Subgroups — C₂×C₁₃×#3025 #15746733

Order 3328.

5086 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#585	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#525	C₂	1	3	yes	maximal, complemented
3	C₁₃×#3025	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#458	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₃×B(4,𝔽₂)	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#410	C₂	1	3	yes	maximal, complemented
7	C₁₃×#585	—	2	12	no	—
8	C₁₃×#585	C₂²	1	8	yes	complemented
9	C₂×C₁₃×2₋¹⁺⁴	—	2	3	no	—
10	C₂×C₁₃×H(5,𝔽₂)	—	2	3	no	—
11	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	4	yes	—
12	C₂²×C₁₃×#41	—	2	6	no	—
13	C₂²×C₁₃×#41	C₂²	1	3	yes	—
14	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
15	C₁₃×#525	—	2	12	no	—
16	C₁₃×#525	C₂²	1	24	yes	complemented
17	C₂×C₁₃×#123	C₂²	1	6	yes	complemented
18	C₂×C₁₃×C₂²⋊Q₈	—	2	3	no	—
19	C₂×C₁₃×#121	—	2	3	no	—
20	C₂×C₁₃×#120	C₂²	1	6	yes	complemented
21	C₂×C₄×D₄×C₁₃	—	2	6	no	—
22	C₂×C₁₃×#117	C₂²	1	3	yes	complemented
23	C₁₃×#458	C₂²	1	32	yes	complemented
24	C₁₃×B(4,𝔽₂)	C₂²	1	32	yes	complemented
25	C₁₃×#410	C₂²	1	24	yes	complemented
26	C₂×C₁₃×#99	C₂²	1	12	yes	complemented
27	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
28	C₁₃×2₋¹⁺⁴	—	2	24	no	—
29	C₁₃×2₋¹⁺⁴	—	2	24	no	—
30	C₁₃×H(5,𝔽₂)	—	2	24	no	—
31	C₁₃×H(5,𝔽₂)	—	2	24	no	—
32	C₁₃×H(5,𝔽₂)	—	2	24	no	—
33	C₁₃×H(5,𝔽₂)	C₂³	1	16	yes	—
34	C₂×C₁₃×#41	—	2	4	no	—
35	C₂×C₁₃×#41	—	2	12	no	—
36	C₂×C₁₃×#41	—	2	48	no	—
37	C₂×C₁₃×#41	—	2	6	no	—
38	C₂×C₁₃×#41	—	2	12	no	—
39	C₂×C₁₃×#41	—	2	6	no	—
40	C₂×C₁₃×#41	—	2	12	no	—
41	C₂×C₁₃×#41	—	2	48	no	—
42	C₂×C₁₃×#41	D₄	1	12	yes	complemented
43	C₂×C₁₃×#41	C₂³	1	12	yes	—
44	C₂²×Q₈×C₁₃	—	2	6	no	—
45	C₂²×Q₈×C₁₃	D₄	1	3	yes	complemented
46	C₂²×D₄×C₁₃	—	2	6	no	—
47	C₂²×D₄×C₁₃	—	2	12	no	—
48	C₂²×D₄×C₁₃	—	2	6	no	—
49	C₂²×D₄×C₁₃	D₄	1	3	yes	complemented
50	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
51	C₂³×C₄×C₁₃	—	2	4	no	—
52	C₂³×C₄×C₁₃	—	2	3	no	—
53	C₂³×C₄×C₁₃	—	2	3	no	—
54	C₂³×C₄×C₁₃	—	2	6	no	—
55	C₂³×C₄×C₁₃	D₄	1	6	yes	complemented
56	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₁₃	C₂³	1	4	yes	complemented
59	C₁₃×#123	—	2	12	no	—
60	C₁₃×#123	C₂³	1	24	yes	complemented
61	C₁₃×C₂²⋊Q₈	—	2	24	no	—
62	C₁₃×#121	—	2	24	no	—
63	C₁₃×#120	—	2	12	no	—
64	C₁₃×#120	C₂³	1	24	yes	complemented
65	C₄×D₄×C₁₃	—	2	48	no	—
66	C₁₃×#117	—	2	6	no	—
67	C₁₃×#117	C₂³	1	12	yes	complemented
68	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	6	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	6	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	6	no	—
72	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
73	C₂×C₄²×C₁₃	—	2	3	no	—
74	C₁₃×#99	C₂³	1	48	yes	complemented
75	C₂×#3025	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂⁴×C₁₃	—	2	4	no	—
77	C₂⁴×C₁₃	—	2	3	no	—
78	C₂⁴×C₁₃	—	2	3	no	—
79	C₂⁴×C₁₃	—	4	4	no	—
80	C₂⁴×C₁₃	C₂×D₄	1	6	yes	—
81	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
82	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
83	C₁₃×#41	—	2	32	no	—
84	C₁₃×#41	—	2	48	no	—
85	C₁₃×#41	—	2	96	no	—
86	C₁₃×#41	—	2	24	no	—
87	C₁₃×#41	—	2	24	no	—
88	C₁₃×#41	—	2	24	no	—
89	C₁₃×#41	—	2	48	no	—
90	C₁₃×#41	—	2	24	no	—
91	C₂×Q₈×C₁₃	—	2	4	no	—
92	C₂×Q₈×C₁₃	—	2	48	no	—
93	C₂×Q₈×C₁₃	—	2	6	no	—
94	C₂×Q₈×C₁₃	—	2	6	no	—
95	C₂×Q₈×C₁₃	C₂×D₄	1	12	yes	complemented
96	C₂×D₄×C₁₃	—	2	12	no	—
97	C₂×D₄×C₁₃	—	2	48	no	—
98	C₂×D₄×C₁₃	—	2	48	no	—
99	C₂×D₄×C₁₃	—	2	12	no	—
100	C₂×D₄×C₁₃	—	2	48	no	—
101	C₂×D₄×C₁₃	—	2	12	no	—
102	C₂×D₄×C₁₃	—	2	24	no	—
103	C₂×D₄×C₁₃	—	2	6	no	—
104	C₂×D₄×C₁₃	—	2	6	no	—
105	C₂×D₄×C₁₃	—	4	24	no	—
106	C₂×D₄×C₁₃	C₂×D₄	1	12	yes	—
107	C₂×D₄×C₁₃	C₂×D₄	1	12	yes	complemented
108	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
109	C₂²×C₄×C₁₃	—	2	12	no	—
110	C₂²×C₄×C₁₃	—	2	32	no	—
111	C₂²×C₄×C₁₃	—	2	6	no	—
112	C₂²×C₄×C₁₃	—	2	12	no	—
113	C₂²×C₄×C₁₃	—	2	6	no	—
114	C₂²×C₄×C₁₃	—	2	6	no	—
115	C₂²×C₄×C₁₃	—	2	3	no	—
116	C₂²×C₄×C₁₃	—	2	3	no	—
117	C₂²×C₄×C₁₃	—	2	12	no	—
118	C₂²×C₄×C₁₃	—	2	12	no	—
119	C₂²×C₄×C₁₃	—	4	3	no	—
120	C₂²×C₄×C₁₃	—	4	6	no	—
121	C₂²×C₄×C₁₃	—	4	6	no	—
122	C₂²×C₄×C₁₃	—	4	1	no	—
123	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
124	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
125	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
126	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
127	C₂²×C₄×C₁₃	C₂×D₄	1	24	yes	complemented
128	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
129	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
130	C₁₃×C₄⋊C₄	—	2	12	no	—
131	C₁₃×C₄⋊C₄	—	2	24	no	—
132	C₁₃×C₂²⋊C₄	—	2	24	no	—
133	C₁₃×C₂²⋊C₄	—	2	6	no	—
134	C₁₃×C₂²⋊C₄	—	2	24	no	—
135	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
136	C₄²×C₁₃	—	2	12	no	—
137	C₂×#585	C₂×C₁₃	1	1	yes	characteristic, complemented
138	C₂×#525	C₂×C₁₃	1	3	yes	complemented
139	#3025	C₂×C₁₃	1	16	yes	direct product factor
140	C₂×#458	C₂×C₁₃	1	4	yes	complemented
141	C₂×B(4,𝔽₂)	C₂×C₁₃	1	4	yes	complemented
142	C₂×#410	C₂×C₁₃	1	3	yes	complemented
143	C₂³×C₁₃	—	2	12	no	—
144	C₂³×C₁₃	—	2	16	no	—
145	C₂³×C₁₃	—	2	6	no	—
146	C₂³×C₁₃	—	2	6	no	—
147	C₂³×C₁₃	—	2	6	no	—
148	C₂³×C₁₃	—	4	2	no	—
149	C₂³×C₁₃	—	4	4	no	—
150	C₂³×C₁₃	—	4	6	no	—
151	C₂³×C₁₃	—	4	12	no	—
152	C₂³×C₁₃	—	4	12	no	—
153	C₂³×C₁₃	—	4	3	no	—
154	C₂³×C₁₃	—	4	1	no	—
155	C₂³×C₁₃	—	8	8	no	—
156	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
157	C₂³×C₁₃	C₂²×D₄	1	12	yes	—
158	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
159	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
160	Q₈×C₁₃	—	2	16	no	—
161	Q₈×C₁₃	—	2	24	no	—
162	D₄×C₁₃	—	2	48	no	—
163	D₄×C₁₃	—	2	24	no	—
164	D₄×C₁₃	—	2	24	no	—
165	D₄×C₁₃	—	2	24	no	—
166	D₄×C₁₃	—	4	48	no	—
167	C₂×C₄×C₁₃	—	2	48	no	—
168	C₂×C₄×C₁₃	—	2	6	no	—
169	C₂×C₄×C₁₃	—	2	6	no	—
170	C₂×C₄×C₁₃	—	2	24	no	—
171	C₂×C₄×C₁₃	—	2	24	no	—
172	C₂×C₄×C₁₃	—	2	12	no	—
173	C₂×C₄×C₁₃	—	2	6	no	—
174	C₂×C₄×C₁₃	—	4	12	no	—
175	C₂×C₄×C₁₃	—	4	3	no	—
176	C₂×C₄×C₁₃	—	4	1	no	—
177	C₂×C₄×C₁₃	—	4	4	no	—
178	C₂×C₄×C₁₃	—	4	12	no	—
179	C₂×C₄×C₁₃	#120	1	3	yes	—
180	C₂×C₄×C₁₃	#120	1	6	yes	—
181	C₂×C₄×C₁₃	#120	1	6	yes	—
182	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
184	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
185	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
186	#585	—	2	12	no	—
187	#585	C₂²×C₁₃	1	8	yes	complemented
188	C₂×2₋¹⁺⁴	—	2	3	no	—
189	C₂×H(5,𝔽₂)	—	2	3	no	—
190	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	4	yes	—
191	C₂²×#41	—	2	6	no	—
192	C₂²×#41	C₂²×C₁₃	1	3	yes	—
193	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
194	#525	—	2	12	no	—
195	#525	C₂²×C₁₃	1	24	yes	complemented
196	C₂×#123	C₂²×C₁₃	1	6	yes	complemented
197	C₂×C₂²⋊Q₈	—	2	3	no	—
198	C₂×#121	—	2	3	no	—
199	C₂×#120	C₂²×C₁₃	1	6	yes	complemented
200	C₂×C₄×D₄	—	2	6	no	—
201	C₂×#117	C₂²×C₁₃	1	3	yes	complemented
202	#458	C₂²×C₁₃	1	32	yes	complemented
203	B(4,𝔽₂)	C₂²×C₁₃	1	32	yes	complemented
204	#410	C₂²×C₁₃	1	24	yes	complemented
205	C₂×#99	C₂²×C₁₃	1	12	yes	complemented
206	C₂²×C₁₃	—	2	6	no	—
207	C₂²×C₁₃	—	2	12	no	—
208	C₂²×C₁₃	—	2	12	no	—
209	C₂²×C₁₃	—	4	3	no	—
210	C₂²×C₁₃	—	4	1	no	—
211	C₂²×C₁₃	—	4	12	no	—
212	C₂²×C₁₃	—	4	6	no	—
213	C₂²×C₁₃	—	4	12	no	—
214	C₂²×C₁₃	—	4	2	no	—
215	C₂²×C₁₃	—	4	4	no	—
216	C₂²×C₁₃	—	4	12	no	—
217	C₂²×C₁₃	—	8	6	no	—
218	C₂²×C₁₃	—	8	16	no	—
219	C₂²×C₁₃	C₂×#120	1	3	yes	—
220	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
221	C₂²×C₁₃	C₂³×D₄	1	3	yes	—
222	C₄×C₁₃	—	2	12	no	—
223	C₄×C₁₃	—	4	12	no	—
224	C₄×C₁₃	—	4	2	no	—
225	C₄×C₁₃	C₂×#120	1	2	yes	—
226	C₄×C₁₃	C₂×#120	1	6	yes	—
227	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
228	2₋¹⁺⁴	—	2	24	no	—
229	2₋¹⁺⁴	—	2	24	no	—
230	H(5,𝔽₂)	—	2	24	no	—
231	H(5,𝔽₂)	—	2	24	no	—
232	H(5,𝔽₂)	—	2	24	no	—
233	H(5,𝔽₂)	C₂³×C₁₃	1	16	yes	—
234	C₂×#41	—	2	4	no	—
235	C₂×#41	—	2	12	no	—
236	C₂×#41	—	2	48	no	—
237	C₂×#41	—	2	6	no	—
238	C₂×#41	—	2	12	no	—
239	C₂×#41	—	2	6	no	—
240	C₂×#41	—	2	12	no	—
241	C₂×#41	—	2	48	no	—
242	C₂×#41	D₄×C₁₃	1	12	yes	complemented
243	C₂×#41	C₂³×C₁₃	1	12	yes	—
244	C₂²×Q₈	—	2	6	no	—
245	C₂²×Q₈	D₄×C₁₃	1	3	yes	complemented
246	C₂²×D₄	—	2	6	no	—
247	C₂²×D₄	—	2	12	no	—
248	C₂²×D₄	—	2	6	no	—
249	C₂²×D₄	D₄×C₁₃	1	3	yes	complemented
250	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
251	C₂³×C₄	—	2	4	no	—
252	C₂³×C₄	—	2	3	no	—
253	C₂³×C₄	—	2	3	no	—
254	C₂³×C₄	—	2	6	no	—
255	C₂³×C₄	D₄×C₁₃	1	6	yes	complemented
256	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
257	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
258	C₂³×C₄	C₂³×C₁₃	1	4	yes	complemented
259	#123	—	2	12	no	—
260	#123	C₂³×C₁₃	1	24	yes	complemented
261	C₂²⋊Q₈	—	2	24	no	—
262	#121	—	2	24	no	—
263	#120	—	2	12	no	—
264	#120	C₂³×C₁₃	1	24	yes	complemented
265	C₄×D₄	—	2	48	no	—
266	#117	—	2	6	no	—
267	#117	C₂³×C₁₃	1	12	yes	complemented
268	C₂×C₄⋊C₄	—	2	3	no	—
269	C₂×C₄⋊C₄	—	2	6	no	—
270	C₂×C₂²⋊C₄	—	2	6	no	—
271	C₂×C₂²⋊C₄	—	2	6	no	—
272	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
273	C₂×C₄²	—	2	3	no	—
274	#99	C₂³×C₁₃	1	48	yes	complemented
275	C₂×C₁₃	—	2	3	no	—
276	C₂×C₁₃	—	2	3	no	—
277	C₂×C₁₃	—	4	4	no	—
278	C₂×C₁₃	—	4	12	no	—
279	C₂×C₁₃	#3025	1	2	yes	direct product factor
280	C₂×C₁₃	C₂²×#120	1	1	yes	characteristic
281	C₂⁴	—	2	4	no	—
282	C₂⁴	—	2	3	no	—
283	C₂⁴	—	2	3	no	—
284	C₂⁴	—	4	4	no	—
285	C₂⁴	C₂×D₄×C₁₃	1	6	yes	—
286	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
287	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
288	#41	—	2	32	no	—
289	#41	—	2	48	no	—
290	#41	—	2	96	no	—
291	#41	—	2	24	no	—
292	#41	—	2	24	no	—
293	#41	—	2	24	no	—
294	#41	—	2	48	no	—
295	#41	—	2	24	no	—
296	C₂×Q₈	—	2	4	no	—
297	C₂×Q₈	—	2	48	no	—
298	C₂×Q₈	—	2	6	no	—
299	C₂×Q₈	—	2	6	no	—
300	C₂×Q₈	C₂×D₄×C₁₃	1	12	yes	complemented
301	C₂×D₄	—	2	12	no	—
302	C₂×D₄	—	2	48	no	—
303	C₂×D₄	—	2	48	no	—
304	C₂×D₄	—	2	12	no	—
305	C₂×D₄	—	2	48	no	—
306	C₂×D₄	—	2	12	no	—
307	C₂×D₄	—	2	24	no	—
308	C₂×D₄	—	2	6	no	—
309	C₂×D₄	—	2	6	no	—
310	C₂×D₄	—	4	24	no	—
311	C₂×D₄	C₂×D₄×C₁₃	1	12	yes	—
312	C₂×D₄	C₂×D₄×C₁₃	1	12	yes	complemented
313	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
314	C₂²×C₄	—	2	12	no	—
315	C₂²×C₄	—	2	32	no	—
316	C₂²×C₄	—	2	6	no	—
317	C₂²×C₄	—	2	6	no	—
318	C₂²×C₄	—	2	12	no	—
319	C₂²×C₄	—	2	6	no	—
320	C₂²×C₄	—	2	3	no	—
321	C₂²×C₄	—	2	3	no	—
322	C₂²×C₄	—	2	12	no	—
323	C₂²×C₄	—	2	12	no	—
324	C₂²×C₄	—	4	1	no	—
325	C₂²×C₄	—	4	3	no	—
326	C₂²×C₄	—	4	6	no	—
327	C₂²×C₄	—	4	6	no	—
328	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
329	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
330	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
331	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
332	C₂²×C₄	C₂×D₄×C₁₃	1	24	yes	complemented
333	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
334	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
335	C₄⋊C₄	—	2	12	no	—
336	C₄⋊C₄	—	2	24	no	—
337	C₂²⋊C₄	—	2	24	no	—
338	C₂²⋊C₄	—	2	6	no	—
339	C₂²⋊C₄	—	2	24	no	—
340	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
341	C₄²	—	2	12	no	—
342	C₁₃	C₂×#3025	1	1	yes	characteristic, direct product factor, Sylow
343	C₂³	—	2	12	no	—
344	C₂³	—	2	16	no	—
345	C₂³	—	2	6	no	—
346	C₂³	—	2	6	no	—
347	C₂³	—	2	6	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	4	no	—
350	C₂³	—	4	6	no	—
351	C₂³	—	4	12	no	—
352	C₂³	—	4	12	no	—
353	C₂³	—	4	3	no	—
354	C₂³	—	4	1	no	—
355	C₂³	—	8	8	no	—
356	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
357	C₂³	C₂²×D₄×C₁₃	1	12	yes	—
358	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
359	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
360	Q₈	—	2	16	no	—
361	Q₈	—	2	24	no	—
362	D₄	—	2	48	no	—
363	D₄	—	2	24	no	—
364	D₄	—	2	24	no	—
365	D₄	—	2	24	no	—
366	D₄	—	4	48	no	—
367	C₂×C₄	—	2	48	no	—
368	C₂×C₄	—	2	6	no	—
369	C₂×C₄	—	2	6	no	—
370	C₂×C₄	—	2	24	no	—
371	C₂×C₄	—	2	24	no	—
372	C₂×C₄	—	2	12	no	—
373	C₂×C₄	—	2	6	no	—
374	C₂×C₄	—	4	12	no	—
375	C₂×C₄	—	4	3	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	4	12	no	—
379	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
380	C₂×C₄	C₁₃×#120	1	3	yes	—
381	C₂×C₄	C₁₃×#120	1	6	yes	—
382	C₂×C₄	C₁₃×#120	1	6	yes	—
383	C₂×C₄	C₂²×D₄×C₁₃	1	12	yes	—
384	C₂×C₄	C₂²×D₄×C₁₃	1	6	yes	—
385	C₂×C₄	C₂²×D₄×C₁₃	1	6	yes	—
386	C₂²	—	2	6	no	—
387	C₂²	—	2	12	no	—
388	C₂²	—	2	12	no	—
389	C₂²	—	4	3	no	—
390	C₂²	—	4	1	no	—
391	C₂²	—	4	12	no	—
392	C₂²	—	4	6	no	—
393	C₂²	—	4	12	no	—
394	C₂²	—	4	4	no	—
395	C₂²	—	4	12	no	—
396	C₂²	—	4	2	no	—
397	C₂²	—	8	6	no	—
398	C₂²	—	8	16	no	—
399	C₂²	C₂×C₁₃×#120	1	3	yes	—
400	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
401	C₂²	C₂³×D₄×C₁₃	1	3	yes	—
402	C₄	—	2	12	no	—
403	C₄	—	4	12	no	—
404	C₄	—	4	2	no	—
405	C₄	C₂×C₁₃×#120	1	2	yes	—
406	C₄	C₂×C₁₃×#120	1	6	yes	—
407	C₂	—	2	3	no	—
408	C₂	—	2	3	no	—
409	C₂	—	4	4	no	—
410	C₂	—	4	12	no	—
411	C₂	C₁₃×#3025	1	2	yes	direct product factor
412	C₂	C₂²×C₁₃×#120	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	#120
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂×#120
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#585	C₂	semidirect
2. C₂×C₁₃×#525	C₂	semidirect
3. C₁₃×#3025	C₂	direct (N × H)
4. C₂×C₁₃×#458	C₂	semidirect
5. C₂×C₁₃×B(4,𝔽₂)	C₂	semidirect
6. C₂×C₁₃×#410	C₂	semidirect
8. C₁₃×#585	C₂²	semidirect
14. C₂⁴×C₄×C₁₃	C₂²	semidirect
16. C₁₃×#525	C₂²	semidirect
17. C₂×C₁₃×#123	C₂²	semidirect
20. C₂×C₁₃×#120	C₂²	semidirect
22. C₂×C₁₃×#117	C₂²	semidirect
23. C₁₃×#458	C₂²	semidirect
24. C₁₃×B(4,𝔽₂)	C₂²	semidirect
25. C₁₃×#410	C₂²	semidirect
26. C₂×C₁₃×#99	C₂²	semidirect
42. C₂×C₁₃×#41	D₄	semidirect
45. C₂²×Q₈×C₁₃	D₄	semidirect
49. C₂²×D₄×C₁₃	D₄	semidirect
55. C₂³×C₄×C₁₃	D₄	semidirect
58. C₂³×C₄×C₁₃	C₂³	semidirect
60. C₁₃×#123	C₂³	semidirect
64. C₁₃×#120	C₂³	semidirect
67. C₁₃×#117	C₂³	semidirect
74. C₁₃×#99	C₂³	semidirect
75. C₂×#3025	C₁₃	direct (N × H)
95. C₂×Q₈×C₁₃	C₂×D₄	semidirect
107. C₂×D₄×C₁₃	C₂×D₄	semidirect
127. C₂²×C₄×C₁₃	C₂×D₄	semidirect
137. C₂×#585	C₂×C₁₃	semidirect
138. C₂×#525	C₂×C₁₃	semidirect
139. #3025	C₂×C₁₃	direct (N × H)
140. C₂×#458	C₂×C₁₃	semidirect
141. C₂×B(4,𝔽₂)	C₂×C₁₃	semidirect
142. C₂×#410	C₂×C₁₃	semidirect
187. #585	C₂²×C₁₃	semidirect
193. C₂⁴×C₄	C₂²×C₁₃	semidirect
195. #525	C₂²×C₁₃	semidirect
196. C₂×#123	C₂²×C₁₃	semidirect
199. C₂×#120	C₂²×C₁₃	semidirect
201. C₂×#117	C₂²×C₁₃	semidirect
202. #458	C₂²×C₁₃	semidirect
203. B(4,𝔽₂)	C₂²×C₁₃	semidirect
204. #410	C₂²×C₁₃	semidirect
205. C₂×#99	C₂²×C₁₃	semidirect
242. C₂×#41	D₄×C₁₃	semidirect
245. C₂²×Q₈	D₄×C₁₃	semidirect
249. C₂²×D₄	D₄×C₁₃	semidirect
255. C₂³×C₄	D₄×C₁₃	semidirect
258. C₂³×C₄	C₂³×C₁₃	semidirect
260. #123	C₂³×C₁₃	semidirect
264. #120	C₂³×C₁₃	semidirect
267. #117	C₂³×C₁₃	semidirect
274. #99	C₂³×C₁₃	semidirect
279. C₂×C₁₃	#3025	direct (N × H)
300. C₂×Q₈	C₂×D₄×C₁₃	semidirect
312. C₂×D₄	C₂×D₄×C₁₃	semidirect
332. C₂²×C₄	C₂×D₄×C₁₃	semidirect
342. C₁₃	C₂×#3025	direct (N × H)
411. C₂	C₁₃×#3025	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×#585	2
C₂×C₁₃×#525	2
C₁₃×#3025	2
C₂×C₁₃×#458	2
C₂×C₁₃×B(4,𝔽₂)	2
C₂×C₁₃×#410	2
C₂×#3025	13

Subgroups — C2×C13×#3025 #15746733

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3025 #15746733