Subgroups — #15866145

Order 3328.

800 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123480	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#88202	C₂	1	1	yes	maximal, characteristic, complemented
3	#13115486	C₂	1	2	yes	maximal, complemented
4	#13115437	C₂	1	2	yes	maximal, complemented
5	#13115165	C₂	1	2	yes	maximal
6	#13115113	C₂	1	2	yes	maximal, complemented
7	C₄×#88059	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#88077	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#88077	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114581	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
13	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
14	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
15	C₂×#88202	C₂²	1	2	yes	—
16	C₄×C₁₃×Q₁₆	C₄	1	1	yes	characteristic, complemented
17	C₄×C₁₃×Q₁₆	C₄	1	1	yes	characteristic, complemented
18	C₄×C₁₃×SD₁₆	C₄	1	1	yes	characteristic, complemented
19	C₄×C₁₃×SD₁₆	C₄	1	1	yes	characteristic, complemented
20	C₄×C₁₃×SD₁₆	C₄	1	1	yes	characteristic, complemented
21	C₄×C₁₃×SD₁₆	C₄	1	1	yes	characteristic, complemented
22	C₄×C₁₃×D₈	C₄	1	1	yes	characteristic, complemented
23	C₄×C₁₃×D₈	C₄	1	1	yes	characteristic, complemented
24	C₁₃×#427	C₂²	1	1	yes	characteristic
25	C₁₃×#416	C₂²	1	1	yes	characteristic
26	C₁₃×#416	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×#88077	C₂²	1	2	yes	—
29	C₂×#88077	C₂²	1	2	yes	—
30	#11718895	C₂²	1	2	yes	—
31	C₂×#88059	C₂²	1	2	yes	—
32	#11718661	—	2	2	no	—
33	#11718660	C₂²	1	2	yes	—
34	#11718658	—	2	2	no	—
35	#11718658	C₂²	1	2	yes	—
36	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
37	#11718586	—	2	1	no	—
38	#11718586	—	2	1	no	—
39	C₄×#6099	—	2	1	no	—
40	C₄×#6099	C₂²	1	1	yes	characteristic
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	#11718142	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	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
51	C₁₃×#135	—	2	4	no	—
52	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
53	C₂×C₁₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
54	C₂×C₁₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
55	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
59	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
60	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
61	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
62	C₄×D₄×C₁₃	—	2	1	no	—
63	C₄×D₄×C₁₃	—	2	1	no	—
64	C₄×D₄×C₁₃	—	2	1	no	—
65	C₄×D₄×C₁₃	—	2	1	no	—
66	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
67	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
68	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
69	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
70	C₁₃×#117	—	2	1	no	—
71	C₁₃×#117	—	2	1	no	—
72	C₁₃×#117	C₂³	1	1	yes	characteristic
73	C₁₃×#117	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	—	2	1	no	—
75	C₂×C₄²×C₁₃	—	2	1	no	—
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	#88202	—	2	4	no	—
78	#88202	—	2	4	no	—
79	C₂×C₄×Dic₁₃	—	2	1	no	—
80	C₂×C₄×Dic₁₃	—	2	1	no	—
81	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
82	C₂×#6099	—	2	2	no	—
83	C₂×#6099	C₂³	1	2	yes	—
84	C₂×#6099	C₂³	1	2	yes	—
85	C₂²×#1055	—	2	2	no	—
86	C₂²×#1055	C₂³	1	2	yes	—
87	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
88	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
89	C₁₃×#106	C₂×C₄	1	1	yes	characteristic
90	C₁₃×#106	C₂×C₄	1	1	yes	characteristic
91	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
92	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
93	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
94	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
95	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
96	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
97	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
98	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
99	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
100	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
101	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
102	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
103	#88077	—	2	4	no	—
104	#88077	—	2	4	no	—
105	C₂²⋊#1055	—	2	2	no	—
106	C₂²⋊#1055	—	2	2	no	—
107	#88059	—	2	4	no	—
108	C₄⋊#1055	—	2	2	no	—
109	C₄⋊#1055	—	2	2	no	—
110	#88043	—	2	1	no	—
111	#88043	—	2	1	no	—
112	#88043	—	2	2	no	—
113	C₄×#1055	—	2	1	no	—
114	C₄×#1055	—	2	1	no	—
115	C₄×#1055	—	2	2	no	—
116	C₄×#1055	D₄	1	2	yes	—
117	C₄×#1055	D₄	1	1	yes	characteristic
118	C₄×#1055	D₄	1	1	yes	characteristic
119	#21137	—	13	1	no	maximal, Sylow
120	C₁₃×#41	—	2	2	no	—
121	C₁₃×#41	—	2	2	no	—
122	C₁₃×#41	—	2	2	no	—
123	C₁₃×#41	#41	1	4	yes	—
124	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
126	C₂×D₄×C₁₃	—	2	1	no	—
127	C₂×D₄×C₁₃	—	2	1	no	—
128	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	—	2	1	no	—
131	C₂²×C₄×C₁₃	—	2	1	no	—
132	C₂²×C₄×C₁₃	—	2	1	no	—
133	C₂²×C₄×C₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
139	C₂²×Dic₁₃	—	2	2	no	—
140	C₁₃×Q₁₆	—	2	2	no	—
141	C₁₃×SD₁₆	—	2	2	no	—
142	C₁₃×SD₁₆	—	2	2	no	—
143	C₁₃×D₈	—	2	2	no	—
144	C₂×C₈×C₁₃	—	2	2	no	—
145	C₂×C₈×C₁₃	—	2	2	no	—
146	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
150	C₁₃×C₄⋊C₄	—	2	1	no	—
151	C₁₃×C₄⋊C₄	—	2	1	no	—
152	C₁₃×C₄⋊C₄	—	2	1	no	—
153	C₁₃×C₄⋊C₄	—	2	1	no	—
154	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
155	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
156	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
157	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
158	C₁₃×C₂²⋊C₄	—	2	1	no	—
159	C₁₃×C₂²⋊C₄	—	2	1	no	—
160	C₁₃×C₂²⋊C₄	—	2	1	no	—
161	C₁₃×C₂²⋊C₄	—	2	1	no	—
162	C₁₃×C₂²⋊C₄	—	2	1	no	—
163	C₁₃×C₂²⋊C₄	—	2	1	no	—
164	C₄²×C₁₃	—	2	1	no	—
165	C₄²×C₁₃	—	2	1	no	—
166	C₄²×C₁₃	—	2	1	no	—
167	C₄²×C₁₃	—	2	1	no	—
168	C₄²×C₁₃	—	2	1	no	—
169	C₄²×C₁₃	—	2	1	no	—
170	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
171	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
172	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₄×Dic₁₃	—	2	4	no	—
175	C₄×Dic₁₃	—	2	2	no	—
176	C₄×Dic₁₃	—	2	2	no	—
177	C₄×Dic₁₃	—	4	2	no	—
178	#6099	—	2	8	no	—
179	#6099	—	2	2	no	—
180	#6099	—	2	2	no	—
181	#6099	—	2	2	no	—
182	#6099	#41	1	4	yes	—
183	C₂×#1055	—	2	8	no	—
184	C₂×#1055	—	2	2	no	—
185	C₂×#1055	—	2	2	no	—
186	C₂×#1055	—	2	2	no	—
187	C₂×#1055	—	2	2	no	—
188	C₂×#1055	C₂×D₄	1	2	yes	—
189	C₂×#1055	C₂×D₄	1	2	yes	—
190	C₄×#135	D₁₃	1	1	yes	characteristic
191	#2922	—	13	1	no	—
192	C₄×#131	—	13	1	no	—
193	#1929	—	13	2	no	—
194	#1922	—	13	2	no	—
195	#1876	—	13	2	no	—
196	#1866	—	13	2	no	—
197	C₄×#108	—	13	1	no	—
198	C₄×#104	—	13	1	no	—
199	C₄×#104	—	13	1	no	—
200	#1744	—	13	1	no	—
201	C₂³×C₁₃	—	2	1	no	—
202	C₂³×C₁₃	—	2	1	no	—
203	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
204	Q₈×C₁₃	—	2	1	no	—
205	Q₈×C₁₃	—	2	1	no	—
206	Q₈×C₁₃	—	2	1	no	—
207	Q₈×C₁₃	#117	1	2	yes	—
208	D₄×C₁₃	—	2	4	no	—
209	D₄×C₁₃	—	2	1	no	—
210	D₄×C₁₃	—	2	1	no	—
211	D₄×C₁₃	—	2	1	no	—
212	D₄×C₁₃	—	4	2	no	—
213	D₄×C₁₃	#117	1	2	yes	—
214	C₂×C₄×C₁₃	—	2	1	no	—
215	C₂×C₄×C₁₃	—	2	4	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	2	1	no	—
219	C₂×C₄×C₁₃	—	2	1	no	—
220	C₂×C₄×C₁₃	—	2	1	no	—
221	C₂×C₄×C₁₃	—	2	1	no	—
222	C₂×C₄×C₁₃	—	2	1	no	—
223	C₂×C₄×C₁₃	—	4	2	no	—
224	C₂×C₄×C₁₃	—	4	2	no	—
225	C₂×C₄×C₁₃	—	4	2	no	—
226	C₂×C₄×C₁₃	—	4	2	no	—
227	C₂×C₄×C₁₃	—	4	2	no	—
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	C₂³×C₄	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
235	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
236	C₂×Dic₁₃	—	2	4	no	—
237	C₂×Dic₁₃	—	4	2	no	—
238	C₂×Dic₁₃	—	4	2	no	—
239	C₈×C₁₃	—	2	1	no	—
240	C₈×C₁₃	—	2	1	no	—
241	C₈×C₁₃	—	2	1	no	—
242	C₈×C₁₃	—	2	1	no	—
243	#1055	—	2	2	no	—
244	#1055	—	2	4	no	—
245	#1055	—	2	2	no	—
246	#1055	—	4	2	no	—
247	C₂×#135	C₂×D₁₃	1	1	yes	characteristic
248	C₂×#131	—	13	2	no	—
249	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
250	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
251	C₄×Q₁₆	Dic₁₃	1	1	yes	characteristic, complemented
252	C₄×Q₁₆	Dic₁₃	1	1	yes	characteristic, complemented
253	C₄×SD₁₆	Dic₁₃	1	1	yes	characteristic, complemented
254	C₄×SD₁₆	Dic₁₃	1	1	yes	characteristic, complemented
255	C₄×SD₁₆	Dic₁₃	1	1	yes	characteristic, complemented
256	C₄×SD₁₆	Dic₁₃	1	1	yes	characteristic, complemented
257	C₄×D₈	Dic₁₃	1	1	yes	characteristic, complemented
258	C₄×D₈	Dic₁₃	1	1	yes	characteristic, complemented
259	#433	—	26	2	no	—
260	#431	—	26	1	no	—
261	#431	—	26	1	no	—
262	C₂×#108	—	13	2	no	—
263	#427	C₂×D₁₃	1	1	yes	characteristic
264	#424	—	13	2	no	—
265	C₂×#104	—	13	2	no	—
266	C₂×#104	—	13	2	no	—
267	#416	C₂×D₁₃	1	1	yes	characteristic
268	#416	C₂×D₁₃	1	1	yes	characteristic
269	#408	—	13	2	no	—
270	#405	—	13	2	no	—
271	#405	—	26	2	no	—
272	C₄×M₁₆	—	13	1	no	—
273	C₄×M₁₆	—	13	1	no	—
274	C₄×M₁₆	—	26	1	no	—
275	C₂×C₄×C₈	—	13	1	no	—
276	C₂×C₄×C₈	—	26	1	no	—
277	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
278	C₄³	—	13	1	no	—
279	#341	—	13	2	no	—
280	#339	—	13	2	no	—
281	#339	—	13	2	no	—
282	#336	—	13	2	no	—
283	#336	—	13	2	no	—
284	C₂²×C₁₃	—	2	1	no	—
285	C₂²×C₁₃	—	2	1	no	—
286	C₂²×C₁₃	—	2	2	no	—
287	C₂²×C₁₃	—	4	1	no	—
288	C₂²×C₁₃	—	4	1	no	—
289	C₂²×C₁₃	—	4	1	no	—
290	C₂²×C₁₃	—	4	1	no	—
291	C₂²×C₁₃	—	4	1	no	—
292	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
293	C₂²×C₁₃	#529	1	2	yes	—
294	C₄×C₁₃	—	2	1	no	—
295	C₄×C₁₃	—	2	1	no	—
296	C₄×C₁₃	—	2	2	no	—
297	C₄×C₁₃	—	4	1	no	—
298	C₄×C₁₃	—	4	1	no	—
299	C₄×C₁₃	—	4	1	no	—
300	C₄×C₁₃	—	4	1	no	—
301	C₄×C₁₃	—	4	1	no	—
302	C₄×C₁₃	#443	1	2	yes	—
303	C₄×C₁₃	#444	1	2	yes	—
304	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
305	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
306	C₄×C₁₃	#525	1	2	yes	—
307	Dic₁₃	—	4	4	no	—
308	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
309	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
310	#135	—	2	4	no	—
311	C₂×Q₁₆	C₂×Dic₁₃	1	1	yes	characteristic
312	C₂×SD₁₆	C₂×Dic₁₃	1	1	yes	characteristic
313	C₂×SD₁₆	C₂×Dic₁₃	1	1	yes	characteristic
314	C₂×D₈	C₂×Dic₁₃	1	1	yes	characteristic
315	#131	—	26	4	no	—
316	#131	—	26	4	no	—
317	C₂×M₁₆	—	13	2	no	—
318	C₂×M₁₆	—	13	2	no	—
319	C₂×M₁₆	—	26	2	no	—
320	C₂²×C₈	—	13	2	no	—
321	C₂²×C₈	—	26	2	no	—
322	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
323	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
324	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
325	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
326	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
327	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
328	C₄×D₄	—	2	1	no	—
329	C₄×D₄	—	2	1	no	—
330	C₄×D₄	—	2	1	no	—
331	C₄×D₄	—	2	1	no	—
332	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
333	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
334	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
335	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
336	#117	—	2	1	no	—
337	#117	—	2	1	no	—
338	#117	C₂²×D₁₃	1	1	yes	characteristic
339	#117	C₂²×D₁₃	1	1	yes	characteristic
340	C₂×C₄²	—	2	1	no	—
341	C₂×C₄²	—	2	1	no	—
342	C₂×C₄²	—	13	2	no	—
343	C₂×C₄²	—	26	1	no	—
344	C₂×C₄²	—	26	1	no	—
345	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
346	#108	—	26	4	no	—
347	#107	C₂×Dic₁₃	1	1	yes	characteristic
348	#107	C₂×Dic₁₃	1	1	yes	characteristic
349	#106	C₂×Dic₁₃	1	1	yes	characteristic
350	#106	C₂×Dic₁₃	1	1	yes	characteristic
351	C₄⋊C₈	—	26	2	no	—
352	C₄⋊C₈	—	26	2	no	—
353	#104	—	26	4	no	—
354	#104	—	26	4	no	—
355	#103	C₂×Dic₁₃	1	1	yes	characteristic
356	#103	C₂×Dic₁₃	1	1	yes	characteristic
357	#103	C₂×Dic₁₃	1	1	yes	characteristic
358	#103	C₂×Dic₁₃	1	1	yes	characteristic
359	#102	C₂×Dic₁₃	1	1	yes	characteristic
360	#102	C₂×Dic₁₃	1	1	yes	characteristic
361	#102	C₂×Dic₁₃	1	1	yes	characteristic
362	#102	C₂×Dic₁₃	1	1	yes	characteristic
363	C₂²⋊C₈	—	26	2	no	—
364	C₂²⋊C₈	—	26	2	no	—
365	#97	—	26	2	no	—
366	#97	—	26	1	no	—
367	#97	—	26	1	no	—
368	C₄×C₈	—	13	2	no	—
369	C₄×C₈	—	13	1	no	—
370	C₄×C₈	—	13	1	no	—
371	C₄×C₈	—	26	2	no	—
372	C₄×C₈	—	26	1	no	—
373	C₄×C₈	—	26	1	no	—
374	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
375	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
376	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
377	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
378	C₂×C₁₃	—	2	2	no	—
379	C₂×C₁₃	—	4	2	no	—
380	C₂×C₁₃	—	8	1	no	—
381	C₂×C₁₃	#2290	1	1	yes	characteristic
382	C₂×C₁₃	C₂×#443	1	1	yes	characteristic
383	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
384	#41	—	2	2	no	—
385	#41	—	2	2	no	—
386	#41	—	2	2	no	—
387	#41	#6127	1	4	yes	—
388	C₂×Q₈	C₂²×Dic₁₃	1	1	yes	characteristic
389	C₂×Q₈	C₂²×Dic₁₃	1	1	yes	characteristic
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
393	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	26	2	no	—
401	C₂²×C₄	#6129	1	1	yes	characteristic
402	C₂²×C₄	#6129	1	1	yes	characteristic
403	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
404	Q₁₆	—	2	2	no	—
405	SD₁₆	—	2	2	no	—
406	SD₁₆	—	2	2	no	—
407	D₈	—	2	2	no	—
408	M₁₆	—	13	4	no	—
409	M₁₆	—	26	8	no	—
410	M₁₆	—	26	2	no	—
411	M₁₆	—	26	2	no	—
412	M₁₆	—	26	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	13	2	no	—
416	C₂×C₈	—	13	2	no	—
417	C₂×C₈	—	26	8	no	—
418	C₂×C₈	—	26	2	no	—
419	C₂×C₈	—	26	2	no	—
420	C₂×C₈	—	26	2	no	—
421	C₂×C₈	—	26	2	no	—
422	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
423	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
424	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
425	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
431	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
432	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
433	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
434	C₂²⋊C₄	—	2	1	no	—
435	C₂²⋊C₄	—	2	1	no	—
436	C₂²⋊C₄	—	2	1	no	—
437	C₂²⋊C₄	—	2	1	no	—
438	C₂²⋊C₄	—	2	1	no	—
439	C₂²⋊C₄	—	2	1	no	—
440	C₄²	—	2	1	no	—
441	C₄²	—	2	1	no	—
442	C₄²	—	2	1	no	—
443	C₄²	—	2	1	no	—
444	C₄²	—	2	1	no	—
445	C₄²	—	2	1	no	—
446	C₄²	—	26	4	no	—
447	C₄²	—	26	2	no	—
448	C₄²	—	26	2	no	—
449	C₄²	—	52	2	no	—
450	C₄²	D₄×D₁₃	1	1	yes	characteristic
451	C₄²	D₄×D₁₃	1	1	yes	characteristic
452	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
453	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
454	C₁₃	#21137	1	1	yes	characteristic, complemented, Sylow
455	C₂³	—	2	1	no	—
456	C₂³	—	2	1	no	—
457	C₂³	C₂×#6129	1	1	yes	characteristic
458	Q₈	—	2	1	no	—
459	Q₈	—	2	1	no	—
460	Q₈	—	2	1	no	—
461	Q₈	#88180	1	2	yes	—
462	D₄	—	2	4	no	—
463	D₄	—	2	1	no	—
464	D₄	—	2	1	no	—
465	D₄	—	2	1	no	—
466	D₄	—	4	2	no	—
467	D₄	#88180	1	2	yes	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	26	4	no	—
483	C₂×C₄	—	52	2	no	—
484	C₂×C₄	—	52	2	no	—
485	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
486	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
487	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
488	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
489	C₂×C₄	C₂×#6127	1	2	yes	—
490	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
491	C₂×C₄	#41×D₁₃	1	2	yes	—
492	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
493	C₈	—	2	1	no	—
494	C₈	—	2	1	no	—
495	C₈	—	2	1	no	—
496	C₈	—	2	1	no	—
497	C₈	—	26	2	no	—
498	C₈	—	26	2	no	—
499	C₈	—	26	4	no	—
500	C₈	—	52	2	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	2	no	—
504	C₂²	—	4	1	no	—
505	C₂²	—	4	1	no	—
506	C₂²	—	4	1	no	—
507	C₂²	—	4	1	no	—
508	C₂²	—	4	1	no	—
509	C₂²	#11719243	1	2	yes	—
510	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
511	C₄	—	2	2	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	4	1	no	—
515	C₄	—	4	1	no	—
516	C₄	—	4	1	no	—
517	C₄	—	4	1	no	—
518	C₄	—	4	1	no	—
519	C₄	—	52	4	no	—
520	C₄	#11718857	1	2	yes	—
521	C₄	#11718858	1	2	yes	—
522	C₄	#11719252	1	2	yes	—
523	C₄	C₂×#88180	1	1	yes	characteristic
524	C₄	#41×Dic₁₃	1	1	yes	characteristic
525	C₂	—	2	2	no	—
526	C₂	—	4	2	no	—
527	C₂	—	8	1	no	—
528	C₂	#13117281	1	1	yes	characteristic
529	C₂	C₂×#11718857	1	1	yes	characteristic
530	C₂	C₂×#11718858	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₄×C₁₃×#135	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×C₁₃×#135	C₂²
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₄×#135	D₁₃
hypocenter	C₁₃	#21137
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #13123480	C₂	semidirect
2. C₄×#88202	C₂	semidirect
3. #13115486	C₂	semidirect
4. #13115437	C₂	semidirect
6. #13115113	C₂	semidirect
7. C₄×#88059	C₂	semidirect
8. C₄×#88077	C₂	semidirect
9. C₄×#88077	C₂	semidirect
10. #13114581	C₂	semidirect
16. C₄×C₁₃×Q₁₆	C₄	semidirect
17. C₄×C₁₃×Q₁₆	C₄	semidirect
18. C₄×C₁₃×SD₁₆	C₄	semidirect
19. C₄×C₁₃×SD₁₆	C₄	semidirect
20. C₄×C₁₃×SD₁₆	C₄	semidirect
21. C₄×C₁₃×SD₁₆	C₄	semidirect
22. C₄×C₁₃×D₈	C₄	semidirect
23. C₄×C₁₃×D₈	C₄	semidirect
251. C₄×Q₁₆	Dic₁₃	semidirect
252. C₄×Q₁₆	Dic₁₃	semidirect
253. C₄×SD₁₆	Dic₁₃	semidirect
254. C₄×SD₁₆	Dic₁₃	semidirect
255. C₄×SD₁₆	Dic₁₃	semidirect
256. C₄×SD₁₆	Dic₁₃	semidirect
257. C₄×D₈	Dic₁₃	semidirect
258. C₄×D₈	Dic₁₃	semidirect
454. C₁₃	#21137	semidirect

Maximal subgroups

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

subgroup	index
#13123480	2
C₄×#88202	2
#13115486	2
#13115437	2
#13115165	2
#13115113	2
C₄×#88059	2
C₄×#88077	2
#13114581	2
C₄×C₁₃×#135	2
#21137	13