Subgroups — #28377809

Order 13952.

1464 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20295862	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16812745	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295835	C₂	1	4	yes	maximal, complemented
4	#20295833	C₂	1	4	yes	maximal, complemented
5	#20295830	C₂	1	4	yes	maximal, complemented
6	#20295828	C₂	1	4	yes	maximal, complemented
7	#20295825	C₂	1	4	yes	maximal, complemented
8	#20295824	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16812727	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16812724	C₂	1	1	yes	maximal, characteristic, complemented
11	AGL(1,ℤ/8)×D₁₀₉	C₂	1	4	yes	maximal, complemented
12	#20295792	C₂	1	1	yes	maximal, characteristic, complemented
13	#575×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#16812747	C₂²	1	2	yes	complemented
15	#16812746	—	2	1	no	—
16	#16812746	C₂²	1	2	yes	complemented
17	#16812745	—	2	2	no	—
18	#16812745	—	2	2	no	—
19	#16812745	—	2	1	no	—
20	#16812745	C₂²	1	4	yes	complemented
21	#16812745	C₂²	1	4	yes	complemented
22	#16812745	C₂²	1	2	yes	complemented
23	#16812744	—	2	2	no	—
24	#16812744	C₂²	1	2	yes	complemented
25	C₂×#13182030	C₂²	1	2	yes	complemented
26	C₂×#13182029	—	2	2	no	—
27	C₂×#13182029	—	2	1	no	—
28	C₂×#13182029	C₂²	1	1	yes	characteristic
29	C₂×#13182029	C₂²	1	1	yes	characteristic, complemented
30	#41×D₁₀₉	—	2	2	no	—
31	#41×D₁₀₉	C₂²	1	4	yes	complemented
32	C₂²×D₄₃₆	—	2	1	no	—
33	C₂²×D₄₃₆	C₂²	1	1	yes	characteristic, complemented
34	C₂×D₄×D₁₀₉	—	2	2	no	—
35	C₂×D₄×D₁₀₉	C₂²	1	2	yes	complemented
36	#16812731	C₂²	1	8	yes	complemented
37	#16812730	C₂²	1	2	yes	complemented
38	#16812729	C₂²	1	2	yes	complemented
39	#16812727	C₂²	1	4	yes	complemented
40	#16812727	C₂²	1	4	yes	complemented
41	#16812726	C₂²	1	8	yes	complemented
42	#16812726	C₂²	1	8	yes	complemented
43	#16812725	C₂²	1	2	yes	complemented
44	#16812724	C₂²	1	4	yes	complemented
45	#16812724	C₂²	1	2	yes	complemented
46	#16812724	C₂²	1	4	yes	complemented
47	#16812723	C₂²	1	8	yes	complemented
48	#16812722	C₂²	1	8	yes	complemented
49	#16812720	C₂²	1	8	yes	complemented
50	#16812719	C₂²	1	4	yes	complemented
51	C₂×#13182018	C₂²	1	2	yes	complemented
52	C₂×#13182016	C₂²	1	2	yes	complemented
53	SD₁₆×D₁₀₉	C₂²	1	8	yes	complemented
54	C₂×D₈₇₂	C₂²	1	2	yes	complemented
55	C₂×#13182014	C₂²	1	2	yes	complemented
56	D₈×D₁₀₉	C₂²	1	8	yes	complemented
57	#16812707	C₂²	1	4	yes	complemented
58	#16812705	C₂²	1	4	yes	complemented
59	C₂×#13182013	C₂²	1	1	yes	characteristic, complemented
60	M₁₆×D₁₀₉	C₂²	1	4	yes	complemented
61	C₂×#41×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
62	C₂×#41×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
63	#137×C₁₀₉	C₂²	1	2	yes	complemented
64	#137×C₁₀₉	C₂²	1	2	yes	complemented
65	AGL(1,ℤ/8)×C₁₀₉	C₂²	1	2	yes	complemented
66	AGL(1,ℤ/8)×C₁₀₉	C₂²	1	2	yes	complemented
67	#135×C₁₀₉	C₂²	1	4	yes	complemented
68	C₂×M₁₆×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
69	C₂³×D₁₀₉	—	2	1	no	—
70	C₂³×D₁₀₉	—	2	2	no	—
71	#13182030	—	2	2	no	—
72	#13182030	—	2	4	no	—
73	#13182030	C₂³	1	8	yes	—
74	#13182030	C₂³	1	4	yes	complemented
75	#13182029	—	2	1	no	—
76	#13182029	—	2	1	no	—
77	#13182029	—	2	4	no	—
78	#13182029	—	2	2	no	—
79	#13182029	—	2	4	no	—
80	#13182029	—	2	4	no	—
81	#13182029	—	2	4	no	—
82	#13182029	—	2	2	no	—
83	#13182029	D₄	1	2	yes	—
84	#13182029	D₄	1	2	yes	—
85	#13182029	C₂³	1	2	yes	—
86	#13182029	C₂³	1	2	yes	—
87	#13182029	C₂³	1	2	yes	—
88	#13182029	C₂³	1	2	yes	complemented
89	#13182028	—	2	4	no	—
90	#13182028	—	2	4	no	—
91	#13182028	—	2	2	no	—
92	#13182028	C₂³	1	4	yes	complemented
93	C₂×Dic₂₁₈	—	2	2	no	—
94	C₂×Dic₂₁₈	D₄	1	1	yes	characteristic
95	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic, complemented
96	Q₈×D₁₀₉	—	2	2	no	—
97	Q₈×D₁₀₉	C₂³	1	4	yes	complemented
98	C₂×D₄₃₆	—	2	2	no	—
99	C₂×D₄₃₆	—	2	1	no	—
100	C₂×D₄₃₆	—	2	1	no	—
101	C₂×D₄₃₆	—	2	1	no	—
102	C₂×D₄₃₆	—	2	4	no	—
103	C₂×D₄₃₆	—	2	4	no	—
104	C₂×D₄₃₆	—	2	2	no	—
105	C₂×D₄₃₆	D₄	1	1	yes	characteristic
106	C₂×D₄₃₆	C₂³	1	2	yes	—
107	C₂×D₄₃₆	C₂³	1	2	yes	—
108	C₂×D₄₃₆	C₂³	1	2	yes	—
109	C₂×D₄₃₆	C₂³	1	1	yes	characteristic, complemented
110	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
111	C₂×C₂²⋊D₁₀₉	—	2	4	no	—
112	C₂×C₂²⋊D₁₀₉	—	2	2	no	—
113	C₂×C₂²⋊D₁₀₉	D₄	1	2	yes	—
114	D₄×D₁₀₉	—	2	4	no	—
115	D₄×D₁₀₉	—	2	8	no	—
116	D₄×D₁₀₉	—	2	8	no	—
117	D₄×D₁₀₉	—	2	4	no	—
118	D₄×D₁₀₉	—	2	2	no	—
119	D₄×D₁₀₉	—	2	4	no	—
120	D₄×D₁₀₉	C₂³	1	8	yes	—
121	D₄×D₁₀₉	C₂³	1	4	yes	complemented
122	C₂×C₄×D₁₀₉	—	2	1	no	—
123	C₂×C₄×D₁₀₉	—	2	2	no	—
124	C₂×C₄×D₁₀₉	—	2	4	no	—
125	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
126	#13182019	C₂³	1	4	yes	complemented
127	#13182018	C₂³	1	8	yes	complemented
128	#13182017	C₂³	1	4	yes	complemented
129	#13182016	C₂³	1	8	yes	complemented
130	#13182016	C₂³	1	4	yes	complemented
131	D₈₇₂	C₂³	1	8	yes	complemented
132	#13182014	C₂³	1	4	yes	complemented
133	#13182014	C₂³	1	8	yes	complemented
134	#13182013	C₂³	1	2	yes	—
135	#13182013	C₂³	1	2	yes	complemented
136	#13182012	C₂³	1	8	yes	complemented
137	C₂×#11724784	C₂³	1	2	yes	complemented
138	C₈×D₁₀₉	C₂³	1	8	yes	complemented
139	#41×C₁₀₉	—	2	1	no	—
140	#41×C₁₀₉	—	2	1	no	—
141	#41×C₁₀₉	—	2	1	no	—
142	#41×C₁₀₉	—	2	1	no	—
143	#41×C₁₀₉	C₂³	1	2	yes	—
144	#41×C₁₀₉	C₂³	1	2	yes	—
145	#41×C₁₀₉	C₂³	1	2	yes	—
146	#41×C₁₀₉	C₂³	1	2	yes	complemented
147	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
148	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic, complemented
149	C₂×D₄×C₁₀₉	—	2	1	no	—
150	C₂×D₄×C₁₀₉	—	2	1	no	—
151	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
152	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic, complemented
153	C₂²×C₄×C₁₀₉	—	2	1	no	—
154	C₂²×C₄×C₁₀₉	—	2	1	no	—
155	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
156	Q₁₆×C₁₀₉	C₂³	1	4	yes	complemented
157	SD₁₆×C₁₀₉	C₂³	1	4	yes	complemented
158	SD₁₆×C₁₀₉	C₂³	1	4	yes	complemented
159	D₈×C₁₀₉	C₂³	1	4	yes	complemented
160	M₁₆×C₁₀₉	C₂³	1	2	yes	—
161	M₁₆×C₁₀₉	C₂³	1	2	yes	complemented
162	C₂×C₈×C₁₀₉	C₂³	1	2	yes	complemented
163	C₂³×C₁₀₉	—	2	1	no	—
164	C₂³×C₁₀₉	—	2	1	no	—
165	C₂³×C₁₀₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×D₁₀₉	—	2	2	no	—
167	C₂²×D₁₀₉	—	2	1	no	—
168	C₂²×D₁₀₉	—	2	2	no	—
169	C₂²×D₁₀₉	—	2	2	no	—
170	C₂²×D₁₀₉	—	2	4	no	—
171	C₂²×D₁₀₉	—	2	8	no	—
172	C₂²×D₁₀₉	—	8	4	no	—
173	C₂²×D₁₀₉	—	8	2	no	—
174	C₂²×D₁₀₉	C₂×D₄	1	2	yes	—
175	Q₈×C₁₀₉	—	2	1	no	—
176	Q₈×C₁₀₉	—	2	1	no	—
177	Q₈×C₁₀₉	C₂⁴	1	2	yes	—
178	Q₈×C₁₀₉	C₂⁴	1	2	yes	—
179	D₄×C₁₀₉	—	2	2	no	—
180	D₄×C₁₀₉	—	2	2	no	—
181	D₄×C₁₀₉	—	2	2	no	—
182	D₄×C₁₀₉	—	2	2	no	—
183	D₄×C₁₀₉	—	2	1	no	—
184	D₄×C₁₀₉	—	2	1	no	—
185	D₄×C₁₀₉	C₂⁴	1	2	yes	—
186	D₄×C₁₀₉	C₂⁴	1	2	yes	—
187	C₂×C₄×C₁₀₉	—	2	1	no	—
188	C₂×C₄×C₁₀₉	—	2	1	no	—
189	C₂×C₄×C₁₀₉	—	2	2	no	—
190	C₂×C₄×C₁₀₉	—	2	2	no	—
191	C₂×C₄×C₁₀₉	—	2	2	no	—
192	C₂×C₄×C₁₀₉	—	2	2	no	—
193	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
197	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
198	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
199	C₂²⋊D₁₀₉	—	2	2	no	—
200	C₂²⋊D₁₀₉	—	2	2	no	—
201	C₂²⋊D₁₀₉	—	2	4	no	—
202	C₂²⋊D₁₀₉	—	2	8	no	—
203	C₂²⋊D₁₀₉	—	2	4	no	—
204	C₂²⋊D₁₀₉	C₂×D₄	1	4	yes	—
205	C₂²⋊D₁₀₉	C₂×D₄	1	4	yes	—
206	C₂×Dic₁₀₉	—	2	1	no	—
207	C₂×Dic₁₀₉	—	2	4	no	—
208	C₂×Dic₁₀₉	C₂×D₄	1	2	yes	—
209	D₄₃₆	—	2	8	no	—
210	D₄₃₆	—	2	4	no	—
211	D₄₃₆	—	2	2	no	—
212	D₄₃₆	—	2	2	no	—
213	D₄₃₆	—	2	2	no	—
214	D₄₃₆	—	2	1	no	—
215	D₄₃₆	C₂×D₄	1	2	yes	—
216	D₄₃₆	C₂×D₄	1	2	yes	—
217	D₄₃₆	C₂⁴	1	2	yes	—
218	D₄₃₆	C₂⁴	1	4	yes	—
219	C₄×D₁₀₉	—	2	4	no	—
220	C₄×D₁₀₉	—	2	2	no	—
221	C₄×D₁₀₉	—	2	2	no	—
222	C₄×D₁₀₉	—	2	8	no	—
223	C₄×D₁₀₉	—	2	4	no	—
224	C₄×D₁₀₉	C₂×D₄	1	4	yes	—
225	C₄×D₁₀₉	C₂⁴	1	4	yes	—
226	Dic₂₁₈	—	2	1	no	—
227	Dic₂₁₈	—	2	4	no	—
228	Dic₂₁₈	C₂×D₄	1	2	yes	—
229	Dic₂₁₈	C₂×D₄	1	2	yes	—
230	Dic₂₁₈	C₂⁴	1	2	yes	—
231	C₈×C₁₀₉	C₂⁴	1	4	yes	—
232	#11724784	C₂⁴	1	4	yes	—
233	C₂²×C₁₀₉	—	2	2	no	—
234	C₂²×C₁₀₉	—	2	2	no	—
235	C₂²×C₁₀₉	—	4	1	no	—
236	C₂²×C₁₀₉	—	4	2	no	—
237	C₂²×C₁₀₉	—	8	1	no	—
238	C₂²×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
239	C₂²×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
240	C₂²×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
241	C₂×D₁₀₉	—	2	2	no	—
242	C₂×D₁₀₉	—	2	4	no	—
243	C₂×D₁₀₉	—	4	2	no	—
244	C₂×D₁₀₉	—	4	4	no	—
245	C₂×D₁₀₉	—	8	4	no	—
246	C₂×D₁₀₉	—	8	8	no	—
247	C₂×D₁₀₉	—	8	1	no	—
248	C₂×D₁₀₉	—	8	2	no	—
249	C₂×D₁₀₉	—	8	2	no	—
250	C₂×D₁₀₉	C₂²×D₄	1	4	yes	—
251	C₄×C₁₀₉	—	2	2	no	—
252	C₄×C₁₀₉	—	2	2	no	—
253	C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
254	C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
255	C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
256	C₄×C₁₀₉	C₂⁵	1	1	yes	characteristic
257	Dic₁₀₉	—	2	2	no	—
258	Dic₁₀₉	C₂²×D₄	1	4	yes	—
259	C₂×C₁₀₉	—	2	1	no	—
260	C₂×C₁₀₉	—	2	1	no	—
261	C₂×C₁₀₉	—	2	1	no	—
262	C₂×C₁₀₉	—	4	2	no	—
263	C₂×C₁₀₉	—	4	2	no	—
264	C₂×C₁₀₉	C₂³×D₄	1	1	yes	characteristic
265	D₁₀₉	—	2	4	no	—
266	D₁₀₉	—	4	4	no	—
267	D₁₀₉	—	4	2	no	—
268	#3585	—	109	1	no	maximal, Sylow
269	C₁₀₉	#3585	1	1	yes	characteristic, complemented, Sylow
270	#585	—	109	1	no	—
271	C₂×H(5,𝔽₂)	—	109	1	no	—
272	#577	—	109	4	no	—
273	#577	—	109	4	no	—
274	#576	—	109	4	no	—
275	#576	—	109	4	no	—
276	#575	—	109	1	no	—
277	#575	—	109	4	no	—
278	#575	D₁₀₉	1	1	yes	characteristic, complemented
279	C₂×AGL(1,ℤ/8)	—	109	1	no	—
280	C₂×AGL(1,ℤ/8)	—	109	4	no	—
281	C₂×AGL(1,ℤ/8)	—	109	1	no	—
282	#568	—	109	1	no	—
283	2₋¹⁺⁴	—	109	2	no	—
284	2₋¹⁺⁴	—	109	2	no	—
285	2₋¹⁺⁴	—	218	1	no	—
286	H(5,𝔽₂)	—	109	4	no	—
287	H(5,𝔽₂)	—	109	4	no	—
288	H(5,𝔽₂)	—	109	2	no	—
289	H(5,𝔽₂)	—	109	2	no	—
290	H(5,𝔽₂)	—	218	2	no	—
291	H(5,𝔽₂)	—	218	1	no	—
292	H(5,𝔽₂)	—	218	2	no	—
293	H(5,𝔽₂)	—	218	2	no	—
294	C₂×#41	—	109	1	no	—
295	C₂×#41	—	109	4	no	—
296	C₂×#41	—	109	2	no	—
297	C₂×#41	—	109	1	no	—
298	C₂×#41	—	218	1	no	—
299	C₂×#41	—	218	2	no	—
300	C₂×#41	—	218	2	no	—
301	C₂×#41	C₂×D₁₀₉	1	1	yes	characteristic, complemented
302	C₂×#41	C₂×D₁₀₉	1	1	yes	characteristic, complemented
303	C₂²×D₄	—	109	2	no	—
304	C₂²×D₄	—	109	1	no	—
305	C₂²×D₄	—	218	1	no	—
306	C₂²×D₄	—	218	2	no	—
307	#137	—	109	2	no	—
308	#137	—	109	2	no	—
309	#137	—	109	8	no	—
310	#137	C₂×D₁₀₉	1	2	yes	complemented
311	#137	C₂×D₁₀₉	1	2	yes	complemented
312	AGL(1,ℤ/8)	—	109	4	no	—
313	AGL(1,ℤ/8)	—	109	2	no	—
314	AGL(1,ℤ/8)	—	109	4	no	—
315	AGL(1,ℤ/8)	—	109	2	no	—
316	AGL(1,ℤ/8)	—	109	8	no	—
317	AGL(1,ℤ/8)	—	109	8	no	—
318	AGL(1,ℤ/8)	—	109	8	no	—
319	AGL(1,ℤ/8)	—	109	4	no	—
320	AGL(1,ℤ/8)	—	109	4	no	—
321	AGL(1,ℤ/8)	C₂×D₁₀₉	1	2	yes	complemented
322	AGL(1,ℤ/8)	C₂×D₁₀₉	1	2	yes	complemented
323	#135	—	109	4	no	—
324	#135	—	109	8	no	—
325	#135	—	109	8	no	—
326	#135	C₂×D₁₀₉	1	4	yes	complemented
327	C₂×SD₁₆	—	109	2	no	—
328	C₂×SD₁₆	—	109	8	no	—
329	C₂×SD₁₆	—	109	2	no	—
330	C₂×D₈	—	109	2	no	—
331	C₂×D₈	—	109	8	no	—
332	C₂×D₈	—	109	2	no	—
333	#131	—	109	4	no	—
334	#131	—	109	4	no	—
335	C₂×M₁₆	—	109	1	no	—
336	C₂×M₁₆	—	109	4	no	—
337	C₂×M₁₆	C₂×D₁₀₉	1	1	yes	characteristic, complemented
338	C₂⁴	—	218	2	no	—
339	C₂⁴	—	218	1	no	—
340	#41	—	2	1	no	—
341	#41	—	2	1	no	—
342	#41	—	2	1	no	—
343	#41	—	2	1	no	—
344	#41	—	109	2	no	—
345	#41	—	109	2	no	—
346	#41	—	109	2	no	—
347	#41	—	109	2	no	—
348	#41	—	109	8	no	—
349	#41	—	109	4	no	—
350	#41	—	109	4	no	—
351	#41	—	109	2	no	—
352	#41	—	109	2	no	—
353	#41	—	218	4	no	—
354	#41	—	218	4	no	—
355	#41	—	218	2	no	—
356	#41	—	218	4	no	—
357	#41	—	218	4	no	—
358	#41	—	218	2	no	—
359	#41	—	218	4	no	—
360	#41	—	218	4	no	—
361	#41	—	218	4	no	—
362	#41	—	218	2	no	—
363	#41	—	218	2	no	—
364	#41	—	218	1	no	—
365	#41	—	218	1	no	—
366	#41	C₂²×D₁₀₉	1	2	yes	—
367	#41	C₂²×D₁₀₉	1	2	yes	—
368	#41	C₂²×D₁₀₉	1	2	yes	—
369	#41	C₂²×D₁₀₉	1	2	yes	complemented
370	C₂×Q₈	—	109	1	no	—
371	C₂×Q₈	—	109	4	no	—
372	C₂×Q₈	—	109	1	no	—
373	C₂×Q₈	—	218	2	no	—
374	C₂×Q₈	—	218	2	no	—
375	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
376	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic, complemented
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	109	2	no	—
380	C₂×D₄	—	109	8	no	—
381	C₂×D₄	—	109	4	no	—
382	C₂×D₄	—	109	1	no	—
383	C₂×D₄	—	109	2	no	—
384	C₂×D₄	—	109	2	no	—
385	C₂×D₄	—	109	2	no	—
386	C₂×D₄	—	109	1	no	—
387	C₂×D₄	—	218	4	no	—
388	C₂×D₄	—	218	4	no	—
389	C₂×D₄	—	218	2	no	—
390	C₂×D₄	—	218	2	no	—
391	C₂×D₄	—	218	4	no	—
392	C₂×D₄	—	218	2	no	—
393	C₂×D₄	—	218	8	no	—
394	C₂×D₄	—	218	8	no	—
395	C₂×D₄	—	218	4	no	—
396	C₂×D₄	—	218	2	no	—
397	C₂×D₄	—	218	4	no	—
398	C₂×D₄	—	218	4	no	—
399	C₂×D₄	—	218	1	no	—
400	C₂×D₄	—	218	1	no	—
401	C₂×D₄	—	218	1	no	—
402	C₂×D₄	—	218	1	no	—
403	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
404	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic, complemented
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	109	2	no	—
408	C₂²×C₄	—	218	2	no	—
409	C₂²×C₄	—	218	4	no	—
410	C₂²×C₄	—	218	1	no	—
411	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
412	Q₁₆	—	109	4	no	—
413	Q₁₆	C₂²×D₁₀₉	1	4	yes	complemented
414	SD₁₆	—	109	8	no	—
415	SD₁₆	—	109	4	no	—
416	SD₁₆	—	109	4	no	—
417	SD₁₆	—	109	8	no	—
418	SD₁₆	C₂²×D₁₀₉	1	4	yes	complemented
419	SD₁₆	C₂²×D₁₀₉	1	4	yes	complemented
420	D₈	—	109	4	no	—
421	D₈	—	109	8	no	—
422	D₈	—	109	8	no	—
423	D₈	C₂²×D₁₀₉	1	4	yes	complemented
424	M₁₆	—	109	2	no	—
425	M₁₆	—	109	2	no	—
426	M₁₆	—	109	8	no	—
427	M₁₆	C₂²×D₁₀₉	1	2	yes	—
428	M₁₆	C₂²×D₁₀₉	1	2	yes	complemented
429	C₂×C₈	—	109	2	no	—
430	C₂×C₈	—	109	8	no	—
431	C₂×C₈	C₂²×D₁₀₉	1	2	yes	complemented
432	C₂³	—	2	1	no	—
433	C₂³	—	2	1	no	—
434	C₂³	—	872	2	no	—
435	C₂³	—	872	4	no	—
436	C₂³	—	109	2	no	—
437	C₂³	—	218	4	no	—
438	C₂³	—	218	8	no	—
439	C₂³	—	218	1	no	—
440	C₂³	—	218	2	no	—
441	C₂³	—	218	2	no	—
442	C₂³	—	218	2	no	—
443	C₂³	D₄×D₁₀₉	1	1	yes	characteristic
444	Q₈	—	2	1	no	—
445	Q₈	—	2	1	no	—
446	Q₈	—	109	2	no	—
447	Q₈	—	109	2	no	—
448	Q₈	—	109	2	no	—
449	Q₈	—	218	4	no	—
450	Q₈	—	218	1	no	—
451	Q₈	C₂³×D₁₀₉	1	2	yes	—
452	Q₈	C₂³×D₁₀₉	1	2	yes	—
453	D₄	—	2	2	no	—
454	D₄	—	2	2	no	—
455	D₄	—	2	2	no	—
456	D₄	—	2	2	no	—
457	D₄	—	2	1	no	—
458	D₄	—	2	1	no	—
459	D₄	—	109	4	no	—
460	D₄	—	109	4	no	—
461	D₄	—	109	2	no	—
462	D₄	—	109	2	no	—
463	D₄	—	109	2	no	—
464	D₄	—	109	4	no	—
465	D₄	—	218	8	no	—
466	D₄	—	218	4	no	—
467	D₄	—	218	8	no	—
468	D₄	—	218	4	no	—
469	D₄	—	218	4	no	—
470	D₄	—	218	2	no	—
471	D₄	—	218	2	no	—
472	D₄	—	218	2	no	—
473	D₄	—	218	2	no	—
474	D₄	—	218	2	no	—
475	D₄	—	218	1	no	—
476	D₄	C₂³×D₁₀₉	1	2	yes	—
477	D₄	C₂³×D₁₀₉	1	2	yes	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	109	2	no	—
485	C₂×C₄	—	109	4	no	—
486	C₂×C₄	—	109	4	no	—
487	C₂×C₄	—	218	8	no	—
488	C₂×C₄	—	218	4	no	—
489	C₂×C₄	—	218	4	no	—
490	C₂×C₄	—	218	4	no	—
491	C₂×C₄	—	218	1	no	—
492	C₂×C₄	—	218	2	no	—
493	C₂×C₄	—	218	2	no	—
494	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
495	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
496	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
497	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
498	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
499	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
500	C₈	—	109	4	no	—
501	C₈	C₂³×D₁₀₉	1	4	yes	—
502	C₂²	—	2	2	no	—
503	C₂²	—	2	2	no	—
504	C₂²	—	4	1	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	8	1	no	—
507	C₂²	—	872	2	no	—
508	C₂²	—	872	2	no	—
509	C₂²	—	872	1	no	—
510	C₂²	—	872	8	no	—
511	C₂²	—	872	4	no	—
512	C₂²	—	109	4	no	—
513	C₂²	—	436	4	no	—
514	C₂²	—	436	2	no	—
515	C₂²	—	218	2	no	—
516	C₂²	—	218	4	no	—
517	C₂²	C₂×D₄×D₁₀₉	1	1	yes	characteristic
518	C₂²	C₂×D₄×D₁₀₉	1	1	yes	characteristic
519	C₂²	C₂×D₄×D₁₀₉	1	1	yes	characteristic
520	C₄	—	2	2	no	—
521	C₄	—	2	2	no	—
522	C₄	—	109	4	no	—
523	C₄	—	218	2	no	—
524	C₄	C₂×D₄×D₁₀₉	1	1	yes	characteristic
525	C₄	C₂×D₄×D₁₀₉	1	1	yes	characteristic
526	C₄	C₂×D₄×D₁₀₉	1	1	yes	characteristic
527	C₄	C₂⁴×D₁₀₉	1	1	yes	characteristic
528	C₂	—	2	1	no	—
529	C₂	—	2	1	no	—
530	C₂	—	2	1	no	—
531	C₂	—	4	2	no	—
532	C₂	—	4	2	no	—
533	C₂	—	436	4	no	—
534	C₂	—	436	2	no	—
535	C₂	—	218	4	no	—
536	C₂	C₂²×D₄×D₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₄×D₁₀₉
commutator, cosocle	C₄×C₁₀₉	C₂⁵
Frattini	C₄	C₂⁴×D₁₀₉
Fitting	#575×C₁₀₉	C₂
socle	C₂×C₁₀₉	C₂³×D₄
hypercenter	#575	D₁₀₉
hypocenter	C₁₀₉	#3585
LCS	G ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #575

Complements

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

N	H ≅ G/N	type
1. #20295862	C₂	semidirect
2. C₂×#16812745	C₂	semidirect
3. #20295835	C₂	semidirect
4. #20295833	C₂	semidirect
5. #20295830	C₂	semidirect
6. #20295828	C₂	semidirect
7. #20295825	C₂	semidirect
8. #20295824	C₂	semidirect
9. C₂×#16812727	C₂	semidirect
10. C₂×#16812724	C₂	semidirect
11. AGL(1,ℤ/8)×D₁₀₉	C₂	semidirect
12. #20295792	C₂	semidirect
13. #575×C₁₀₉	C₂	semidirect
14. #16812747	C₂²	semidirect
16. #16812746	C₂²	semidirect
20. #16812745	C₂²	semidirect
21. #16812745	C₂²	semidirect
22. #16812745	C₂²	semidirect
24. #16812744	C₂²	semidirect
25. C₂×#13182030	C₂²	semidirect
29. C₂×#13182029	C₂²	semidirect
31. #41×D₁₀₉	C₂²	semidirect
33. C₂²×D₄₃₆	C₂²	semidirect
35. C₂×D₄×D₁₀₉	C₂²	semidirect
36. #16812731	C₂²	semidirect
37. #16812730	C₂²	semidirect
38. #16812729	C₂²	semidirect
39. #16812727	C₂²	semidirect
40. #16812727	C₂²	semidirect
41. #16812726	C₂²	semidirect
42. #16812726	C₂²	semidirect
43. #16812725	C₂²	semidirect
44. #16812724	C₂²	semidirect
45. #16812724	C₂²	semidirect
46. #16812724	C₂²	semidirect
47. #16812723	C₂²	semidirect
48. #16812722	C₂²	semidirect
49. #16812720	C₂²	semidirect
50. #16812719	C₂²	semidirect
51. C₂×#13182018	C₂²	semidirect
52. C₂×#13182016	C₂²	semidirect
53. SD₁₆×D₁₀₉	C₂²	semidirect
54. C₂×D₈₇₂	C₂²	semidirect
55. C₂×#13182014	C₂²	semidirect
56. D₈×D₁₀₉	C₂²	semidirect
57. #16812707	C₂²	semidirect
58. #16812705	C₂²	semidirect
59. C₂×#13182013	C₂²	semidirect
60. M₁₆×D₁₀₉	C₂²	semidirect
61. C₂×#41×C₁₀₉	C₂²	semidirect
62. C₂×#41×C₁₀₉	C₂²	semidirect
63. #137×C₁₀₉	C₂²	semidirect
64. #137×C₁₀₉	C₂²	semidirect
65. AGL(1,ℤ/8)×C₁₀₉	C₂²	semidirect
66. AGL(1,ℤ/8)×C₁₀₉	C₂²	semidirect
67. #135×C₁₀₉	C₂²	semidirect
68. C₂×M₁₆×C₁₀₉	C₂²	semidirect
74. #13182030	C₂³	semidirect
88. #13182029	C₂³	semidirect
92. #13182028	C₂³	semidirect
95. C₂×Dic₂₁₈	C₂³	semidirect
97. Q₈×D₁₀₉	C₂³	semidirect
109. C₂×D₄₃₆	C₂³	semidirect
121. D₄×D₁₀₉	C₂³	semidirect
126. #13182019	C₂³	semidirect
127. #13182018	C₂³	semidirect
128. #13182017	C₂³	semidirect
129. #13182016	C₂³	semidirect
130. #13182016	C₂³	semidirect
131. D₈₇₂	C₂³	semidirect
132. #13182014	C₂³	semidirect
133. #13182014	C₂³	semidirect
135. #13182013	C₂³	semidirect
136. #13182012	C₂³	semidirect
137. C₂×#11724784	C₂³	semidirect
138. C₈×D₁₀₉	C₂³	semidirect
146. #41×C₁₀₉	C₂³	semidirect
148. C₂×Q₈×C₁₀₉	C₂³	semidirect
152. C₂×D₄×C₁₀₉	C₂³	semidirect
156. Q₁₆×C₁₀₉	C₂³	semidirect
157. SD₁₆×C₁₀₉	C₂³	semidirect
158. SD₁₆×C₁₀₉	C₂³	semidirect
159. D₈×C₁₀₉	C₂³	semidirect
161. M₁₆×C₁₀₉	C₂³	semidirect
162. C₂×C₈×C₁₀₉	C₂³	semidirect
269. C₁₀₉	#3585	semidirect
278. #575	D₁₀₉	semidirect
301. C₂×#41	C₂×D₁₀₉	semidirect
302. C₂×#41	C₂×D₁₀₉	semidirect
310. #137	C₂×D₁₀₉	semidirect
311. #137	C₂×D₁₀₉	semidirect
321. AGL(1,ℤ/8)	C₂×D₁₀₉	semidirect
322. AGL(1,ℤ/8)	C₂×D₁₀₉	semidirect
326. #135	C₂×D₁₀₉	semidirect
337. C₂×M₁₆	C₂×D₁₀₉	semidirect
369. #41	C₂²×D₁₀₉	semidirect
376. C₂×Q₈	C₂²×D₁₀₉	semidirect
404. C₂×D₄	C₂²×D₁₀₉	semidirect
413. Q₁₆	C₂²×D₁₀₉	semidirect
418. SD₁₆	C₂²×D₁₀₉	semidirect
419. SD₁₆	C₂²×D₁₀₉	semidirect
423. D₈	C₂²×D₁₀₉	semidirect
428. M₁₆	C₂²×D₁₀₉	semidirect
431. C₂×C₈	C₂²×D₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
#20295862	2
C₂×#16812745	2
#20295835	2
#20295833	2
#20295830	2
#20295828	2
#20295825	2
#20295824	2
C₂×#16812727	2
C₂×#16812724	2
AGL(1,ℤ/8)×D₁₀₉	2
#20295792	2
#575×C₁₀₉	2
#3585	109