Subgroups — #15834371

Order 3328.

654 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123856	C₂	1	1	yes	maximal, characteristic, complemented
2	#13123850	C₂	1	1	yes	maximal, characteristic, complemented
3	#13113727	C₂	1	2	yes	maximal, complemented
4	#13113687	C₂	1	2	yes	maximal, complemented
5	#13113666	C₂	1	2	yes	maximal, complemented
6	SD₁₆×#1055	C₂	1	2	yes	maximal, complemented
7	#13113599	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113270	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113270	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#6099	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#135	C₄	1	1	yes	characteristic
13	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
14	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
15	C₄×C₁₃×Q₁₆	C₄	1	1	yes	characteristic
16	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
17	C₄×C₁₃×SD₁₆	C₄	1	1	yes	characteristic
18	C₄×C₁₃×SD₁₆	C₄	1	1	yes	characteristic
19	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
20	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
21	C₄×C₁₃×D₈	C₄	1	1	yes	characteristic
22	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
23	C₁₃×#427	C₄	1	1	yes	characteristic
24	C₁₃×#416	C₄	1	1	yes	characteristic
25	C₁₃×#416	C₄	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
27	#11718685	C₂²	1	2	yes	—
28	Q₈×#1055	C₂²	1	2	yes	—
29	#11718673	—	2	2	no	—
30	#11718673	C₂²	1	2	yes	—
31	#11718672	—	2	2	no	—
32	D₄×#1055	C₂²	1	2	yes	—
33	#11718587	—	2	1	no	—
34	#11718587	—	2	1	no	—
35	#11718587	C₂²	1	1	yes	characteristic
36	#11718587	C₂²	1	1	yes	characteristic
37	#11718586	C₂²	1	1	yes	characteristic
38	C₄×#6099	—	2	1	no	—
39	C₄×#6099	C₂²	1	1	yes	characteristic
40	C₂×#88043	—	2	1	no	—
41	Q₈⋊#1055	C₂²	1	2	yes	—
42	Q₈⋊#1055	C₂²	1	2	yes	—
43	D₄⋊#1055	C₂²	1	2	yes	—
44	D₄⋊#1055	C₂²	1	2	yes	—
45	#11718050	C₂²	1	2	yes	—
46	#11718049	C₂²	1	2	yes	—
47	#11718046	C₂²	1	2	yes	—
48	C₈×#1055	C₂²	1	2	yes	—
49	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₃×#41	C₂×C₄	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	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂×C₄	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	C₂³	1	1	yes	characteristic
61	C₄×Q₈×C₁₃	C₂³	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	C₂³	1	1	yes	characteristic
69	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₁₃×#117	—	2	1	no	—
71	C₁₃×#117	—	2	1	no	—
72	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
73	C₁₃×#117	C₂×C₄	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	C₂×#6099	—	2	2	no	—
78	C₂×#6099	D₄	1	2	yes	—
79	C₂²×#1055	—	2	2	no	—
80	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
81	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
82	C₁₃×#106	C₂×C₄	1	1	yes	characteristic
83	C₁₃×#106	C₂×C₄	1	1	yes	characteristic
84	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
85	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
86	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
87	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
88	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
89	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
90	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
91	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
92	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
93	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
94	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₂²⋊#1055	—	2	1	no	—
97	C₂²⋊#1055	—	2	1	no	—
98	C₂²⋊#1055	—	2	1	no	—
99	C₂²⋊#1055	—	2	2	no	—
100	C₂²⋊#1055	—	2	2	no	—
101	C₄⋊#1055	—	2	1	no	—
102	C₄⋊#1055	—	2	2	no	—
103	C₄⋊#1055	—	2	2	no	—
104	C₄⋊#1055	C₂³	1	2	yes	—
105	C₄⋊#1055	C₂³	1	2	yes	—
106	#88043	—	2	1	no	—
107	#88043	—	2	1	no	—
108	#88043	—	2	2	no	—
109	#88043	D₄	1	1	yes	characteristic
110	#88043	D₄	1	1	yes	characteristic
111	C₄×#1055	—	2	2	no	—
112	C₄×#1055	C₂³	1	2	yes	—
113	C₄×#1055	C₂³	1	2	yes	—
114	#18037	—	13	1	no	maximal, Sylow
115	C₁₃×#41	—	2	2	no	—
116	C₁₃×#41	—	2	2	no	—
117	C₁₃×#41	—	4	1	no	—
118	C₁₃×#41	—	4	1	no	—
119	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×D₄×C₁₃	—	2	1	no	—
122	C₂×D₄×C₁₃	—	2	1	no	—
123	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
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	—	2	1	no	—
129	C₂²×C₄×C₁₃	—	2	1	no	—
130	C₂²×C₄×C₁₃	—	2	1	no	—
131	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
134	C₁₃×Q₁₆	—	2	2	no	—
135	C₁₃×SD₁₆	—	2	2	no	—
136	C₁₃×SD₁₆	M₁₆	1	4	yes	complemented
137	C₁₃×D₈	—	2	2	no	—
138	C₂×C₈×C₁₃	—	2	2	no	—
139	C₂×C₈×C₁₃	—	4	1	no	—
140	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
144	C₁₃×C₄⋊C₄	—	2	1	no	—
145	C₁₃×C₄⋊C₄	—	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×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
151	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
152	C₁₃×C₂²⋊C₄	—	2	1	no	—
153	C₁₃×C₂²⋊C₄	—	2	1	no	—
154	C₁₃×C₂²⋊C₄	—	2	1	no	—
155	C₁₃×C₂²⋊C₄	—	2	1	no	—
156	C₁₃×C₂²⋊C₄	—	2	1	no	—
157	C₁₃×C₂²⋊C₄	—	2	1	no	—
158	C₄²×C₁₃	—	2	1	no	—
159	C₄²×C₁₃	—	2	1	no	—
160	C₄²×C₁₃	—	2	1	no	—
161	C₄²×C₁₃	—	2	1	no	—
162	C₄²×C₁₃	—	2	1	no	—
163	C₄²×C₁₃	—	2	1	no	—
164	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
165	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₁₃	#41	1	1	yes	characteristic
167	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
168	#6099	—	2	4	no	—
169	#6099	—	4	4	no	—
170	C₂×#1055	—	2	2	no	—
171	C₂×#1055	—	2	2	no	—
172	C₂×#1055	—	2	2	no	—
173	C₂×#1055	—	4	4	no	—
174	C₂×#1055	C₂×D₄	1	2	yes	—
175	C₂×#1055	C₂×D₄	1	2	yes	—
176	#2971	—	13	1	no	—
177	#2970	—	13	1	no	—
178	C₄×#135	D₁₃	1	1	yes	characteristic
179	#1590	—	13	2	no	—
180	#1584	—	13	2	no	—
181	#1581	—	13	2	no	—
182	C₈×SD₁₆	—	13	2	no	—
183	#1568	—	13	1	no	—
184	#1488	—	13	1	no	—
185	#1488	—	13	1	no	—
186	C₈×M₁₆	—	13	1	no	—
187	C₂³×C₁₃	—	2	1	no	—
188	C₂³×C₁₃	—	2	1	no	—
189	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
190	Q₈×C₁₃	—	2	1	no	—
191	Q₈×C₁₃	—	2	1	no	—
192	Q₈×C₁₃	—	2	1	no	—
193	Q₈×C₁₃	C₂×M₁₆	1	2	yes	—
194	D₄×C₁₃	—	2	1	no	—
195	D₄×C₁₃	—	2	1	no	—
196	D₄×C₁₃	—	2	1	no	—
197	D₄×C₁₃	—	4	2	no	—
198	D₄×C₁₃	—	4	2	no	—
199	D₄×C₁₃	C₂×M₁₆	1	2	yes	—
200	C₂×C₄×C₁₃	—	2	1	no	—
201	C₂×C₄×C₁₃	—	2	1	no	—
202	C₂×C₄×C₁₃	—	2	1	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	1	no	—
205	C₂×C₄×C₁₃	—	2	1	no	—
206	C₂×C₄×C₁₃	—	2	1	no	—
207	C₂×C₄×C₁₃	—	2	1	no	—
208	C₂×C₄×C₁₃	—	2	1	no	—
209	C₂×C₄×C₁₃	—	4	1	no	—
210	C₂×C₄×C₁₃	—	4	2	no	—
211	C₂×C₄×C₁₃	—	4	2	no	—
212	C₂×C₄×C₁₃	—	4	2	no	—
213	C₂×C₄×C₁₃	—	4	2	no	—
214	C₂×C₄×C₁₃	—	8	1	no	—
215	C₂×C₄×C₁₃	—	8	1	no	—
216	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
217	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
218	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
222	C₈×C₁₃	—	2	1	no	—
223	C₈×C₁₃	—	2	1	no	—
224	C₈×C₁₃	—	2	1	no	—
225	C₈×C₁₃	C₂×M₁₆	1	2	yes	—
226	#1055	—	2	2	no	—
227	#1055	—	4	2	no	—
228	#1055	—	4	2	no	—
229	#1055	—	4	2	no	—
230	#1055	#135	1	4	yes	complemented
231	C₂×#135	Dic₁₃	1	1	yes	characteristic
232	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
233	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
234	#446	—	13	2	no	—
235	C₈×Q₈	—	13	2	no	—
236	C₄×Q₁₆	Dic₁₃	1	1	yes	characteristic
237	C₄×Q₁₆	C₂×D₁₃	1	1	yes	characteristic
238	C₄×SD₁₆	Dic₁₃	1	1	yes	characteristic
239	C₄×SD₁₆	Dic₁₃	1	1	yes	characteristic
240	C₄×SD₁₆	C₂×D₁₃	1	1	yes	characteristic
241	C₄×SD₁₆	C₂×D₁₃	1	1	yes	characteristic
242	C₄×D₈	Dic₁₃	1	1	yes	characteristic
243	C₄×D₈	C₂×D₁₃	1	1	yes	characteristic
244	#436	—	13	2	no	—
245	#436	—	26	2	no	—
246	#435	—	26	2	no	—
247	C₈×D₄	—	13	2	no	—
248	#432	—	13	1	no	—
249	#432	—	13	1	no	—
250	#432	—	26	1	no	—
251	#432	—	26	1	no	—
252	#431	—	13	1	no	—
253	#427	Dic₁₃	1	1	yes	characteristic
254	#416	Dic₁₃	1	1	yes	characteristic
255	#416	Dic₁₃	1	1	yes	characteristic
256	C₄×M₁₆	—	13	1	no	—
257	C₄×M₁₆	—	26	1	no	—
258	C₂×#97	—	26	1	no	—
259	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
260	#335	—	13	2	no	—
261	#334	—	13	2	no	—
262	Q₈⋊C₈	—	13	2	no	—
263	Q₈⋊C₈	—	13	2	no	—
264	D₄⋊C₈	—	13	2	no	—
265	D₄⋊C₈	—	13	2	no	—
266	#322	—	13	2	no	—
267	C₈²	—	13	2	no	—
268	C₂²×C₁₃	—	2	1	no	—
269	C₂²×C₁₃	—	2	2	no	—
270	C₂²×C₁₃	—	2	1	no	—
271	C₂²×C₁₃	—	2	1	no	—
272	C₂²×C₁₃	—	4	1	no	—
273	C₂²×C₁₃	—	4	1	no	—
274	C₂²×C₁₃	—	4	1	no	—
275	C₂²×C₁₃	—	4	1	no	—
276	C₂²×C₁₃	—	4	1	no	—
277	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
278	C₄×C₁₃	—	2	1	no	—
279	C₄×C₁₃	—	2	2	no	—
280	C₄×C₁₃	—	2	1	no	—
281	C₄×C₁₃	—	2	1	no	—
282	C₄×C₁₃	—	2	1	no	—
283	C₄×C₁₃	—	4	1	no	—
284	C₄×C₁₃	—	4	1	no	—
285	C₄×C₁₃	—	4	1	no	—
286	C₄×C₁₃	—	4	1	no	—
287	C₄×C₁₃	—	4	1	no	—
288	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
289	C₄×C₁₃	#568	1	1	yes	characteristic
290	C₄×C₁₃	C₂×#135	1	2	yes	—
291	C₂×#41	C₂×Dic₁₃	1	1	yes	characteristic
292	C₂×#41	C₂×Dic₁₃	1	1	yes	characteristic
293	#135	—	2	4	no	—
294	C₂×Q₁₆	C₂×Dic₁₃	1	1	yes	characteristic
295	C₂×SD₁₆	C₂×Dic₁₃	1	1	yes	characteristic
296	C₂×SD₁₆	C₂×Dic₁₃	1	1	yes	characteristic
297	C₂×D₈	C₂×Dic₁₃	1	1	yes	characteristic
298	C₂×M₁₆	—	13	2	no	—
299	C₂×M₁₆	—	26	2	no	—
300	C₂²×C₈	—	26	2	no	—
301	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
302	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
303	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
304	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
305	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
306	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
307	C₄×D₄	—	2	1	no	—
308	C₄×D₄	—	2	1	no	—
309	C₄×D₄	—	2	1	no	—
310	C₄×D₄	—	2	1	no	—
311	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
312	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
313	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
314	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
315	#117	—	2	1	no	—
316	#117	—	2	1	no	—
317	#117	C₂×Dic₁₃	1	1	yes	characteristic
318	#117	C₂×Dic₁₃	1	1	yes	characteristic
319	C₂×C₄²	—	2	1	no	—
320	C₂×C₄²	—	2	1	no	—
321	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
322	#107	C₂×Dic₁₃	1	1	yes	characteristic
323	#107	C₂×Dic₁₃	1	1	yes	characteristic
324	#106	C₂×Dic₁₃	1	1	yes	characteristic
325	#106	C₂×Dic₁₃	1	1	yes	characteristic
326	C₄⋊C₈	—	13	2	no	—
327	C₄⋊C₈	—	13	2	no	—
328	C₄⋊C₈	—	26	2	no	—
329	C₄⋊C₈	—	26	2	no	—
330	C₄⋊C₈	—	26	1	no	—
331	#103	C₂×Dic₁₃	1	1	yes	characteristic
332	#103	C₂×Dic₁₃	1	1	yes	characteristic
333	#103	C₂×Dic₁₃	1	1	yes	characteristic
334	#103	C₂×Dic₁₃	1	1	yes	characteristic
335	#102	C₂×Dic₁₃	1	1	yes	characteristic
336	#102	C₂×Dic₁₃	1	1	yes	characteristic
337	#102	C₂×Dic₁₃	1	1	yes	characteristic
338	#102	C₂×Dic₁₃	1	1	yes	characteristic
339	C₂²⋊C₈	—	26	2	no	—
340	C₂²⋊C₈	—	26	2	no	—
341	C₂²⋊C₈	—	26	1	no	—
342	C₂²⋊C₈	—	26	1	no	—
343	C₂²⋊C₈	—	26	1	no	—
344	#97	—	13	1	no	—
345	#97	—	13	1	no	—
346	#97	—	26	2	no	—
347	#97	—	26	1	no	—
348	#97	—	26	1	no	—
349	C₄×C₈	—	13	2	no	—
350	C₄×C₈	—	13	2	no	—
351	C₄×C₈	—	26	2	no	—
352	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
353	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
354	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
355	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
356	C₂×C₁₃	—	4	1	no	—
357	C₂×C₁₃	—	4	2	no	—
358	C₂×C₁₃	—	8	1	no	—
359	C₂×C₁₃	D₄×M₁₆	1	1	yes	characteristic
360	C₂×C₁₃	C₄×#135	1	1	yes	characteristic
361	C₂×C₁₃	#2957	1	1	yes	characteristic
362	#41	—	2	2	no	—
363	#41	—	2	2	no	—
364	#41	—	4	1	no	—
365	#41	—	4	1	no	—
366	C₂×Q₈	C₂²×Dic₁₃	1	1	yes	characteristic
367	C₂×Q₈	C₂²×Dic₁₃	1	1	yes	characteristic
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
371	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
379	C₂²×C₄	#6129	1	1	yes	characteristic
380	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
381	Q₁₆	—	2	2	no	—
382	SD₁₆	—	2	2	no	—
383	SD₁₆	#6099	1	4	yes	complemented
384	D₈	—	2	2	no	—
385	M₁₆	—	26	4	no	—
386	M₁₆	—	52	4	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	4	1	no	—
389	C₂×C₈	—	13	2	no	—
390	C₂×C₈	—	13	2	no	—
391	C₂×C₈	—	26	2	no	—
392	C₂×C₈	—	26	2	no	—
393	C₂×C₈	—	26	2	no	—
394	C₂×C₈	—	52	4	no	—
395	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
396	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
397	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
398	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
404	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
405	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
406	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
407	C₂²⋊C₄	—	2	1	no	—
408	C₂²⋊C₄	—	2	1	no	—
409	C₂²⋊C₄	—	2	1	no	—
410	C₂²⋊C₄	—	2	1	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	1	no	—
413	C₄²	—	2	1	no	—
414	C₄²	—	2	1	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	2	1	no	—
418	C₄²	—	2	1	no	—
419	C₄²	D₄×D₁₃	1	1	yes	characteristic
420	C₄²	#6129	1	1	yes	characteristic
421	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
422	C₄²	C₂³×D₁₃	1	1	yes	characteristic
423	C₁₃	#18037	1	1	yes	characteristic, complemented, Sylow
424	C₂³	—	2	1	no	—
425	C₂³	—	2	1	no	—
426	C₂³	D₄×Dic₁₃	1	1	yes	characteristic
427	Q₈	—	2	1	no	—
428	Q₈	—	2	1	no	—
429	Q₈	—	2	1	no	—
430	Q₈	C₂×#6099	1	2	yes	—
431	D₄	—	2	1	no	—
432	D₄	—	2	1	no	—
433	D₄	—	2	1	no	—
434	D₄	—	4	2	no	—
435	D₄	—	4	2	no	—
436	D₄	C₂×#6099	1	2	yes	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	8	1	no	—
452	C₂×C₄	—	8	1	no	—
453	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
454	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
455	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
456	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
457	C₂×C₄	C₂×#6129	1	1	yes	characteristic
458	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
459	C₈	—	2	1	no	—
460	C₈	—	2	1	no	—
461	C₈	—	2	1	no	—
462	C₈	—	13	4	no	—
463	C₈	—	26	2	no	—
464	C₈	—	52	2	no	—
465	C₈	—	52	2	no	—
466	C₈	—	52	2	no	—
467	C₈	C₂×#6099	1	2	yes	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	4	1	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	4	1	no	—
477	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	2	2	no	—
483	C₄	—	4	1	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	1	no	—
486	C₄	—	4	1	no	—
487	C₄	—	4	1	no	—
488	C₄	D₁₃×#135	1	2	yes	—
489	C₄	C₂²×#6099	1	1	yes	characteristic
490	C₄	#11719524	1	1	yes	characteristic
491	C₂	—	4	1	no	—
492	C₂	—	4	2	no	—
493	C₂	—	8	1	no	—
494	C₂	D₄×#6099	1	1	yes	characteristic
495	C₂	#135×Dic₁₃	1	1	yes	characteristic
496	C₂	#13123753	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₄×C₁₃×#135	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×C₁₃×#135	C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₄×#135	D₁₃
hypocenter	C₁₃	#18037
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #13123856	C₂	semidirect
2. #13123850	C₂	semidirect
3. #13113727	C₂	semidirect
4. #13113687	C₂	semidirect
5. #13113666	C₂	semidirect
6. SD₁₆×#1055	C₂	semidirect
7. #13113599	C₂	semidirect
8. #13113270	C₂	semidirect
9. #13113270	C₂	semidirect
10. C₈×#6099	C₂	semidirect
136. C₁₃×SD₁₆	M₁₆	semidirect
230. #1055	#135	semidirect
383. SD₁₆	#6099	semidirect
423. C₁₃	#18037	semidirect

Maximal subgroups

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

subgroup	index
#13123856	2
#13123850	2
#13113727	2
#13113687	2
#13113666	2
SD₁₆×#1055	2
#13113599	2
#13113270	2
C₈×#6099	2
C₄×C₁₃×#135	2
#18037	13