	characteristic
206	C₂³×C₁₃	#123	1	1	yes	characteristic
207	C₂³×C₁₃	#124	1	1	yes	characteristic
208	C₂³×C₁₃	#126	1	1	yes	characteristic
209	C₂³×C₁₃	#126	1	1	yes	characteristic
210	C₂²×D₁₃	—	2	2	no	—
211	C₂²×D₁₃	—	4	1	no	—
212	C₂²×D₁₃	—	4	1	no	—
213	C₂²×D₁₃	—	4	2	no	—
214	C₂²×D₁₃	—	4	2	no	—
215	C₂×C₄×C₁₃	—	2	4	no	—
216	C₂×C₄×C₁₃	—	4	4	no	—
217	C₂×C₄×C₁₃	—	4	4	no	—
218	C₂×C₄×C₁₃	—	4	2	no	—
219	C₂×C₄×C₁₃	—	4	2	no	—
220	C₂×C₄×C₁₃	—	4	2	no	—
221	C₂×C₄×C₁₃	—	4	2	no	—
222	C₂×C₄×C₁₃	—	4	2	no	—
223	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
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	#120	1	1	yes	characteristic
230	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
231	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
232	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
233	C₂×C₄×C₁₃	#121	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	#123	1	1	yes	characteristic
241	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
242	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
243	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
244	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
245	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
246	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
247	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
248	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
249	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
250	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
251	C₂²⋊D₁₃	—	4	2	no	—
252	C₂²⋊D₁₃	—	4	2	no	—
253	C₂²⋊D₁₃	—	4	2	no	—
254	C₂²⋊D₁₃	—	4	2	no	—
255	C₂×Dic₁₃	—	2	2	no	—
256	C₂×Dic₁₃	—	4	1	no	—
257	C₂×Dic₁₃	—	4	1	no	—
258	D₅₂	—	2	2	no	—
259	D₅₂	—	2	2	no	—
260	D₅₂	—	4	1	no	—
261	D₅₂	—	4	1	no	—
262	C₄×D₁₃	—	4	2	no	—
263	C₄×D₁₃	—	4	2	no	—
264	C₄×D₁₃	—	4	2	no	—
265	C₄×D₁₃	—	4	2	no	—
266	Dic₂₆	—	2	2	no	—
267	Dic₂₆	—	2	2	no	—
268	Dic₂₆	—	4	1	no	—
269	Dic₂₆	—	4	1	no	—
270	C₈×C₁₃	—	4	2	no	—
271	#1055	—	4	2	no	—
272	#1055	—	4	2	no	—
273	#1055	—	4	2	no	—
274	C₂²×#41	—	13	1	no	—
275	C₂²×M₁₆	—	13	1	no	—
276	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
277	C₂³×C₈	—	13	1	no	—
278	C₂³×C₈	—	13	1	no	—
279	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
280	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
281	C₂×#104	—	26	2	no	—
282	C₂×#104	—	26	2	no	—
283	C₂×#104	—	26	2	no	—
284	#416	—	26	2	no	—
285	#416	—	26	2	no	—
286	C₂×#103	—	13	2	no	—
287	C₂×#102	—	13	2	no	—
288	#408	—	26	2	no	—
289	#408	—	26	2	no	—
290	C₂×C₂²⋊C₈	—	26	2	no	—
291	#341	—	26	2	no	—
292	#339	—	2	2	no	—
293	#336	—	26	2	no	—
294	#336	—	26	2	no	—
295	C₂²×C₁₃	—	2	2	no	—
296	C₂²×C₁₃	—	2	2	no	—
297	C₂²×C₁₃	—	2	2	no	—
298	C₂²×C₁₃	—	2	2	no	—
299	C₂²×C₁₃	—	2	1	no	—
300	C₂²×C₁₃	—	2	1	no	—
301	C₂²×C₁₃	—	2	1	no	—
302	C₂²×C₁₃	—	2	1	no	—
303	C₂²×C₁₃	#386	1	1	yes	characteristic
304	C₂²×C₁₃	#388	1	1	yes	characteristic
305	C₂²×C₁₃	#388	1	1	yes	characteristic
306	C₂²×C₁₃	#394	1	1	yes	characteristic
307	C₂²×C₁₃	#397	1	1	yes	characteristic
308	C₂²×C₁₃	#397	1	1	yes	characteristic
309	C₂²×C₁₃	#397	1	1	yes	characteristic
310	C₂²×C₁₃	#443	1	2	yes	—
311	C₂²×C₁₃	#444	1	2	yes	—
312	C₂×D₁₃	—	4	4	no	—
313	C₂×D₁₃	—	4	2	no	—
314	C₂×D₁₃	—	8	2	no	—
315	C₂×D₁₃	—	8	1	no	—
316	C₂×D₁₃	—	8	1	no	—
317	C₄×C₁₃	—	4	4	no	—
318	C₄×C₁₃	—	8	2	no	—
319	C₄×C₁₃	#381	1	1	yes	characteristic
320	C₄×C₁₃	#386	1	1	yes	characteristic
321	C₄×C₁₃	#388	1	1	yes	characteristic
322	C₄×C₁₃	#388	1	1	yes	characteristic
323	C₄×C₁₃	#394	1	1	yes	characteristic
324	C₄×C₁₃	#394	1	1	yes	characteristic
325	C₄×C₁₃	#394	1	1	yes	characteristic
326	C₄×C₁₃	#397	1	1	yes	characteristic
327	Dic₁₃	—	4	2	no	—
328	C₂×#41	—	13	2	no	—
329	C₂×#41	—	13	2	no	—
330	C₂×#41	—	26	1	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	C₂²×Q₈	—	13	1	no	—
341	C₂²×D₄	—	13	1	no	—
342	C₂²×D₄	—	26	1	no	—
343	C₂³×C₄	—	2	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	—	2	1	no	—
350	C₂×M₁₆	—	2	1	no	—
351	C₂×M₁₆	—	13	2	no	—
352	C₂×M₁₆	—	26	1	no	—
353	C₂×M₁₆	—	26	1	no	—
354	C₂×M₁₆	—	26	1	no	—
355	C₂×M₁₆	—	26	1	no	—
356	C₂×M₁₆	—	26	1	no	—
357	C₂×M₁₆	C₂²⋊D₁₃	1	2	yes	—
358	C₂²×C₈	—	2	1	no	—
359	C₂²×C₈	—	13	2	no	—
360	C₂²×C₈	—	13	2	no	—
361	C₂²×C₈	—	26	1	no	—
362	C₂²×C₈	—	26	1	no	—
363	C₂²×C₈	—	26	1	no	—
364	C₂²×C₈	—	26	1	no	—
365	C₂²×C₈	—	26	1	no	—
366	C₂²×C₈	—	26	1	no	—
367	C₂²×C₈	—	26	1	no	—
368	C₂²×C₈	—	26	1	no	—
369	C₂²×C₈	—	26	1	no	—
370	C₂²×C₈	—	26	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	C₂×C₄⋊C₄	C₄×D₁₃	1	2	yes	—
379	C₂×C₂²⋊C₄	—	2	1	no	—
380	C₂×C₄²	—	2	1	no	—
381	C₂×C₄²	—	2	1	no	—
382	C₂×C₄²	—	2	1	no	—
383	C₂×C₄²	—	2	1	no	—
384	C₂×C₄²	—	2	1	no	—
385	C₂×C₄²	—	2	1	no	—
386	C₂×C₄²	D₅₂	1	2	yes	—
387	#104	—	26	8	no	—
388	#103	—	26	4	no	—
389	#102	—	26	4	no	—
390	C₂²⋊C₈	—	26	8	no	—
391	C₂×C₁₃	—	2	1	no	—
392	C₂×C₁₃	—	2	1	no	—
393	C₂×C₁₃	—	2	1	no	—
394	C₂×C₁₃	—	2	1	no	—
395	C₂×C₁₃	#1440	1	1	yes	characteristic
396	C₂×C₁₃	#1876	1	2	yes	—
397	C₂×C₁₃	#1929	1	2	yes	—
398	C₂×C₁₃	#1937	1	1	yes	characteristic
399	C₂×C₁₃	#1938	1	1	yes	characteristic
400	D₁₃	—	8	2	no	—
401	C₂⁴	—	26	1	no	—
402	C₂⁴	#6129	1	1	yes	characteristic
403	#41	—	26	2	no	—
404	#41	—	26	2	no	—
405	#41	—	26	2	no	—
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	—	52	1	no	—
412	#41	—	52	1	no	—
413	#41	—	52	1	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	C₂×Q₈	—	13	2	no	—
420	C₂×Q₈	—	26	1	no	—
421	C₂×Q₈	—	26	1	no	—
422	C₂×Q₈	—	26	1	no	—
423	C₂×Q₈	—	26	1	no	—
424	C₂×Q₈	—	26	1	no	—
425	C₂×D₄	—	13	2	no	—
426	C₂×D₄	—	26	2	no	—
427	C₂×D₄	—	26	2	no	—
428	C₂×D₄	—	26	1	no	—
429	C₂×D₄	—	26	1	no	—
430	C₂×D₄	—	26	1	no	—
431	C₂×D₄	—	26	1	no	—
432	C₂×D₄	—	26	1	no	—
433	C₂×D₄	—	52	1	no	—
434	C₂×D₄	—	52	1	no	—
435	C₂×D₄	—	52	1	no	—
436	C₂×D₄	—	52	1	no	—
437	C₂²×C₄	—	2	4	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	4	2	no	—
441	C₂²×C₄	—	4	1	no	—
442	C₂²×C₄	—	4	1	no	—
443	C₂²×C₄	—	26	1	no	—
444	C₂²×C₄	—	26	2	no	—
445	C₂²×C₄	—	26	2	no	—
446	C₂²×C₄	—	52	1	no	—
447	C₂²×C₄	—	52	1	no	—
448	C₂²×C₄	—	52	1	no	—
449	C₂²×C₄	—	52	1	no	—
450	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
452	C₂²×C₄	#6127	1	1	yes	characteristic
453	C₂²×C₄	#6127	1	1	yes	characteristic
454	C₂²×C₄	#6127	1	1	yes	characteristic
455	C₂²×C₄	#6127	1	1	yes	characteristic
456	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
457	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
458	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
459	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
460	C₂²×C₄	#6129	1	1	yes	characteristic
461	C₂²×C₄	#6131	1	1	yes	characteristic
462	C₂²×C₄	#6131	1	1	yes	characteristic
463	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
464	M₁₆	—	2	2	no	—
465	M₁₆	—	2	2	no	—
466	M₁₆	—	4	1	no	—
467	M₁₆	—	4	1	no	—
468	M₁₆	—	26	2	no	—
469	M₁₆	—	26	2	no	—
470	M₁₆	—	52	1	no	—
471	M₁₆	—	52	1	no	—
472	C₂×C₈	—	2	2	no	—
473	C₂×C₈	—	4	1	no	—
474	C₂×C₈	—	4	1	no	—
475	C₂×C₈	—	26	2	no	—
476	C₂×C₈	—	26	2	no	—
477	C₂×C₈	—	26	2	no	—
478	C₂×C₈	—	26	2	no	—
479	C₂×C₈	—	26	2	no	—
480	C₂×C₈	—	26	2	no	—
481	C₂×C₈	—	26	2	no	—
482	C₂×C₈	—	52	1	no	—
483	C₂×C₈	—	52	1	no	—
484	C₂×C₈	—	52	1	no	—
485	C₂×C₈	—	52	1	no	—
486	C₂×C₈	—	52	1	no	—
487	C₂×C₈	—	52	1	no	—
488	C₂×C₈	—	52	1	no	—
489	C₂×C₈	—	52	1	no	—
490	C₂×C₈	—	52	1	no	—
491	C₂×C₈	—	52	1	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₂²⋊C₄	—	4	1	no	—
495	C₂²⋊C₄	—	4	1	no	—
496	C₄²	—	2	2	no	—
497	C₄²	—	2	2	no	—
498	C₄²	—	4	1	no	—
499	C₄²	—	4	1	no	—
500	C₄²	—	4	1	no	—
501	C₄²	—	4	1	no	—
502	C₁₃	#11191	1	1	yes	characteristic, complemented, Sylow
503	C₂³	—	2	2	no	—
504	C₂³	—	2	2	no	—
505	C₂³	—	26	2	no	—
506	C₂³	—	52	2	no	—
507	C₂³	—	52	2	no	—
508	C₂³	—	52	1	no	—
509	C₂³	—	52	1	no	—
510	C₂³	#88135	1	1	yes	characteristic
511	C₂³	#88137	1	1	yes	characteristic
512	C₂³	#88139	1	1	yes	characteristic
513	C₂³	#88140	1	1	yes	characteristic
514	C₂³	#88152	1	1	yes	characteristic
515	C₂³	#88152	1	1	yes	characteristic
516	C₂³	#88192	1	1	yes	characteristic
517	Q₈	—	26	2	no	—
518	Q₈	—	26	2	no	—
519	Q₈	—	52	1	no	—
520	Q₈	—	52	1	no	—
521	D₄	—	26	2	no	—
522	D₄	—	26	2	no	—
523	D₄	—	52	2	no	—
524	D₄	—	52	2	no	—
525	D₄	—	52	2	no	—
526	D₄	—	52	2	no	—
527	D₄	—	52	1	no	—
528	D₄	—	52	1	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	4	4	no	—
531	C₂×C₄	—	4	4	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	26	2	no	—
538	C₂×C₄	—	52	1	no	—
539	C₂×C₄	—	52	1	no	—
540	C₂×C₄	—	52	2	no	—
541	C₂×C₄	—	52	2	no	—
542	C₂×C₄	—	52	2	no	—
543	C₂×C₄	—	52	2	no	—
544	C₂×C₄	#88126	1	1	yes	characteristic
545	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
546	C₂×C₄	#88129	1	1	yes	characteristic
547	C₂×C₄	#88130	1	1	yes	characteristic
548	C₂×C₄	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
549	C₂×C₄	#88136	1	1	yes	characteristic
550	C₂×C₄	#88137	1	1	yes	characteristic
551	C₂×C₄	#88137	1	1	yes	characteristic
552	C₂×C₄	#88138	1	1	yes	characteristic
553	C₂×C₄	#88138	1	1	yes	characteristic
554	C₂×C₄	#88138	1	1	yes	characteristic
555	C₂×C₄	#88139	1	1	yes	characteristic
556	C₂×C₄	#88146	1	1	yes	characteristic
557	C₂×C₄	#88147	1	1	yes	characteristic
558	C₂×C₄	#88148	1	1	yes	characteristic
559	C₂×C₄	#88148	1	1	yes	characteristic
560	C₂×C₄	#88148	1	1	yes	characteristic
561	C₂×C₄	#88148	1	1	yes	characteristic
562	C₂×C₄	#88148	1	1	yes	characteristic
563	C₂×C₄	#88149	1	1	yes	characteristic
564	C₂×C₄	#88149	1	1	yes	characteristic
565	C₂×C₄	#88152	1	1	yes	characteristic
566	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
567	C₂×C₄	#88183	1	1	yes	characteristic
568	C₂×C₄	#88184	1	1	yes	characteristic
569	C₂×C₄	#88191	1	1	yes	characteristic
570	C₂×C₄	#88193	1	1	yes	characteristic
571	C₂×C₄	#88201	1	1	yes	characteristic
572	C₈	—	4	2	no	—
573	C₈	—	52	2	no	—
574	C₈	—	52	2	no	—
575	C₈	—	52	2	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	2	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	52	4	no	—
585	C₂²	—	52	2	no	—
586	C₂²	—	104	2	no	—
587	C₂²	—	104	1	no	—
588	C₂²	—	104	1	no	—
589	C₂²	#11718330	1	1	yes	characteristic
590	C₂²	#11718331	1	1	yes	characteristic
591	C₂²	#11718335	1	1	yes	characteristic
592	C₂²	#11718336	1	1	yes	characteristic
593	C₂²	#11718484	1	2	yes	—
594	C₂²	#11718485	1	2	yes	—
595	C₂²	#11718617	1	1	yes	characteristic
596	C₂²	#11718622	1	1	yes	characteristic
597	C₂²	#11718654	1	1	yes	characteristic
598	C₄	—	4	4	no	—
599	C₄	—	8	2	no	—
600	C₄	—	52	2	no	—
601	C₄	#11718325	1	1	yes	characteristic
602	C₄	#11718326	1	1	yes	characteristic
603	C₄	#11718333	1	1	yes	characteristic
604	C₄	#11718336	1	1	yes	characteristic
605	C₄	#11718601	1	1	yes	characteristic
606	C₄	#11718620	1	1	yes	characteristic
607	C₄	#11718651	1	1	yes	characteristic
608	C₄	#11718652	1	1	yes	characteristic
609	C₂	—	2	1	no	—
610	C₂	—	2	1	no	—
611	C₂	—	2	1	no	—
612	C₂	—	2	1	no	—
613	C₂	—	104	2	no	—
614	C₂	#13113084	1	1	yes	characteristic
615	C₂	#13115160	1	2	yes	—
616	C₂	#13115482	1	2	yes	—
617	C₂	#13115541	1	1	yes	characteristic
618	C₂	#13115548	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₃
commutator	C₂²×C₄×C₁₃	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₃
Fitting	C₂×C₁₃×#339	C₂
socle	C₂³×C₁₃	C₄×D₄
prime radical	C₂²×#6127	C₂²
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	C₂×#339	D₁₃
hypocenter	C₁₃	#11191
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂×#339

Complements

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

N	H ≅ G/N	type
4. C₂×#11718150	C₂	semidirect
5. #13114533	C₂	semidirect
6. C₂×#11718116	C₂	semidirect
7. C₂×C₁₃×#339	C₂	semidirect
20. C₂×#88050	C₄	semidirect
21. C₂×#88049	C₄	semidirect
198. C₂×#339	D₁₃	semidirect
502. C₁₃	#11191	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#88045	2
C₂×#11718663	2
C₂×#11718790	2
C₂×#11718150	2
#13114533	2
C₂×#11718116	2
C₂×C₁₃×#339	2
#11191	13