Subgroups — #15885423

Order 3328.

892 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13124291	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718485	C₂	1	2	yes	maximal, complemented
3	#13123582	C₂	1	1	yes	maximal, characteristic, complemented
4	#13123404	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115664	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115611	C₂	1	1	yes	maximal, characteristic, complemented
7	#13115541	C₂	1	2	yes	maximal, complemented
8	#13115161	C₂	1	2	yes	maximal, complemented
9	#13115112	C₂	1	2	yes	maximal, complemented
10	C₄×C₄⋊#1055	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×#104	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₂×#88204	C₂²	1	2	yes	—
14	C₂×#88202	C₂²	1	2	yes	—
15	C₂×#88161	C₂²	1	2	yes	—
16	#11719182	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
19	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
20	C₄³×C₁₃	C₂²	1	1	yes	characteristic
21	#11718790	C₂²	1	2	yes	—
22	C₂×#88062	C₂²	1	2	yes	—
23	#11718692	C₄	1	1	yes	characteristic, complemented
24	#11718689	C₄	1	2	yes	complemented
25	#11718688	C₄	1	1	yes	characteristic, complemented
26	#11718680	C₄	1	1	yes	characteristic, complemented
27	#11718677	C₄	1	2	yes	complemented
28	#11718676	C₄	1	1	yes	characteristic, complemented
29	#11718663	C₂²	1	2	yes	—
30	#11718660	—	2	2	no	—
31	#11718660	C₂²	1	2	yes	—
32	C₂×#88045	C₂²	1	2	yes	—
33	C₂×#88045	C₂²	1	2	yes	—
34	#11718585	—	2	1	no	—
35	#11718585	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊#1055	—	2	1	no	—
37	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
39	C₂×C₄×#1055	C₂²	1	2	yes	—
40	#11718485	—	2	8	no	—
41	#11718367	—	2	2	no	—
42	#11718349	—	2	1	no	—
43	C₈×D₅₂	—	2	1	no	—
44	C₁₃×#339	C₂²	1	1	yes	characteristic
45	C₁₃×#339	C₂²	1	1	yes	characteristic
46	#11718150	C₂²	1	2	yes	—
47	#11718116	C₂²	1	2	yes	—
48	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
49	C₂×#6127	C₂³	1	2	yes	—
50	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
51	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
52	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
53	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
54	C₄×D₄×C₁₃	—	2	1	no	—
55	C₄×D₄×C₁₃	—	2	1	no	—
56	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
57	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
58	C₁₃×#117	—	2	1	no	—
59	C₁₃×#117	C₂³	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
66	#88204	—	2	4	no	—
67	#88204	—	2	4	no	—
68	#88202	—	2	4	no	—
69	#88202	—	4	2	no	—
70	C₂×#6107	C₂×C₄	1	2	yes	—
71	C₂×#6106	C₂×C₄	1	2	yes	—
72	C₂×#6105	C₂×C₄	1	2	yes	—
73	C₂×#6104	C₂×C₄	1	2	yes	—
74	#88184	—	2	1	no	—
75	#88184	—	2	1	no	—
76	C₂×#6099	—	2	2	no	—
77	C₂×#6099	C₂³	1	2	yes	—
78	C₂²×#1055	—	2	2	no	—
79	C₂²×#1055	C₂³	1	2	yes	—
80	C₂²×#1055	C₂³	1	2	yes	—
81	#88161	—	2	4	no	—
82	#88161	—	4	2	no	—
83	C₂×#6094	—	2	2	no	—
84	C₂×C₈×D₁₃	—	2	2	no	—
85	#88129	C₂×C₄	1	2	yes	—
86	#88128	C₂×C₄	1	1	yes	characteristic
87	C₄×D₅₂	—	2	1	no	—
88	C₄×D₅₂	—	2	1	no	—
89	#88123	C₂×C₄	1	1	yes	characteristic
90	C₁₃×#104	—	2	2	no	—
91	C₁₃×#104	D₄	1	4	yes	complemented
92	C₁₃×#97	—	2	1	no	—
93	C₄×C₈×C₁₃	—	2	1	no	—
94	#88062	—	2	4	no	—
95	#88060	—	2	2	no	—
96	#88060	—	2	2	no	—
97	#88050	C₂×C₄	1	2	yes	—
98	#88050	C₂×C₄	1	2	yes	—
99	#88049	C₂×C₄	1	2	yes	—
100	#88049	C₂×C₄	1	2	yes	—
101	#88045	—	2	4	no	—
102	#88045	—	4	2	no	—
103	C₄⋊#1055	—	2	1	no	—
104	C₄⋊#1055	—	2	1	no	—
105	C₄⋊#1055	—	2	2	no	—
106	C₄⋊#1055	—	2	2	no	—
107	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
108	C₄⋊#1055	C₂×C₄	1	2	yes	—
109	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
110	C₄⋊#1055	D₄	1	2	yes	—
111	C₄⋊#1055	D₄	1	1	yes	characteristic
112	C₄⋊#1055	D₄	1	1	yes	characteristic
113	C₄×#1055	—	2	4	no	—
114	#23015	—	13	1	no	maximal, Sylow
115	C₁₃×#41	—	2	1	no	—
116	C₁₃×#41	—	2	1	no	—
117	C₁₃×#41	C₂×D₄	1	2	yes	—
118	C₁₃×#41	#41	1	2	yes	—
119	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₂×D₄×C₁₃	—	2	1	no	—
121	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	—	2	1	no	—
124	C₂²×C₄×C₁₃	—	2	1	no	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
130	C₂×C₂²⋊D₁₃	—	2	2	no	—
131	#6127	—	2	2	no	—
132	#6127	—	2	2	no	—
133	#6127	—	2	2	no	—
134	#6127	—	2	2	no	—
135	C₂×D₅₂	—	2	1	no	—
136	C₂×D₅₂	—	2	1	no	—
137	C₂×D₅₂	C₂²×C₄	1	2	yes	—
138	C₂×C₄×D₁₃	—	2	2	no	—
139	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
140	C₁₃×M₁₆	—	2	1	no	—
141	C₁₃×M₁₆	—	2	1	no	—
142	C₁₃×M₁₆	—	2	1	no	—
143	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
144	C₂×C₈×C₁₃	—	2	1	no	—
145	C₂×C₈×C₁₃	—	2	1	no	—
146	C₁₃×C₄⋊C₄	—	2	1	no	—
147	C₁₃×C₄⋊C₄	—	2	1	no	—
148	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
149	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
150	C₁₃×C₂²⋊C₄	—	2	1	no	—
151	C₁₃×C₂²⋊C₄	—	2	1	no	—
152	C₁₃×C₂²⋊C₄	—	2	1	no	—
153	C₄²×C₁₃	—	2	4	no	—
154	C₄²×C₁₃	—	2	1	no	—
155	C₄²×C₁₃	—	2	1	no	—
156	C₄²×C₁₃	—	2	1	no	—
157	C₄²×C₁₃	—	2	1	no	—
158	C₄²×C₁₃	—	2	1	no	—
159	C₄²×C₁₃	—	2	1	no	—
160	C₄²×C₁₃	—	4	2	no	—
161	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
162	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
163	C₄²×C₁₃	C₂×D₄	1	2	yes	—
164	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
166	#6107	—	2	4	no	—
167	#6106	—	2	4	no	—
168	#6105	—	2	4	no	—
169	#6104	—	2	4	no	—
170	#6103	—	2	2	no	—
171	#6103	—	2	2	no	—
172	C₄⋊Dic₁₃	—	2	1	no	—
173	C₄⋊Dic₁₃	—	2	1	no	—
174	#6099	—	2	2	no	—
175	#6099	—	2	2	no	—
176	#6099	—	4	4	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	—	4	4	no	—
183	C₂×#1055	C₂²×C₄	1	2	yes	—
184	C₂×#1055	C₂²×C₄	1	2	yes	—
185	C₂×#1055	C₂×D₄	1	2	yes	—
186	C₂×#1055	C₂×D₄	1	2	yes	—
187	#6094	—	4	4	no	—
188	C₈×D₁₃	—	4	4	no	—
189	#3035	—	13	1	no	—
190	C₂×#443	—	13	2	no	—
191	#2935	—	13	1	no	—
192	#2906	—	13	1	no	—
193	#1962	—	13	1	no	—
194	#1950	—	13	1	no	—
195	#1937	—	13	2	no	—
196	#1876	—	13	2	no	—
197	#1866	—	13	2	no	—
198	C₄×C₄⋊C₈	—	13	1	no	—
199	C₄×#104	D₁₃	1	1	yes	characteristic, complemented
200	C₂³×C₁₃	—	2	1	no	—
201	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
202	C₂²×D₁₃	—	2	2	no	—
203	Q₈×C₁₃	—	2	1	no	—
204	Q₈×C₁₃	C₄×D₄	1	2	yes	—
205	D₄×C₁₃	—	2	2	no	—
206	D₄×C₁₃	—	2	2	no	—
207	D₄×C₁₃	—	2	1	no	—
208	D₄×C₁₃	C₄×D₄	1	2	yes	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	1	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	1	no	—
218	C₂×C₄×C₁₃	—	2	1	no	—
219	C₂×C₄×C₁₃	—	4	1	no	—
220	C₂×C₄×C₁₃	—	4	1	no	—
221	C₂×C₄×C₁₃	—	4	1	no	—
222	C₂×C₄×C₁₃	—	4	2	no	—
223	C₂×C₄×C₁₃	—	8	1	no	—
224	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₄×D₄	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	C₂³×C₄	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
233	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
234	C₂²⋊D₁₃	—	4	2	no	—
235	C₂²⋊D₁₃	—	4	2	no	—
236	C₂×Dic₁₃	—	2	2	no	—
237	D₅₂	—	2	2	no	—
238	D₅₂	—	2	2	no	—
239	D₅₂	—	4	2	no	—
240	D₅₂	—	8	1	no	—
241	C₄×D₁₃	—	4	2	no	—
242	C₄×D₁₃	—	4	2	no	—
243	Dic₂₆	—	2	2	no	—
244	Dic₂₆	—	2	2	no	—
245	C₈×C₁₃	—	2	2	no	—
246	C₈×C₁₃	—	4	1	no	—
247	#1055	—	2	2	no	—
248	#1055	—	2	2	no	—
249	#1055	—	2	2	no	—
250	#1055	—	2	2	no	—
251	#1055	—	4	2	no	—
252	C₂×#135	—	13	2	no	—
253	C₂×#131	—	13	2	no	—
254	C₂×#131	—	13	2	no	—
255	#532	—	13	1	no	—
256	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
257	#464	—	13	2	no	—
258	#463	—	13	2	no	—
259	#462	—	13	1	no	—
260	#461	—	13	1	no	—
261	#460	—	13	1	no	—
262	#459	—	13	1	no	—
263	#443	—	26	8	no	—
264	#436	—	26	1	no	—
265	#435	—	26	2	no	—
266	C₈×D₄	—	26	1	no	—
267	C₂×#108	—	13	2	no	—
268	#424	—	13	2	no	—
269	#424	—	26	2	no	—
270	#423	—	13	1	no	—
271	#423	—	26	1	no	—
272	C₂×C₄⋊C₈	—	13	1	no	—
273	C₂×C₄⋊C₈	—	13	1	no	—
274	C₂×C₄⋊C₈	—	26	1	no	—
275	C₂×#104	—	13	2	no	—
276	C₂×#104	—	13	2	no	—
277	C₂×#104	C₂×D₁₃	1	1	yes	characteristic
278	C₂×#104	C₂×D₁₃	1	1	yes	characteristic
279	#416	—	13	2	no	—
280	#408	—	13	2	no	—
281	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
282	C₂×C₄×C₈	—	13	2	no	—
283	C₄³	C₂×D₁₃	1	1	yes	characteristic
284	#341	—	13	2	no	—
285	#339	C₂×D₁₃	1	1	yes	characteristic
286	#339	C₂×D₁₃	1	1	yes	characteristic
287	#336	—	13	2	no	—
288	C₂²×C₁₃	—	2	1	no	—
289	C₂²×C₁₃	—	2	1	no	—
290	C₂²×C₁₃	—	2	2	no	—
291	C₂²×C₁₃	—	4	1	no	—
292	C₂²×C₁₃	—	4	1	no	—
293	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
294	C₂²×C₁₃	#547	1	1	yes	characteristic
295	C₂²×C₁₃	#553	1	1	yes	characteristic
296	C₂×D₁₃	—	4	2	no	—
297	C₂×D₁₃	—	4	2	no	—
298	C₂×D₁₃	—	4	2	no	—
299	C₄×C₁₃	—	2	4	no	—
300	C₄×C₁₃	—	2	2	no	—
301	C₄×C₁₃	—	2	1	no	—
302	C₄×C₁₃	—	2	1	no	—
303	C₄×C₁₃	—	2	1	no	—
304	C₄×C₁₃	—	4	2	no	—
305	C₄×C₁₃	—	4	1	no	—
306	C₄×C₁₃	—	4	1	no	—
307	C₄×C₁₃	#443	1	2	yes	complemented
308	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
309	C₄×C₁₃	#520	1	1	yes	characteristic
310	C₄×C₁₃	D₄²	1	1	yes	characteristic
311	C₄×C₁₃	#548	1	1	yes	characteristic
312	Dic₁₃	—	4	2	no	—
313	C₂×#41	—	13	2	no	—
314	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
315	#135	—	26	4	no	—
316	#135	—	26	4	no	—
317	C₂×Q₁₆	—	13	2	no	—
318	C₂×SD₁₆	—	13	2	no	—
319	C₂×SD₁₆	—	13	2	no	—
320	C₂×D₈	—	13	2	no	—
321	#131	—	26	4	no	—
322	#131	—	26	4	no	—
323	#131	—	52	2	no	—
324	#131	—	52	2	no	—
325	C₂×M₁₆	—	13	2	no	—
326	C₂×M₁₆	—	26	2	no	—
327	C₂×M₁₆	—	26	2	no	—
328	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
329	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
330	C₂²×C₈	—	13	2	no	—
331	C₂²×C₈	—	13	2	no	—
332	C₂²×C₈	—	26	2	no	—
333	C₂²×C₈	—	26	2	no	—
334	C₄⋊Q₈	—	13	1	no	—
335	#127	—	13	1	no	—
336	#124	—	13	2	no	—
337	#121	—	26	1	no	—
338	#121	—	26	1	no	—
339	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
340	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
341	C₄×D₄	—	2	1	no	—
342	C₄×D₄	—	2	1	no	—
343	C₄×D₄	—	26	1	no	—
344	C₄×D₄	—	26	1	no	—
345	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
346	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
347	#117	—	2	1	no	—
348	#117	C₂²×D₁₃	1	1	yes	characteristic
349	C₂×C₄²	—	2	1	no	—
350	C₂×C₄²	—	2	1	no	—
351	C₂×C₄²	—	2	1	no	—
352	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
353	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
354	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
355	#108	—	26	4	no	—
356	C₄⋊C₈	—	13	1	no	—
357	C₄⋊C₈	—	13	1	no	—
358	C₄⋊C₈	—	13	2	no	—
359	C₄⋊C₈	—	13	1	no	—
360	C₄⋊C₈	—	13	1	no	—
361	C₄⋊C₈	—	13	2	no	—
362	C₄⋊C₈	—	26	2	no	—
363	C₄⋊C₈	—	26	2	no	—
364	C₄⋊C₈	—	26	1	no	—
365	C₄⋊C₈	—	26	1	no	—
366	#104	—	2	2	no	—
367	#104	—	26	4	no	—
368	#104	—	52	2	no	—
369	#104	D₅₂	1	4	yes	complemented
370	#103	—	13	2	no	—
371	#103	—	13	2	no	—
372	#102	—	13	2	no	—
373	#102	—	13	2	no	—
374	C₂²⋊C₈	—	26	2	no	—
375	C₂²⋊C₈	—	26	2	no	—
376	#97	—	2	1	no	—
377	C₄×C₈	—	2	1	no	—
378	C₄×C₈	—	26	4	no	—
379	C₂×C₁₃	—	2	1	no	—
380	C₂×C₁₃	—	2	1	no	—
381	C₂×C₁₃	—	4	2	no	—
382	C₂×C₁₃	#2361	1	1	yes	characteristic
383	C₂×C₁₃	C₂×#443	1	1	yes	characteristic
384	C₂×C₁₃	#2956	1	1	yes	characteristic
385	D₁₃	—	8	2	no	—
386	#41	—	2	1	no	—
387	#41	—	2	1	no	—
388	#41	—	26	2	no	—
389	#41	—	26	2	no	—
390	#41	—	26	2	no	—
391	#41	—	26	2	no	—
392	#41	C₂×D₅₂	1	2	yes	—
393	#41	#6127	1	2	yes	—
394	C₂×Q₈	—	13	2	no	—
395	C₂×Q₈	C₂×C₄×D₁₃	1	1	yes	characteristic
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	13	2	no	—
398	C₂×D₄	—	26	2	no	—
399	C₂×D₄	—	26	1	no	—
400	C₂×D₄	—	26	1	no	—
401	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	26	2	no	—
408	C₂²×C₄	#6129	1	1	yes	characteristic
409	C₂²×C₄	#6129	1	1	yes	characteristic
410	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
411	Q₁₆	—	26	4	no	—
412	SD₁₆	—	26	4	no	—
413	SD₁₆	—	26	4	no	—
414	D₈	—	26	4	no	—
415	M₁₆	—	2	1	no	—
416	M₁₆	—	2	1	no	—
417	M₁₆	—	2	1	no	—
418	M₁₆	—	26	2	no	—
419	M₁₆	—	26	2	no	—
420	M₁₆	—	52	4	no	—
421	M₁₆	—	52	4	no	—
422	M₁₆	C₂×D₅₂	1	2	yes	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	13	2	no	—
426	C₂×C₈	—	13	2	no	—
427	C₂×C₈	—	13	2	no	—
428	C₂×C₈	—	13	2	no	—
429	C₂×C₈	—	26	2	no	—
430	C₂×C₈	—	26	2	no	—
431	C₂×C₈	—	26	2	no	—
432	C₂×C₈	—	26	2	no	—
433	C₂×C₈	—	26	2	no	—
434	C₂×C₈	—	52	4	no	—
435	C₂×C₈	—	52	4	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	26	1	no	—
439	C₄⋊C₄	—	26	1	no	—
440	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
441	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
442	C₂²⋊C₄	—	2	1	no	—
443	C₂²⋊C₄	—	2	1	no	—
444	C₂²⋊C₄	—	2	1	no	—
445	C₂²⋊C₄	—	26	2	no	—
446	C₂²⋊C₄	—	26	2	no	—
447	C₄²	—	2	4	no	—
448	C₄²	—	2	1	no	—
449	C₄²	—	2	1	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	2	1	no	—
454	C₄²	—	4	2	no	—
455	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
456	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
457	C₄²	C₂×D₅₂	1	2	yes	—
458	C₄²	D₄×D₁₃	1	1	yes	characteristic
459	C₄²	D₄×D₁₃	1	1	yes	characteristic
460	C₁₃	#23015	1	1	yes	characteristic, complemented, Sylow
461	C₂³	—	2	1	no	—
462	C₂³	—	26	2	no	—
463	C₂³	C₂×#6129	1	1	yes	characteristic
464	Q₈	—	2	1	no	—
465	Q₈	—	26	2	no	—
466	Q₈	—	26	2	no	—
467	Q₈	C₄×D₅₂	1	2	yes	—
468	D₄	—	2	2	no	—
469	D₄	—	2	2	no	—
470	D₄	—	2	1	no	—
471	D₄	—	26	2	no	—
472	D₄	—	26	2	no	—
473	D₄	—	52	2	no	—
474	D₄	—	52	2	no	—
475	D₄	—	52	2	no	—
476	D₄	—	104	1	no	—
477	D₄	C₄×D₅₂	1	2	yes	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	8	1	no	—
493	C₂×C₄	—	26	2	no	—
494	C₂×C₄	—	52	2	no	—
495	C₂×C₄	—	52	2	no	—
496	C₂×C₄	#88135	1	1	yes	characteristic
497	C₂×C₄	#88135	1	1	yes	characteristic
498	C₂×C₄	#88135	1	1	yes	characteristic
499	C₂×C₄	#88135	1	1	yes	characteristic
500	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
501	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
502	C₂×C₄	C₂×#6127	1	1	yes	characteristic
503	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
504	C₂×C₄	#88256	1	1	yes	characteristic
505	C₂×C₄	#88257	1	1	yes	characteristic
506	C₈	—	2	2	no	—
507	C₈	—	4	1	no	—
508	C₈	—	26	2	no	—
509	C₈	—	26	2	no	—
510	C₈	—	26	2	no	—
511	C₈	—	26	2	no	—
512	C₈	—	52	2	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	4	1	no	—
517	C₂²	—	4	1	no	—
518	C₂²	—	52	2	no	—
519	C₂²	—	52	2	no	—
520	C₂²	—	52	2	no	—
521	C₂²	C₂×#88135	1	1	yes	characteristic
522	C₂²	#11719260	1	1	yes	characteristic
523	C₂²	#11719270	1	1	yes	characteristic
524	C₄	—	2	4	no	—
525	C₄	—	2	1	no	—
526	C₄	—	2	2	no	—
527	C₄	—	2	1	no	—
528	C₄	—	2	1	no	—
529	C₄	—	4	2	no	—
530	C₄	—	4	1	no	—
531	C₄	—	4	1	no	—
532	C₄	—	52	2	no	—
533	C₄	#11718485	1	2	yes	complemented
534	C₄	C₂×C₄×D₅₂	1	1	yes	characteristic
535	C₄	#11719228	1	1	yes	characteristic
536	C₄	D₄×D₅₂	1	1	yes	characteristic
537	C₄	#11719257	1	1	yes	characteristic
538	C₂	—	2	1	no	—
539	C₂	—	2	1	no	—
540	C₂	—	4	2	no	—
541	C₂	—	104	2	no	—
542	C₂	#13117850	1	1	yes	characteristic
543	C₂	C₂×#11718485	1	1	yes	characteristic
544	C₂	#13123742	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	C₄×C₁₃×#104	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	#13124291	C₂
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₄×#104	D₁₃
hypocenter	C₁₃	#23015
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#104

Complements

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

N	H ≅ G/N	type
2. C₂×#11718485	C₂	semidirect
3. #13123582	C₂	semidirect
4. #13123404	C₂	semidirect
5. #13115664	C₂	semidirect
6. #13115611	C₂	semidirect
7. #13115541	C₂	semidirect
8. #13115161	C₂	semidirect
9. #13115112	C₂	semidirect
10. C₄×C₄⋊#1055	C₂	semidirect
11. C₄×C₁₃×#104	C₂	semidirect
23. #11718692	C₄	semidirect
24. #11718689	C₄	semidirect
25. #11718688	C₄	semidirect
26. #11718680	C₄	semidirect
27. #11718677	C₄	semidirect
28. #11718676	C₄	semidirect
91. C₁₃×#104	D₄	semidirect
199. C₄×#104	D₁₃	semidirect
307. C₄×C₁₃	#443	semidirect
369. #104	D₅₂	semidirect
460. C₁₃	#23015	semidirect
533. C₄	#11718485	semidirect

Maximal subgroups

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

subgroup	index
#13124291	2
C₂×#11718485	2
#13123582	2
#13123404	2
#13115664	2
#13115611	2
#13115541	2
#13115161	2
#13115112	2
C₄×C₄⋊#1055	2
C₄×C₁₃×#104	2
#23015	13