Subgroups — C₄×C₁₃×#510 #15719792

Order 3328.

674 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#510	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2176	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2175	C₂	1	2	yes	maximal, complemented
6	C₄×C₁₃×Q₃₂	C₂	1	2	yes	maximal, complemented
7	C₄×C₁₃×SD₃₂	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2159	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2141	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2139	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
14	C₄×C₁₃×#41	—	2	1	no	—
15	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
16	C₁₃×#510	C₄	1	8	yes	direct product factor
17	C₂×C₁₃×Q₃₂	C₂²	1	2	yes	—
18	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
19	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
21	C₄×C₁₃×Q₁₆	—	2	1	no	—
22	C₄×C₁₃×Q₁₆	—	2	1	no	—
23	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
24	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
25	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
26	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
27	C₄×C₁₃×SD₁₆	—	2	1	no	—
28	C₄×C₁₃×SD₁₆	—	2	1	no	—
29	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
30	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
31	C₁₃×#427	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
33	C₁₃×#416	—	2	1	no	—
34	C₂×C₁₃×#103	—	2	1	no	—
35	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₁₃×#367	C₂²	1	2	yes	—
37	C₁₃×#366	C₂²	1	2	yes	—
38	C₁₃×#358	C₂²	1	2	yes	—
39	C₁₃×#358	C₂²	1	2	yes	—
40	C₁₃×#358	C₂²	1	2	yes	—
41	C₁₃×#357	C₂²	1	2	yes	—
42	C₁₃×#346	C₂²	1	2	yes	—
43	C₄×C₁₃×C₁₆	C₂²	1	2	yes	—
44	C₂×C₁₃×#41	—	2	1	no	—
45	C₂²×Q₈×C₁₃	—	2	1	no	—
46	C₁₃×#135	—	2	2	no	—
47	C₁₃×#135	C₂×C₄	1	4	yes	—
48	C₂×C₁₃×Q₁₆	—	2	1	no	—
49	C₂×C₁₃×Q₁₆	—	2	2	no	—
50	C₂×C₁₃×Q₁₆	C₂×C₄	1	4	yes	complemented
51	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
52	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
53	C₂×C₁₃×SD₁₆	—	2	1	no	—
54	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₄×Q₈×C₁₃	—	2	1	no	—
58	C₄×Q₈×C₁₃	—	2	1	no	—
59	C₄×Q₈×C₁₃	—	2	2	no	—
60	C₄×Q₈×C₁₃	—	2	2	no	—
61	C₄×Q₈×C₁₃	—	4	1	no	—
62	C₄×Q₈×C₁₃	—	4	1	no	—
63	C₄×D₄×C₁₃	—	2	1	no	—
64	C₄×D₄×C₁₃	—	2	1	no	—
65	C₄×D₄×C₁₃	—	4	1	no	—
66	C₄×D₄×C₁₃	—	4	1	no	—
67	C₁₃×#117	—	2	1	no	—
68	C₁₃×#117	—	4	1	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
71	C₂×C₄²×C₁₃	—	4	1	no	—
72	C₂×C₄²×C₁₃	—	4	1	no	—
73	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
74	C₁₃×Q₃₂	C₂×C₄	1	8	yes	complemented
75	C₁₃×SD₃₂	C₂×C₄	1	8	yes	complemented
76	C₁₃×M₃₂	—	2	2	no	—
77	C₁₃×M₃₂	C₂×C₄	1	4	yes	complemented
78	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
79	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
80	C₁₃×#107	—	2	1	no	—
81	C₁₃×#107	C₂³	1	2	yes	—
82	C₁₃×#107	C₂³	1	1	yes	characteristic
83	C₁₃×#107	C₂³	1	1	yes	characteristic
84	C₁₃×#106	—	2	1	no	—
85	C₁₃×#103	—	2	2	no	—
86	C₁₃×#103	—	2	2	no	—
87	C₁₃×#103	—	2	1	no	—
88	C₁₃×#103	—	2	1	no	—
89	C₁₃×#102	—	2	1	no	—
90	C₁₃×#102	—	2	1	no	—
91	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
92	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
93	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₄×#510	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₁₃×#41	—	2	4	no	—
97	C₁₃×#41	—	4	2	no	—
98	C₂×Q₈×C₁₃	—	2	4	no	—
99	C₂×Q₈×C₁₃	—	2	1	no	—
100	C₂×Q₈×C₁₃	—	2	2	no	—
101	C₂×Q₈×C₁₃	—	4	1	no	—
102	C₂×Q₈×C₁₃	—	4	2	no	—
103	C₂×D₄×C₁₃	—	2	1	no	—
104	C₂×D₄×C₁₃	—	4	1	no	—
105	C₂²×C₄×C₁₃	—	4	1	no	—
106	C₂²×C₄×C₁₃	—	4	1	no	—
107	C₂²×C₄×C₁₃	—	4	1	no	—
108	C₂²×C₄×C₁₃	—	4	1	no	—
109	C₂²×C₄×C₁₃	—	4	1	no	—
110	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₁₃×Q₁₆	—	2	4	no	—
114	C₁₃×Q₁₆	—	2	2	no	—
115	C₁₃×Q₁₆	—	2	1	no	—
116	C₁₃×Q₁₆	C₂²×C₄	1	4	yes	—
117	C₁₃×Q₁₆	C₂²×C₄	1	2	yes	—
118	C₁₃×SD₁₆	—	2	4	no	—
119	C₁₃×D₈	—	2	1	no	—
120	C₁₃×D₈	C₂²×C₄	1	2	yes	—
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
123	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₁₃	#41	1	2	yes	—
127	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
128	C₁₃×C₄⋊C₄	—	2	1	no	—
129	C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	4	1	no	—
132	C₁₃×C₄⋊C₄	—	4	2	no	—
133	C₁₃×C₄⋊C₄	—	4	2	no	—
134	C₁₃×C₄⋊C₄	—	4	1	no	—
135	C₁₃×C₄⋊C₄	—	4	1	no	—
136	C₁₃×C₂²⋊C₄	—	4	1	no	—
137	C₁₃×C₂²⋊C₄	—	4	1	no	—
138	C₁₃×C₂²⋊C₄	—	4	1	no	—
139	C₄²×C₁₃	—	4	1	no	—
140	C₄²×C₁₃	—	4	1	no	—
141	C₄²×C₁₃	—	4	2	no	—
142	C₄²×C₁₃	—	4	1	no	—
143	C₄²×C₁₃	—	4	2	no	—
144	C₄²×C₁₃	D₈	1	1	yes	characteristic
145	C₄²×C₁₃	D₈	1	1	yes	characteristic
146	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₁₃×C₁₆	—	2	2	no	—
149	C₁₃×C₁₆	C₂²×C₄	1	4	yes	—
150	C₂×#510	C₂×C₁₃	1	1	yes	characteristic
151	C₄×#135	C₂×C₁₃	1	1	yes	characteristic
152	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
153	#2176	C₂×C₁₃	1	2	yes	complemented
154	#2175	C₂×C₁₃	1	2	yes	complemented
155	C₄×Q₃₂	C₂×C₁₃	1	2	yes	complemented
156	C₄×SD₃₂	C₂×C₁₃	1	2	yes	complemented
157	#2159	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#2141	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#2139	C₂×C₁₃	1	1	yes	characteristic
160	C₄×M₃₂	C₂×C₁₃	1	1	yes	characteristic, complemented
161	C₂³×C₁₃	—	4	1	no	—
162	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
163	Q₈×C₁₃	—	2	2	no	—
164	Q₈×C₁₃	—	2	4	no	—
165	Q₈×C₁₃	—	4	2	no	—
166	Q₈×C₁₃	—	4	1	no	—
167	Q₈×C₁₃	—	4	4	no	—
168	D₄×C₁₃	—	2	2	no	—
169	D₄×C₁₃	—	4	4	no	—
170	D₄×C₁₃	—	4	1	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	4	1	no	—
173	C₂×C₄×C₁₃	—	4	1	no	—
174	C₂×C₄×C₁₃	—	4	2	no	—
175	C₂×C₄×C₁₃	—	4	4	no	—
176	C₂×C₄×C₁₃	—	4	4	no	—
177	C₂×C₄×C₁₃	—	4	1	no	—
178	C₂×C₄×C₁₃	—	4	1	no	—
179	C₂×C₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	—	8	2	no	—
181	C₂×C₄×C₁₃	—	8	2	no	—
182	C₂×C₄×C₁₃	—	8	2	no	—
183	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
184	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
189	C₂×C₄×C₁₃	#135	1	2	yes	—
190	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
191	C₈×C₁₃	—	2	1	no	—
192	C₈×C₁₃	—	2	1	no	—
193	C₈×C₁₃	C₄×D₄	1	2	yes	—
194	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
195	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
196	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
197	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
198	C₄×#41	—	2	1	no	—
199	C₂×C₄×Q₈	—	2	1	no	—
200	#510	C₄×C₁₃	1	8	yes	direct product factor
201	C₂×Q₃₂	C₂²×C₁₃	1	2	yes	—
202	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
203	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
204	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
205	C₄×Q₁₆	—	2	1	no	—
206	C₄×Q₁₆	—	2	1	no	—
207	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
208	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
209	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
210	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
211	C₄×SD₁₆	—	2	1	no	—
212	C₄×SD₁₆	—	2	1	no	—
213	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
214	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
215	#427	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
217	#416	—	2	1	no	—
218	C₂×#103	—	2	1	no	—
219	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
220	#367	C₂²×C₁₃	1	2	yes	—
221	#366	C₂²×C₁₃	1	2	yes	—
222	#358	C₂²×C₁₃	1	2	yes	—
223	#358	C₂²×C₁₃	1	2	yes	—
224	#358	C₂²×C₁₃	1	2	yes	—
225	#357	C₂²×C₁₃	1	2	yes	—
226	#346	C₂²×C₁₃	1	2	yes	—
227	C₄×C₁₆	C₂²×C₁₃	1	2	yes	—
228	C₂²×C₁₃	—	2	1	no	—
229	C₂²×C₁₃	—	2	1	no	—
230	C₂²×C₁₃	—	4	2	no	—
231	C₂²×C₁₃	—	8	1	no	—
232	C₂²×C₁₃	—	8	1	no	—
233	C₂²×C₁₃	C₄×D₈	1	2	yes	—
234	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
235	C₄×C₁₃	—	2	1	no	—
236	C₄×C₁₃	—	2	1	no	—
237	C₄×C₁₃	—	2	1	no	—
238	C₄×C₁₃	—	4	2	no	—
239	C₄×C₁₃	—	4	4	no	—
240	C₄×C₁₃	—	8	1	no	—
241	C₄×C₁₃	—	8	1	no	—
242	C₄×C₁₃	—	8	2	no	—
243	C₄×C₁₃	C₄×D₈	1	2	yes	—
244	C₄×C₁₃	#510	1	2	yes	direct product factor
245	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
246	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
247	C₂×#41	—	2	1	no	—
248	C₂²×Q₈	—	2	1	no	—
249	#135	—	2	2	no	—
250	#135	C₂×C₄×C₁₃	1	4	yes	—
251	C₂×Q₁₆	—	2	1	no	—
252	C₂×Q₁₆	—	2	2	no	—
253	C₂×Q₁₆	C₂×C₄×C₁₃	1	4	yes	complemented
254	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
255	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
256	C₂×SD₁₆	—	2	1	no	—
257	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
258	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
260	C₄×Q₈	—	2	2	no	—
261	C₄×Q₈	—	2	2	no	—
262	C₄×Q₈	—	2	1	no	—
263	C₄×Q₈	—	2	1	no	—
264	C₄×Q₈	—	4	1	no	—
265	C₄×Q₈	—	4	1	no	—
266	C₄×D₄	—	2	1	no	—
267	C₄×D₄	—	2	1	no	—
268	C₄×D₄	—	4	1	no	—
269	C₄×D₄	—	4	1	no	—
270	#117	—	2	1	no	—
271	#117	—	4	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	4	1	no	—
274	C₂×C₄²	—	4	1	no	—
275	C₂×C₄²	—	4	1	no	—
276	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
277	Q₃₂	C₂×C₄×C₁₃	1	8	yes	complemented
278	SD₃₂	C₂×C₄×C₁₃	1	8	yes	complemented
279	M₃₂	—	2	2	no	—
280	M₃₂	C₂×C₄×C₁₃	1	4	yes	complemented
281	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
282	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
283	#107	—	2	1	no	—
284	#107	C₂³×C₁₃	1	2	yes	—
285	#107	C₂³×C₁₃	1	1	yes	characteristic
286	#107	C₂³×C₁₃	1	1	yes	characteristic
287	#106	—	2	1	no	—
288	#103	—	2	2	no	—
289	#103	—	2	2	no	—
290	#103	—	2	1	no	—
291	#103	—	2	1	no	—
292	#102	—	2	1	no	—
293	#102	—	2	1	no	—
294	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
295	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
296	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
297	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
298	C₂×C₁₃	—	2	2	no	—
299	C₂×C₁₃	—	8	2	no	—
300	C₂×C₁₃	C₂×C₄×D₈	1	1	yes	characteristic
301	C₂×C₁₃	C₂×#510	1	1	yes	characteristic
302	C₂×C₁₃	#3414	1	1	yes	characteristic
303	#41	—	2	4	no	—
304	#41	—	4	2	no	—
305	C₂×Q₈	—	2	4	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	4	1	no	—
309	C₂×Q₈	—	4	2	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂²×C₄	—	4	1	no	—
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	—	4	1	no	—
315	C₂²×C₄	—	4	1	no	—
316	C₂²×C₄	—	4	1	no	—
317	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
318	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
320	Q₁₆	—	2	4	no	—
321	Q₁₆	—	2	2	no	—
322	Q₁₆	—	2	1	no	—
323	Q₁₆	C₂²×C₄×C₁₃	1	4	yes	—
324	Q₁₆	C₂²×C₄×C₁₃	1	2	yes	—
325	SD₁₆	—	2	4	no	—
326	D₈	—	2	1	no	—
327	D₈	C₂²×C₄×C₁₃	1	2	yes	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
330	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
331	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
332	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
333	C₂×C₈	C₁₃×#41	1	2	yes	—
334	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₄⋊C₄	—	4	2	no	—
340	C₄⋊C₄	—	4	2	no	—
341	C₄⋊C₄	—	4	1	no	—
342	C₄⋊C₄	—	4	1	no	—
343	C₂²⋊C₄	—	4	1	no	—
344	C₂²⋊C₄	—	4	1	no	—
345	C₂²⋊C₄	—	4	1	no	—
346	C₄²	—	4	1	no	—
347	C₄²	—	4	1	no	—
348	C₄²	—	4	1	no	—
349	C₄²	—	4	2	no	—
350	C₄²	—	4	2	no	—
351	C₄²	C₁₃×D₈	1	1	yes	characteristic
352	C₄²	C₁₃×D₈	1	1	yes	characteristic
353	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
354	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
355	C₁₆	—	2	2	no	—
356	C₁₆	C₂²×C₄×C₁₃	1	4	yes	—
357	C₁₃	C₄×#510	1	1	yes	characteristic, direct product factor, Sylow
358	C₂³	—	4	1	no	—
359	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
360	Q₈	—	2	2	no	—
361	Q₈	—	2	4	no	—
362	Q₈	—	4	4	no	—
363	Q₈	—	4	2	no	—
364	Q₈	—	4	1	no	—
365	D₄	—	2	2	no	—
366	D₄	—	4	4	no	—
367	D₄	—	4	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	8	2	no	—
378	C₂×C₄	—	8	2	no	—
379	C₂×C₄	—	8	2	no	—
380	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
381	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
382	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
383	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
384	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
385	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
386	C₂×C₄	C₁₃×#135	1	2	yes	—
387	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
388	C₈	—	2	1	no	—
389	C₈	—	2	1	no	—
390	C₈	C₄×D₄×C₁₃	1	2	yes	—
391	C₈	C₂³×C₄×C₁₃	1	1	yes	characteristic
392	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	8	1	no	—
397	C₂²	—	8	1	no	—
398	C₂²	C₄×C₁₃×D₈	1	2	yes	—
399	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	4	2	no	—
404	C₄	—	4	4	no	—
405	C₄	—	8	1	no	—
406	C₄	—	8	1	no	—
407	C₄	—	8	2	no	—
408	C₄	C₄×C₁₃×D₈	1	2	yes	—
409	C₄	C₁₃×#510	1	2	yes	direct product factor
410	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
411	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	8	2	no	—
414	C₂	C₂×C₄×C₁₃×D₈	1	1	yes	characteristic
415	C₂	C₂×C₁₃×#510	1	1	yes	characteristic
416	C₂	C₁₃×#3414	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂×D₈
commutator	C₈	C₂³×C₄×C₁₃
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂²×D₈
prime radical	C₂×C₁₃×#135	C₂²
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
4. C₁₃×#2176	C₂	semidirect
5. C₁₃×#2175	C₂	semidirect
6. C₄×C₁₃×Q₃₂	C₂	semidirect
7. C₄×C₁₃×SD₃₂	C₂	semidirect
8. C₁₃×#2159	C₂	semidirect
9. C₁₃×#2141	C₂	semidirect
11. C₄×C₁₃×M₃₂	C₂	semidirect
16. C₁₃×#510	C₄	direct (N × H)
50. C₂×C₁₃×Q₁₆	C₂×C₄	semidirect
74. C₁₃×Q₃₂	C₂×C₄	semidirect
75. C₁₃×SD₃₂	C₂×C₄	semidirect
77. C₁₃×M₃₂	C₂×C₄	semidirect
95. C₄×#510	C₁₃	direct (N × H)
152. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
153. #2176	C₂×C₁₃	semidirect
154. #2175	C₂×C₁₃	semidirect
155. C₄×Q₃₂	C₂×C₁₃	semidirect
156. C₄×SD₃₂	C₂×C₁₃	semidirect
157. #2159	C₂×C₁₃	semidirect
158. #2141	C₂×C₁₃	semidirect
160. C₄×M₃₂	C₂×C₁₃	semidirect
200. #510	C₄×C₁₃	direct (N × H)
244. C₄×C₁₃	#510	direct (N × H)
253. C₂×Q₁₆	C₂×C₄×C₁₃	semidirect
277. Q₃₂	C₂×C₄×C₁₃	semidirect
278. SD₃₂	C₂×C₄×C₁₃	semidirect
280. M₃₂	C₂×C₄×C₁₃	semidirect
357. C₁₃	C₄×#510	direct (N × H)
409. C₄	C₁₃×#510	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#510	2
C₄×C₁₃×#135	2
C₂×C₄×C₁₃×Q₁₆	2
C₁₃×#2176	2
C₁₃×#2175	2
C₄×C₁₃×Q₃₂	2
C₄×C₁₃×SD₃₂	2
C₁₃×#2159	2
C₁₃×#2141	2
C₁₃×#2139	2
C₄×C₁₃×M₃₂	2
C₄×#510	13

Subgroups — C4×C13×#510 #15719792

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₃×#510 #15719792