Subgroups — C₁₃×#34547 #15720886

Order 3328.

2938 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₃×#41	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2399	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2398	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2397	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2396	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2395	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2392	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2392	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2388	C₂	1	4	yes	maximal, complemented
10	C₄²×D₄×C₁₃	C₂	1	4	yes	maximal, complemented
11	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	C₂²	1	2	yes	—
13	C₄×C₁₃×#41	—	2	16	no	—
14	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
17	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
18	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
19	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
20	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
22	C₂×C₁₃×#117	C₂²	1	2	yes	—
23	C₂×C₁₃×#117	C₂²	1	4	yes	—
24	C₂×C₁₃×#117	C₂²	1	2	yes	—
25	C₂²×C₄²×C₁₃	C₂²	1	4	yes	—
26	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#400	C₂²	1	4	yes	—
28	C₁₃×#399	C₂²	1	4	yes	—
29	C₁₃×#398	C₂²	1	4	yes	—
30	C₁₃×#398	C₂²	1	4	yes	—
31	C₁₃×#397	C₂²	1	4	yes	—
32	C₁₃×#397	C₂²	1	4	yes	—
33	C₁₃×#396	C₂²	1	8	yes	—
34	C₁₃×#395	C₂²	1	4	yes	—
35	C₁₃×#394	C₂²	1	8	yes	—
36	C₁₃×#394	C₂²	1	4	yes	—
37	C₁₃×#394	C₂²	1	4	yes	—
38	C₁₃×#393	C₂²	1	4	yes	—
39	C₁₃×#392	C₂²	1	4	yes	—
40	C₁₃×#392	C₂²	1	4	yes	—
41	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
42	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
43	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	—
44	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
45	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
46	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
47	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
48	C₁₃×#376	C₂²	1	1	yes	characteristic
49	C₁₃×#376	C₂²	1	1	yes	characteristic
50	C₄³×C₁₃	C₂²	1	2	yes	—
51	C₂×C₁₃×#41	—	2	8	no	—
52	C₂×C₁₃×#41	—	2	16	no	—
53	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
54	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
55	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
56	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
57	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
58	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
59	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
60	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
62	C₄×Q₈×C₁₃	—	2	8	no	—
63	C₄×Q₈×C₁₃	—	2	8	no	—
64	C₄×D₄×C₁₃	—	2	16	no	—
65	C₄×D₄×C₁₃	—	2	16	no	—
66	C₄×D₄×C₁₃	—	2	32	no	—
67	C₄×D₄×C₁₃	—	2	8	no	—
68	C₄×D₄×C₁₃	—	2	8	no	—
69	C₄×D₄×C₁₃	—	2	16	no	—
70	C₁₃×#117	—	2	8	no	—
71	C₁₃×#117	—	2	16	no	—
72	C₁₃×#117	—	2	8	no	—
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
80	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
81	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
82	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
83	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
84	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
85	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
86	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
87	C₂×C₄²×C₁₃	—	2	16	no	—
88	C₂×C₄²×C₁₃	D₄	1	8	yes	complemented
89	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
90	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
91	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
92	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
93	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
94	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
95	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
97	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
98	C₁₃×#95	C₂³	1	4	yes	—
99	C₁₃×#95	C₂³	1	8	yes	—
100	C₁₃×#95	C₂³	1	4	yes	—
101	C₁₃×#95	C₂³	1	8	yes	—
102	C₁₃×#95	C₂³	1	4	yes	—
103	C₁₃×#95	C₂³	1	4	yes	—
104	#34547	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
105	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
106	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
107	C₁₃×#41	—	2	64	no	—
108	C₂×Q₈×C₁₃	—	2	4	no	—
109	C₂×Q₈×C₁₃	—	2	8	no	—
110	C₂×D₄×C₁₃	—	2	8	no	—
111	C₂×D₄×C₁₃	—	2	16	no	—
112	C₂×D₄×C₁₃	—	2	8	no	—
113	C₂×D₄×C₁₃	—	2	8	no	—
114	C₂×D₄×C₁₃	—	2	4	no	—
115	C₂×D₄×C₁₃	—	2	8	no	—
116	C₂×D₄×C₁₃	—	2	8	no	—
117	C₂²×C₄×C₁₃	—	2	8	no	—
118	C₂²×C₄×C₁₃	—	2	4	no	—
119	C₂²×C₄×C₁₃	—	2	8	no	—
120	C₂²×C₄×C₁₃	—	2	8	no	—
121	C₂²×C₄×C₁₃	—	2	8	no	—
122	C₂²×C₄×C₁₃	—	2	8	no	—
123	C₂²×C₄×C₁₃	—	2	16	no	—
124	C₂²×C₄×C₁₃	—	2	16	no	—
125	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
126	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
127	C₂²×C₄×C₁₃	#41	1	16	yes	complemented
128	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
129	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
130	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
131	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
132	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
136	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
137	C₁₃×C₄⋊C₄	—	2	8	no	—
138	C₁₃×C₄⋊C₄	—	2	8	no	—
139	C₁₃×C₄⋊C₄	—	2	4	no	—
140	C₁₃×C₄⋊C₄	—	2	4	no	—
141	C₁₃×C₄⋊C₄	—	2	8	no	—
142	C₁₃×C₄⋊C₄	—	2	16	no	—
143	C₁₃×C₄⋊C₄	—	2	8	no	—
144	C₁₃×C₂²⋊C₄	—	2	8	no	—
145	C₁₃×C₂²⋊C₄	—	2	16	no	—
146	C₁₃×C₂²⋊C₄	—	2	8	no	—
147	C₁₃×C₂²⋊C₄	—	2	8	no	—
148	C₁₃×C₂²⋊C₄	—	2	8	no	—
149	C₁₃×C₂²⋊C₄	—	2	16	no	—
150	C₁₃×C₂²⋊C₄	—	2	16	no	—
151	C₄²×C₁₃	—	2	8	no	—
152	C₄²×C₁₃	—	2	8	no	—
153	C₄²×C₁₃	—	2	8	no	—
154	C₄²×C₁₃	—	2	4	no	—
155	C₄²×C₁₃	—	2	16	no	—
156	C₄²×C₁₃	C₂×D₄	1	4	yes	—
157	C₄²×C₁₃	C₂×D₄	1	8	yes	—
158	C₄²×C₁₃	C₂×D₄	1	4	yes	—
159	C₄²×C₁₃	#41	1	8	yes	complemented
160	C₂×C₄×#41	C₂×C₁₃	1	2	yes	complemented
161	#2399	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#2398	C₂×C₁₃	1	2	yes	complemented
163	#2397	C₂×C₁₃	1	1	yes	characteristic, complemented
164	#2396	C₂×C₁₃	1	4	yes	complemented
165	#2395	C₂×C₁₃	1	4	yes	complemented
166	#2392	C₂×C₁₃	1	4	yes	complemented
167	#2392	C₂×C₁₃	1	4	yes	complemented
168	#2388	C₂×C₁₃	1	4	yes	complemented
169	C₄²×D₄	C₂×C₁₃	1	4	yes	complemented
170	C₄×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
171	C₂³×C₁₃	—	2	4	no	—
172	C₂³×C₁₃	—	2	2	no	—
173	C₂³×C₁₃	—	2	8	no	—
174	C₂³×C₁₃	—	2	8	no	—
175	C₂³×C₁₃	—	2	4	no	—
176	C₂³×C₁₃	—	2	4	no	—
177	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
178	C₂³×C₁₃	C₂×#41	1	8	yes	—
179	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
180	Q₈×C₁₃	—	2	16	no	—
181	D₄×C₁₃	—	2	32	no	—
182	D₄×C₁₃	—	2	16	no	—
183	D₄×C₁₃	—	2	32	no	—
184	C₂×C₄×C₁₃	—	2	4	no	—
185	C₂×C₄×C₁₃	—	2	8	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	4	no	—
188	C₂×C₄×C₁₃	—	2	4	no	—
189	C₂×C₄×C₁₃	—	2	16	no	—
190	C₂×C₄×C₁₃	—	2	32	no	—
191	C₂×C₄×C₁₃	—	2	8	no	—
192	C₂×C₄×C₁₃	—	2	4	no	—
193	C₂×C₄×C₁₃	—	2	4	no	—
194	C₂×C₄×C₁₃	—	2	8	no	—
195	C₂×C₄×C₁₃	—	2	4	no	—
196	C₂×C₄×C₁₃	—	2	8	no	—
197	C₂×C₄×C₁₃	—	2	8	no	—
198	C₂×C₄×C₁₃	—	4	16	no	—
199	C₂×C₄×C₁₃	—	4	16	no	—
200	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
201	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
202	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
203	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
204	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
205	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
206	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
207	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
208	C₂²×#41	C₂²×C₁₃	1	2	yes	—
209	C₄×#41	—	2	16	no	—
210	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
211	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
212	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
213	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
214	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
215	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
216	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
217	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
218	C₂×#117	C₂²×C₁₃	1	2	yes	—
219	C₂×#117	C₂²×C₁₃	1	4	yes	—
220	C₂×#117	C₂²×C₁₃	1	2	yes	—
221	C₂²×C₄²	C₂²×C₁₃	1	4	yes	—
222	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
223	#400	C₂²×C₁₃	1	4	yes	—
224	#399	C₂²×C₁₃	1	4	yes	—
225	#398	C₂²×C₁₃	1	4	yes	—
226	#398	C₂²×C₁₃	1	4	yes	—
227	#397	C₂²×C₁₃	1	4	yes	—
228	#397	C₂²×C₁₃	1	4	yes	—
229	#396	C₂²×C₁₃	1	8	yes	—
230	#395	C₂²×C₁₃	1	4	yes	—
231	#394	C₂²×C₁₃	1	8	yes	—
232	#394	C₂²×C₁₃	1	4	yes	—
233	#394	C₂²×C₁₃	1	4	yes	—
234	#393	C₂²×C₁₃	1	4	yes	—
235	#392	C₂²×C₁₃	1	4	yes	—
236	#392	C₂²×C₁₃	1	4	yes	—
237	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
238	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
239	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	—
240	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
241	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
242	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
243	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
244	#376	C₂²×C₁₃	1	1	yes	characteristic
245	#376	C₂²×C₁₃	1	1	yes	characteristic
246	C₄³	C₂²×C₁₃	1	2	yes	—
247	C₂²×C₁₃	—	2	4	no	—
248	C₂²×C₁₃	—	2	8	no	—
249	C₂²×C₁₃	—	2	2	no	—
250	C₂²×C₁₃	—	2	16	no	—
251	C₂²×C₁₃	—	4	4	no	—
252	C₂²×C₁₃	—	4	4	no	—
253	C₂²×C₁₃	—	4	4	no	—
254	C₂²×C₁₃	—	4	8	no	—
255	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
256	C₂²×C₁₃	C₂²×#41	1	4	yes	—
257	C₂²×C₁₃	C₂²×#41	1	2	yes	—
258	C₄×C₁₃	—	2	4	no	—
259	C₄×C₁₃	—	2	8	no	—
260	C₄×C₁₃	—	2	2	no	—
261	C₄×C₁₃	—	2	8	no	—
262	C₄×C₁₃	—	4	4	no	—
263	C₄×C₁₃	—	4	4	no	—
264	C₄×C₁₃	—	4	4	no	—
265	C₄×C₁₃	#525	1	8	yes	—
266	C₄×C₁₃	#532	1	4	yes	—
267	C₂×#41	—	2	8	no	—
268	C₂×#41	—	2	16	no	—
269	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
270	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
271	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
272	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
273	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
274	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
275	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
276	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
277	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
278	C₄×Q₈	—	2	8	no	—
279	C₄×Q₈	—	2	8	no	—
280	C₄×D₄	—	2	16	no	—
281	C₄×D₄	—	2	16	no	—
282	C₄×D₄	—	2	32	no	—
283	C₄×D₄	—	2	8	no	—
284	C₄×D₄	—	2	8	no	—
285	C₄×D₄	—	2	16	no	—
286	#117	—	2	8	no	—
287	#117	—	2	16	no	—
288	#117	—	2	8	no	—
289	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
290	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
291	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
294	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
295	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
296	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
297	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
298	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
299	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
300	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
301	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
302	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
303	C₂×C₄²	—	2	16	no	—
304	C₂×C₄²	D₄×C₁₃	1	8	yes	complemented
305	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
306	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
307	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
308	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
309	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
310	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
311	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
312	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
313	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
314	#95	C₂³×C₁₃	1	4	yes	—
315	#95	C₂³×C₁₃	1	4	yes	—
316	#95	C₂³×C₁₃	1	4	yes	—
317	#95	C₂³×C₁₃	1	8	yes	—
318	#95	C₂³×C₁₃	1	4	yes	—
319	#95	C₂³×C₁₃	1	8	yes	—
320	C₂×C₁₃	—	4	2	no	—
321	C₂×C₁₃	—	4	8	no	—
322	C₂×C₁₃	C₂×#525	1	2	yes	—
323	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
324	C₂×C₁₃	#3444	1	4	yes	—
325	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
326	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
327	#41	—	2	64	no	—
328	C₂×Q₈	—	2	4	no	—
329	C₂×Q₈	—	2	8	no	—
330	C₂×D₄	—	2	8	no	—
331	C₂×D₄	—	2	16	no	—
332	C₂×D₄	—	2	8	no	—
333	C₂×D₄	—	2	8	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	8	no	—
336	C₂×D₄	—	2	8	no	—
337	C₂²×C₄	—	2	8	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	8	no	—
340	C₂²×C₄	—	2	8	no	—
341	C₂²×C₄	—	2	8	no	—
342	C₂²×C₄	—	2	8	no	—
343	C₂²×C₄	—	2	16	no	—
344	C₂²×C₄	—	2	16	no	—
345	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
346	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
347	C₂²×C₄	C₁₃×#41	1	16	yes	complemented
348	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
349	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
350	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
351	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
352	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
353	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
354	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
355	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
356	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
357	C₄⋊C₄	—	2	8	no	—
358	C₄⋊C₄	—	2	8	no	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	8	no	—
362	C₄⋊C₄	—	2	16	no	—
363	C₄⋊C₄	—	2	8	no	—
364	C₂²⋊C₄	—	2	8	no	—
365	C₂²⋊C₄	—	2	16	no	—
366	C₂²⋊C₄	—	2	8	no	—
367	C₂²⋊C₄	—	2	8	no	—
368	C₂²⋊C₄	—	2	8	no	—
369	C₂²⋊C₄	—	2	16	no	—
370	C₂²⋊C₄	—	2	16	no	—
371	C₄²	—	2	8	no	—
372	C₄²	—	2	8	no	—
373	C₄²	—	2	8	no	—
374	C₄²	—	2	4	no	—
375	C₄²	—	2	16	no	—
376	C₄²	C₂×D₄×C₁₃	1	4	yes	—
377	C₄²	C₂×D₄×C₁₃	1	8	yes	—
378	C₄²	C₂×D₄×C₁₃	1	4	yes	—
379	C₄²	C₁₃×#41	1	8	yes	complemented
380	C₁₃	#34547	1	1	yes	characteristic, direct product factor, Sylow
381	C₂³	—	2	4	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	2	8	no	—
384	C₂³	—	2	8	no	—
385	C₂³	—	2	4	no	—
386	C₂³	—	2	4	no	—
387	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
388	C₂³	C₂×C₁₃×#41	1	8	yes	—
389	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
390	Q₈	—	2	16	no	—
391	D₄	—	2	32	no	—
392	D₄	—	2	16	no	—
393	D₄	—	2	32	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	8	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	16	no	—
400	C₂×C₄	—	2	32	no	—
401	C₂×C₄	—	2	8	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	8	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	8	no	—
407	C₂×C₄	—	2	8	no	—
408	C₂×C₄	—	4	16	no	—
409	C₂×C₄	—	4	16	no	—
410	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
411	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
412	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
413	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
414	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
415	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
416	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
417	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
418	C₂²	—	2	4	no	—
419	C₂²	—	2	8	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	16	no	—
422	C₂²	—	4	4	no	—
423	C₂²	—	4	4	no	—
424	C₂²	—	4	4	no	—
425	C₂²	—	4	8	no	—
426	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
427	C₂²	C₂²×C₁₃×#41	1	4	yes	—
428	C₂²	C₂²×C₁₃×#41	1	2	yes	—
429	C₄	—	2	4	no	—
430	C₄	—	2	8	no	—
431	C₄	—	2	2	no	—
432	C₄	—	2	8	no	—
433	C₄	—	4	4	no	—
434	C₄	—	4	4	no	—
435	C₄	—	4	4	no	—
436	C₄	C₁₃×#525	1	8	yes	—
437	C₄	C₁₃×#532	1	4	yes	—
438	C₂	—	4	2	no	—
439	C₂	—	4	8	no	—
440	C₂	C₂×C₁₃×#525	1	2	yes	—
441	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
442	C₂	C₁₃×#3444	1	4	yes	—

	subgroup	G/H
center	C₂×C₄²×C₁₃	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×C₁₃×#41	C₂	semidirect
2. C₁₃×#2399	C₂	semidirect
3. C₁₃×#2398	C₂	semidirect
4. C₁₃×#2397	C₂	semidirect
5. C₁₃×#2396	C₂	semidirect
6. C₁₃×#2395	C₂	semidirect
7. C₁₃×#2392	C₂	semidirect
8. C₁₃×#2392	C₂	semidirect
9. C₁₃×#2388	C₂	semidirect
10. C₄²×D₄×C₁₃	C₂	semidirect
11. C₄×C₁₃×#117	C₂	semidirect
88. C₂×C₄²×C₁₃	D₄	semidirect
104. #34547	C₁₃	direct (N × H)
127. C₂²×C₄×C₁₃	#41	semidirect
159. C₄²×C₁₃	#41	semidirect
160. C₂×C₄×#41	C₂×C₁₃	semidirect
161. #2399	C₂×C₁₃	semidirect
162. #2398	C₂×C₁₃	semidirect
163. #2397	C₂×C₁₃	semidirect
164. #2396	C₂×C₁₃	semidirect
165. #2395	C₂×C₁₃	semidirect
166. #2392	C₂×C₁₃	semidirect
167. #2392	C₂×C₁₃	semidirect
168. #2388	C₂×C₁₃	semidirect
169. C₄²×D₄	C₂×C₁₃	semidirect
170. C₄×#117	C₂×C₁₃	semidirect
304. C₂×C₄²	D₄×C₁₃	semidirect
347. C₂²×C₄	C₁₃×#41	semidirect
379. C₄²	C₁₃×#41	semidirect
380. C₁₃	#34547	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×C₄×C₁₃×#41	2
C₁₃×#2399	2
C₁₃×#2398	2
C₁₃×#2397	2
C₁₃×#2396	2
C₁₃×#2395	2
C₁₃×#2392	2
C₁₃×#2388	2
C₄²×D₄×C₁₃	2
C₄×C₁₃×#117	2
#34547	13

Subgroups — C13×#34547 #15720886

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34547 #15720886