Subgroups — #28376585

Order 13952.

1132 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20295747	C₂	1	1	yes	maximal, characteristic, complemented
2	#20295739	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295734	C₂	1	1	yes	maximal, characteristic, complemented
4	#20295729	C₂	1	1	yes	maximal, characteristic, complemented
5	#20295722	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295717	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295708	C₂	1	2	yes	maximal, complemented
8	#20295701	C₂	1	2	yes	maximal, complemented
9	#20295700	C₂	1	2	yes	maximal, complemented
10	#20295677	C₂	1	1	yes	maximal, characteristic, complemented
11	#20295668	C₂	1	2	yes	maximal, complemented
12	#20295582	C₂	1	1	yes	maximal, characteristic, complemented
13	#20295561	C₂	1	2	yes	maximal, complemented
14	#20295559	C₂	1	2	yes	maximal, complemented
15	#20295553	C₂	1	2	yes	maximal, complemented
16	#20295539	C₂	1	1	yes	maximal, characteristic, complemented
17	#20295539	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#13182030	C₂	1	1	yes	maximal, characteristic, complemented
19	#20295494	C₂	1	2	yes	maximal, complemented
20	C₄×D₄×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#16812657	C₂	1	1	yes	maximal, characteristic, complemented
22	#117×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#552×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13182030	C₂²	1	1	yes	characteristic
25	C₂×#13182029	C₂²	1	2	yes	—
26	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
29	#16812698	C₂²	1	1	yes	characteristic, complemented
30	#16812698	C₂²	1	1	yes	characteristic, complemented
31	#16812694	C₂²	1	2	yes	complemented
32	#16812694	C₂²	1	2	yes	complemented
33	#16812694	C₂²	1	2	yes	complemented
34	#16812693	C₂²	1	2	yes	complemented
35	#16812692	C₂²	1	2	yes	complemented
36	#16812691	C₂²	1	1	yes	characteristic, complemented
37	#16812689	C₂²	1	2	yes	complemented
38	#16812689	C₂²	1	2	yes	complemented
39	#16812687	C₂²	1	2	yes	complemented
40	#16812685	C₂²	1	2	yes	—
41	#16812685	C₂²	1	2	yes	complemented
42	#16812684	C₂²	1	2	yes	—
43	#16812684	C₂²	1	2	yes	—
44	#16812684	C₂²	1	2	yes	—
45	#16812684	C₂²	1	2	yes	complemented
46	#16812684	C₂²	1	2	yes	complemented
47	#16812682	C₂²	1	2	yes	complemented
48	#16812681	C₂²	1	2	yes	complemented
49	#16812679	C₂²	1	2	yes	complemented
50	#16812677	C₂²	1	2	yes	—
51	#16812677	C₂²	1	2	yes	—
52	#16812677	C₂²	1	2	yes	complemented
53	#16812676	C₂²	1	2	yes	complemented
54	#16812675	C₂²	1	1	yes	characteristic, complemented
55	#16812675	C₂²	1	1	yes	characteristic, complemented
56	#16812674	C₂²	1	2	yes	—
57	#16812674	C₂²	1	1	yes	characteristic, complemented
58	#16812674	C₂²	1	1	yes	characteristic, complemented
59	#16812673	C₂²	1	1	yes	characteristic, complemented
60	#16812673	C₂²	1	1	yes	characteristic, complemented
61	#16812672	C₂²	1	2	yes	—
62	#16812671	C₂²	1	2	yes	—
63	#16812669	C₂²	1	2	yes	—
64	#16812669	C₂²	1	2	yes	—
65	Q₈×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
66	#16812664	C₂²	1	2	yes	complemented
67	#16812664	C₂²	1	2	yes	complemented
68	#16812664	C₂²	1	2	yes	complemented
69	C₄×D₄₃₆	C₂²	1	2	yes	—
70	C₄×D₄₃₆	C₂²	1	1	yes	characteristic
71	C₄×D₄₃₆	C₂²	1	1	yes	characteristic, complemented
72	D₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
73	#16812661	C₂²	1	2	yes	—
74	#16812661	C₂²	1	1	yes	characteristic
75	#16812661	C₂²	1	2	yes	complemented
76	#16812661	C₂²	1	1	yes	characteristic, complemented
77	#16812661	C₂²	1	2	yes	complemented
78	#16812661	C₂²	1	2	yes	complemented
79	C₄×C₂²⋊D₁₀₉	C₂²	1	1	yes	characteristic
80	C₄×C₂²⋊D₁₀₉	C₂²	1	1	yes	characteristic
81	#16812659	C₂²	1	2	yes	—
82	#16812659	C₂²	1	1	yes	characteristic
83	#16812659	C₂²	1	1	yes	characteristic
84	#16812659	C₂²	1	2	yes	complemented
85	#16812659	C₂²	1	2	yes	complemented
86	#16812659	C₂²	1	2	yes	complemented
87	#16812658	C₂²	1	1	yes	characteristic, complemented
88	#16812657	C₂²	1	2	yes	—
89	#16812657	C₂²	1	1	yes	characteristic
90	#16812657	C₂²	1	1	yes	characteristic
91	#16812657	C₂²	1	1	yes	characteristic
92	#16812657	C₂²	1	1	yes	characteristic, complemented
93	#16812657	C₂²	1	1	yes	characteristic, complemented
94	#16812657	C₂²	1	2	yes	complemented
95	#16812657	C₂²	1	2	yes	complemented
96	#16812656	C₂²	1	2	yes	—
97	#16812656	C₂²	1	2	yes	complemented
98	#16812656	C₂²	1	2	yes	complemented
99	#16812655	C₂²	1	2	yes	complemented
100	C₂×C₄⋊Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
101	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
102	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
103	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
104	C₂×#13182006	C₂²	1	2	yes	—
105	C₂²⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
106	C₂²⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
107	C₂²⋊C₄×D₁₀₉	C₂²	1	2	yes	—
108	C₂×C₄×Dic₁₀₉	C₂²	1	2	yes	complemented
109	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic
110	C₄²×D₁₀₉	C₂²	1	2	yes	complemented
111	C₄²×D₁₀₉	C₂²	1	2	yes	complemented
112	#126×C₁₀₉	C₂²	1	2	yes	complemented
113	#125×C₁₀₉	C₂²	1	2	yes	complemented
114	#125×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
115	#123×C₁₀₉	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
117	C₂²⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
120	#117×C₁₀₉	C₂²	1	2	yes	complemented
121	#117×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₀₉	C₂³	1	1	yes	characteristic
124	C₂³×D₁₀₉	C₂³	1	1	yes	characteristic
125	#13182030	—	2	4	no	—
126	#13182029	—	2	8	no	—
127	C₂×Dic₂₁₈	C₂³	1	2	yes	—
128	C₂×Dic₂₁₈	C₂³	1	2	yes	—
129	C₂×D₄₃₆	C₂³	1	2	yes	—
130	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
131	C₂×D₄₃₆	C₂³	1	2	yes	—
132	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
133	C₂×D₄₃₆	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₀₉	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₀₉	C₂³	1	1	yes	characteristic
138	D₄×D₁₀₉	—	2	4	no	—
139	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
140	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
141	C₂²×Dic₁₀₉	C₂³	1	2	yes	—
142	C₂×C₄×D₁₀₉	—	2	4	no	—
143	C₂×C₄×D₁₀₉	—	2	4	no	—
144	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
147	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
148	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
149	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
156	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
157	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
158	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
159	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
162	C₄⋊Dic₁₀₉	C₂³	1	2	yes	—
163	C₄⋊Dic₁₀₉	C₂³	1	2	yes	—
164	#13182008	C₂³	1	1	yes	characteristic
165	#13182008	C₂³	1	1	yes	characteristic
166	#13182008	C₂³	1	2	yes	—
167	#13182008	C₂³	1	2	yes	—
168	#13182008	C₂³	1	2	yes	—
169	#13182008	C₂³	1	2	yes	—
170	#13182008	C₂³	1	2	yes	—
171	#13182008	C₂³	1	2	yes	—
172	#13182008	C₂³	1	2	yes	—
173	#13182008	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
177	#13182006	C₂³	1	2	yes	—
178	#13182006	C₂³	1	2	yes	—
179	#13182006	C₂³	1	1	yes	characteristic
180	#13182006	C₂³	1	1	yes	characteristic
181	#13182006	C₂³	1	1	yes	characteristic
182	#13182006	C₂³	1	1	yes	characteristic
183	#13182006	C₂³	1	2	yes	—
184	#13182006	C₂³	1	2	yes	—
185	#13182006	C₂³	1	2	yes	—
186	#13182006	C₂³	1	2	yes	—
187	#13182006	C₂³	1	2	yes	—
188	#13182006	C₂³	1	2	yes	—
189	#13182006	C₂³	1	2	yes	—
190	#13182006	C₂³	1	2	yes	—
191	#13182006	C₂³	1	2	yes	—
192	#13182006	C₂³	1	2	yes	—
193	#13182006	C₂³	1	2	yes	—
194	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
195	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
196	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
197	C₄×Dic₁₀₉	C₂³	1	2	yes	—
198	C₄×Dic₁₀₉	C₂³	1	2	yes	—
199	C₄×Dic₁₀₉	C₂³	1	2	yes	—
200	C₄×Dic₁₀₉	C₂³	1	2	yes	—
201	C₄×Dic₁₀₉	C₂³	1	2	yes	—
202	C₄×Dic₁₀₉	C₂³	1	2	yes	—
203	C₄×Dic₁₀₉	C₂³	1	2	yes	—
204	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
205	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
206	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
207	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
208	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
209	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
210	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
212	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
214	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
215	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
216	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
217	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
218	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
220	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
223	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
224	C₄²×C₁₀₉	C₂³	1	2	yes	—
225	C₄²×C₁₀₉	C₂³	1	2	yes	—
226	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
227	C₂³×C₁₀₉	C₂⁴	1	1	yes	characteristic
228	C₂³×C₁₀₉	C₂⁴	1	1	yes	characteristic
229	C₂²×D₁₀₉	—	2	2	no	—
230	C₂²×D₁₀₉	—	2	2	no	—
231	C₂²×D₁₀₉	—	2	2	no	—
232	C₂²×D₁₀₉	—	2	2	no	—
233	C₂²×D₁₀₉	—	4	1	no	—
234	C₂²×D₁₀₉	—	4	1	no	—
235	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
236	C₂²×D₁₀₉	C₂⁴	1	2	yes	—
237	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
238	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
239	Q₈×C₁₀₉	—	2	2	no	—
240	D₄×C₁₀₉	—	2	2	no	—
241	C₂×C₄×C₁₀₉	—	2	4	no	—
242	C₂×C₄×C₁₀₉	—	2	2	no	—
243	C₂×C₄×C₁₀₉	—	2	2	no	—
244	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
247	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
248	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
249	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
251	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
253	C₂²⋊D₁₀₉	—	2	4	no	—
254	C₂²⋊D₁₀₉	—	2	2	no	—
255	C₂²⋊D₁₀₉	—	4	2	no	—
256	C₂²⋊D₁₀₉	#41	1	4	yes	complemented
257	C₂×Dic₁₀₉	—	2	2	no	—
258	C₂×Dic₁₀₉	—	2	2	no	—
259	C₂×Dic₁₀₉	—	4	2	no	—
260	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
262	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
264	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
265	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
268	D₄₃₆	—	2	2	no	—
269	D₄₃₆	—	2	4	no	—
270	D₄₃₆	—	2	4	no	—
271	D₄₃₆	—	2	2	no	—
272	D₄₃₆	—	4	2	no	—
273	C₄×D₁₀₉	—	2	2	no	—
274	C₄×D₁₀₉	—	2	2	no	—
275	C₄×D₁₀₉	—	2	4	no	—
276	C₄×D₁₀₉	—	2	2	no	—
277	C₄×D₁₀₉	—	2	2	no	—
278	C₄×D₁₀₉	—	2	2	no	—
279	C₄×D₁₀₉	—	2	2	no	—
280	C₄×D₁₀₉	—	2	2	no	—
281	C₄×D₁₀₉	—	2	4	no	—
282	C₄×D₁₀₉	—	2	4	no	—
283	C₄×D₁₀₉	—	4	1	no	—
284	C₄×D₁₀₉	—	4	2	no	—
285	C₄×D₁₀₉	—	4	2	no	—
286	C₄×D₁₀₉	#41	1	4	yes	complemented
287	Dic₂₁₈	—	2	4	no	—
288	Dic₂₁₈	—	4	2	no	—
289	C₂²×C₁₀₉	—	2	1	no	—
290	C₂²×C₁₀₉	—	2	1	no	—
291	C₂²×C₁₀₉	—	2	1	no	—
292	C₂²×C₁₀₉	—	2	1	no	—
293	C₂²×C₁₀₉	—	2	1	no	—
294	C₂²×C₁₀₉	C₂×#41	1	2	yes	—
295	C₂²×C₁₀₉	C₂⁵	1	1	yes	characteristic
296	C₂×D₁₀₉	—	2	1	no	—
297	C₂×D₁₀₉	—	2	1	no	—
298	C₂×D₁₀₉	—	2	1	no	—
299	C₂×D₁₀₉	—	2	1	no	—
300	C₂×D₁₀₉	—	2	1	no	—
301	C₂×D₁₀₉	—	2	2	no	—
302	C₂×D₁₀₉	—	2	2	no	—
303	C₂×D₁₀₉	—	2	1	no	—
304	C₂×D₁₀₉	—	2	2	no	—
305	C₂×D₁₀₉	—	2	1	no	—
306	C₂×D₁₀₉	—	4	4	no	—
307	C₂×D₁₀₉	—	4	4	no	—
308	C₂×D₁₀₉	C₂×#41	1	2	yes	—
309	C₂×D₁₀₉	C₂×#41	1	2	yes	—
310	C₄×C₁₀₉	—	2	2	no	—
311	C₄×C₁₀₉	—	2	2	no	—
312	C₄×C₁₀₉	—	2	1	no	—
313	C₄×C₁₀₉	—	2	1	no	—
314	C₄×C₁₀₉	—	2	1	no	—
315	C₄×C₁₀₉	—	2	2	no	—
316	C₄×C₁₀₉	—	2	2	no	—
317	C₄×C₁₀₉	—	2	1	no	—
318	C₄×C₁₀₉	C₂×#41	1	2	yes	—
319	Dic₁₀₉	—	2	2	no	—
320	Dic₁₀₉	—	2	1	no	—
321	Dic₁₀₉	—	2	1	no	—
322	Dic₁₀₉	—	2	1	no	—
323	Dic₁₀₉	—	2	2	no	—
324	Dic₁₀₉	—	2	2	no	—
325	Dic₁₀₉	C₂×#41	1	2	yes	—
326	Dic₁₀₉	C₂×#41	1	2	yes	—
327	C₂×C₁₀₉	—	2	2	no	—
328	C₂×C₁₀₉	—	4	1	no	—
329	C₂×C₁₀₉	C₂²×#41	1	1	yes	characteristic
330	C₂×C₁₀₉	C₂²×#41	1	1	yes	characteristic
331	C₂×C₁₀₉	#585	1	1	yes	characteristic
332	D₁₀₉	—	2	2	no	—
333	D₁₀₉	—	2	2	no	—
334	D₁₀₉	—	4	2	no	—
335	D₁₀₉	—	4	1	no	—
336	#3475	—	109	1	no	maximal, Sylow
337	C₁₀₉	#3475	1	1	yes	characteristic, complemented, Sylow
338	#556	—	109	1	no	—
339	#555	—	109	1	no	—
340	#554	—	109	1	no	—
341	#553	—	109	1	no	—
342	#553	—	109	1	no	—
343	#552	—	109	2	no	—
344	#552	—	109	1	no	—
345	#552	D₁₀₉	1	1	yes	characteristic, complemented
346	#551	—	109	2	no	—
347	#551	—	109	2	no	—
348	#547	—	109	1	no	—
349	#546	—	109	2	no	—
350	#533	—	109	1	no	—
351	#529	—	109	2	no	—
352	#529	—	109	2	no	—
353	#529	—	109	2	no	—
354	#525	—	109	1	no	—
355	#525	—	109	1	no	—
356	C₄×#41	—	109	1	no	—
357	C₄×#41	—	109	2	no	—
358	C₂×C₄×D₄	—	109	1	no	—
359	C₂×#117	—	109	1	no	—
360	C₂×#117	—	109	1	no	—
361	C₂×#41	—	109	1	no	—
362	C₂×#41	—	109	2	no	—
363	C₂²×D₄	—	109	1	no	—
364	C₂³×C₄	—	109	1	no	—
365	C₂³×C₄	—	109	1	no	—
366	C₄⋊Q₈	—	109	1	no	—
367	C₄⋊Q₈	—	109	1	no	—
368	#126	—	109	2	no	—
369	#126	—	109	2	no	—
370	#126	—	109	2	no	—
371	#126	—	109	2	no	—
372	#126	—	109	2	no	—
373	#126	C₂×D₁₀₉	1	2	yes	complemented
374	#125	—	109	2	no	—
375	#125	—	109	2	no	—
376	#125	—	109	1	no	—
377	#125	C₂×D₁₀₉	1	2	yes	complemented
378	#125	C₂×D₁₀₉	1	1	yes	characteristic, complemented
379	#124	—	109	2	no	—
380	#124	—	109	2	no	—
381	#124	—	109	2	no	—
382	#123	—	109	2	no	—
383	#123	—	109	2	no	—
384	#123	—	109	2	no	—
385	#123	—	109	2	no	—
386	#123	—	109	2	no	—
387	#123	—	109	2	no	—
388	#123	—	109	2	no	—
389	#123	C₂×D₁₀₉	1	2	yes	—
390	C₂²⋊Q₈	—	109	1	no	—
391	C₂²⋊Q₈	—	109	1	no	—
392	C₂²⋊Q₈	—	109	2	no	—
393	C₂²⋊Q₈	—	109	2	no	—
394	C₂²⋊Q₈	—	109	2	no	—
395	C₂²⋊Q₈	—	109	2	no	—
396	C₂²⋊Q₈	—	109	2	no	—
397	C₂²⋊Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
398	C₂²⋊Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
399	#121	—	109	2	no	—
400	#121	—	109	1	no	—
401	#121	—	109	1	no	—
402	#121	—	109	1	no	—
403	#121	—	109	1	no	—
404	#121	—	109	2	no	—
405	#121	—	109	2	no	—
406	#120	—	109	2	no	—
407	#120	—	109	2	no	—
408	C₄×Q₈	—	109	1	no	—
409	C₄×Q₈	—	109	2	no	—
410	C₄×Q₈	—	109	2	no	—
411	C₄×Q₈	—	109	2	no	—
412	C₄×Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
413	C₄×D₄	—	109	1	no	—
414	C₄×D₄	—	109	1	no	—
415	C₄×D₄	—	109	1	no	—
416	C₄×D₄	—	109	1	no	—
417	C₄×D₄	—	109	2	no	—
418	C₄×D₄	—	109	2	no	—
419	C₄×D₄	—	109	1	no	—
420	C₄×D₄	—	109	2	no	—
421	C₄×D₄	—	109	2	no	—
422	C₄×D₄	—	109	1	no	—
423	C₄×D₄	—	109	1	no	—
424	C₄×D₄	—	109	2	no	—
425	C₄×D₄	—	109	2	no	—
426	C₄×D₄	—	109	2	no	—
427	C₄×D₄	—	109	2	no	—
428	C₄×D₄	—	109	1	no	—
429	C₄×D₄	—	109	2	no	—
430	C₄×D₄	—	109	1	no	—
431	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic
432	#117	—	109	1	no	—
433	#117	—	109	1	no	—
434	#117	—	109	1	no	—
435	#117	—	109	1	no	—
436	#117	—	109	2	no	—
437	#117	—	109	2	no	—
438	#117	—	109	1	no	—
439	#117	—	109	1	no	—
440	#117	—	109	2	no	—
441	#117	—	109	2	no	—
442	#117	—	109	2	no	—
443	#117	—	109	2	no	—
444	#117	—	109	2	no	—
445	#117	C₂×D₁₀₉	1	1	yes	characteristic, complemented
446	#117	C₂×D₁₀₉	1	2	yes	complemented
447	C₂×C₄⋊C₄	—	109	1	no	—
448	C₂×C₄⋊C₄	—	109	1	no	—
449	C₂×C₄⋊C₄	—	109	1	no	—
450	C₂×C₄⋊C₄	—	109	1	no	—
451	C₂×C₄⋊C₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
452	C₂×C₂²⋊C₄	—	109	2	no	—
453	C₂×C₂²⋊C₄	—	109	2	no	—
454	C₂×C₂²⋊C₄	—	109	1	no	—
455	C₂×C₂²⋊C₄	—	109	1	no	—
456	C₂×C₄²	—	109	2	no	—
457	C₂×C₄²	—	109	2	no	—
458	C₂×C₄²	—	109	1	no	—
459	C₂×C₄²	—	109	2	no	—
460	C₂⁴	—	109	1	no	—
461	C₂⁴	—	109	1	no	—
462	#41	—	218	8	no	—
463	#41	—	218	4	no	—
464	C₂×Q₈	—	109	2	no	—
465	C₂×Q₈	—	109	2	no	—
466	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
467	C₂×D₄	—	109	1	no	—
468	C₂×D₄	—	109	2	no	—
469	C₂×D₄	—	109	2	no	—
470	C₂×D₄	—	109	1	no	—
471	C₂×D₄	—	109	2	no	—
472	C₂×D₄	—	109	2	no	—
473	C₂×D₄	—	109	2	no	—
474	C₂×D₄	—	109	1	no	—
475	C₂×D₄	—	109	1	no	—
476	C₂×D₄	—	218	4	no	—
477	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
478	C₂²×C₄	—	109	1	no	—
479	C₂²×C₄	—	109	2	no	—
480	C₂²×C₄	—	109	1	no	—
481	C₂²×C₄	—	109	1	no	—
482	C₂²×C₄	—	109	1	no	—
483	C₂²×C₄	—	109	2	no	—
484	C₂²×C₄	—	109	2	no	—
485	C₂²×C₄	—	109	1	no	—
486	C₂²×C₄	—	109	2	no	—
487	C₂²×C₄	—	109	1	no	—
488	C₂²×C₄	—	109	2	no	—
489	C₂²×C₄	—	109	2	no	—
490	C₂²×C₄	—	109	1	no	—
491	C₂²×C₄	—	109	1	no	—
492	C₂²×C₄	—	109	1	no	—
493	C₂²×C₄	—	109	1	no	—
494	C₂²×C₄	—	109	1	no	—
495	C₂²×C₄	—	218	4	no	—
496	C₂²×C₄	—	218	4	no	—
497	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	—
498	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
499	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
500	C₄⋊C₄	—	109	1	no	—
501	C₄⋊C₄	—	109	2	no	—
502	C₄⋊C₄	—	109	2	no	—
503	C₄⋊C₄	—	109	1	no	—
504	C₄⋊C₄	—	109	2	no	—
505	C₄⋊C₄	—	109	2	no	—
506	C₄⋊C₄	—	109	2	no	—
507	C₄⋊C₄	—	109	2	no	—
508	C₄⋊C₄	—	109	2	no	—
509	C₄⋊C₄	—	109	2	no	—
510	C₄⋊C₄	—	109	1	no	—
511	C₄⋊C₄	—	109	1	no	—
512	C₄⋊C₄	—	109	1	no	—
513	C₄⋊C₄	—	109	2	no	—
514	C₄⋊C₄	—	109	1	no	—
515	C₄⋊C₄	—	109	2	no	—
516	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
517	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
518	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
519	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
520	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
521	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
522	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
523	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
524	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
525	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
526	C₂²⋊C₄	—	109	2	no	—
527	C₂²⋊C₄	—	109	1	no	—
528	C₂²⋊C₄	—	109	1	no	—
529	C₂²⋊C₄	—	109	2	no	—
530	C₂²⋊C₄	—	109	1	no	—
531	C₂²⋊C₄	—	109	2	no	—
532	C₂²⋊C₄	—	109	2	no	—
533	C₂²⋊C₄	—	109	2	no	—
534	C₂²⋊C₄	—	109	2	no	—
535	C₂²⋊C₄	—	109	1	no	—
536	C₂²⋊C₄	—	109	1	no	—
537	C₂²⋊C₄	—	109	1	no	—
538	C₂²⋊C₄	—	109	2	no	—
539	C₂²⋊C₄	—	109	2	no	—
540	C₂²⋊C₄	—	109	2	no	—
541	C₂²⋊C₄	—	109	2	no	—
542	C₂²⋊C₄	—	109	2	no	—
543	C₂²⋊C₄	—	109	2	no	—
544	C₂²⋊C₄	—	109	2	no	—
545	C₂²⋊C₄	—	109	2	no	—
546	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
547	C₂²⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
548	C₂²⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
549	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
550	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
551	C₄²	—	109	2	no	—
552	C₄²	—	109	1	no	—
553	C₄²	—	109	2	no	—
554	C₄²	—	109	1	no	—
555	C₄²	—	109	2	no	—
556	C₄²	—	109	2	no	—
557	C₄²	—	109	2	no	—
558	C₄²	—	109	2	no	—
559	C₄²	—	109	1	no	—
560	C₄²	—	109	2	no	—
561	C₄²	C₂²×D₁₀₉	1	2	yes	—
562	C₄²	C₂²×D₁₀₉	1	2	yes	—
563	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
564	C₂³	—	109	1	no	—
565	C₂³	—	109	1	no	—
566	C₂³	—	109	1	no	—
567	C₂³	—	109	2	no	—
568	C₂³	—	436	1	no	—
569	C₂³	—	436	1	no	—
570	C₂³	—	218	2	no	—
571	C₂³	—	218	2	no	—
572	C₂³	—	218	2	no	—
573	C₂³	—	218	2	no	—
574	C₂³	C₂³×D₁₀₉	1	1	yes	characteristic
575	C₂³	C₂³×D₁₀₉	1	1	yes	characteristic
576	Q₈	—	2	2	no	—
577	Q₈	—	436	2	no	—
578	Q₈	—	218	4	no	—
579	D₄	—	2	2	no	—
580	D₄	—	109	4	no	—
581	D₄	—	436	2	no	—
582	D₄	—	436	2	no	—
583	D₄	—	218	2	no	—
584	D₄	—	218	4	no	—
585	D₄	—	218	4	no	—
586	D₄	—	218	2	no	—
587	D₄	—	218	4	no	—
588	D₄	—	218	2	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	109	1	no	—
593	C₂×C₄	—	109	1	no	—
594	C₂×C₄	—	109	4	no	—
595	C₂×C₄	—	109	1	no	—
596	C₂×C₄	—	109	2	no	—
597	C₂×C₄	—	109	1	no	—
598	C₂×C₄	—	109	2	no	—
599	C₂×C₄	—	109	2	no	—
600	C₂×C₄	—	109	1	no	—
601	C₂×C₄	—	436	2	no	—
602	C₂×C₄	—	436	1	no	—
603	C₂×C₄	—	436	2	no	—
604	C₂×C₄	—	436	2	no	—
605	C₂×C₄	—	218	2	no	—
606	C₂×C₄	—	218	2	no	—
607	C₂×C₄	—	218	2	no	—
608	C₂×C₄	—	218	4	no	—
609	C₂×C₄	—	218	4	no	—
610	C₂×C₄	—	218	2	no	—
611	C₂×C₄	—	218	2	no	—
612	C₂×C₄	—	218	4	no	—
613	C₂×C₄	—	218	2	no	—
614	C₂×C₄	—	218	2	no	—
615	C₂×C₄	—	218	2	no	—
616	C₂×C₄	—	218	2	no	—
617	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
618	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
619	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
620	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
622	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
623	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	109	2	no	—
632	C₂²	—	109	2	no	—
633	C₂²	—	436	4	no	—
634	C₂²	—	436	4	no	—
635	C₂²	—	218	1	no	—
636	C₂²	—	218	2	no	—
637	C₂²	—	218	2	no	—
638	C₂²	—	218	1	no	—
639	C₂²	—	218	2	no	—
640	C₂²	—	218	1	no	—
641	C₂²	—	218	1	no	—
642	C₂²	—	218	1	no	—
643	C₂²	—	218	1	no	—
644	C₂²	—	218	1	no	—
645	C₂²	#41×D₁₀₉	1	2	yes	—
646	C₂²	C₂⁴×D₁₀₉	1	1	yes	characteristic
647	C₄	—	2	2	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	2	no	—
655	C₄	—	109	2	no	—
656	C₄	—	109	2	no	—
657	C₄	—	218	1	no	—
658	C₄	—	218	1	no	—
659	C₄	—	218	2	no	—
660	C₄	—	218	2	no	—
661	C₄	—	218	2	no	—
662	C₄	—	218	1	no	—
663	C₄	#41×D₁₀₉	1	2	yes	—
664	C₂	—	2	2	no	—
665	C₂	—	4	1	no	—
666	C₂	—	436	1	no	—
667	C₂	—	436	2	no	—
668	C₂	—	218	2	no	—
669	C₂	—	218	2	no	—
670	C₂	C₂×#41×D₁₀₉	1	1	yes	characteristic
671	C₂	C₂×#41×D₁₀₉	1	1	yes	characteristic
672	C₂	#20295863	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₀₉
commutator, socle, cosocle	C₂²×C₁₀₉	C₂⁵
Fitting	#552×C₁₀₉	C₂
hypercenter	#552	D₁₀₉
hypocenter	C₁₀₉	#3475
LCS	G ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. #20295747	C₂	semidirect
2. #20295739	C₂	semidirect
3. #20295734	C₂	semidirect
4. #20295729	C₂	semidirect
5. #20295722	C₂	semidirect
6. #20295717	C₂	semidirect
7. #20295708	C₂	semidirect
8. #20295701	C₂	semidirect
9. #20295700	C₂	semidirect
10. #20295677	C₂	semidirect
11. #20295668	C₂	semidirect
12. #20295582	C₂	semidirect
13. #20295561	C₂	semidirect
14. #20295559	C₂	semidirect
15. #20295553	C₂	semidirect
16. #20295539	C₂	semidirect
17. #20295539	C₂	semidirect
18. C₄×#13182030	C₂	semidirect
19. #20295494	C₂	semidirect
20. C₄×D₄×D₁₀₉	C₂	semidirect
21. C₂×#16812657	C₂	semidirect
22. #117×D₁₀₉	C₂	semidirect
23. #552×C₁₀₉	C₂	semidirect
29. #16812698	C₂²	semidirect
30. #16812698	C₂²	semidirect
31. #16812694	C₂²	semidirect
32. #16812694	C₂²	semidirect
33. #16812694	C₂²	semidirect
34. #16812693	C₂²	semidirect
35. #16812692	C₂²	semidirect
36. #16812691	C₂²	semidirect
37. #16812689	C₂²	semidirect
38. #16812689	C₂²	semidirect
39. #16812687	C₂²	semidirect
41. #16812685	C₂²	semidirect
45. #16812684	C₂²	semidirect
46. #16812684	C₂²	semidirect
47. #16812682	C₂²	semidirect
48. #16812681	C₂²	semidirect
49. #16812679	C₂²	semidirect
52. #16812677	C₂²	semidirect
53. #16812676	C₂²	semidirect
54. #16812675	C₂²	semidirect
55. #16812675	C₂²	semidirect
57. #16812674	C₂²	semidirect
58. #16812674	C₂²	semidirect
59. #16812673	C₂²	semidirect
60. #16812673	C₂²	semidirect
65. Q₈×Dic₁₀₉	C₂²	semidirect
66. #16812664	C₂²	semidirect
67. #16812664	C₂²	semidirect
68. #16812664	C₂²	semidirect
71. C₄×D₄₃₆	C₂²	semidirect
75. #16812661	C₂²	semidirect
76. #16812661	C₂²	semidirect
77. #16812661	C₂²	semidirect
78. #16812661	C₂²	semidirect
84. #16812659	C₂²	semidirect
85. #16812659	C₂²	semidirect
86. #16812659	C₂²	semidirect
87. #16812658	C₂²	semidirect
92. #16812657	C₂²	semidirect
93. #16812657	C₂²	semidirect
94. #16812657	C₂²	semidirect
95. #16812657	C₂²	semidirect
97. #16812656	C₂²	semidirect
98. #16812656	C₂²	semidirect
99. #16812655	C₂²	semidirect
100. C₂×C₄⋊Dic₁₀₉	C₂²	semidirect
102. C₄⋊C₄×D₁₀₉	C₂²	semidirect
103. C₄⋊C₄×D₁₀₉	C₂²	semidirect
108. C₂×C₄×Dic₁₀₉	C₂²	semidirect
110. C₄²×D₁₀₉	C₂²	semidirect
111. C₄²×D₁₀₉	C₂²	semidirect
112. #126×C₁₀₉	C₂²	semidirect
113. #125×C₁₀₉	C₂²	semidirect
114. #125×C₁₀₉	C₂²	semidirect
116. C₂²⋊Q₈×C₁₀₉	C₂²	semidirect
117. C₂²⋊Q₈×C₁₀₉	C₂²	semidirect
118. C₄×Q₈×C₁₀₉	C₂²	semidirect
120. #117×C₁₀₉	C₂²	semidirect
121. #117×C₁₀₉	C₂²	semidirect
122. C₂×C₄⋊C₄×C₁₀₉	C₂²	semidirect
256. C₂²⋊D₁₀₉	#41	semidirect
286. C₄×D₁₀₉	#41	semidirect
337. C₁₀₉	#3475	semidirect
345. #552	D₁₀₉	semidirect
373. #126	C₂×D₁₀₉	semidirect
377. #125	C₂×D₁₀₉	semidirect
378. #125	C₂×D₁₀₉	semidirect
397. C₂²⋊Q₈	C₂×D₁₀₉	semidirect
398. C₂²⋊Q₈	C₂×D₁₀₉	semidirect
412. C₄×Q₈	C₂×D₁₀₉	semidirect
445. #117	C₂×D₁₀₉	semidirect
446. #117	C₂×D₁₀₉	semidirect
451. C₂×C₄⋊C₄	C₂×D₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
#20295747	2
#20295739	2
#20295734	2
#20295729	2
#20295722	2
#20295717	2
#20295708	2
#20295701	2
#20295700	2
#20295677	2
#20295668	2
#20295582	2
#20295561	2
#20295559	2
#20295553	2
#20295539	2
C₄×#13182030	2
#20295494	2
C₄×D₄×D₁₀₉	2
C₂×#16812657	2
#117×D₁₀₉	2
#552×C₁₀₉	2
#3475	109