Subgroups — #28372289

Order 13952.

754 conjugacy classes of subgroups.

The subgroup lattice has 468 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
2	C₂×#16812731	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16812728	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²⋊Q₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#20295190	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295188	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295186	C₂	1	1	yes	maximal, characteristic, complemented
8	#20295183	C₂	1	1	yes	maximal, characteristic, complemented
9	#20295180	C₂	1	1	yes	maximal, characteristic, complemented
10	#20295178	C₂	1	1	yes	maximal, characteristic, complemented
11	#20295175	C₂	1	1	yes	maximal, characteristic, complemented
12	#20295026	C₂	1	1	yes	maximal, characteristic, complemented
13	#20295024	C₂	1	1	yes	maximal, characteristic, complemented
14	#20294988	C₂	1	1	yes	maximal, characteristic, complemented
15	#452×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13182030	C₂²	1	1	yes	characteristic
17	C₂×#13182029	—	2	1	no	—
18	C₂×#13182029	C₂²	1	1	yes	characteristic
19	C₂×#13182028	—	2	1	no	—
20	C₂×#13182028	C₂²	1	1	yes	characteristic
21	#41×D₁₀₉	—	2	4	no	—
22	#41×D₁₀₉	—	2	4	no	—
23	C₂×Q₈×D₁₀₉	C₂²	1	1	yes	characteristic
24	C₂×Q₈×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
25	C₂×D₄×D₁₀₉	—	2	1	no	—
26	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₁₀₉	—	2	1	no	—
28	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
29	#16812731	—	2	4	no	—
30	#16812728	—	2	4	no	—
31	C₂×Dic₄₃₆	C₂²	1	1	yes	characteristic, complemented
32	C₂×#13182019	C₂²	1	1	yes	characteristic, complemented
33	C₂×#13182019	C₂²	1	1	yes	characteristic, complemented
34	C₂×#13182018	C₂²	1	1	yes	characteristic, complemented
35	C₂×#13182017	C₂²	1	1	yes	characteristic, complemented
36	C₂×#13182016	C₂²	1	1	yes	characteristic, complemented
37	C₂×#13182012	C₂²	1	1	yes	characteristic, complemented
38	C₂×#13182012	C₂²	1	1	yes	characteristic, complemented
39	#16812679	C₂²	1	1	yes	characteristic
40	#16812678	C₂²	1	1	yes	characteristic, complemented
41	#16812677	—	2	1	no	—
42	#16812676	—	2	1	no	—
43	#16812675	C₂²	1	1	yes	characteristic
44	C₄⋊C₄×D₁₀₉	—	2	1	no	—
45	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
46	C₂²⋊C₄×D₁₀₉	—	2	1	no	—
47	#16812624	C₂²	1	1	yes	characteristic, complemented
48	#16812623	C₂²	1	1	yes	characteristic, complemented
49	#16812622	C₂²	1	1	yes	characteristic, complemented
50	#16812621	C₂²	1	1	yes	characteristic, complemented
51	#16812620	C₂²	1	1	yes	characteristic, complemented
52	#16812619	C₂²	1	1	yes	characteristic, complemented
53	C₂²⋊#11724784	C₂²	1	1	yes	characteristic, complemented
54	#16812611	C₂²	1	1	yes	characteristic
55	#16812611	C₂²	1	1	yes	characteristic
56	C₂×#41×C₁₀₉	C₂²	1	1	yes	characteristic
57	C₂×Q₁₆×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
58	C₂×SD₁₆×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
59	C₂²⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
60	#103×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
61	#102×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
62	C₂²⋊C₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
63	C₂³×D₁₀₉	—	2	1	no	—
64	C₂³×D₁₀₉	D₄	1	1	yes	characteristic
65	#13182030	—	2	2	no	—
66	#13182030	D₄	1	4	yes	—
67	#13182029	—	2	8	no	—
68	#13182029	—	2	2	no	—
69	#13182029	—	2	2	no	—
70	#13182028	—	2	8	no	—
71	#13182028	—	2	2	no	—
72	#13182028	D₄	1	4	yes	—
73	C₂×Dic₂₁₈	—	2	1	no	—
74	C₂×Dic₂₁₈	—	2	1	no	—
75	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
76	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
77	Q₈×D₁₀₉	—	2	2	no	—
78	Q₈×D₁₀₉	—	2	2	no	—
79	Q₈×D₁₀₉	—	2	2	no	—
80	Q₈×D₁₀₉	—	2	2	no	—
81	C₂×D₄₃₆	—	2	1	no	—
82	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
83	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
84	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
85	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
86	D₄×D₁₀₉	—	2	8	no	—
87	D₄×D₁₀₉	—	2	2	no	—
88	D₄×D₁₀₉	—	2	2	no	—
89	C₂²×Dic₁₀₉	—	2	1	no	—
90	C₂²×Dic₁₀₉	D₄	1	1	yes	characteristic
91	C₂×C₄×D₁₀₉	—	2	8	no	—
92	C₂×C₄×D₁₀₉	—	2	1	no	—
93	C₂×C₄×D₁₀₉	—	2	1	no	—
94	C₂×C₄×D₁₀₉	—	2	1	no	—
95	C₂×C₄×D₁₀₉	—	2	2	no	—
96	C₂×C₄×D₁₀₉	—	2	2	no	—
97	C₂×C₄×D₁₀₉	—	2	1	no	—
98	C₂×C₄×D₁₀₉	—	2	1	no	—
99	C₂×C₄×D₁₀₉	D₄	1	1	yes	characteristic
100	C₂×C₄×D₁₀₉	D₄	1	1	yes	characteristic
101	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
102	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
103	Dic₄₃₆	—	2	2	no	—
104	#13182019	—	2	2	no	—
105	#13182019	—	2	2	no	—
106	#13182018	—	2	2	no	—
107	#13182017	—	2	2	no	—
108	#13182016	—	2	2	no	—
109	#13182012	—	2	2	no	—
110	#13182012	—	2	2	no	—
111	C₂×#11724784	C₂³	1	1	yes	characteristic
112	C₂×#11724784	C₂³	1	1	yes	characteristic
113	C₄⋊Dic₁₀₉	—	2	1	no	—
114	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
115	#13182008	—	2	1	no	—
116	#13182008	—	2	1	no	—
117	#13182008	—	2	1	no	—
118	C₂²⋊Dic₁₀₉	—	2	1	no	—
119	#13182006	—	2	1	no	—
120	#13182006	—	2	1	no	—
121	#41×C₁₀₉	—	2	2	no	—
122	#41×C₁₀₉	—	2	2	no	—
123	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₁₀₉	—	2	1	no	—
126	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₁₀₉	—	2	1	no	—
128	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
129	Q₁₆×C₁₀₉	—	2	2	no	—
130	SD₁₆×C₁₀₉	—	2	2	no	—
131	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
132	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
133	C₄⋊C₄×C₁₀₉	—	2	1	no	—
134	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
135	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
136	C₂³×C₁₀₉	—	2	1	no	—
137	C₂³×C₁₀₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×D₁₀₉	—	2	4	no	—
139	C₂²×D₁₀₉	—	2	1	no	—
140	C₂²×D₁₀₉	—	2	2	no	—
141	C₂²×D₁₀₉	—	2	2	no	—
142	C₂²×D₁₀₉	—	4	1	no	—
143	C₂²×D₁₀₉	—	4	2	no	—
144	C₂²×D₁₀₉	—	4	2	no	—
145	C₂²×D₁₀₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×D₁₀₉	C₂×D₄	1	1	yes	characteristic
147	Q₈×C₁₀₉	—	2	1	no	—
148	Q₈×C₁₀₉	—	2	1	no	—
149	Q₈×C₁₀₉	—	2	1	no	—
150	Q₈×C₁₀₉	C₂×D₄	1	2	yes	—
151	D₄×C₁₀₉	—	2	4	no	—
152	D₄×C₁₀₉	—	2	1	no	—
153	D₄×C₁₀₉	C₂×D₄	1	2	yes	—
154	C₂×C₄×C₁₀₉	—	2	4	no	—
155	C₂×C₄×C₁₀₉	—	2	1	no	—
156	C₂×C₄×C₁₀₉	—	2	1	no	—
157	C₂×C₄×C₁₀₉	—	2	1	no	—
158	C₂×C₄×C₁₀₉	—	2	1	no	—
159	C₂×C₄×C₁₀₉	—	2	1	no	—
160	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
161	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
162	C₂²⋊D₁₀₉	—	2	4	no	—
163	C₂²⋊D₁₀₉	—	2	4	no	—
164	C₂²⋊D₁₀₉	—	2	4	no	—
165	C₂×Dic₁₀₉	—	2	1	no	—
166	C₂×Dic₁₀₉	—	2	4	no	—
167	C₂×Dic₁₀₉	—	2	2	no	—
168	C₂×Dic₁₀₉	—	2	1	no	—
169	C₂×Dic₁₀₉	—	2	1	no	—
170	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
171	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
172	D₄₃₆	—	2	4	no	—
173	D₄₃₆	—	2	1	no	—
174	D₄₃₆	C₂×D₄	1	2	yes	—
175	C₄×D₁₀₉	—	2	4	no	—
176	C₄×D₁₀₉	—	2	4	no	—
177	C₄×D₁₀₉	—	2	2	no	—
178	C₄×D₁₀₉	—	2	1	no	—
179	C₄×D₁₀₉	—	2	1	no	—
180	C₄×D₁₀₉	—	2	2	no	—
181	C₄×D₁₀₉	—	2	4	no	—
182	C₄×D₁₀₉	—	4	2	no	—
183	C₄×D₁₀₉	—	4	2	no	—
184	C₄×D₁₀₉	C₂×D₄	1	2	yes	—
185	C₄×D₁₀₉	C₂×D₄	1	2	yes	—
186	Dic₂₁₈	—	2	4	no	—
187	Dic₂₁₈	—	2	1	no	—
188	Dic₂₁₈	—	2	1	no	—
189	Dic₂₁₈	—	2	1	no	—
190	Dic₂₁₈	—	4	2	no	—
191	Dic₂₁₈	C₂×D₄	1	2	yes	—
192	C₈×C₁₀₉	—	2	1	no	—
193	C₈×C₁₀₉	—	2	1	no	—
194	#11724784	—	2	1	no	—
195	#11724784	—	2	1	no	—
196	C₂²×C₁₀₉	—	2	1	no	—
197	C₂²×C₁₀₉	—	2	2	no	—
198	C₂²×C₁₀₉	—	2	1	no	—
199	C₂²×C₁₀₉	—	2	1	no	—
200	C₂²×C₁₀₉	—	4	1	no	—
201	C₂²×C₁₀₉	—	4	1	no	—
202	C₂²×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
203	C₂×D₁₀₉	—	2	1	no	—
204	C₂×D₁₀₉	—	2	1	no	—
205	C₂×D₁₀₉	—	2	1	no	—
206	C₂×D₁₀₉	—	2	1	no	—
207	C₂×D₁₀₉	—	2	2	no	—
208	C₂×D₁₀₉	—	4	4	no	—
209	C₂×D₁₀₉	—	4	8	no	—
210	C₂×D₁₀₉	—	4	1	no	—
211	C₂×D₁₀₉	—	4	1	no	—
212	C₂×D₁₀₉	#120	1	2	yes	—
213	C₂×D₁₀₉	#137	1	2	yes	complemented
214	C₄×C₁₀₉	—	2	2	no	—
215	C₄×C₁₀₉	—	2	1	no	—
216	C₄×C₁₀₉	—	4	1	no	—
217	C₄×C₁₀₉	—	4	1	no	—
218	C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
219	C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
220	Dic₁₀₉	—	2	1	no	—
221	Dic₁₀₉	—	2	2	no	—
222	Dic₁₀₉	—	4	1	no	—
223	Dic₁₀₉	—	4	1	no	—
224	Dic₁₀₉	#120	1	2	yes	—
225	C₂×C₁₀₉	—	4	1	no	—
226	C₂×C₁₀₉	—	4	2	no	—
227	C₂×C₁₀₉	C₂×#120	1	1	yes	characteristic
228	C₂×C₁₀₉	C₂×#137	1	1	yes	characteristic
229	C₂×C₁₀₉	#575	1	1	yes	characteristic
230	D₁₀₉	—	2	2	no	—
231	D₁₀₉	—	2	2	no	—
232	D₁₀₉	—	4	2	no	—
233	#3007	—	109	1	no	maximal, Sylow
234	C₁₀₉	#3007	1	1	yes	characteristic, complemented, Sylow
235	C₂²×#41	—	109	1	no	—
236	C₂×#137	—	109	1	no	—
237	C₂×#137	—	109	1	no	—
238	C₂×C₂²⋊Q₈	—	109	1	no	—
239	#452	—	109	1	no	—
240	#452	—	109	1	no	—
241	#452	—	109	1	no	—
242	#452	D₁₀₉	1	1	yes	characteristic, complemented
243	#451	—	109	1	no	—
244	#451	—	109	1	no	—
245	#450	—	109	1	no	—
246	#450	—	109	1	no	—
247	#417	—	109	1	no	—
248	#417	—	109	1	no	—
249	#407	—	109	1	no	—
250	C₂×#41	—	109	1	no	—
251	C₂×#41	—	109	1	no	—
252	C₂×#41	—	109	1	no	—
253	C₂×#41	—	218	1	no	—
254	C₂×#41	—	218	1	no	—
255	C₂×#41	—	218	4	no	—
256	C₂×#41	—	218	4	no	—
257	C₂×#41	C₂×D₁₀₉	1	1	yes	characteristic
258	C₂²×Q₈	—	109	1	no	—
259	C₂²×Q₈	—	109	1	no	—
260	C₂²×D₄	—	109	1	no	—
261	C₂²×D₄	—	218	1	no	—
262	C₂³×C₄	—	109	1	no	—
263	C₂³×C₄	—	218	1	no	—
264	#137	—	218	4	no	—
265	#137	—	218	4	no	—
266	C₂×Q₁₆	—	109	1	no	—
267	C₂×Q₁₆	—	109	1	no	—
268	C₂×Q₁₆	—	109	1	no	—
269	C₂×Q₁₆	C₂×D₁₀₉	1	1	yes	characteristic, complemented
270	C₂×SD₁₆	—	109	1	no	—
271	C₂×SD₁₆	—	109	1	no	—
272	C₂×SD₁₆	—	109	1	no	—
273	C₂×SD₁₆	C₂×D₁₀₉	1	1	yes	characteristic, complemented
274	C₂×M₁₆	—	109	1	no	—
275	C₂×M₁₆	—	109	1	no	—
276	C₂²⋊Q₈	—	109	1	no	—
277	C₂²⋊Q₈	—	109	1	no	—
278	C₂²⋊Q₈	—	109	1	no	—
279	C₂²⋊Q₈	—	218	1	no	—
280	C₂²⋊Q₈	—	218	1	no	—
281	C₂²⋊Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
282	C₂×C₄⋊C₄	—	109	1	no	—
283	C₂×C₄⋊C₄	—	218	1	no	—
284	C₂×C₂²⋊C₄	—	218	1	no	—
285	#103	—	109	1	no	—
286	#103	—	109	1	no	—
287	#103	—	109	1	no	—
288	#103	C₂×D₁₀₉	1	1	yes	characteristic, complemented
289	#102	—	109	1	no	—
290	#102	—	109	1	no	—
291	#102	—	109	1	no	—
292	#102	C₂×D₁₀₉	1	1	yes	characteristic, complemented
293	C₂²⋊C₈	—	109	1	no	—
294	C₂²⋊C₈	—	109	1	no	—
295	C₂²⋊C₈	—	109	1	no	—
296	C₂²⋊C₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
297	C₂⁴	—	109	1	no	—
298	C₂⁴	—	218	1	no	—
299	#41	—	2	2	no	—
300	#41	—	2	2	no	—
301	#41	—	109	4	no	—
302	#41	—	109	4	no	—
303	#41	—	218	2	no	—
304	#41	—	218	2	no	—
305	#41	—	218	8	no	—
306	#41	—	218	2	no	—
307	#41	—	218	2	no	—
308	#41	—	218	8	no	—
309	C₂×Q₈	—	109	1	no	—
310	C₂×Q₈	—	109	1	no	—
311	C₂×Q₈	—	218	1	no	—
312	C₂×Q₈	—	218	1	no	—
313	C₂×Q₈	—	218	2	no	—
314	C₂×Q₈	—	218	2	no	—
315	C₂×Q₈	—	218	2	no	—
316	C₂×Q₈	—	218	2	no	—
317	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
318	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	109	1	no	—
321	C₂×D₄	—	218	1	no	—
322	C₂×D₄	—	218	1	no	—
323	C₂×D₄	—	218	2	no	—
324	C₂×D₄	—	218	8	no	—
325	C₂×D₄	—	218	1	no	—
326	C₂×D₄	—	218	1	no	—
327	C₂×D₄	—	218	2	no	—
328	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	109	1	no	—
331	C₂²×C₄	—	109	1	no	—
332	C₂²×C₄	—	109	1	no	—
333	C₂²×C₄	—	109	1	no	—
334	C₂²×C₄	—	109	1	no	—
335	C₂²×C₄	—	218	2	no	—
336	C₂²×C₄	—	218	2	no	—
337	C₂²×C₄	—	218	1	no	—
338	C₂²×C₄	—	218	1	no	—
339	C₂²×C₄	—	218	1	no	—
340	C₂²×C₄	—	218	1	no	—
341	C₂²×C₄	—	218	8	no	—
342	C₂²×C₄	—	218	1	no	—
343	C₂²×C₄	—	218	1	no	—
344	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
345	Q₁₆	—	2	2	no	—
346	Q₁₆	—	218	2	no	—
347	Q₁₆	—	218	2	no	—
348	Q₁₆	—	218	2	no	—
349	SD₁₆	—	2	2	no	—
350	SD₁₆	—	218	2	no	—
351	SD₁₆	—	218	2	no	—
352	SD₁₆	—	218	2	no	—
353	M₁₆	—	218	2	no	—
354	M₁₆	—	218	2	no	—
355	C₂×C₈	—	109	1	no	—
356	C₂×C₈	—	109	1	no	—
357	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
358	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	109	1	no	—
361	C₄⋊C₄	—	218	1	no	—
362	C₄⋊C₄	—	218	1	no	—
363	C₄⋊C₄	—	218	1	no	—
364	C₄⋊C₄	—	218	1	no	—
365	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
366	C₂²⋊C₄	—	2	1	no	—
367	C₂²⋊C₄	—	218	1	no	—
368	C₂²⋊C₄	—	218	1	no	—
369	C₂²⋊C₄	—	218	1	no	—
370	C₂³	—	2	1	no	—
371	C₂³	—	109	1	no	—
372	C₂³	—	109	1	no	—
373	C₂³	—	436	1	no	—
374	C₂³	—	436	2	no	—
375	C₂³	—	436	2	no	—
376	C₂³	—	218	2	no	—
377	C₂³	—	218	2	no	—
378	C₂³	—	218	4	no	—
379	C₂³	—	218	1	no	—
380	C₂³	D₄×D₁₀₉	1	1	yes	characteristic
381	Q₈	—	2	1	no	—
382	Q₈	—	2	1	no	—
383	Q₈	—	2	1	no	—
384	Q₈	—	109	2	no	—
385	Q₈	—	436	2	no	—
386	Q₈	—	218	4	no	—
387	Q₈	—	218	1	no	—
388	Q₈	—	218	1	no	—
389	Q₈	—	218	1	no	—
390	Q₈	D₄×D₁₀₉	1	2	yes	—
391	D₄	—	2	4	no	—
392	D₄	—	2	1	no	—
393	D₄	—	109	2	no	—
394	D₄	—	218	4	no	—
395	D₄	—	218	4	no	—
396	D₄	—	218	4	no	—
397	D₄	—	218	4	no	—
398	D₄	—	218	1	no	—
399	D₄	D₄×D₁₀₉	1	2	yes	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	109	1	no	—
407	C₂×C₄	—	109	2	no	—
408	C₂×C₄	—	109	2	no	—
409	C₂×C₄	—	109	1	no	—
410	C₂×C₄	—	436	2	no	—
411	C₂×C₄	—	436	2	no	—
412	C₂×C₄	—	218	2	no	—
413	C₂×C₄	—	218	4	no	—
414	C₂×C₄	—	218	2	no	—
415	C₂×C₄	—	218	4	no	—
416	C₂×C₄	—	218	4	no	—
417	C₂×C₄	—	218	2	no	—
418	C₂×C₄	—	218	4	no	—
419	C₂×C₄	—	218	1	no	—
420	C₂×C₄	—	218	1	no	—
421	C₂×C₄	—	218	1	no	—
422	C₂×C₄	—	218	1	no	—
423	C₂×C₄	—	218	1	no	—
424	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
425	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
426	C₈	—	2	1	no	—
427	C₈	—	2	1	no	—
428	C₈	—	218	1	no	—
429	C₈	—	218	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	109	2	no	—
437	C₂²	—	109	2	no	—
438	C₂²	—	436	8	no	—
439	C₂²	—	436	4	no	—
440	C₂²	—	436	1	no	—
441	C₂²	—	436	1	no	—
442	C₂²	—	218	2	no	—
443	C₂²	—	218	1	no	—
444	C₂²	—	218	1	no	—
445	C₂²	—	218	1	no	—
446	C₂²	—	218	1	no	—
447	C₂²	C₂×D₄×D₁₀₉	1	1	yes	characteristic
448	C₄	—	2	1	no	—
449	C₄	—	2	2	no	—
450	C₄	—	4	1	no	—
451	C₄	—	4	1	no	—
452	C₄	—	109	2	no	—
453	C₄	—	436	1	no	—
454	C₄	—	436	1	no	—
455	C₄	—	218	1	no	—
456	C₄	—	218	2	no	—
457	C₄	C₂×D₄×D₁₀₉	1	1	yes	characteristic
458	C₄	C₂×D₄×D₁₀₉	1	1	yes	characteristic
459	C₂	—	4	1	no	—
460	C₂	—	4	2	no	—
461	C₂	—	436	2	no	—
462	C₂	—	218	2	no	—
463	C₂	—	218	2	no	—
464	C₂	#120×D₁₀₉	1	1	yes	characteristic
465	C₂	#137×D₁₀₉	1	1	yes	characteristic
466	C₂	#20295823	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₀₉
commutator, cosocle	C₂×C₄×C₁₀₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₀₉
Fitting	#452×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂²×D₄
prime radical	C₂×#41×D₁₀₉	C₂
hypercenter	#452	D₁₀₉
hypocenter	C₁₀₉	#3007
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #452

Complements

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

N	H ≅ G/N	type
2. C₂×#16812731	C₂	semidirect
3. C₂×#16812728	C₂	semidirect
4. C₂²⋊Q₈×D₁₀₉	C₂	semidirect
5. #20295190	C₂	semidirect
6. #20295188	C₂	semidirect
7. #20295186	C₂	semidirect
8. #20295183	C₂	semidirect
9. #20295180	C₂	semidirect
10. #20295178	C₂	semidirect
11. #20295175	C₂	semidirect
12. #20295026	C₂	semidirect
13. #20295024	C₂	semidirect
14. #20294988	C₂	semidirect
15. #452×C₁₀₉	C₂	semidirect
24. C₂×Q₈×D₁₀₉	C₂²	semidirect
31. C₂×Dic₄₃₆	C₂²	semidirect
32. C₂×#13182019	C₂²	semidirect
33. C₂×#13182019	C₂²	semidirect
34. C₂×#13182018	C₂²	semidirect
35. C₂×#13182017	C₂²	semidirect
36. C₂×#13182016	C₂²	semidirect
37. C₂×#13182012	C₂²	semidirect
38. C₂×#13182012	C₂²	semidirect
40. #16812678	C₂²	semidirect
45. C₄⋊C₄×D₁₀₉	C₂²	semidirect
47. #16812624	C₂²	semidirect
48. #16812623	C₂²	semidirect
49. #16812622	C₂²	semidirect
50. #16812621	C₂²	semidirect
51. #16812620	C₂²	semidirect
52. #16812619	C₂²	semidirect
53. C₂²⋊#11724784	C₂²	semidirect
57. C₂×Q₁₆×C₁₀₉	C₂²	semidirect
58. C₂×SD₁₆×C₁₀₉	C₂²	semidirect
59. C₂²⋊Q₈×C₁₀₉	C₂²	semidirect
60. #103×C₁₀₉	C₂²	semidirect
61. #102×C₁₀₉	C₂²	semidirect
62. C₂²⋊C₈×C₁₀₉	C₂²	semidirect
213. C₂×D₁₀₉	#137	semidirect
234. C₁₀₉	#3007	semidirect
242. #452	D₁₀₉	semidirect
269. C₂×Q₁₆	C₂×D₁₀₉	semidirect
273. C₂×SD₁₆	C₂×D₁₀₉	semidirect
281. C₂²⋊Q₈	C₂×D₁₀₉	semidirect
288. #103	C₂×D₁₀₉	semidirect
292. #102	C₂×D₁₀₉	semidirect
296. C₂²⋊C₈	C₂×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
C₂×#16812731	2
C₂×#16812728	2
C₂²⋊Q₈×D₁₀₉	2
#20295190	2
#20295188	2
#20295186	2
#20295183	2
#20295180	2
#20295178	2
#20295175	2
#20295026	2
#20295024	2
#20294988	2
#452×C₁₀₉	2
#3007	109