Subgroups — C₂×C₁₃×#3283 #15747382

Order 3328.

2806 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	C₂²×C₁₃×#135	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₃×#547	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3283	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#467	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#461	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#452	C₂	1	4	yes	maximal, complemented
8	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₈×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×#41	C₂²	1	4	yes	—
11	C₂×C₁₃×#135	—	2	16	no	—
12	C₂×C₁₃×#135	C₂²	1	16	yes	complemented
13	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
14	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
15	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	—
16	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
18	C₁₃×#547	—	2	8	no	—
19	C₁₃×#547	C₂²	1	16	yes	complemented
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₁₃×#123	—	2	4	no	—
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
23	C₂×C₁₃×#121	—	2	2	no	—
24	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
26	C₂²×C₁₃×C₄⋊C₄	—	2	2	no	—
27	C₁₃×#494	C₂²	1	8	yes	complemented
28	C₁₃×#467	C₂²	1	16	yes	complemented
29	C₁₃×#461	C₂²	1	16	yes	complemented
30	C₁₃×#452	C₂²	1	32	yes	complemented
31	C₄×C₁₃×D₈	C₂²	1	8	yes	complemented
32	C₈×D₄×C₁₃	C₂²	1	8	yes	complemented
33	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#103	C₂²	1	4	yes	—
36	C₂×C₁₃×#102	C₂²	1	2	yes	—
37	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#41	—	2	8	no	—
40	C₂×C₁₃×#41	—	2	16	no	—
41	C₂×C₁₃×#41	—	4	8	no	—
42	C₂×C₁₃×#41	C₂³	1	16	yes	—
43	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
44	C₂²×D₄×C₁₃	—	2	4	no	—
45	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
46	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₃	—	2	2	no	—
48	C₂³×C₄×C₁₃	—	2	4	no	—
49	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
50	C₁₃×#135	—	2	64	no	—
51	C₂×C₁₃×Q₁₆	—	2	8	no	—
52	C₂×C₁₃×Q₁₆	—	4	4	no	—
53	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
54	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
55	C₂×C₁₃×SD₁₆	—	2	16	no	—
56	C₂×C₁₃×SD₁₆	C₂³	1	16	yes	—
57	C₂×C₁₃×D₈	D₄	1	8	yes	complemented
58	C₂×C₁₃×D₈	C₂³	1	4	yes	—
59	C₂²×C₈×C₁₃	—	2	8	no	—
60	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
62	C₂²×C₈×C₁₃	C₂³	1	8	yes	—
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₁₃×C₄⋊Q₈	—	2	4	no	—
65	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
66	C₁₃×#123	—	2	32	no	—
67	C₁₃×C₂²⋊Q₈	—	2	8	no	—
68	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
69	C₁₃×#121	—	2	16	no	—
70	C₄×D₄×C₁₃	—	2	4	no	—
71	C₄×D₄×C₁₃	D₄	1	4	yes	—
72	C₄×D₄×C₁₃	C₂³	1	8	yes	—
73	C₄×D₄×C₁₃	C₂³	1	4	yes	—
74	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	16	no	—
78	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
81	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
82	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
83	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
84	C₁₃×#107	C₂³	1	4	yes	—
85	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
86	C₁₃×#103	C₂³	1	16	yes	—
87	C₁₃×#102	C₂³	1	8	yes	—
88	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
89	C₄×C₈×C₁₃	C₂³	1	4	yes	—
90	C₂×#3283	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
91	C₂⁴×C₁₃	—	2	2	no	—
92	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
93	C₁₃×#41	—	2	32	no	—
94	C₁₃×#41	—	4	16	no	—
95	C₁₃×#41	—	4	32	no	—
96	C₂×Q₈×C₁₃	—	2	4	no	—
97	C₂×Q₈×C₁₃	—	2	8	no	—
98	C₂×Q₈×C₁₃	—	2	8	no	—
99	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
100	C₂×D₄×C₁₃	—	2	16	no	—
101	C₂×D₄×C₁₃	—	2	4	no	—
102	C₂×D₄×C₁₃	—	2	2	no	—
103	C₂×D₄×C₁₃	—	2	4	no	—
104	C₂×D₄×C₁₃	—	4	16	no	—
105	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
106	C₂×D₄×C₁₃	C₂×D₄	1	8	yes	—
107	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
108	C₂²×C₄×C₁₃	—	2	4	no	—
109	C₂²×C₄×C₁₃	—	2	4	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	2	4	no	—
112	C₂²×C₄×C₁₃	—	2	8	no	—
113	C₂²×C₄×C₁₃	—	2	16	no	—
114	C₂²×C₄×C₁₃	—	4	16	no	—
115	C₂²×C₄×C₁₃	—	4	8	no	—
116	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
121	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
122	C₁₃×Q₁₆	—	2	16	no	—
123	C₁₃×Q₁₆	—	4	8	no	—
124	C₁₃×SD₁₆	—	2	32	no	—
125	C₁₃×D₈	C₂×D₄	1	16	yes	complemented
126	C₂×C₈×C₁₃	—	2	4	no	—
127	C₂×C₈×C₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	—	2	16	no	—
129	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
130	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
131	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
132	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
133	C₁₃×C₄⋊C₄	—	2	8	no	—
134	C₁₃×C₄⋊C₄	—	2	16	no	—
135	C₁₃×C₄⋊C₄	—	2	8	no	—
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
138	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
139	C₁₃×C₂²⋊C₄	—	2	16	no	—
140	C₁₃×C₂²⋊C₄	—	2	8	no	—
141	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
142	C₄²×C₁₃	C₂×D₄	1	2	yes	—
143	C₄²×C₁₃	C₂⁴	1	2	yes	—
144	C₂²×#135	C₂×C₁₃	1	2	yes	complemented
145	C₂×#547	C₂×C₁₃	1	2	yes	complemented
146	#3283	C₂×C₁₃	1	16	yes	direct product factor
147	C₂×#494	C₂×C₁₃	1	1	yes	characteristic, complemented
148	C₂×#467	C₂×C₁₃	1	2	yes	complemented
149	C₂×#461	C₂×C₁₃	1	2	yes	complemented
150	C₂×#452	C₂×C₁₃	1	4	yes	complemented
151	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
152	C₂×C₈×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
153	C₂³×C₁₃	—	2	4	no	—
154	C₂³×C₁₃	—	2	8	no	—
155	C₂³×C₁₃	—	2	4	no	—
156	C₂³×C₁₃	—	2	4	no	—
157	C₂³×C₁₃	—	2	4	no	—
158	C₂³×C₁₃	—	4	4	no	—
159	C₂³×C₁₃	—	4	4	no	—
160	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
161	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
162	Q₈×C₁₃	—	2	8	no	—
163	Q₈×C₁₃	—	2	8	no	—
164	Q₈×C₁₃	—	4	8	no	—
165	D₄×C₁₃	—	2	8	no	—
166	D₄×C₁₃	—	2	8	no	—
167	D₄×C₁₃	—	2	4	no	—
168	D₄×C₁₃	—	4	32	no	—
169	D₄×C₁₃	C₂²×D₄	1	8	yes	—
170	C₂×C₄×C₁₃	—	2	4	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	8	no	—
173	C₂×C₄×C₁₃	—	2	4	no	—
174	C₂×C₄×C₁₃	—	2	4	no	—
175	C₂×C₄×C₁₃	—	2	4	no	—
176	C₂×C₄×C₁₃	—	2	8	no	—
177	C₂×C₄×C₁₃	—	4	32	no	—
178	C₂×C₄×C₁₃	—	4	8	no	—
179	C₂×C₄×C₁₃	—	4	4	no	—
180	C₂×C₄×C₁₃	—	4	16	no	—
181	C₂×C₄×C₁₃	#135	1	4	yes	complemented
182	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
183	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
184	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
186	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
187	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
188	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
189	C₈×C₁₃	—	2	4	no	—
190	C₈×C₁₃	—	2	2	no	—
191	C₈×C₁₃	C₂²×D₄	1	4	yes	—
192	C₂²×#41	C₂²×C₁₃	1	4	yes	—
193	C₂×#135	—	2	16	no	—
194	C₂×#135	C₂²×C₁₃	1	16	yes	complemented
195	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
196	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
197	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	—
198	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
199	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
200	#547	—	2	8	no	—
201	#547	C₂²×C₁₃	1	16	yes	complemented
202	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
203	C₂×#123	—	2	4	no	—
204	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
205	C₂×#121	—	2	2	no	—
206	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
207	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
208	C₂²×C₄⋊C₄	—	2	2	no	—
209	#494	C₂²×C₁₃	1	8	yes	complemented
210	#467	C₂²×C₁₃	1	16	yes	complemented
211	#461	C₂²×C₁₃	1	16	yes	complemented
212	#452	C₂²×C₁₃	1	32	yes	complemented
213	C₄×D₈	C₂²×C₁₃	1	8	yes	complemented
214	C₈×D₄	C₂²×C₁₃	1	8	yes	complemented
215	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×#103	C₂²×C₁₃	1	4	yes	—
218	C₂×#102	C₂²×C₁₃	1	2	yes	—
219	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
220	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
221	C₂²×C₁₃	—	2	4	no	—
222	C₂²×C₁₃	—	2	8	no	—
223	C₂²×C₁₃	—	2	4	no	—
224	C₂²×C₁₃	—	2	4	no	—
225	C₂²×C₁₃	—	4	8	no	—
226	C₂²×C₁₃	—	4	16	no	—
227	C₂²×C₁₃	—	4	4	no	—
228	C₂²×C₁₃	—	4	4	no	—
229	C₂²×C₁₃	D₄²	1	2	yes	—
230	C₂²×C₁₃	C₂×#135	1	2	yes	—
231	C₂²×C₁₃	#578	1	2	yes	—
232	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
233	C₄×C₁₃	—	2	4	no	—
234	C₄×C₁₃	—	2	2	no	—
235	C₄×C₁₃	—	4	8	no	—
236	C₄×C₁₃	—	4	4	no	—
237	C₄×C₁₃	D₄²	1	2	yes	—
238	C₄×C₁₃	C₂×#135	1	4	yes	complemented
239	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
240	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
241	C₂×#41	—	2	8	no	—
242	C₂×#41	—	2	16	no	—
243	C₂×#41	—	4	8	no	—
244	C₂×#41	C₂³×C₁₃	1	16	yes	—
245	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
246	C₂²×D₄	—	2	4	no	—
247	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
248	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
249	C₂³×C₄	—	2	2	no	—
250	C₂³×C₄	—	2	4	no	—
251	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
252	#135	—	2	64	no	—
253	C₂×Q₁₆	—	2	8	no	—
254	C₂×Q₁₆	—	4	4	no	—
255	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
256	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
257	C₂×SD₁₆	—	2	16	no	—
258	C₂×SD₁₆	C₂³×C₁₃	1	16	yes	—
259	C₂×D₈	D₄×C₁₃	1	8	yes	complemented
260	C₂×D₈	C₂³×C₁₃	1	4	yes	—
261	C₂²×C₈	—	2	8	no	—
262	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
263	C₂²×C₈	C₂³×C₁₃	1	8	yes	—
264	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
266	C₄⋊Q₈	—	2	4	no	—
267	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
268	#123	—	2	32	no	—
269	C₂²⋊Q₈	—	2	8	no	—
270	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
271	#121	—	2	16	no	—
272	C₄×D₄	—	2	4	no	—
273	C₄×D₄	D₄×C₁₃	1	4	yes	—
274	C₄×D₄	C₂³×C₁₃	1	8	yes	—
275	C₄×D₄	C₂³×C₁₃	1	4	yes	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	4	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	16	no	—
280	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
282	C₂×C₂²⋊C₄	—	2	4	no	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
285	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
286	#107	C₂³×C₁₃	1	4	yes	—
287	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
288	#103	C₂³×C₁₃	1	16	yes	—
289	#102	C₂³×C₁₃	1	8	yes	—
290	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
291	C₄×C₈	C₂³×C₁₃	1	4	yes	—
292	C₂×C₁₃	—	4	4	no	—
293	C₂×C₁₃	—	4	8	no	—
294	C₂×C₁₃	#3283	1	4	yes	direct product factor
295	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
296	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
297	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
298	C₂⁴	—	2	2	no	—
299	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
300	#41	—	2	32	no	—
301	#41	—	4	16	no	—
302	#41	—	4	32	no	—
303	C₂×Q₈	—	2	4	no	—
304	C₂×Q₈	—	2	8	no	—
305	C₂×Q₈	—	2	8	no	—
306	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
307	C₂×D₄	—	2	16	no	—
308	C₂×D₄	—	2	4	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	4	no	—
311	C₂×D₄	—	4	16	no	—
312	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
313	C₂×D₄	C₂×D₄×C₁₃	1	8	yes	—
314	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	8	no	—
320	C₂²×C₄	—	2	16	no	—
321	C₂²×C₄	—	4	16	no	—
322	C₂²×C₄	—	4	8	no	—
323	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
324	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
325	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
326	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
327	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
328	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
329	Q₁₆	—	2	16	no	—
330	Q₁₆	—	4	8	no	—
331	SD₁₆	—	2	32	no	—
332	D₈	C₂×D₄×C₁₃	1	16	yes	complemented
333	C₂×C₈	—	2	4	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	16	no	—
336	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
337	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
338	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
339	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
340	C₄⋊C₄	—	2	8	no	—
341	C₄⋊C₄	—	2	16	no	—
342	C₄⋊C₄	—	2	8	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
345	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
346	C₂²⋊C₄	—	2	16	no	—
347	C₂²⋊C₄	—	2	8	no	—
348	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
349	C₄²	C₂×D₄×C₁₃	1	2	yes	—
350	C₄²	C₂⁴×C₁₃	1	2	yes	—
351	C₁₃	C₂×#3283	1	1	yes	characteristic, direct product factor, Sylow
352	C₂³	—	2	4	no	—
353	C₂³	—	2	8	no	—
354	C₂³	—	2	4	no	—
355	C₂³	—	2	4	no	—
356	C₂³	—	2	4	no	—
357	C₂³	—	4	4	no	—
358	C₂³	—	4	4	no	—
359	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
360	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
361	Q₈	—	2	8	no	—
362	Q₈	—	2	8	no	—
363	Q₈	—	4	8	no	—
364	D₄	—	2	8	no	—
365	D₄	—	2	8	no	—
366	D₄	—	2	4	no	—
367	D₄	—	4	32	no	—
368	D₄	C₂²×D₄×C₁₃	1	8	yes	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	8	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	8	no	—
376	C₂×C₄	—	4	32	no	—
377	C₂×C₄	—	4	8	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	—	4	16	no	—
380	C₂×C₄	C₁₃×#135	1	4	yes	complemented
381	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
382	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
383	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
384	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
385	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
386	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
387	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
388	C₈	—	2	4	no	—
389	C₈	—	2	2	no	—
390	C₈	C₂²×D₄×C₁₃	1	4	yes	—
391	C₂²	—	2	4	no	—
392	C₂²	—	2	4	no	—
393	C₂²	—	2	4	no	—
394	C₂²	—	2	8	no	—
395	C₂²	—	4	8	no	—
396	C₂²	—	4	16	no	—
397	C₂²	—	4	4	no	—
398	C₂²	—	4	4	no	—
399	C₂²	D₄²×C₁₃	1	2	yes	—
400	C₂²	C₂×C₁₃×#135	1	2	yes	—
401	C₂²	C₁₃×#578	1	2	yes	—
402	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
403	C₄	—	2	2	no	—
404	C₄	—	2	4	no	—
405	C₄	—	4	4	no	—
406	C₄	—	4	8	no	—
407	C₄	D₄²×C₁₃	1	2	yes	—
408	C₄	C₂×C₁₃×#135	1	4	yes	complemented
409	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
410	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
411	C₂	—	4	4	no	—
412	C₂	—	4	8	no	—
413	C₂	C₁₃×#3283	1	4	yes	direct product factor
414	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
415	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
416	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×#135	C₂	semidirect
2. C₂×C₁₃×#547	C₂	semidirect
3. C₁₃×#3283	C₂	direct (N × H)
4. C₂×C₁₃×#494	C₂	semidirect
5. C₂×C₁₃×#467	C₂	semidirect
6. C₂×C₁₃×#461	C₂	semidirect
7. C₂×C₁₃×#452	C₂	semidirect
8. C₂×C₄×C₁₃×D₈	C₂	semidirect
9. C₂×C₈×D₄×C₁₃	C₂	semidirect
12. C₂×C₁₃×#135	C₂²	semidirect
19. C₁₃×#547	C₂²	semidirect
27. C₁₃×#494	C₂²	semidirect
28. C₁₃×#467	C₂²	semidirect
29. C₁₃×#461	C₂²	semidirect
30. C₁₃×#452	C₂²	semidirect
31. C₄×C₁₃×D₈	C₂²	semidirect
32. C₈×D₄×C₁₃	C₂²	semidirect
57. C₂×C₁₃×D₈	D₄	semidirect
90. C₂×#3283	C₁₃	direct (N × H)
125. C₁₃×D₈	C₂×D₄	semidirect
144. C₂²×#135	C₂×C₁₃	semidirect
145. C₂×#547	C₂×C₁₃	semidirect
146. #3283	C₂×C₁₃	direct (N × H)
147. C₂×#494	C₂×C₁₃	semidirect
148. C₂×#467	C₂×C₁₃	semidirect
149. C₂×#461	C₂×C₁₃	semidirect
150. C₂×#452	C₂×C₁₃	semidirect
151. C₂×C₄×D₈	C₂×C₁₃	semidirect
152. C₂×C₈×D₄	C₂×C₁₃	semidirect
181. C₂×C₄×C₁₃	#135	semidirect
194. C₂×#135	C₂²×C₁₃	semidirect
201. #547	C₂²×C₁₃	semidirect
209. #494	C₂²×C₁₃	semidirect
210. #467	C₂²×C₁₃	semidirect
211. #461	C₂²×C₁₃	semidirect
212. #452	C₂²×C₁₃	semidirect
213. C₄×D₈	C₂²×C₁₃	semidirect
214. C₈×D₄	C₂²×C₁₃	semidirect
238. C₄×C₁₃	C₂×#135	semidirect
259. C₂×D₈	D₄×C₁₃	semidirect
294. C₂×C₁₃	#3283	direct (N × H)
332. D₈	C₂×D₄×C₁₃	semidirect
351. C₁₃	C₂×#3283	direct (N × H)
380. C₂×C₄	C₁₃×#135	semidirect
408. C₄	C₂×C₁₃×#135	semidirect
413. C₂	C₁₃×#3283	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#135	2
C₂×C₁₃×#547	2
C₁₃×#3283	2
C₂×C₁₃×#494	2
C₂×C₁₃×#467	2
C₂×C₁₃×#461	2
C₂×C₁₃×#452	2
C₂×C₄×C₁₃×D₈	2
C₂×C₈×D₄×C₁₃	2
C₂×#3283	13

Subgroups — C2×C13×#3283 #15747382

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3283 #15747382