Subgroups — #28376446

Order 13952.

1140 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20295653	C₂	1	1	yes	maximal, characteristic, complemented
2	#20295650	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295643	C₂	1	1	yes	maximal, characteristic, complemented
4	#20295640	C₂	1	2	yes	maximal, complemented
5	#20295630	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295629	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295626	C₂	1	2	yes	maximal, complemented
8	#20295610	C₂	1	2	yes	maximal, complemented
9	#20295608	C₂	1	2	yes	maximal, complemented
10	#20295605	C₂	1	1	yes	maximal, characteristic, complemented
11	#20295592	C₂	1	1	yes	maximal, characteristic, complemented
12	#20295589	C₂	1	1	yes	maximal, characteristic, complemented
13	#20295573	C₂	1	1	yes	maximal, characteristic, complemented
14	#20295572	C₂	1	2	yes	maximal, complemented
15	#20295560	C₂	1	1	yes	maximal, characteristic, complemented
16	#20295558	C₂	1	1	yes	maximal, characteristic, complemented
17	#20295556	C₂	1	2	yes	maximal, complemented
18	#20295535	C₂	1	2	yes	maximal, complemented
19	#20295533	C₂	1	2	yes	maximal, complemented
20	C₄×#13182029	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#13182028	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₄×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#532×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13182029	C₂²	1	1	yes	characteristic
25	C₂×#13182029	C₂²	1	2	yes	complemented
26	C₂×#13182028	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₁₀₉	C₂²	1	2	yes	—
29	#16812698	C₂²	1	1	yes	characteristic, complemented
30	#16812697	C₂²	1	2	yes	complemented
31	#16812695	C₂²	1	2	yes	—
32	#16812695	C₂²	1	1	yes	characteristic
33	#16812694	C₂²	1	2	yes	complemented
34	#16812693	C₂²	1	2	yes	complemented
35	#16812692	C₂²	1	2	yes	complemented
36	#16812692	C₂²	1	2	yes	complemented
37	#16812691	C₂²	1	1	yes	characteristic, complemented
38	#16812690	C₂²	1	1	yes	characteristic, complemented
39	#16812689	C₂²	1	2	yes	complemented
40	#16812688	C₂²	1	2	yes	complemented
41	#16812687	C₂²	1	1	yes	characteristic
42	#16812686	C₂²	1	1	yes	characteristic
43	#16812686	C₂²	1	2	yes	complemented
44	#16812685	C₂²	1	2	yes	—
45	#16812685	C₂²	1	2	yes	complemented
46	#16812684	C₂²	1	2	yes	complemented
47	#16812683	C₂²	1	2	yes	complemented
48	#16812682	C₂²	1	2	yes	complemented
49	#16812681	C₂²	1	2	yes	complemented
50	#16812681	C₂²	1	2	yes	complemented
51	#16812680	C₂²	1	2	yes	complemented
52	#16812680	C₂²	1	2	yes	complemented
53	#16812680	C₂²	1	2	yes	complemented
54	#16812679	C₂²	1	1	yes	characteristic, complemented
55	#16812678	C₂²	1	1	yes	characteristic, complemented
56	#16812677	C₂²	1	2	yes	—
57	#16812676	C₂²	1	2	yes	complemented
58	#16812676	C₂²	1	2	yes	complemented
59	#16812675	C₂²	1	2	yes	—
60	#16812675	C₂²	1	2	yes	complemented
61	#16812674	C₂²	1	1	yes	characteristic
62	#16812673	C₂²	1	1	yes	characteristic
63	#16812672	C₂²	1	2	yes	—
64	#16812672	C₂²	1	2	yes	complemented
65	#16812671	C₂²	1	2	yes	—
66	#16812671	C₂²	1	2	yes	—
67	#16812671	C₂²	1	2	yes	complemented
68	#16812671	C₂²	1	2	yes	complemented
69	#16812671	C₂²	1	2	yes	complemented
70	#16812671	C₂²	1	2	yes	complemented
71	#16812670	C₂²	1	2	yes	—
72	#16812670	C₂²	1	1	yes	characteristic
73	#16812670	C₂²	1	2	yes	complemented
74	#16812670	C₂²	1	1	yes	characteristic, complemented
75	#16812669	C₂²	1	2	yes	—
76	#16812667	C₂²	1	2	yes	—
77	#16812667	C₂²	1	2	yes	—
78	#16812667	C₂²	1	2	yes	—
79	C₄×Dic₂₁₈	C₂²	1	1	yes	characteristic, complemented
80	C₄×Dic₂₁₈	C₂²	1	1	yes	characteristic, complemented
81	C₄×Dic₂₁₈	C₂²	1	1	yes	characteristic, complemented
82	#16812664	C₂²	1	1	yes	characteristic, complemented
83	C₄×D₄₃₆	C₂²	1	1	yes	characteristic
84	C₄×D₄₃₆	C₂²	1	1	yes	characteristic
85	C₄×D₄₃₆	C₂²	1	1	yes	characteristic
86	D₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
87	D₄×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
88	#16812661	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊D₁₀₉	C₂²	1	2	yes	—
90	C₄×C₂²⋊D₁₀₉	C₂²	1	2	yes	—
91	C₄×C₂²⋊D₁₀₉	C₂²	1	1	yes	characteristic
92	C₄×C₂²⋊D₁₀₉	C₂²	1	1	yes	characteristic
93	C₄×C₂²⋊D₁₀₉	C₂²	1	1	yes	characteristic, complemented
94	C₄×C₂²⋊D₁₀₉	C₂²	1	1	yes	characteristic, complemented
95	C₄×C₂²⋊D₁₀₉	C₂²	1	2	yes	complemented
96	C₄×C₂²⋊D₁₀₉	C₂²	1	2	yes	complemented
97	C₄×C₂²⋊D₁₀₉	C₂²	1	2	yes	complemented
98	#16812659	C₂²	1	2	yes	—
99	#16812659	C₂²	1	2	yes	—
100	#16812658	C₂²	1	1	yes	characteristic, complemented
101	#16812658	C₂²	1	2	yes	complemented
102	#16812657	C₂²	1	1	yes	characteristic
103	#16812656	C₂²	1	1	yes	characteristic
104	#16812656	C₂²	1	1	yes	characteristic, complemented
105	#16812656	C₂²	1	2	yes	complemented
106	#16812655	C₂²	1	2	yes	complemented
107	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
108	C₂²⋊C₄×D₁₀₉	C₂²	1	2	yes	—
109	C₂×C₄×Dic₁₀₉	C₂²	1	2	yes	complemented
110	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic
111	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
112	C₂×#41×C₁₀₉	C₂²	1	2	yes	complemented
113	C₄⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
114	#127×C₁₀₉	C₂²	1	1	yes	characteristic
115	#124×C₁₀₉	C₂²	1	2	yes	complemented
116	#121×C₁₀₉	C₂²	1	1	yes	characteristic
117	#121×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
118	#121×C₁₀₉	C₂²	1	2	yes	complemented
119	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
120	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₁₀₉	C₂²	1	2	yes	complemented
122	C₂×C₄²×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₀₉	C₂³	1	2	yes	—
124	#13182029	—	2	4	no	—
125	#13182029	—	4	4	no	—
126	#13182028	—	2	4	no	—
127	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
128	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
129	C₂×Dic₂₁₈	C₂³	1	2	yes	—
130	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
131	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
132	C₂×D₄₃₆	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₀₉	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₁₀₉	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
142	D₄×D₁₀₉	—	2	4	no	—
143	C₂²×Dic₁₀₉	C₂³	1	2	yes	—
144	C₂²×Dic₁₀₉	C₂³	1	2	yes	—
145	C₂²×Dic₁₀₉	C₂³	1	2	yes	—
146	C₂×C₄×D₁₀₉	—	4	4	no	—
147	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
151	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
154	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
155	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
156	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₁₀₉	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	2	yes	—
161	C₄⋊Dic₁₀₉	C₂³	1	2	yes	—
162	#13182008	C₂³	1	2	yes	—
163	#13182008	C₂³	1	2	yes	—
164	#13182008	C₂³	1	2	yes	—
165	#13182008	C₂³	1	1	yes	characteristic
166	#13182008	C₂³	1	1	yes	characteristic
167	#13182008	C₂³	1	1	yes	characteristic
168	#13182008	C₂³	1	1	yes	characteristic
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	2	yes	—
176	C₂²⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	—
183	#13182006	C₂³	1	2	yes	—
184	#13182006	C₂³	1	2	yes	—
185	#13182006	C₂³	1	1	yes	characteristic
186	#13182006	C₂³	1	1	yes	characteristic
187	#13182006	C₂³	1	1	yes	characteristic
188	#13182006	C₂³	1	1	yes	characteristic
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	#13182006	C₂³	1	2	yes	—
195	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
196	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
197	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
198	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
199	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
200	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
201	C₄×Dic₁₀₉	C₂³	1	2	yes	—
202	C₄×Dic₁₀₉	C₂³	1	2	yes	—
203	C₄×Dic₁₀₉	C₂³	1	2	yes	—
204	#41×C₁₀₉	—	4	4	no	—
205	C₂×Q₈×C₁₀₉	C₂³	1	2	yes	—
206	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
207	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₁₀₉	C₂³	1	2	yes	—
209	C₂×D₄×C₁₀₉	C₂³	1	2	yes	—
210	C₂×D₄×C₁₀₉	C₂³	1	2	yes	—
211	C₂×D₄×C₁₀₉	C₂³	1	2	yes	—
212	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
213	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
214	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
215	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
216	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
219	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
224	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
225	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
226	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
227	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
228	C₂³×C₁₀₉	C₂⁴	1	2	yes	—
229	C₂³×C₁₀₉	C₂⁴	1	2	yes	—
230	C₂³×C₁₀₉	C₂⁴	1	1	yes	characteristic
231	C₂²×D₁₀₉	—	2	4	no	—
232	C₂²×D₁₀₉	—	4	2	no	—
233	C₂²×D₁₀₉	—	4	2	no	—
234	C₂²×D₁₀₉	C₂⁴	1	2	yes	—
235	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
236	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
237	Q₈×C₁₀₉	—	4	2	no	—
238	D₄×C₁₀₉	—	2	2	no	—
239	D₄×C₁₀₉	—	2	2	no	—
240	D₄×C₁₀₉	—	4	2	no	—
241	D₄×C₁₀₉	—	4	2	no	—
242	D₄×C₁₀₉	—	4	2	no	—
243	D₄×C₁₀₉	—	4	2	no	—
244	C₂×C₄×C₁₀₉	—	2	2	no	—
245	C₂×C₄×C₁₀₉	—	2	2	no	—
246	C₂×C₄×C₁₀₉	—	2	4	no	—
247	C₂×C₄×C₁₀₉	—	2	4	no	—
248	C₂×C₄×C₁₀₉	—	4	1	no	—
249	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
254	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
255	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
257	C₂²⋊D₁₀₉	—	2	4	no	—
258	C₂²⋊D₁₀₉	—	2	2	no	—
259	C₂²⋊D₁₀₉	—	2	4	no	—
260	C₂²⋊D₁₀₉	—	2	2	no	—
261	C₂²⋊D₁₀₉	—	4	2	no	—
262	C₂²⋊D₁₀₉	—	4	2	no	—
263	C₂²⋊D₁₀₉	—	4	2	no	—
264	C₂²⋊D₁₀₉	—	4	2	no	—
265	C₂²⋊D₁₀₉	—	4	2	no	—
266	C₂×Dic₁₀₉	—	2	4	no	—
267	C₂×Dic₁₀₉	—	4	2	no	—
268	C₂×Dic₁₀₉	—	4	2	no	—
269	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
271	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
273	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
277	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
278	D₄₃₆	—	2	2	no	—
279	D₄₃₆	—	2	2	no	—
280	D₄₃₆	—	4	2	no	—
281	C₄×D₁₀₉	—	2	2	no	—
282	C₄×D₁₀₉	—	2	2	no	—
283	C₄×D₁₀₉	—	2	4	no	—
284	C₄×D₁₀₉	—	2	2	no	—
285	C₄×D₁₀₉	—	4	2	no	—
286	C₄×D₁₀₉	—	4	2	no	—
287	C₄×D₁₀₉	—	4	1	no	—
288	C₄×D₁₀₉	—	4	1	no	—
289	C₄×D₁₀₉	#41	1	4	yes	complemented
290	Dic₂₁₈	—	2	2	no	—
291	Dic₂₁₈	—	2	2	no	—
292	Dic₂₁₈	—	4	2	no	—
293	C₂²×C₁₀₉	—	2	2	no	—
294	C₂²×C₁₀₉	—	2	1	no	—
295	C₂²×C₁₀₉	—	2	2	no	—
296	C₂²×C₁₀₉	—	2	2	no	—
297	C₂²×C₁₀₉	—	2	2	no	—
298	C₂²×C₁₀₉	—	2	1	no	—
299	C₂²×C₁₀₉	—	2	2	no	—
300	C₂²×C₁₀₉	—	2	1	no	—
301	C₂²×C₁₀₉	—	2	2	no	—
302	C₂²×C₁₀₉	C₂⁵	1	1	yes	characteristic
303	C₂×D₁₀₉	—	2	1	no	—
304	C₂×D₁₀₉	—	2	1	no	—
305	C₂×D₁₀₉	—	2	1	no	—
306	C₂×D₁₀₉	—	2	2	no	—
307	C₂×D₁₀₉	—	2	2	no	—
308	C₂×D₁₀₉	—	2	1	no	—
309	C₂×D₁₀₉	—	2	1	no	—
310	C₂×D₁₀₉	—	2	2	no	—
311	C₂×D₁₀₉	—	4	8	no	—
312	C₂×D₁₀₉	C₂×#41	1	2	yes	—
313	C₄×C₁₀₉	—	2	1	no	—
314	C₄×C₁₀₉	—	2	2	no	—
315	C₄×C₁₀₉	—	2	2	no	—
316	C₄×C₁₀₉	—	2	1	no	—
317	C₄×C₁₀₉	—	2	1	no	—
318	C₄×C₁₀₉	—	2	1	no	—
319	C₄×C₁₀₉	C₂×#41	1	2	yes	—
320	C₄×C₁₀₉	H(5,𝔽₂)	1	2	yes	—
321	Dic₁₀₉	—	2	1	no	—
322	Dic₁₀₉	—	2	2	no	—
323	Dic₁₀₉	—	2	1	no	—
324	Dic₁₀₉	—	2	2	no	—
325	Dic₁₀₉	—	2	1	no	—
326	Dic₁₀₉	—	2	1	no	—
327	Dic₁₀₉	—	2	1	no	—
328	Dic₁₀₉	—	2	2	no	—
329	Dic₁₀₉	C₂×#41	1	2	yes	—
330	C₂×C₁₀₉	—	4	2	no	—
331	C₂×C₁₀₉	—	4	2	no	—
332	C₂×C₁₀₉	—	4	1	no	—
333	C₂×C₁₀₉	C₂²×#41	1	1	yes	characteristic
334	C₂×C₁₀₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
335	C₂×C₁₀₉	#585	1	1	yes	characteristic
336	D₁₀₉	—	2	2	no	—
337	D₁₀₉	—	4	1	no	—
338	D₁₀₉	—	4	2	no	—
339	#3460	—	109	1	no	maximal, Sylow
340	C₁₀₉	#3460	1	1	yes	characteristic, complemented, Sylow
341	#544	—	109	1	no	—
342	#542	—	109	1	no	—
343	#542	—	109	2	no	—
344	#542	—	109	1	no	—
345	#540	—	109	1	no	—
346	#540	—	109	2	no	—
347	#540	—	109	1	no	—
348	#538	—	109	2	no	—
349	#538	—	109	2	no	—
350	#537	—	109	1	no	—
351	#535	—	109	1	no	—
352	#535	—	109	1	no	—
353	#532	—	109	2	no	—
354	#532	—	109	1	no	—
355	#532	D₁₀₉	1	1	yes	characteristic, complemented
356	#529	—	109	1	no	—
357	#529	—	109	2	no	—
358	#529	—	109	1	no	—
359	#525	—	109	2	no	—
360	#525	—	109	2	no	—
361	C₄×#41	—	109	1	no	—
362	C₄×#41	—	109	1	no	—
363	C₂×C₄×D₄	—	109	1	no	—
364	C₂×#41	—	109	1	no	—
365	C₂×#41	—	109	2	no	—
366	C₂×#41	—	109	1	no	—
367	C₂×#41	C₂×D₁₀₉	1	2	yes	complemented
368	C₂²×D₄	—	109	1	no	—
369	C₂³×C₄	—	109	2	no	—
370	C₄⋊Q₈	—	109	2	no	—
371	C₄⋊Q₈	—	109	1	no	—
372	C₄⋊Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
373	#127	—	109	1	no	—
374	#127	—	109	2	no	—
375	#127	C₂×D₁₀₉	1	1	yes	characteristic
376	#126	—	109	2	no	—
377	#126	—	109	2	no	—
378	#126	—	109	2	no	—
379	#126	—	109	2	no	—
380	#125	—	109	2	no	—
381	#125	—	109	1	no	—
382	#125	—	109	1	no	—
383	#124	—	109	2	no	—
384	#124	—	109	1	no	—
385	#124	—	109	2	no	—
386	#124	—	109	2	no	—
387	#124	—	109	2	no	—
388	#124	—	109	1	no	—
389	#124	C₂×D₁₀₉	1	2	yes	complemented
390	#123	—	109	2	no	—
391	#123	—	109	2	no	—
392	#123	—	109	2	no	—
393	#123	—	109	2	no	—
394	#123	—	109	2	no	—
395	#123	—	109	2	no	—
396	#123	—	109	2	no	—
397	#123	—	109	2	no	—
398	C₂²⋊Q₈	—	109	2	no	—
399	C₂²⋊Q₈	—	109	2	no	—
400	C₂²⋊Q₈	—	109	1	no	—
401	C₂²⋊Q₈	—	109	2	no	—
402	C₂²⋊Q₈	—	109	1	no	—
403	C₂²⋊Q₈	—	109	2	no	—
404	C₂²⋊Q₈	—	109	2	no	—
405	#121	—	109	2	no	—
406	#121	—	109	2	no	—
407	#121	—	109	2	no	—
408	#121	—	109	1	no	—
409	#121	—	109	2	no	—
410	#121	—	109	2	no	—
411	#121	—	109	1	no	—
412	#121	—	109	2	no	—
413	#121	—	109	2	no	—
414	#121	—	109	2	no	—
415	#121	—	109	1	no	—
416	#121	—	109	1	no	—
417	#121	—	109	2	no	—
418	#121	—	109	2	no	—
419	#121	C₂×D₁₀₉	1	1	yes	characteristic
420	#121	C₂×D₁₀₉	1	1	yes	characteristic, complemented
421	#121	C₂×D₁₀₉	1	2	yes	complemented
422	#120	—	109	2	no	—
423	#120	—	109	2	no	—
424	#120	—	109	2	no	—
425	#120	—	109	2	no	—
426	C₄×Q₈	—	109	1	no	—
427	C₄×Q₈	—	109	1	no	—
428	C₄×Q₈	—	109	1	no	—
429	C₄×Q₈	—	109	1	no	—
430	C₄×D₄	—	109	1	no	—
431	C₄×D₄	—	109	1	no	—
432	C₄×D₄	—	109	2	no	—
433	C₄×D₄	—	109	2	no	—
434	C₄×D₄	—	109	1	no	—
435	C₄×D₄	—	109	1	no	—
436	C₄×D₄	—	109	1	no	—
437	C₄×D₄	—	109	1	no	—
438	C₄×D₄	—	109	2	no	—
439	C₄×D₄	—	109	2	no	—
440	C₄×D₄	—	109	2	no	—
441	C₄×D₄	—	109	1	no	—
442	C₄×D₄	—	109	2	no	—
443	C₄×D₄	—	109	2	no	—
444	C₄×D₄	—	109	1	no	—
445	C₄×D₄	—	109	1	no	—
446	C₄×D₄	—	109	1	no	—
447	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic
448	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
449	C₄×D₄	C₂×D₁₀₉	1	2	yes	complemented
450	#117	—	109	1	no	—
451	#117	—	109	2	no	—
452	#117	—	109	1	no	—
453	#117	—	109	2	no	—
454	#117	—	109	1	no	—
455	#117	—	109	1	no	—
456	#117	—	109	2	no	—
457	C₂×C₄⋊C₄	—	109	1	no	—
458	C₂×C₂²⋊C₄	—	109	2	no	—
459	C₂×C₄²	—	109	2	no	—
460	C₂×C₄²	—	109	1	no	—
461	C₂×C₄²	—	109	1	no	—
462	C₂×C₄²	C₂×D₁₀₉	1	1	yes	characteristic, complemented
463	C₂⁴	—	109	2	no	—
464	#41	—	4	4	no	—
465	#41	—	436	4	no	—
466	#41	—	218	4	no	—
467	#41	—	218	4	no	—
468	C₂×Q₈	—	109	2	no	—
469	C₂×Q₈	—	109	1	no	—
470	C₂×Q₈	—	109	1	no	—
471	C₂×Q₈	C₂²×D₁₀₉	1	2	yes	—
472	C₂×D₄	—	109	2	no	—
473	C₂×D₄	—	109	2	no	—
474	C₂×D₄	—	109	2	no	—
475	C₂×D₄	—	109	2	no	—
476	C₂×D₄	—	109	2	no	—
477	C₂×D₄	—	109	1	no	—
478	C₂×D₄	—	109	2	no	—
479	C₂×D₄	—	109	2	no	—
480	C₂×D₄	—	109	1	no	—
481	C₂×D₄	—	109	2	no	—
482	C₂×D₄	—	109	1	no	—
483	C₂×D₄	—	109	1	no	—
484	C₂×D₄	—	218	4	no	—
485	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
486	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
487	C₂×D₄	C₂²×D₁₀₉	1	2	yes	—
488	C₂×D₄	C₂²×D₁₀₉	1	2	yes	—
489	C₂×D₄	C₂²×D₁₀₉	1	2	yes	—
490	C₂×D₄	C₂²×D₁₀₉	1	2	yes	—
491	C₂²×C₄	—	109	1	no	—
492	C₂²×C₄	—	109	2	no	—
493	C₂²×C₄	—	109	2	no	—
494	C₂²×C₄	—	109	2	no	—
495	C₂²×C₄	—	109	1	no	—
496	C₂²×C₄	—	109	1	no	—
497	C₂²×C₄	—	109	2	no	—
498	C₂²×C₄	—	109	2	no	—
499	C₂²×C₄	—	109	1	no	—
500	C₂²×C₄	—	109	1	no	—
501	C₂²×C₄	—	109	1	no	—
502	C₂²×C₄	—	109	2	no	—
503	C₂²×C₄	—	436	4	no	—
504	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
505	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	—
506	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
507	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	—
508	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
509	C₄⋊C₄	—	109	2	no	—
510	C₄⋊C₄	—	109	1	no	—
511	C₄⋊C₄	—	109	1	no	—
512	C₄⋊C₄	—	109	2	no	—
513	C₄⋊C₄	—	109	1	no	—
514	C₄⋊C₄	—	109	1	no	—
515	C₄⋊C₄	—	109	2	no	—
516	C₄⋊C₄	—	109	2	no	—
517	C₄⋊C₄	—	109	2	no	—
518	C₄⋊C₄	—	109	2	no	—
519	C₄⋊C₄	—	109	2	no	—
520	C₄⋊C₄	—	109	2	no	—
521	C₄⋊C₄	—	109	1	no	—
522	C₄⋊C₄	—	109	1	no	—
523	C₄⋊C₄	—	109	1	no	—
524	C₄⋊C₄	—	109	1	no	—
525	C₄⋊C₄	—	109	2	no	—
526	C₄⋊C₄	—	109	2	no	—
527	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
528	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
529	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
530	C₂²⋊C₄	—	109	2	no	—
531	C₂²⋊C₄	—	109	1	no	—
532	C₂²⋊C₄	—	109	2	no	—
533	C₂²⋊C₄	—	109	1	no	—
534	C₂²⋊C₄	—	109	2	no	—
535	C₂²⋊C₄	—	109	2	no	—
536	C₂²⋊C₄	—	109	2	no	—
537	C₂²⋊C₄	—	109	2	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	1	no	—
543	C₂²⋊C₄	—	109	1	no	—
544	C₂²⋊C₄	—	109	1	no	—
545	C₂²⋊C₄	—	109	1	no	—
546	C₂²⋊C₄	—	109	2	no	—
547	C₂²⋊C₄	—	109	2	no	—
548	C₂²⋊C₄	—	109	2	no	—
549	C₂²⋊C₄	—	109	2	no	—
550	C₂²⋊C₄	—	109	2	no	—
551	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
552	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
553	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
555	C₄²	—	109	1	no	—
556	C₄²	—	109	1	no	—
557	C₄²	—	109	2	no	—
558	C₄²	—	109	1	no	—
559	C₄²	—	109	2	no	—
560	C₄²	—	109	1	no	—
561	C₄²	—	109	1	no	—
562	C₄²	—	109	1	no	—
563	C₄²	—	109	2	no	—
564	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
565	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
566	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
567	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
568	C₂³	—	109	1	no	—
569	C₂³	—	109	2	no	—
570	C₂³	—	109	1	no	—
571	C₂³	—	436	2	no	—
572	C₂³	—	436	2	no	—
573	C₂³	—	218	4	no	—
574	C₂³	C₂³×D₁₀₉	1	2	yes	—
575	C₂³	C₂³×D₁₀₉	1	1	yes	characteristic
576	C₂³	C₂³×D₁₀₉	1	2	yes	—
577	Q₈	—	4	2	no	—
578	Q₈	—	436	2	no	—
579	Q₈	—	218	2	no	—
580	Q₈	—	218	2	no	—
581	D₄	—	2	2	no	—
582	D₄	—	2	2	no	—
583	D₄	—	4	2	no	—
584	D₄	—	4	2	no	—
585	D₄	—	4	2	no	—
586	D₄	—	4	2	no	—
587	D₄	—	436	2	no	—
588	D₄	—	436	2	no	—
589	D₄	—	436	2	no	—
590	D₄	—	436	2	no	—
591	D₄	—	436	2	no	—
592	D₄	—	436	2	no	—
593	D₄	—	218	2	no	—
594	D₄	—	218	4	no	—
595	D₄	—	218	2	no	—
596	D₄	—	218	2	no	—
597	D₄	—	218	4	no	—
598	D₄	—	218	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	4	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	109	1	no	—
605	C₂×C₄	—	109	4	no	—
606	C₂×C₄	—	109	1	no	—
607	C₂×C₄	—	109	1	no	—
608	C₂×C₄	—	109	2	no	—
609	C₂×C₄	—	109	1	no	—
610	C₂×C₄	—	109	2	no	—
611	C₂×C₄	—	109	1	no	—
612	C₂×C₄	—	109	1	no	—
613	C₂×C₄	—	109	2	no	—
614	C₂×C₄	—	436	2	no	—
615	C₂×C₄	—	436	2	no	—
616	C₂×C₄	—	436	1	no	—
617	C₂×C₄	—	436	1	no	—
618	C₂×C₄	—	436	2	no	—
619	C₂×C₄	—	436	2	no	—
620	C₂×C₄	—	218	4	no	—
621	C₂×C₄	—	218	2	no	—
622	C₂×C₄	—	218	2	no	—
623	C₂×C₄	—	218	4	no	—
624	C₂×C₄	—	218	2	no	—
625	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
627	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
628	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
629	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
630	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
631	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
632	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
633	C₂²	—	2	1	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	109	2	no	—
643	C₂²	—	436	8	no	—
644	C₂²	—	218	1	no	—
645	C₂²	—	218	2	no	—
646	C₂²	—	218	2	no	—
647	C₂²	—	218	1	no	—
648	C₂²	—	218	1	no	—
649	C₂²	—	218	2	no	—
650	C₂²	—	218	1	no	—
651	C₂²	—	218	1	no	—
652	C₂²	C₂⁴×D₁₀₉	1	1	yes	characteristic
653	C₄	—	2	1	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	1	no	—
658	C₄	—	2	1	no	—
659	C₄	—	109	2	no	—
660	C₄	—	218	2	no	—
661	C₄	—	218	1	no	—
662	C₄	—	218	1	no	—
663	C₄	—	218	2	no	—
664	C₄	—	218	1	no	—
665	C₄	—	218	1	no	—
666	C₄	—	218	1	no	—
667	C₄	—	218	2	no	—
668	C₄	#41×D₁₀₉	1	2	yes	—
669	C₄	#16812744	1	2	yes	—
670	C₂	—	4	2	no	—
671	C₂	—	4	1	no	—
672	C₂	—	4	2	no	—
673	C₂	—	436	2	no	—
674	C₂	—	436	1	no	—
675	C₂	—	218	2	no	—
676	C₂	C₂×#41×D₁₀₉	1	1	yes	characteristic
677	C₂	C₂×#16812744	1	1	yes	characteristic
678	C₂	#20295862	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₀₉
commutator, socle, cosocle	C₂²×C₁₀₉	C₂⁵
Frattini	C₂²	C₂⁴×D₁₀₉
Fitting	#532×C₁₀₉	C₂
hypercenter	#532	D₁₀₉
hypocenter	C₁₀₉	#3460
LCS	G ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂×C₄ ◁ #532

Complements

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

N	H ≅ G/N	type
1. #20295653	C₂	semidirect
2. #20295650	C₂	semidirect
3. #20295643	C₂	semidirect
4. #20295640	C₂	semidirect
5. #20295630	C₂	semidirect
6. #20295629	C₂	semidirect
7. #20295626	C₂	semidirect
8. #20295610	C₂	semidirect
9. #20295608	C₂	semidirect
10. #20295605	C₂	semidirect
11. #20295592	C₂	semidirect
12. #20295589	C₂	semidirect
13. #20295573	C₂	semidirect
14. #20295572	C₂	semidirect
15. #20295560	C₂	semidirect
16. #20295558	C₂	semidirect
17. #20295556	C₂	semidirect
18. #20295535	C₂	semidirect
19. #20295533	C₂	semidirect
20. C₄×#13182029	C₂	semidirect
21. C₄×#13182028	C₂	semidirect
22. C₄×D₄×D₁₀₉	C₂	semidirect
23. #532×C₁₀₉	C₂	semidirect
25. C₂×#13182029	C₂²	semidirect
29. #16812698	C₂²	semidirect
30. #16812697	C₂²	semidirect
33. #16812694	C₂²	semidirect
34. #16812693	C₂²	semidirect
35. #16812692	C₂²	semidirect
36. #16812692	C₂²	semidirect
37. #16812691	C₂²	semidirect
38. #16812690	C₂²	semidirect
39. #16812689	C₂²	semidirect
40. #16812688	C₂²	semidirect
43. #16812686	C₂²	semidirect
45. #16812685	C₂²	semidirect
46. #16812684	C₂²	semidirect
47. #16812683	C₂²	semidirect
48. #16812682	C₂²	semidirect
49. #16812681	C₂²	semidirect
50. #16812681	C₂²	semidirect
51. #16812680	C₂²	semidirect
52. #16812680	C₂²	semidirect
53. #16812680	C₂²	semidirect
54. #16812679	C₂²	semidirect
55. #16812678	C₂²	semidirect
57. #16812676	C₂²	semidirect
58. #16812676	C₂²	semidirect
60. #16812675	C₂²	semidirect
64. #16812672	C₂²	semidirect
67. #16812671	C₂²	semidirect
68. #16812671	C₂²	semidirect
69. #16812671	C₂²	semidirect
70. #16812671	C₂²	semidirect
73. #16812670	C₂²	semidirect
74. #16812670	C₂²	semidirect
79. C₄×Dic₂₁₈	C₂²	semidirect
80. C₄×Dic₂₁₈	C₂²	semidirect
81. C₄×Dic₂₁₈	C₂²	semidirect
82. #16812664	C₂²	semidirect
87. D₄×Dic₁₀₉	C₂²	semidirect
93. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
94. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
95. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
96. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
97. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
100. #16812658	C₂²	semidirect
101. #16812658	C₂²	semidirect
104. #16812656	C₂²	semidirect
105. #16812656	C₂²	semidirect
106. #16812655	C₂²	semidirect
109. C₂×C₄×Dic₁₀₉	C₂²	semidirect
111. C₄²×D₁₀₉	C₂²	semidirect
112. C₂×#41×C₁₀₉	C₂²	semidirect
113. C₄⋊Q₈×C₁₀₉	C₂²	semidirect
115. #124×C₁₀₉	C₂²	semidirect
117. #121×C₁₀₉	C₂²	semidirect
118. #121×C₁₀₉	C₂²	semidirect
120. C₄×D₄×C₁₀₉	C₂²	semidirect
121. C₄×D₄×C₁₀₉	C₂²	semidirect
122. C₂×C₄²×C₁₀₉	C₂²	semidirect
289. C₄×D₁₀₉	#41	semidirect
340. C₁₀₉	#3460	semidirect
355. #532	D₁₀₉	semidirect
367. C₂×#41	C₂×D₁₀₉	semidirect
372. C₄⋊Q₈	C₂×D₁₀₉	semidirect
389. #124	C₂×D₁₀₉	semidirect
420. #121	C₂×D₁₀₉	semidirect
421. #121	C₂×D₁₀₉	semidirect
448. C₄×D₄	C₂×D₁₀₉	semidirect
449. C₄×D₄	C₂×D₁₀₉	semidirect
462. C₂×C₄²	C₂×D₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
#20295653	2
#20295650	2
#20295643	2
#20295640	2
#20295630	2
#20295629	2
#20295626	2
#20295610	2
#20295608	2
#20295605	2
#20295592	2
#20295589	2
#20295573	2
#20295572	2
#20295560	2
#20295558	2
#20295556	2
#20295535	2
#20295533	2
C₄×#13182029	2
C₄×#13182028	2
C₄×D₄×D₁₀₉	2
#532×C₁₀₉	2
#3460	109