Subgroups — #28377810

Order 13952.

1464 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20295863	C₂	1	1	yes	maximal, characteristic, complemented
2	H(5,𝔽₂)×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295835	C₂	1	3	yes	maximal, complemented
4	#20295834	C₂	1	1	yes	maximal, characteristic, complemented
5	#20295832	C₂	1	3	yes	maximal, complemented
6	#20295831	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295830	C₂	1	3	yes	maximal, complemented
8	#20295829	C₂	1	1	yes	maximal, characteristic, complemented
9	#20295828	C₂	1	3	yes	maximal, complemented
10	#20295825	C₂	1	3	yes	maximal, complemented
11	#20295823	C₂	1	3	yes	maximal, complemented
12	C₂×#16812726	C₂	1	3	yes	maximal, complemented
13	AGL(1,ℤ/8)×D₁₀₉	C₂	1	3	yes	maximal, complemented
14	#20295791	C₂	1	1	yes	maximal, characteristic, complemented
15	#577×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#16812747	—	2	1	no	—
17	#16812747	C₂²	1	3	yes	complemented
18	#16812745	—	2	1	no	—
19	#16812745	—	2	3	no	—
20	#16812745	C₂²	1	1	yes	characteristic, complemented
21	#16812745	C₂²	1	1	yes	characteristic, complemented
22	#16812745	C₂²	1	3	yes	complemented
23	#16812745	C₂²	1	3	yes	complemented
24	#16812744	—	2	3	no	—
25	#16812744	C₂²	1	3	yes	complemented
26	C₂×#13182030	—	2	1	no	—
27	C₂×#13182030	C₂²	1	3	yes	complemented
28	#41×D₁₀₉	—	2	3	no	—
29	#41×D₁₀₉	—	2	1	no	—
30	#41×D₁₀₉	C₂²	1	1	yes	characteristic
31	#41×D₁₀₉	C₂²	1	3	yes	complemented
32	#41×D₁₀₉	C₂²	1	3	yes	complemented
33	C₂×D₄×D₁₀₉	—	2	3	no	—
34	C₂×D₄×D₁₀₉	C₂²	1	3	yes	complemented
35	#16812731	C₂²	1	3	yes	complemented
36	#16812731	C₂²	1	3	yes	complemented
37	#16812730	C₂²	1	3	yes	complemented
38	#16812728	C₂²	1	1	yes	characteristic, complemented
39	#16812728	C₂²	1	3	yes	complemented
40	#16812727	C₂²	1	3	yes	complemented
41	#16812727	C₂²	1	3	yes	complemented
42	#16812726	C₂²	1	6	yes	complemented
43	#16812726	C₂²	1	3	yes	complemented
44	#16812726	C₂²	1	6	yes	complemented
45	#16812726	C₂²	1	6	yes	complemented
46	#16812726	C₂²	1	3	yes	complemented
47	#16812725	C₂²	1	3	yes	complemented
48	#16812724	C₂²	1	3	yes	complemented
49	#16812724	C₂²	1	3	yes	complemented
50	#16812723	C₂²	1	3	yes	complemented
51	#16812723	C₂²	1	3	yes	complemented
52	#16812722	C₂²	1	6	yes	complemented
53	#16812721	C₂²	1	3	yes	complemented
54	#16812720	C₂²	1	6	yes	complemented
55	#16812719	C₂²	1	3	yes	complemented
56	#16812719	C₂²	1	3	yes	complemented
57	C₂×#13182016	C₂²	1	3	yes	complemented
58	SD₁₆×D₁₀₉	C₂²	1	6	yes	complemented
59	C₂×D₈₇₂	C₂²	1	3	yes	complemented
60	C₂×#13182014	C₂²	1	3	yes	complemented
61	D₈×D₁₀₉	C₂²	1	6	yes	complemented
62	#16812707	C₂²	1	3	yes	complemented
63	#16812706	C₂²	1	1	yes	characteristic, complemented
64	#16812705	C₂²	1	3	yes	complemented
65	C₂×#13182012	C₂²	1	3	yes	complemented
66	M₁₆×D₁₀₉	C₂²	1	3	yes	complemented
67	2₋¹⁺⁴×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
68	H(5,𝔽₂)×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
69	#137×C₁₀₉	C₂²	1	3	yes	complemented
70	AGL(1,ℤ/8)×C₁₀₉	C₂²	1	3	yes	complemented
71	#135×C₁₀₉	C₂²	1	3	yes	complemented
72	C₂×SD₁₆×C₁₀₉	C₂²	1	3	yes	complemented
73	#131×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
74	C₂³×D₁₀₉	—	2	3	no	—
75	#13182030	—	2	1	no	—
76	#13182030	—	2	1	no	—
77	#13182030	—	2	3	no	—
78	#13182030	—	2	3	no	—
79	#13182030	—	2	3	no	—
80	#13182030	D₄	1	1	yes	characteristic
81	#13182030	C₂³	1	3	yes	—
82	#13182030	C₂³	1	3	yes	—
83	#13182030	C₂³	1	6	yes	complemented
84	#13182029	—	2	6	no	—
85	#13182029	—	2	3	no	—
86	#13182029	—	2	3	no	—
87	#13182029	—	2	3	no	—
88	#13182029	—	2	3	no	—
89	#13182029	C₂³	1	3	yes	—
90	#13182029	C₂³	1	3	yes	—
91	#13182029	C₂³	1	3	yes	complemented
92	#13182028	—	2	3	no	—
93	#13182028	—	2	3	no	—
94	#13182028	—	2	3	no	—
95	#13182028	D₄	1	3	yes	—
96	#13182028	C₂³	1	3	yes	—
97	#13182028	C₂³	1	1	yes	characteristic
98	Q₈×D₁₀₉	—	2	3	no	—
99	Q₈×D₁₀₉	D₄	1	1	yes	characteristic
100	Q₈×D₁₀₉	C₂³	1	1	yes	characteristic
101	Q₈×D₁₀₉	C₂³	1	3	yes	complemented
102	C₂×D₄₃₆	—	2	3	no	—
103	C₂×D₄₃₆	—	2	3	no	—
104	C₂×D₄₃₆	—	2	3	no	—
105	C₂×D₄₃₆	C₂³	1	3	yes	—
106	C₂×D₄₃₆	C₂³	1	3	yes	complemented
107	C₂×C₂²⋊D₁₀₉	—	2	6	no	—
108	C₂×C₂²⋊D₁₀₉	—	2	3	no	—
109	D₄×D₁₀₉	—	2	3	no	—
110	D₄×D₁₀₉	—	2	3	no	—
111	D₄×D₁₀₉	—	2	3	no	—
112	D₄×D₁₀₉	—	2	3	no	—
113	D₄×D₁₀₉	—	2	6	no	—
114	D₄×D₁₀₉	—	2	6	no	—
115	D₄×D₁₀₉	—	2	3	no	—
116	D₄×D₁₀₉	—	2	3	no	—
117	D₄×D₁₀₉	—	2	3	no	—
118	D₄×D₁₀₉	D₄	1	3	yes	—
119	D₄×D₁₀₉	C₂³	1	6	yes	—
120	D₄×D₁₀₉	C₂³	1	3	yes	—
121	D₄×D₁₀₉	C₂³	1	3	yes	complemented
122	C₂×C₄×D₁₀₉	—	2	3	no	—
123	C₂×C₄×D₁₀₉	—	2	3	no	—
124	C₂×C₄×D₁₀₉	—	2	3	no	—
125	C₂×C₄×D₁₀₉	C₂³	1	3	yes	—
126	Dic₄₃₆	C₂³	1	1	yes	characteristic, complemented
127	#13182019	C₂³	1	1	yes	characteristic, complemented
128	#13182019	C₂³	1	3	yes	complemented
129	#13182018	C₂³	1	3	yes	complemented
130	#13182018	C₂³	1	3	yes	complemented
131	#13182017	C₂³	1	3	yes	complemented
132	#13182017	C₂³	1	1	yes	characteristic, complemented
133	#13182016	C₂³	1	6	yes	complemented
134	#13182016	C₂³	1	3	yes	complemented
135	#13182016	C₂³	1	3	yes	complemented
136	D₈₇₂	C₂³	1	6	yes	complemented
137	D₈₇₂	C₂³	1	3	yes	complemented
138	#13182014	C₂³	1	3	yes	complemented
139	#13182014	C₂³	1	6	yes	complemented
140	#13182014	C₂³	1	3	yes	complemented
141	#13182013	C₂³	1	3	yes	complemented
142	#13182012	C₂³	1	3	yes	—
143	#13182012	C₂³	1	1	yes	characteristic
144	#13182012	C₂³	1	3	yes	complemented
145	#13182012	C₂³	1	3	yes	complemented
146	C₂×#11724784	C₂³	1	3	yes	complemented
147	C₈×D₁₀₉	C₂³	1	6	yes	complemented
148	#41×C₁₀₉	—	2	1	no	—
149	#41×C₁₀₉	—	2	3	no	—
150	#41×C₁₀₉	C₂³	1	3	yes	—
151	#41×C₁₀₉	C₂³	1	1	yes	characteristic
152	#41×C₁₀₉	C₂³	1	3	yes	complemented
153	C₂×Q₈×C₁₀₉	—	2	1	no	—
154	C₂×Q₈×C₁₀₉	C₂³	1	3	yes	complemented
155	C₂×D₄×C₁₀₉	—	2	3	no	—
156	C₂×D₄×C₁₀₉	C₂³	1	3	yes	—
157	Q₁₆×C₁₀₉	C₂³	1	3	yes	complemented
158	SD₁₆×C₁₀₉	C₂³	1	3	yes	complemented
159	SD₁₆×C₁₀₉	C₂³	1	6	yes	complemented
160	SD₁₆×C₁₀₉	C₂³	1	1	yes	characteristic, complemented
161	D₈×C₁₀₉	C₂³	1	3	yes	complemented
162	M₁₆×C₁₀₉	C₂³	1	3	yes	complemented
163	C₂×C₈×C₁₀₉	C₂³	1	3	yes	complemented
164	C₂³×C₁₀₉	—	2	3	no	—
165	C₂²×D₁₀₉	—	2	3	no	—
166	C₂²×D₁₀₉	—	2	3	no	—
167	C₂²×D₁₀₉	—	2	3	no	—
168	C₂²×D₁₀₉	—	2	3	no	—
169	C₂²×D₁₀₉	—	2	6	no	—
170	C₂²×D₁₀₉	—	8	6	no	—
171	C₂²×D₁₀₉	C₂×D₄	1	3	yes	—
172	Q₈×C₁₀₉	—	2	3	no	—
173	Q₈×C₁₀₉	C₂×D₄	1	1	yes	characteristic
174	Q₈×C₁₀₉	C₂⁴	1	3	yes	—
175	Q₈×C₁₀₉	C₂⁴	1	1	yes	characteristic
176	D₄×C₁₀₉	—	2	3	no	—
177	D₄×C₁₀₉	—	2	3	no	—
178	D₄×C₁₀₉	—	2	3	no	—
179	D₄×C₁₀₉	C₂×D₄	1	3	yes	—
180	D₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
181	D₄×C₁₀₉	C₂⁴	1	3	yes	—
182	C₂×C₄×C₁₀₉	—	2	3	no	—
183	C₂×C₄×C₁₀₉	—	2	3	no	—
184	C₂×C₄×C₁₀₉	—	2	3	no	—
185	C₂×C₄×C₁₀₉	C₂⁴	1	3	yes	—
186	C₂²⋊D₁₀₉	—	2	3	no	—
187	C₂²⋊D₁₀₉	—	2	3	no	—
188	C₂²⋊D₁₀₉	—	2	3	no	—
189	C₂²⋊D₁₀₉	—	2	1	no	—
190	C₂²⋊D₁₀₉	—	2	6	no	—
191	C₂²⋊D₁₀₉	—	2	3	no	—
192	C₂²⋊D₁₀₉	—	2	3	no	—
193	C₂²⋊D₁₀₉	C₂×D₄	1	6	yes	—
194	C₂×Dic₁₀₉	—	2	1	no	—
195	C₂×Dic₁₀₉	—	2	3	no	—
196	C₂×Dic₁₀₉	C₂×D₄	1	3	yes	—
197	D₄₃₆	—	2	3	no	—
198	D₄₃₆	—	2	3	no	—
199	D₄₃₆	—	2	6	no	—
200	D₄₃₆	—	2	3	no	—
201	D₄₃₆	—	2	3	no	—
202	D₄₃₆	C₂×D₄	1	3	yes	—
203	D₄₃₆	C₂⁴	1	3	yes	—
204	D₄₃₆	C₂⁴	1	3	yes	—
205	C₄×D₁₀₉	—	2	1	no	—
206	C₄×D₁₀₉	—	2	3	no	—
207	C₄×D₁₀₉	—	2	3	no	—
208	C₄×D₁₀₉	—	2	3	no	—
209	C₄×D₁₀₉	—	2	3	no	—
210	C₄×D₁₀₉	—	2	3	no	—
211	C₄×D₁₀₉	—	2	6	no	—
212	C₄×D₁₀₉	C₂×D₄	1	3	yes	—
213	C₄×D₁₀₉	C₂×D₄	1	3	yes	—
214	C₄×D₁₀₉	C₂⁴	1	3	yes	—
215	C₄×D₁₀₉	C₂⁴	1	1	yes	characteristic
216	Dic₂₁₈	—	2	3	no	—
217	Dic₂₁₈	—	2	1	no	—
218	Dic₂₁₈	C₂×D₄	1	3	yes	—
219	Dic₂₁₈	C₂⁴	1	1	yes	characteristic
220	Dic₂₁₈	C₂⁴	1	1	yes	characteristic
221	C₈×C₁₀₉	C₂⁴	1	1	yes	characteristic
222	C₈×C₁₀₉	C₂⁴	1	3	yes	—
223	#11724784	C₂⁴	1	3	yes	—
224	#11724784	C₂⁴	1	1	yes	characteristic
225	C₂²×C₁₀₉	—	2	1	no	—
226	C₂²×C₁₀₉	—	2	3	no	—
227	C₂²×C₁₀₉	—	8	3	no	—
228	C₂²×C₁₀₉	C₂²×D₄	1	3	yes	—
229	C₂×D₁₀₉	—	2	3	no	—
230	C₂×D₁₀₉	—	2	3	no	—
231	C₂×D₁₀₉	—	4	3	no	—
232	C₂×D₁₀₉	—	4	6	no	—
233	C₂×D₁₀₉	—	8	3	no	—
234	C₂×D₁₀₉	—	8	6	no	—
235	C₂×D₁₀₉	—	8	3	no	—
236	C₂×D₁₀₉	—	8	3	no	—
237	C₂×D₁₀₉	C₂²×D₄	1	1	yes	characteristic
238	C₂×D₁₀₉	C₂²×D₄	1	3	yes	—
239	C₄×C₁₀₉	—	2	1	no	—
240	C₄×C₁₀₉	—	2	3	no	—
241	C₄×C₁₀₉	C₂²×D₄	1	3	yes	—
242	C₄×C₁₀₉	C₂⁵	1	1	yes	characteristic
243	Dic₁₀₉	—	2	1	no	—
244	Dic₁₀₉	—	2	1	no	—
245	Dic₁₀₉	C₂²×D₄	1	3	yes	—
246	Dic₁₀₉	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₁₀₉	—	2	3	no	—
248	C₂×C₁₀₉	—	4	3	no	—
249	C₂×C₁₀₉	—	4	1	no	—
250	C₂×C₁₀₉	C₂³×D₄	1	1	yes	characteristic
251	D₁₀₉	—	2	1	no	—
252	D₁₀₉	—	2	3	no	—
253	D₁₀₉	—	4	3	no	—
254	D₁₀₉	—	4	3	no	—
255	#3585	—	109	1	no	maximal, Sylow
256	C₁₀₉	#3585	1	1	yes	characteristic, complemented, Sylow
257	#585	—	109	1	no	—
258	C₂×H(5,𝔽₂)	—	109	1	no	—
259	#577	—	109	1	no	—
260	#577	—	109	3	no	—
261	#577	—	109	3	no	—
262	#577	D₁₀₉	1	1	yes	characteristic, complemented
263	#576	—	109	1	no	—
264	#576	—	109	3	no	—
265	#576	—	109	3	no	—
266	#576	—	109	1	no	—
267	#575	—	109	3	no	—
268	#575	—	109	3	no	—
269	C₂×AGL(1,ℤ/8)	—	109	3	no	—
270	C₂×AGL(1,ℤ/8)	—	109	3	no	—
271	#568	—	109	1	no	—
272	2₋¹⁺⁴	—	109	3	no	—
273	2₋¹⁺⁴	—	218	1	no	—
274	2₋¹⁺⁴	C₂×D₁₀₉	1	1	yes	characteristic, complemented
275	H(5,𝔽₂)	—	109	3	no	—
276	H(5,𝔽₂)	—	109	1	no	—
277	H(5,𝔽₂)	—	109	1	no	—
278	H(5,𝔽₂)	—	109	3	no	—
279	H(5,𝔽₂)	—	109	3	no	—
280	H(5,𝔽₂)	—	218	3	no	—
281	H(5,𝔽₂)	—	218	3	no	—
282	H(5,𝔽₂)	—	218	1	no	—
283	H(5,𝔽₂)	C₂×D₁₀₉	1	1	yes	characteristic, complemented
284	C₂×#41	—	109	1	no	—
285	C₂×#41	—	109	3	no	—
286	C₂×#41	—	109	3	no	—
287	C₂×#41	—	109	3	no	—
288	C₂×#41	—	218	1	no	—
289	C₂×#41	—	218	1	no	—
290	C₂×#41	—	218	3	no	—
291	C₂²×D₄	—	109	3	no	—
292	C₂²×D₄	—	218	3	no	—
293	#137	—	109	3	no	—
294	#137	—	109	3	no	—
295	#137	—	109	3	no	—
296	#137	—	109	1	no	—
297	#137	—	109	3	no	—
298	#137	C₂×D₁₀₉	1	3	yes	complemented
299	AGL(1,ℤ/8)	—	109	3	no	—
300	AGL(1,ℤ/8)	—	109	3	no	—
301	AGL(1,ℤ/8)	—	109	3	no	—
302	AGL(1,ℤ/8)	—	109	6	no	—
303	AGL(1,ℤ/8)	—	109	3	no	—
304	AGL(1,ℤ/8)	—	109	6	no	—
305	AGL(1,ℤ/8)	—	109	6	no	—
306	AGL(1,ℤ/8)	—	109	3	no	—
307	AGL(1,ℤ/8)	—	109	3	no	—
308	AGL(1,ℤ/8)	—	109	3	no	—
309	AGL(1,ℤ/8)	—	109	3	no	—
310	AGL(1,ℤ/8)	—	109	3	no	—
311	AGL(1,ℤ/8)	C₂×D₁₀₉	1	3	yes	complemented
312	#135	—	109	3	no	—
313	#135	—	109	3	no	—
314	#135	—	109	6	no	—
315	#135	—	109	6	no	—
316	#135	—	109	3	no	—
317	#135	C₂×D₁₀₉	1	3	yes	complemented
318	C₂×SD₁₆	—	109	3	no	—
319	C₂×SD₁₆	—	109	6	no	—
320	C₂×SD₁₆	C₂×D₁₀₉	1	3	yes	complemented
321	C₂×D₈	—	109	3	no	—
322	C₂×D₈	—	109	6	no	—
323	C₂×D₈	—	109	3	no	—
324	#131	—	109	1	no	—
325	#131	—	109	3	no	—
326	#131	—	109	3	no	—
327	#131	C₂×D₁₀₉	1	1	yes	characteristic, complemented
328	C₂×M₁₆	—	109	3	no	—
329	C₂×M₁₆	—	109	3	no	—
330	C₂⁴	—	218	3	no	—
331	#41	—	2	1	no	—
332	#41	—	2	3	no	—
333	#41	—	109	1	no	—
334	#41	—	109	3	no	—
335	#41	—	109	3	no	—
336	#41	—	109	3	no	—
337	#41	—	109	3	no	—
338	#41	—	109	6	no	—
339	#41	—	109	3	no	—
340	#41	—	109	1	no	—
341	#41	—	109	3	no	—
342	#41	—	109	3	no	—
343	#41	—	218	3	no	—
344	#41	—	218	3	no	—
345	#41	—	218	6	no	—
346	#41	—	218	3	no	—
347	#41	—	218	3	no	—
348	#41	—	218	3	no	—
349	#41	—	218	3	no	—
350	#41	—	218	3	no	—
351	#41	—	218	3	no	—
352	#41	—	218	3	no	—
353	#41	—	218	3	no	—
354	#41	—	218	1	no	—
355	#41	—	218	1	no	—
356	#41	C₂²×D₁₀₉	1	3	yes	—
357	#41	C₂²×D₁₀₉	1	1	yes	characteristic
358	#41	C₂²×D₁₀₉	1	3	yes	complemented
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	109	1	no	—
361	C₂×Q₈	—	109	1	no	—
362	C₂×Q₈	—	109	3	no	—
363	C₂×Q₈	—	218	3	no	—
364	C₂×Q₈	C₂²×D₁₀₉	1	3	yes	complemented
365	C₂×D₄	—	2	3	no	—
366	C₂×D₄	—	109	3	no	—
367	C₂×D₄	—	109	6	no	—
368	C₂×D₄	—	109	3	no	—
369	C₂×D₄	—	109	3	no	—
370	C₂×D₄	—	109	3	no	—
371	C₂×D₄	—	109	3	no	—
372	C₂×D₄	—	218	3	no	—
373	C₂×D₄	—	218	3	no	—
374	C₂×D₄	—	218	3	no	—
375	C₂×D₄	—	218	3	no	—
376	C₂×D₄	—	218	3	no	—
377	C₂×D₄	—	218	3	no	—
378	C₂×D₄	—	218	6	no	—
379	C₂×D₄	—	218	3	no	—
380	C₂×D₄	—	218	6	no	—
381	C₂×D₄	—	218	3	no	—
382	C₂×D₄	—	218	3	no	—
383	C₂×D₄	—	218	6	no	—
384	C₂×D₄	—	218	3	no	—
385	C₂×D₄	—	218	3	no	—
386	C₂×D₄	C₂²×D₁₀₉	1	3	yes	—
387	C₂²×C₄	—	109	3	no	—
388	C₂²×C₄	—	218	3	no	—
389	C₂²×C₄	—	218	3	no	—
390	C₂²×C₄	—	218	3	no	—
391	Q₁₆	—	109	1	no	—
392	Q₁₆	—	109	3	no	—
393	Q₁₆	—	109	1	no	—
394	Q₁₆	C₂²×D₁₀₉	1	3	yes	complemented
395	SD₁₆	—	109	6	no	—
396	SD₁₆	—	109	3	no	—
397	SD₁₆	—	109	3	no	—
398	SD₁₆	—	109	3	no	—
399	SD₁₆	—	109	1	no	—
400	SD₁₆	—	109	3	no	—
401	SD₁₆	—	109	3	no	—
402	SD₁₆	C₂²×D₁₀₉	1	6	yes	complemented
403	SD₁₆	C₂²×D₁₀₉	1	3	yes	complemented
404	SD₁₆	C₂²×D₁₀₉	1	1	yes	characteristic, complemented
405	D₈	—	109	6	no	—
406	D₈	—	109	3	no	—
407	D₈	—	109	3	no	—
408	D₈	—	109	6	no	—
409	D₈	—	109	3	no	—
410	D₈	C₂²×D₁₀₉	1	3	yes	complemented
411	M₁₆	—	109	3	no	—
412	M₁₆	—	109	3	no	—
413	M₁₆	—	109	1	no	—
414	M₁₆	—	109	3	no	—
415	M₁₆	—	109	3	no	—
416	M₁₆	C₂²×D₁₀₉	1	3	yes	complemented
417	C₂×C₈	—	109	3	no	—
418	C₂×C₈	—	109	6	no	—
419	C₂×C₈	C₂²×D₁₀₉	1	3	yes	complemented
420	C₂³	—	2	3	no	—
421	C₂³	—	872	6	no	—
422	C₂³	—	109	3	no	—
423	C₂³	—	218	3	no	—
424	C₂³	—	218	6	no	—
425	C₂³	—	218	3	no	—
426	C₂³	—	218	3	no	—
427	C₂³	—	218	3	no	—
428	Q₈	—	2	3	no	—
429	Q₈	—	109	3	no	—
430	Q₈	—	109	1	no	—
431	Q₈	—	109	1	no	—
432	Q₈	—	218	3	no	—
433	Q₈	—	218	1	no	—
434	Q₈	D₄×D₁₀₉	1	1	yes	characteristic
435	Q₈	C₂³×D₁₀₉	1	3	yes	—
436	Q₈	C₂³×D₁₀₉	1	1	yes	characteristic
437	D₄	—	2	3	no	—
438	D₄	—	2	3	no	—
439	D₄	—	2	3	no	—
440	D₄	—	109	6	no	—
441	D₄	—	109	3	no	—
442	D₄	—	109	3	no	—
443	D₄	—	109	3	no	—
444	D₄	—	218	3	no	—
445	D₄	—	218	3	no	—
446	D₄	—	218	6	no	—
447	D₄	—	218	3	no	—
448	D₄	—	218	6	no	—
449	D₄	—	218	3	no	—
450	D₄	—	218	3	no	—
451	D₄	—	218	1	no	—
452	D₄	—	218	3	no	—
453	D₄	—	218	3	no	—
454	D₄	—	218	3	no	—
455	D₄	—	218	3	no	—
456	D₄	D₄×D₁₀₉	1	3	yes	—
457	D₄	C₂³×D₁₀₉	1	1	yes	characteristic
458	D₄	C₂³×D₁₀₉	1	3	yes	—
459	C₂×C₄	—	2	3	no	—
460	C₂×C₄	—	2	3	no	—
461	C₂×C₄	—	2	3	no	—
462	C₂×C₄	—	109	3	no	—
463	C₂×C₄	—	109	3	no	—
464	C₂×C₄	—	109	3	no	—
465	C₂×C₄	—	109	3	no	—
466	C₂×C₄	—	109	1	no	—
467	C₂×C₄	—	218	3	no	—
468	C₂×C₄	—	218	3	no	—
469	C₂×C₄	—	218	6	no	—
470	C₂×C₄	—	218	1	no	—
471	C₂×C₄	—	218	3	no	—
472	C₂×C₄	—	218	1	no	—
473	C₂×C₄	—	218	3	no	—
474	C₂×C₄	—	218	3	no	—
475	C₂×C₄	—	218	3	no	—
476	C₂×C₄	C₂³×D₁₀₉	1	3	yes	—
477	C₈	—	109	1	no	—
478	C₈	—	109	3	no	—
479	C₈	C₂³×D₁₀₉	1	3	yes	—
480	C₈	C₂³×D₁₀₉	1	1	yes	characteristic
481	C₂²	—	2	1	no	—
482	C₂²	—	2	3	no	—
483	C₂²	—	8	3	no	—
484	C₂²	—	872	3	no	—
485	C₂²	—	872	3	no	—
486	C₂²	—	872	6	no	—
487	C₂²	—	872	3	no	—
488	C₂²	—	109	1	no	—
489	C₂²	—	109	3	no	—
490	C₂²	—	436	3	no	—
491	C₂²	—	436	6	no	—
492	C₂²	—	218	3	no	—
493	C₂²	—	218	3	no	—
494	C₂²	C₂×D₄×D₁₀₉	1	3	yes	—
495	C₄	—	2	1	no	—
496	C₄	—	2	3	no	—
497	C₄	—	109	1	no	—
498	C₄	—	109	3	no	—
499	C₄	—	218	1	no	—
500	C₄	—	218	1	no	—
501	C₄	C₂×D₄×D₁₀₉	1	3	yes	—
502	C₄	C₂⁴×D₁₀₉	1	1	yes	characteristic
503	C₂	—	2	3	no	—
504	C₂	—	4	3	no	—
505	C₂	—	4	1	no	—
506	C₂	—	436	3	no	—
507	C₂	—	436	3	no	—
508	C₂	—	218	3	no	—
509	C₂	—	218	1	no	—
510	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	#577×C₁₀₉	C₂
socle	C₂×C₁₀₉	C₂³×D₄
hypercenter	#577	D₁₀₉
hypocenter	C₁₀₉	#3585
LCS	G ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂ ◁ #41 ◁ #577

Complements

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

N	H ≅ G/N	type
1. #20295863	C₂	semidirect
2. H(5,𝔽₂)×D₁₀₉	C₂	semidirect
3. #20295835	C₂	semidirect
4. #20295834	C₂	semidirect
5. #20295832	C₂	semidirect
6. #20295831	C₂	semidirect
7. #20295830	C₂	semidirect
8. #20295829	C₂	semidirect
9. #20295828	C₂	semidirect
10. #20295825	C₂	semidirect
11. #20295823	C₂	semidirect
12. C₂×#16812726	C₂	semidirect
13. AGL(1,ℤ/8)×D₁₀₉	C₂	semidirect
14. #20295791	C₂	semidirect
15. #577×C₁₀₉	C₂	semidirect
17. #16812747	C₂²	semidirect
20. #16812745	C₂²	semidirect
21. #16812745	C₂²	semidirect
22. #16812745	C₂²	semidirect
23. #16812745	C₂²	semidirect
25. #16812744	C₂²	semidirect
27. C₂×#13182030	C₂²	semidirect
31. #41×D₁₀₉	C₂²	semidirect
32. #41×D₁₀₉	C₂²	semidirect
34. C₂×D₄×D₁₀₉	C₂²	semidirect
35. #16812731	C₂²	semidirect
36. #16812731	C₂²	semidirect
37. #16812730	C₂²	semidirect
38. #16812728	C₂²	semidirect
39. #16812728	C₂²	semidirect
40. #16812727	C₂²	semidirect
41. #16812727	C₂²	semidirect
42. #16812726	C₂²	semidirect
43. #16812726	C₂²	semidirect
44. #16812726	C₂²	semidirect
45. #16812726	C₂²	semidirect
46. #16812726	C₂²	semidirect
47. #16812725	C₂²	semidirect
48. #16812724	C₂²	semidirect
49. #16812724	C₂²	semidirect
50. #16812723	C₂²	semidirect
51. #16812723	C₂²	semidirect
52. #16812722	C₂²	semidirect
53. #16812721	C₂²	semidirect
54. #16812720	C₂²	semidirect
55. #16812719	C₂²	semidirect
56. #16812719	C₂²	semidirect
57. C₂×#13182016	C₂²	semidirect
58. SD₁₆×D₁₀₉	C₂²	semidirect
59. C₂×D₈₇₂	C₂²	semidirect
60. C₂×#13182014	C₂²	semidirect
61. D₈×D₁₀₉	C₂²	semidirect
62. #16812707	C₂²	semidirect
63. #16812706	C₂²	semidirect
64. #16812705	C₂²	semidirect
65. C₂×#13182012	C₂²	semidirect
66. M₁₆×D₁₀₉	C₂²	semidirect
67. 2₋¹⁺⁴×C₁₀₉	C₂²	semidirect
68. H(5,𝔽₂)×C₁₀₉	C₂²	semidirect
69. #137×C₁₀₉	C₂²	semidirect
70. AGL(1,ℤ/8)×C₁₀₉	C₂²	semidirect
71. #135×C₁₀₉	C₂²	semidirect
72. C₂×SD₁₆×C₁₀₉	C₂²	semidirect
73. #131×C₁₀₉	C₂²	semidirect
83. #13182030	C₂³	semidirect
91. #13182029	C₂³	semidirect
101. Q₈×D₁₀₉	C₂³	semidirect
106. C₂×D₄₃₆	C₂³	semidirect
121. D₄×D₁₀₉	C₂³	semidirect
126. Dic₄₃₆	C₂³	semidirect
127. #13182019	C₂³	semidirect
128. #13182019	C₂³	semidirect
129. #13182018	C₂³	semidirect
130. #13182018	C₂³	semidirect
131. #13182017	C₂³	semidirect
132. #13182017	C₂³	semidirect
133. #13182016	C₂³	semidirect
134. #13182016	C₂³	semidirect
135. #13182016	C₂³	semidirect
136. D₈₇₂	C₂³	semidirect
137. D₈₇₂	C₂³	semidirect
138. #13182014	C₂³	semidirect
139. #13182014	C₂³	semidirect
140. #13182014	C₂³	semidirect
141. #13182013	C₂³	semidirect
144. #13182012	C₂³	semidirect
145. #13182012	C₂³	semidirect
146. C₂×#11724784	C₂³	semidirect
147. C₈×D₁₀₉	C₂³	semidirect
152. #41×C₁₀₉	C₂³	semidirect
154. C₂×Q₈×C₁₀₉	C₂³	semidirect
157. Q₁₆×C₁₀₉	C₂³	semidirect
158. SD₁₆×C₁₀₉	C₂³	semidirect
159. SD₁₆×C₁₀₉	C₂³	semidirect
160. SD₁₆×C₁₀₉	C₂³	semidirect
161. D₈×C₁₀₉	C₂³	semidirect
162. M₁₆×C₁₀₉	C₂³	semidirect
163. C₂×C₈×C₁₀₉	C₂³	semidirect
256. C₁₀₉	#3585	semidirect
262. #577	D₁₀₉	semidirect
274. 2₋¹⁺⁴	C₂×D₁₀₉	semidirect
283. H(5,𝔽₂)	C₂×D₁₀₉	semidirect
298. #137	C₂×D₁₀₉	semidirect
311. AGL(1,ℤ/8)	C₂×D₁₀₉	semidirect
317. #135	C₂×D₁₀₉	semidirect
320. C₂×SD₁₆	C₂×D₁₀₉	semidirect
327. #131	C₂×D₁₀₉	semidirect
358. #41	C₂²×D₁₀₉	semidirect
364. C₂×Q₈	C₂²×D₁₀₉	semidirect
394. Q₁₆	C₂²×D₁₀₉	semidirect
402. SD₁₆	C₂²×D₁₀₉	semidirect
403. SD₁₆	C₂²×D₁₀₉	semidirect
404. SD₁₆	C₂²×D₁₀₉	semidirect
410. D₈	C₂²×D₁₀₉	semidirect
416. M₁₆	C₂²×D₁₀₉	semidirect
419. 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
#20295863	2
H(5,𝔽₂)×D₁₀₉	2
#20295835	2
#20295834	2
#20295832	2
#20295831	2
#20295830	2
#20295829	2
#20295828	2
#20295825	2
#20295823	2
C₂×#16812726	2
AGL(1,ℤ/8)×D₁₀₉	2
#20295791	2
#577×C₁₀₉	2
#3585	109