Subgroups — #525×D₁₀₉ #28376268

Order 13952.

1880 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₄×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295539	C₂	1	2	yes	maximal, complemented
4	#20295538	C₂	1	1	yes	maximal, characteristic, complemented
5	#20295537	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295536	C₂	1	2	yes	maximal, complemented
7	#20295535	C₂	1	4	yes	maximal, complemented
8	#20295534	C₂	1	2	yes	maximal, complemented
9	#20295533	C₂	1	1	yes	maximal, characteristic, complemented
10	#20295532	C₂	1	2	yes	maximal, complemented
11	#123×D₁₀₉	C₂	1	2	yes	maximal, complemented
12	C₂²⋊Q₈×D₁₀₉	C₂	1	2	yes	maximal, complemented
13	#121×D₁₀₉	C₂	1	2	yes	maximal, complemented
14	#120×D₁₀₉	C₂	1	2	yes	maximal, complemented
15	C₄×D₄×D₁₀₉	C₂	1	4	yes	maximal, complemented
16	#117×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#525×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂⁴×D₁₀₉	C₂²	1	1	yes	characteristic
19	C₂×#13182030	C₂²	1	1	yes	characteristic, complemented
20	C₂×#13182029	C₂²	1	1	yes	characteristic, complemented
21	C₂×#13182029	C₂²	1	2	yes	complemented
22	C₂×#13182028	C₂²	1	2	yes	complemented
23	C₂×#13182028	C₂²	1	1	yes	characteristic, complemented
24	#41×D₁₀₉	—	2	8	no	—
25	C₂×Q₈×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
26	C₂×D₄×D₁₀₉	C₂²	1	4	yes	—
27	C₂×D₄×D₁₀₉	C₂²	1	2	yes	—
28	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
29	C₂³×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₄×D₁₀₉	—	2	8	no	—
31	C₂²×C₄×D₁₀₉	C₂²	1	2	yes	—
32	C₂²×C₄×D₁₀₉	C₂²	1	2	yes	—
33	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
34	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
36	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₄×D₁₀₉	C₂²	1	2	yes	complemented
38	C₂²×C₄×D₁₀₉	C₂²	1	2	yes	complemented
39	C₂²×C₄×D₁₀₉	C₂²	1	2	yes	complemented
40	#16812684	C₂²	1	4	yes	complemented
41	#16812683	C₂²	1	2	yes	complemented
42	#16812682	C₂²	1	2	yes	complemented
43	#16812681	C₂²	1	4	yes	complemented
44	#16812680	C₂²	1	2	yes	complemented
45	#16812679	C₂²	1	2	yes	complemented
46	#16812678	C₂²	1	2	yes	complemented
47	#16812677	C₂²	1	4	yes	complemented
48	#16812676	C₂²	1	4	yes	complemented
49	#16812675	C₂²	1	2	yes	complemented
50	#16812674	C₂²	1	2	yes	complemented
51	#16812673	C₂²	1	2	yes	complemented
52	#16812672	C₂²	1	4	yes	complemented
53	#16812671	C₂²	1	4	yes	complemented
54	#16812670	C₂²	1	2	yes	complemented
55	#16812669	C₂²	1	2	yes	complemented
56	#16812669	C₂²	1	4	yes	complemented
57	#16812668	C₂²	1	2	yes	complemented
58	#16812667	C₂²	1	2	yes	complemented
59	#16812667	C₂²	1	4	yes	complemented
60	C₄×D₄₃₆	C₂²	1	4	yes	complemented
61	D₄×Dic₁₀₉	C₂²	1	4	yes	complemented
62	#16812661	C₂²	1	4	yes	complemented
63	C₄×C₂²⋊D₁₀₉	C₂²	1	4	yes	complemented
64	C₄×C₂²⋊D₁₀₉	C₂²	1	4	yes	complemented
65	#16812659	C₂²	1	4	yes	complemented
66	#16812659	C₂²	1	4	yes	complemented
67	#16812658	C₂²	1	1	yes	characteristic, complemented
68	#16812657	C₂²	1	2	yes	complemented
69	#16812656	C₂²	1	2	yes	complemented
70	#16812655	C₂²	1	2	yes	complemented
71	C₄⋊C₄×D₁₀₉	C₂²	1	2	yes	complemented
72	C₄⋊C₄×D₁₀₉	C₂²	1	4	yes	complemented
73	C₂²⋊C₄×D₁₀₉	C₂²	1	2	yes	—
74	C₂²⋊C₄×D₁₀₉	C₂²	1	4	yes	—
75	C₂²⋊C₄×D₁₀₉	C₂²	1	4	yes	complemented
76	C₄²×D₁₀₉	C₂²	1	2	yes	complemented
77	C₂×#41×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
78	C₂³×C₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
79	#123×C₁₀₉	C₂²	1	2	yes	complemented
80	C₂²⋊Q₈×C₁₀₉	C₂²	1	2	yes	complemented
81	#121×C₁₀₉	C₂²	1	2	yes	complemented
82	#120×C₁₀₉	C₂²	1	2	yes	complemented
83	C₄×D₄×C₁₀₉	C₂²	1	4	yes	complemented
84	#117×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
85	C₂³×D₁₀₉	—	2	4	no	—
86	C₂³×D₁₀₉	—	2	8	no	—
87	C₂³×D₁₀₉	C₂³	1	2	yes	—
88	C₂³×D₁₀₉	C₂³	1	1	yes	characteristic
89	C₂³×D₁₀₉	C₂³	1	2	yes	—
90	C₂³×D₁₀₉	C₂³	1	1	yes	characteristic
91	C₂³×D₁₀₉	C₂³	1	2	yes	—
92	#13182030	—	2	4	no	—
93	#13182029	—	2	4	no	—
94	#13182029	—	2	8	no	—
95	#13182028	—	2	8	no	—
96	#13182028	—	2	4	no	—
97	C₂×Dic₂₁₈	C₂³	1	2	yes	complemented
98	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic, complemented
99	Q₈×D₁₀₉	—	2	4	no	—
100	C₂×D₄₃₆	C₂³	1	4	yes	—
101	C₂×D₄₃₆	C₂³	1	2	yes	—
102	C₂×D₄₃₆	C₂³	1	1	yes	characteristic, complemented
103	C₂×C₂²⋊D₁₀₉	C₂³	1	4	yes	—
104	C₂×C₂²⋊D₁₀₉	C₂³	1	4	yes	—
105	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
106	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
107	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	complemented
108	D₄×D₁₀₉	—	2	8	no	—
109	D₄×D₁₀₉	—	2	16	no	—
110	D₄×D₁₀₉	—	2	4	no	—
111	C₂²×Dic₁₀₉	—	2	4	no	—
112	C₂²×Dic₁₀₉	C₂³	1	2	yes	—
113	C₂²×Dic₁₀₉	C₂³	1	2	yes	—
114	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
115	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
116	C₂²×Dic₁₀₉	C₂³	1	2	yes	complemented
117	C₂×C₄×D₁₀₉	—	2	4	no	—
118	C₂×C₄×D₁₀₉	—	2	4	no	—
119	C₂×C₄×D₁₀₉	—	2	4	no	—
120	C₂×C₄×D₁₀₉	—	2	8	no	—
121	C₂×C₄×D₁₀₉	—	2	8	no	—
122	C₂×C₄×D₁₀₉	—	2	8	no	—
123	C₂×C₄×D₁₀₉	—	2	8	no	—
124	C₂×C₄×D₁₀₉	—	2	8	no	—
125	C₂×C₄×D₁₀₉	D₄	1	8	yes	complemented
126	C₂×C₄×D₁₀₉	C₂³	1	4	yes	—
127	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
128	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
129	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
130	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
131	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
132	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
133	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
134	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
135	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
136	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
137	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
138	C₂×C₄×D₁₀₉	C₂³	1	2	yes	complemented
139	C₂×C₄×D₁₀₉	C₂³	1	2	yes	complemented
140	C₄⋊Dic₁₀₉	C₂³	1	2	yes	complemented
141	C₄⋊Dic₁₀₉	C₂³	1	4	yes	complemented
142	#13182008	C₂³	1	4	yes	complemented
143	#13182008	C₂³	1	4	yes	complemented
144	#13182008	C₂³	1	4	yes	complemented
145	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	—
146	C₂²⋊Dic₁₀₉	C₂³	1	4	yes	—
147	C₂²⋊Dic₁₀₉	C₂³	1	4	yes	complemented
148	#13182006	C₂³	1	4	yes	—
149	#13182006	C₂³	1	4	yes	—
150	#13182006	C₂³	1	4	yes	—
151	#13182006	C₂³	1	4	yes	complemented
152	#13182006	C₂³	1	4	yes	complemented
153	C₄×Dic₁₀₉	C₂³	1	4	yes	complemented
154	C₄×Dic₁₀₉	C₂³	1	2	yes	complemented
155	C₂⁴×C₁₀₉	C₂³	1	1	yes	characteristic
156	#41×C₁₀₉	—	2	4	no	—
157	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic, complemented
158	C₂×D₄×C₁₀₉	C₂³	1	4	yes	—
159	C₂×D₄×C₁₀₉	C₂³	1	2	yes	—
160	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic, complemented
161	C₂²×C₄×C₁₀₉	—	2	4	no	—
162	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
163	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
164	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
165	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
166	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	complemented
167	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	complemented
168	C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	complemented
169	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
170	C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
171	C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	complemented
172	C₄²×C₁₀₉	C₂³	1	2	yes	complemented
173	C₂³×C₁₀₉	—	2	2	no	—
174	C₂³×C₁₀₉	—	2	4	no	—
175	C₂³×C₁₀₉	C₂⁴	1	2	yes	—
176	C₂³×C₁₀₉	C₂⁴	1	1	yes	characteristic
177	C₂³×C₁₀₉	C₂⁴	1	2	yes	—
178	C₂²×D₁₀₉	—	2	32	no	—
179	C₂²×D₁₀₉	—	2	2	no	—
180	C₂²×D₁₀₉	—	2	4	no	—
181	C₂²×D₁₀₉	—	2	4	no	—
182	C₂²×D₁₀₉	—	2	4	no	—
183	C₂²×D₁₀₉	—	2	4	no	—
184	C₂²×D₁₀₉	—	2	4	no	—
185	C₂²×D₁₀₉	—	2	4	no	—
186	C₂²×D₁₀₉	—	2	4	no	—
187	C₂²×D₁₀₉	—	2	4	no	—
188	C₂²×D₁₀₉	—	2	8	no	—
189	C₂²×D₁₀₉	C₂×D₄	1	4	yes	—
190	C₂²×D₁₀₉	#41	1	8	yes	complemented
191	C₂²×D₁₀₉	C₂⁴	1	2	yes	—
192	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
193	C₂²×D₁₀₉	C₂⁴	1	2	yes	—
194	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
195	Q₈×C₁₀₉	—	2	2	no	—
196	D₄×C₁₀₉	—	2	4	no	—
197	D₄×C₁₀₉	—	2	8	no	—
198	D₄×C₁₀₉	—	2	2	no	—
199	C₂×C₄×C₁₀₉	—	2	2	no	—
200	C₂×C₄×C₁₀₉	—	2	4	no	—
201	C₂×C₄×C₁₀₉	—	2	4	no	—
202	C₂×C₄×C₁₀₉	—	2	4	no	—
203	C₂×C₄×C₁₀₉	C₂×D₄	1	4	yes	complemented
204	C₂×C₄×C₁₀₉	C₂⁴	1	4	yes	—
205	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
206	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
207	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
208	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
209	C₂²⋊D₁₀₉	—	2	4	no	—
210	C₂²⋊D₁₀₉	—	2	8	no	—
211	C₂²⋊D₁₀₉	—	2	4	no	—
212	C₂²⋊D₁₀₉	—	2	8	no	—
213	C₂²⋊D₁₀₉	—	2	4	no	—
214	C₂×Dic₁₀₉	—	2	2	no	—
215	C₂×Dic₁₀₉	—	2	4	no	—
216	C₂×Dic₁₀₉	—	2	4	no	—
217	C₂×Dic₁₀₉	—	2	4	no	—
218	C₂×Dic₁₀₉	C₂×D₄	1	4	yes	complemented
219	C₂×Dic₁₀₉	C₂⁴	1	4	yes	—
220	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
221	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
222	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
223	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
224	D₄₃₆	—	2	4	no	—
225	D₄₃₆	—	2	8	no	—
226	D₄₃₆	—	2	2	no	—
227	C₄×D₁₀₉	—	2	4	no	—
228	C₄×D₁₀₉	—	2	4	no	—
229	C₄×D₁₀₉	—	2	4	no	—
230	C₄×D₁₀₉	—	2	8	no	—
231	C₄×D₁₀₉	—	2	4	no	—
232	C₄×D₁₀₉	—	2	4	no	—
233	C₄×D₁₀₉	—	2	4	no	—
234	C₄×D₁₀₉	—	2	4	no	—
235	C₄×D₁₀₉	—	2	4	no	—
236	C₄×D₁₀₉	—	2	4	no	—
237	C₄×D₁₀₉	C₂×D₄	1	4	yes	—
238	C₄×D₁₀₉	C₂×D₄	1	4	yes	—
239	C₄×D₁₀₉	C₂×D₄	1	4	yes	complemented
240	C₄×D₁₀₉	C₂×D₄	1	4	yes	complemented
241	Dic₂₁₈	—	2	2	no	—
242	Dic₂₁₈	—	2	4	no	—
243	C₂²×C₁₀₉	—	2	8	no	—
244	C₂²×C₁₀₉	—	2	2	no	—
245	C₂²×C₁₀₉	—	2	2	no	—
246	C₂²×C₁₀₉	—	2	2	no	—
247	C₂²×C₁₀₉	—	2	2	no	—
248	C₂²×C₁₀₉	—	2	4	no	—
249	C₂²×C₁₀₉	C₂²×D₄	1	2	yes	—
250	C₂²×C₁₀₉	C₂×#41	1	4	yes	complemented
251	C₂²×C₁₀₉	C₂⁵	1	1	yes	characteristic
252	C₂×D₁₀₉	—	2	16	no	—
253	C₂×D₁₀₉	—	2	8	no	—
254	C₂×D₁₀₉	—	2	2	no	—
255	C₂×D₁₀₉	—	2	2	no	—
256	C₂×D₁₀₉	—	2	2	no	—
257	C₂×D₁₀₉	—	2	8	no	—
258	C₂×D₁₀₉	—	2	16	no	—
259	C₂×D₁₀₉	—	2	2	no	—
260	C₂×D₁₀₉	—	2	4	no	—
261	C₂×D₁₀₉	—	4	8	no	—
262	C₂×D₁₀₉	C₂²×D₄	1	2	yes	—
263	C₂×D₁₀₉	C₂²×D₄	1	2	yes	—
264	C₂×D₁₀₉	C₂×#41	1	4	yes	—
265	C₂×D₁₀₉	C₂×#41	1	4	yes	complemented
266	C₄×C₁₀₉	—	2	2	no	—
267	C₄×C₁₀₉	—	2	2	no	—
268	C₄×C₁₀₉	—	2	4	no	—
269	C₄×C₁₀₉	C₂²×D₄	1	2	yes	—
270	C₄×C₁₀₉	C₂²×D₄	1	2	yes	—
271	Dic₁₀₉	—	2	2	no	—
272	Dic₁₀₉	—	2	2	no	—
273	Dic₁₀₉	—	2	4	no	—
274	Dic₁₀₉	C₂²×D₄	1	2	yes	—
275	Dic₁₀₉	C₂²×D₄	1	2	yes	—
276	C₂×C₁₀₉	—	2	2	no	—
277	C₂×C₁₀₉	—	2	4	no	—
278	C₂×C₁₀₉	—	4	2	no	—
279	C₂×C₁₀₉	C₂³×D₄	1	1	yes	characteristic
280	C₂×C₁₀₉	C₂²×#41	1	2	yes	—
281	D₁₀₉	—	2	2	no	—
282	D₁₀₉	—	2	4	no	—
283	D₁₀₉	—	4	2	no	—
284	D₁₀₉	#525	1	4	yes	direct product factor
285	C₂×#525	—	109	1	no	maximal, Sylow
286	C₁₀₉	C₂×#525	1	1	yes	characteristic, complemented, Sylow
287	C₂²×#41	—	109	1	no	—
288	C₂⁴×C₄	—	109	1	no	—
289	#525	—	109	1	no	—
290	#525	—	109	1	no	—
291	#525	—	109	2	no	—
292	#525	—	109	2	no	—
293	#525	—	109	2	no	—
294	#525	—	109	2	no	—
295	#525	—	109	4	no	—
296	#525	—	109	1	no	—
297	#525	D₁₀₉	1	1	yes	characteristic, direct product factor
298	C₂×#123	—	109	2	no	—
299	C₂×C₂²⋊Q₈	—	109	2	no	—
300	C₂×#121	—	109	2	no	—
301	C₂×#120	—	109	2	no	—
302	C₂×C₄×D₄	—	109	4	no	—
303	C₂×#117	—	109	1	no	—
304	C₂⁵	—	109	1	no	—
305	C₂×#41	—	109	1	no	—
306	C₂×#41	—	109	2	no	—
307	C₂×#41	—	109	1	no	—
308	C₂×#41	—	109	1	no	—
309	C₂×#41	—	109	2	no	—
310	C₂×#41	—	218	8	no	—
311	C₂×#41	C₂×D₁₀₉	1	1	yes	characteristic, complemented
312	C₂²×Q₈	—	109	1	no	—
313	C₂²×D₄	—	109	4	no	—
314	C₂²×D₄	—	109	2	no	—
315	C₂²×D₄	—	109	1	no	—
316	C₂³×C₄	—	109	1	no	—
317	C₂³×C₄	—	109	1	no	—
318	C₂³×C₄	—	109	2	no	—
319	C₂³×C₄	—	109	2	no	—
320	C₂³×C₄	—	109	1	no	—
321	C₂³×C₄	—	109	1	no	—
322	C₂³×C₄	—	109	2	no	—
323	C₂³×C₄	—	109	2	no	—
324	C₂³×C₄	—	109	1	no	—
325	C₂³×C₄	—	109	2	no	—
326	C₂³×C₄	—	218	8	no	—
327	C₂³×C₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
328	#123	—	109	2	no	—
329	#123	—	109	2	no	—
330	#123	—	109	4	no	—
331	#123	—	109	2	no	—
332	#123	—	109	4	no	—
333	#123	C₂×D₁₀₉	1	2	yes	complemented
334	C₂²⋊Q₈	—	109	2	no	—
335	C₂²⋊Q₈	—	109	2	no	—
336	C₂²⋊Q₈	—	109	4	no	—
337	C₂²⋊Q₈	—	109	2	no	—
338	C₂²⋊Q₈	—	109	4	no	—
339	C₂²⋊Q₈	C₂×D₁₀₉	1	2	yes	complemented
340	#121	—	109	4	no	—
341	#121	—	109	2	no	—
342	#121	—	109	2	no	—
343	#121	—	109	2	no	—
344	#121	—	109	4	no	—
345	#121	C₂×D₁₀₉	1	2	yes	complemented
346	#120	—	109	2	no	—
347	#120	—	109	2	no	—
348	#120	—	109	4	no	—
349	#120	—	109	4	no	—
350	#120	—	109	2	no	—
351	#120	C₂×D₁₀₉	1	2	yes	complemented
352	C₄×D₄	—	109	4	no	—
353	C₄×D₄	—	109	4	no	—
354	C₄×D₄	—	109	4	no	—
355	C₄×D₄	—	109	4	no	—
356	C₄×D₄	—	109	4	no	—
357	C₄×D₄	—	109	4	no	—
358	C₄×D₄	—	109	4	no	—
359	C₄×D₄	C₂×D₁₀₉	1	4	yes	complemented
360	#117	—	109	1	no	—
361	#117	—	109	2	no	—
362	#117	—	109	2	no	—
363	#117	—	109	2	no	—
364	#117	C₂×D₁₀₉	1	1	yes	characteristic, complemented
365	C₂×C₄⋊C₄	—	109	2	no	—
366	C₂×C₄⋊C₄	—	109	4	no	—
367	C₂×C₂²⋊C₄	—	109	2	no	—
368	C₂×C₂²⋊C₄	—	109	4	no	—
369	C₂×C₂²⋊C₄	—	109	4	no	—
370	C₂×C₄²	—	109	2	no	—
371	C₂⁴	—	109	1	no	—
372	C₂⁴	—	109	2	no	—
373	C₂⁴	—	109	2	no	—
374	C₂⁴	—	109	2	no	—
375	C₂⁴	—	109	1	no	—
376	C₂⁴	—	218	4	no	—
377	C₂⁴	—	218	8	no	—
378	C₂⁴	C₂²×D₁₀₉	1	1	yes	characteristic
379	#41	—	2	4	no	—
380	#41	—	218	8	no	—
381	#41	—	218	8	no	—
382	#41	—	218	4	no	—
383	#41	—	218	4	no	—
384	#41	—	218	4	no	—
385	C₂×Q₈	—	109	2	no	—
386	C₂×Q₈	—	109	1	no	—
387	C₂×Q₈	—	218	4	no	—
388	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic, complemented
389	C₂×D₄	—	109	4	no	—
390	C₂×D₄	—	109	4	no	—
391	C₂×D₄	—	109	2	no	—
392	C₂×D₄	—	109	2	no	—
393	C₂×D₄	—	109	2	no	—
394	C₂×D₄	—	109	4	no	—
395	C₂×D₄	—	109	2	no	—
396	C₂×D₄	—	109	1	no	—
397	C₂×D₄	—	218	4	no	—
398	C₂×D₄	—	218	16	no	—
399	C₂×D₄	—	218	8	no	—
400	C₂×D₄	C₂²×D₁₀₉	1	4	yes	—
401	C₂×D₄	C₂²×D₁₀₉	1	2	yes	—
402	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic, complemented
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	109	1	no	—
405	C₂²×C₄	—	109	8	no	—
406	C₂²×C₄	—	109	1	no	—
407	C₂²×C₄	—	109	1	no	—
408	C₂²×C₄	—	109	1	no	—
409	C₂²×C₄	—	109	1	no	—
410	C₂²×C₄	—	109	2	no	—
411	C₂²×C₄	—	109	2	no	—
412	C₂²×C₄	—	109	1	no	—
413	C₂²×C₄	—	109	2	no	—
414	C₂²×C₄	—	109	4	no	—
415	C₂²×C₄	—	109	2	no	—
416	C₂²×C₄	—	109	2	no	—
417	C₂²×C₄	—	109	2	no	—
418	C₂²×C₄	—	109	2	no	—
419	C₂²×C₄	—	109	2	no	—
420	C₂²×C₄	—	109	2	no	—
421	C₂²×C₄	—	109	2	no	—
422	C₂²×C₄	—	109	2	no	—
423	C₂²×C₄	—	109	2	no	—
424	C₂²×C₄	—	218	4	no	—
425	C₂²×C₄	—	218	8	no	—
426	C₂²×C₄	—	218	8	no	—
427	C₂²×C₄	—	218	8	no	—
428	C₂²×C₄	—	218	8	no	—
429	C₂²×C₄	—	218	8	no	—
430	C₂²×C₄	—	218	4	no	—
431	C₂²×C₄	—	218	4	no	—
432	C₂²×C₄	—	218	4	no	—
433	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	—
434	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
435	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	—
436	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
437	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	complemented
438	C₄⋊C₄	—	109	4	no	—
439	C₄⋊C₄	—	109	4	no	—
440	C₄⋊C₄	—	109	4	no	—
441	C₄⋊C₄	—	109	2	no	—
442	C₄⋊C₄	—	109	4	no	—
443	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	complemented
444	C₄⋊C₄	C₂²×D₁₀₉	1	4	yes	complemented
445	C₂²⋊C₄	—	109	2	no	—
446	C₂²⋊C₄	—	109	4	no	—
447	C₂²⋊C₄	—	109	4	no	—
448	C₂²⋊C₄	—	109	4	no	—
449	C₂²⋊C₄	—	109	4	no	—
450	C₂²⋊C₄	—	109	4	no	—
451	C₂²⋊C₄	—	109	4	no	—
452	C₂²⋊C₄	—	109	4	no	—
453	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
454	C₂²⋊C₄	C₂²×D₁₀₉	1	4	yes	—
455	C₂²⋊C₄	C₂²×D₁₀₉	1	4	yes	complemented
456	C₄²	—	109	4	no	—
457	C₄²	—	109	2	no	—
458	C₄²	C₂²×D₁₀₉	1	2	yes	complemented
459	C₂³	—	2	2	no	—
460	C₂³	—	2	4	no	—
461	C₂³	—	109	1	no	—
462	C₂³	—	109	4	no	—
463	C₂³	—	109	8	no	—
464	C₂³	—	109	1	no	—
465	C₂³	—	109	2	no	—
466	C₂³	—	109	2	no	—
467	C₂³	—	218	4	no	—
468	C₂³	—	218	8	no	—
469	C₂³	—	218	4	no	—
470	C₂³	—	218	4	no	—
471	C₂³	—	218	4	no	—
472	C₂³	—	218	4	no	—
473	C₂³	—	218	4	no	—
474	C₂³	—	218	4	no	—
475	C₂³	—	218	32	no	—
476	C₂³	—	218	2	no	—
477	C₂³	—	218	4	no	—
478	C₂³	C₂³×D₁₀₉	1	2	yes	—
479	C₂³	C₂³×D₁₀₉	1	1	yes	characteristic
480	C₂³	C₂³×D₁₀₉	1	2	yes	—
481	Q₈	—	2	2	no	—
482	Q₈	—	218	4	no	—
483	Q₈	—	218	2	no	—
484	D₄	—	2	4	no	—
485	D₄	—	2	8	no	—
486	D₄	—	2	2	no	—
487	D₄	—	218	4	no	—
488	D₄	—	218	8	no	—
489	D₄	—	218	4	no	—
490	D₄	—	218	4	no	—
491	D₄	—	218	8	no	—
492	D₄	—	218	4	no	—
493	D₄	—	218	8	no	—
494	D₄	—	218	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	109	4	no	—
500	C₂×C₄	—	109	1	no	—
501	C₂×C₄	—	109	1	no	—
502	C₂×C₄	—	109	4	no	—
503	C₂×C₄	—	109	4	no	—
504	C₂×C₄	—	109	4	no	—
505	C₂×C₄	—	109	4	no	—
506	C₂×C₄	—	109	4	no	—
507	C₂×C₄	—	109	2	no	—
508	C₂×C₄	—	109	2	no	—
509	C₂×C₄	—	218	4	no	—
510	C₂×C₄	—	218	4	no	—
511	C₂×C₄	—	218	4	no	—
512	C₂×C₄	—	218	4	no	—
513	C₂×C₄	—	218	4	no	—
514	C₂×C₄	—	218	4	no	—
515	C₂×C₄	—	218	8	no	—
516	C₂×C₄	—	218	4	no	—
517	C₂×C₄	—	218	4	no	—
518	C₂×C₄	—	218	4	no	—
519	C₂×C₄	—	218	2	no	—
520	C₂×C₄	—	218	4	no	—
521	C₂×C₄	—	218	4	no	—
522	C₂×C₄	—	218	4	no	—
523	C₂×C₄	D₄×D₁₀₉	1	4	yes	complemented
524	C₂×C₄	C₂³×D₁₀₉	1	4	yes	—
525	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
526	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
527	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
528	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
529	C₂²	—	2	8	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	2	4	no	—
535	C₂²	—	109	2	no	—
536	C₂²	—	109	4	no	—
537	C₂²	—	109	2	no	—
538	C₂²	—	109	4	no	—
539	C₂²	—	436	8	no	—
540	C₂²	—	218	8	no	—
541	C₂²	—	218	16	no	—
542	C₂²	—	218	8	no	—
543	C₂²	—	218	16	no	—
544	C₂²	—	218	2	no	—
545	C₂²	—	218	4	no	—
546	C₂²	—	218	2	no	—
547	C₂²	—	218	2	no	—
548	C₂²	—	218	2	no	—
549	C₂²	C₂×D₄×D₁₀₉	1	2	yes	—
550	C₂²	#41×D₁₀₉	1	4	yes	complemented
551	C₂²	C₂⁴×D₁₀₉	1	1	yes	characteristic
552	C₄	—	2	2	no	—
553	C₄	—	2	2	no	—
554	C₄	—	2	4	no	—
555	C₄	—	109	2	no	—
556	C₄	—	109	2	no	—
557	C₄	—	218	2	no	—
558	C₄	—	218	2	no	—
559	C₄	—	218	4	no	—
560	C₄	C₂×D₄×D₁₀₉	1	2	yes	—
561	C₄	C₂×D₄×D₁₀₉	1	2	yes	—
562	C₂	—	2	2	no	—
563	C₂	—	2	4	no	—
564	C₂	—	4	2	no	—
565	C₂	—	109	4	no	—
566	C₂	—	436	2	no	—
567	C₂	—	218	2	no	—
568	C₂	—	218	4	no	—
569	C₂	C₂²×D₄×D₁₀₉	1	1	yes	characteristic
570	C₂	C₂×#41×D₁₀₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₀₉
commutator, socle, cosocle	C₂²×C₁₀₉	C₂⁵
Frattini	C₂²	C₂⁴×D₁₀₉
Fitting	#525×C₁₀₉	C₂
hypercenter	#525	D₁₀₉
hypocenter	C₁₀₉	C₂×#525
LCS	G ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂×C₄ ◁ #525

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₁₀₉	C₂	semidirect
2. C₂³×C₄×D₁₀₉	C₂	semidirect
3. #20295539	C₂	semidirect
4. #20295538	C₂	semidirect
5. #20295537	C₂	semidirect
6. #20295536	C₂	semidirect
7. #20295535	C₂	semidirect
8. #20295534	C₂	semidirect
9. #20295533	C₂	semidirect
10. #20295532	C₂	semidirect
11. #123×D₁₀₉	C₂	semidirect
12. C₂²⋊Q₈×D₁₀₉	C₂	semidirect
13. #121×D₁₀₉	C₂	semidirect
14. #120×D₁₀₉	C₂	semidirect
15. C₄×D₄×D₁₀₉	C₂	semidirect
16. #117×D₁₀₉	C₂	semidirect
17. #525×C₁₀₉	C₂	semidirect
19. C₂×#13182030	C₂²	semidirect
20. C₂×#13182029	C₂²	semidirect
21. C₂×#13182029	C₂²	semidirect
22. C₂×#13182028	C₂²	semidirect
23. C₂×#13182028	C₂²	semidirect
25. C₂×Q₈×D₁₀₉	C₂²	semidirect
28. C₂×D₄×D₁₀₉	C₂²	semidirect
29. C₂³×Dic₁₀₉	C₂²	semidirect
35. C₂²×C₄×D₁₀₉	C₂²	semidirect
36. C₂²×C₄×D₁₀₉	C₂²	semidirect
37. C₂²×C₄×D₁₀₉	C₂²	semidirect
38. C₂²×C₄×D₁₀₉	C₂²	semidirect
39. C₂²×C₄×D₁₀₉	C₂²	semidirect
40. #16812684	C₂²	semidirect
41. #16812683	C₂²	semidirect
42. #16812682	C₂²	semidirect
43. #16812681	C₂²	semidirect
44. #16812680	C₂²	semidirect
45. #16812679	C₂²	semidirect
46. #16812678	C₂²	semidirect
47. #16812677	C₂²	semidirect
48. #16812676	C₂²	semidirect
49. #16812675	C₂²	semidirect
50. #16812674	C₂²	semidirect
51. #16812673	C₂²	semidirect
52. #16812672	C₂²	semidirect
53. #16812671	C₂²	semidirect
54. #16812670	C₂²	semidirect
55. #16812669	C₂²	semidirect
56. #16812669	C₂²	semidirect
57. #16812668	C₂²	semidirect
58. #16812667	C₂²	semidirect
59. #16812667	C₂²	semidirect
60. C₄×D₄₃₆	C₂²	semidirect
61. D₄×Dic₁₀₉	C₂²	semidirect
62. #16812661	C₂²	semidirect
63. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
64. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
65. #16812659	C₂²	semidirect
66. #16812659	C₂²	semidirect
67. #16812658	C₂²	semidirect
68. #16812657	C₂²	semidirect
69. #16812656	C₂²	semidirect
70. #16812655	C₂²	semidirect
71. C₄⋊C₄×D₁₀₉	C₂²	semidirect
72. C₄⋊C₄×D₁₀₉	C₂²	semidirect
75. C₂²⋊C₄×D₁₀₉	C₂²	semidirect
76. C₄²×D₁₀₉	C₂²	semidirect
77. C₂×#41×C₁₀₉	C₂²	semidirect
78. C₂³×C₄×C₁₀₉	C₂²	semidirect
79. #123×C₁₀₉	C₂²	semidirect
80. C₂²⋊Q₈×C₁₀₉	C₂²	semidirect
81. #121×C₁₀₉	C₂²	semidirect
82. #120×C₁₀₉	C₂²	semidirect
83. C₄×D₄×C₁₀₉	C₂²	semidirect
84. #117×C₁₀₉	C₂²	semidirect
97. C₂×Dic₂₁₈	C₂³	semidirect
98. C₂×Dic₂₁₈	C₂³	semidirect
102. C₂×D₄₃₆	C₂³	semidirect
107. C₂×C₂²⋊D₁₀₉	C₂³	semidirect
116. C₂²×Dic₁₀₉	C₂³	semidirect
125. C₂×C₄×D₁₀₉	D₄	semidirect
138. C₂×C₄×D₁₀₉	C₂³	semidirect
139. C₂×C₄×D₁₀₉	C₂³	semidirect
140. C₄⋊Dic₁₀₉	C₂³	semidirect
141. C₄⋊Dic₁₀₉	C₂³	semidirect
142. #13182008	C₂³	semidirect
143. #13182008	C₂³	semidirect
144. #13182008	C₂³	semidirect
147. C₂²⋊Dic₁₀₉	C₂³	semidirect
151. #13182006	C₂³	semidirect
152. #13182006	C₂³	semidirect
153. C₄×Dic₁₀₉	C₂³	semidirect
154. C₄×Dic₁₀₉	C₂³	semidirect
157. C₂×Q₈×C₁₀₉	C₂³	semidirect
160. C₂×D₄×C₁₀₉	C₂³	semidirect
166. C₂²×C₄×C₁₀₉	C₂³	semidirect
167. C₄⋊C₄×C₁₀₉	C₂³	semidirect
168. C₄⋊C₄×C₁₀₉	C₂³	semidirect
171. C₂²⋊C₄×C₁₀₉	C₂³	semidirect
172. C₄²×C₁₀₉	C₂³	semidirect
190. C₂²×D₁₀₉	#41	semidirect
203. C₂×C₄×C₁₀₉	C₂×D₄	semidirect
218. C₂×Dic₁₀₉	C₂×D₄	semidirect
239. C₄×D₁₀₉	C₂×D₄	semidirect
240. C₄×D₁₀₉	C₂×D₄	semidirect
250. C₂²×C₁₀₉	C₂×#41	semidirect
265. C₂×D₁₀₉	C₂×#41	semidirect
284. D₁₀₉	#525	direct (N × H)
286. C₁₀₉	C₂×#525	semidirect
297. #525	D₁₀₉	direct (N × H)
311. C₂×#41	C₂×D₁₀₉	semidirect
327. C₂³×C₄	C₂×D₁₀₉	semidirect
333. #123	C₂×D₁₀₉	semidirect
339. C₂²⋊Q₈	C₂×D₁₀₉	semidirect
345. #121	C₂×D₁₀₉	semidirect
351. #120	C₂×D₁₀₉	semidirect
359. C₄×D₄	C₂×D₁₀₉	semidirect
364. #117	C₂×D₁₀₉	semidirect
388. C₂×Q₈	C₂²×D₁₀₉	semidirect
402. C₂×D₄	C₂²×D₁₀₉	semidirect
437. C₂²×C₄	C₂²×D₁₀₉	semidirect
443. C₄⋊C₄	C₂²×D₁₀₉	semidirect
444. C₄⋊C₄	C₂²×D₁₀₉	semidirect
455. C₂²⋊C₄	C₂²×D₁₀₉	semidirect
458. C₄²	C₂²×D₁₀₉	semidirect
523. C₂×C₄	D₄×D₁₀₉	semidirect
550. C₂²	#41×D₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×D₁₀₉	2
C₂³×C₄×D₁₀₉	2
#20295539	2
#20295538	2
#20295537	2
#20295536	2
#20295535	2
#20295534	2
#20295533	2
#20295532	2
#123×D₁₀₉	2
C₂²⋊Q₈×D₁₀₉	2
#121×D₁₀₉	2
#120×D₁₀₉	2
C₄×D₄×D₁₀₉	2
#117×D₁₀₉	2
#525×C₁₀₉	2
C₂×#525	109

Subgroups — #525×D109 #28376268

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #525×D₁₀₉ #28376268