Subgroups — #28377817

Order 13952.

1412 conjugacy classes of subgroups.

The subgroup lattice has 504 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	2₋¹⁺⁴×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295842	C₂	1	3	yes	maximal, complemented
4	#20295841	C₂	1	1	yes	maximal, characteristic, complemented
5	#20295839	C₂	1	3	yes	maximal, complemented
6	#20295838	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295835	C₂	1	3	yes	maximal, complemented
8	#20295834	C₂	1	1	yes	maximal, characteristic, complemented
9	#20295833	C₂	1	3	yes	maximal, complemented
10	#20295825	C₂	1	3	yes	maximal, complemented
11	#20295823	C₂	1	3	yes	maximal, complemented
12	C₂×#16812731	C₂	1	3	yes	maximal, complemented
13	#137×D₁₀₉	C₂	1	3	yes	maximal, complemented
14	#20295791	C₂	1	1	yes	maximal, characteristic, complemented
15	#578×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#16812747	—	2	1	no	—
17	#16812747	—	2	1	no	—
18	#16812747	C₂²	1	3	yes	complemented
19	#16812747	C₂²	1	3	yes	complemented
20	#16812746	—	2	3	no	—
21	#16812746	C₂²	1	1	yes	characteristic, complemented
22	#16812746	C₂²	1	3	yes	complemented
23	#16812745	—	2	3	no	—
24	#16812745	C₂²	1	1	yes	characteristic, complemented
25	#16812745	C₂²	1	3	yes	complemented
26	C₂×#13182030	—	2	1	no	—
27	C₂×#13182030	C₂²	1	3	yes	—
28	#41×D₁₀₉	—	2	3	no	—
29	#41×D₁₀₉	—	2	3	no	—
30	#41×D₁₀₉	C₂²	1	3	yes	—
31	#41×D₁₀₉	C₂²	1	1	yes	characteristic
32	#41×D₁₀₉	C₂²	1	3	yes	complemented
33	C₂×Q₈×D₁₀₉	—	2	1	no	—
34	C₂×Q₈×D₁₀₉	C₂²	1	3	yes	complemented
35	#16812732	C₂²	1	3	yes	complemented
36	#16812731	C₂²	1	6	yes	complemented
37	#16812731	C₂²	1	3	yes	complemented
38	#16812731	C₂²	1	6	yes	complemented
39	#16812731	C₂²	1	6	yes	complemented
40	#16812731	C₂²	1	3	yes	complemented
41	#16812730	C₂²	1	3	yes	complemented
42	#16812730	C₂²	1	3	yes	complemented
43	#16812729	C₂²	1	3	yes	complemented
44	#16812728	C₂²	1	3	yes	complemented
45	#16812728	C₂²	1	3	yes	complemented
46	#16812727	C₂²	1	3	yes	complemented
47	#16812726	C₂²	1	3	yes	complemented
48	#16812726	C₂²	1	3	yes	complemented
49	#16812724	C₂²	1	3	yes	complemented
50	#16812723	C₂²	1	1	yes	characteristic, 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×#13182019	C₂²	1	3	yes	complemented
58	Q₁₆×D₁₀₉	C₂²	1	6	yes	complemented
59	C₂×#13182018	C₂²	1	3	yes	complemented
60	C₂×#13182016	C₂²	1	3	yes	complemented
61	SD₁₆×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	2₋¹⁺⁴×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
69	#137×C₁₀₉	C₂²	1	3	yes	complemented
70	#137×C₁₀₉	C₂²	1	3	yes	complemented
71	#135×C₁₀₉	C₂²	1	3	yes	complemented
72	C₂×Q₁₆×C₁₀₉	C₂²	1	3	yes	complemented
73	#131×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
74	#13182030	—	2	1	no	—
75	#13182030	—	2	3	no	—
76	#13182030	—	2	3	no	—
77	#13182030	—	2	3	no	—
78	#13182030	—	2	3	no	—
79	#13182030	D₄	1	1	yes	characteristic
80	#13182030	C₂³	1	6	yes	—
81	#13182030	C₂³	1	3	yes	—
82	#13182030	C₂³	1	3	yes	—
83	#13182029	—	2	6	no	—
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	—
92	#13182028	—	2	3	no	—
93	#13182028	—	2	6	no	—
94	#13182028	—	2	3	no	—
95	#13182028	—	2	3	no	—
96	#13182028	D₄	1	3	yes	—
97	#13182028	C₂³	1	3	yes	—
98	#13182028	C₂³	1	1	yes	characteristic
99	C₂×Dic₂₁₈	—	2	3	no	—
100	C₂×Dic₂₁₈	—	2	3	no	—
101	C₂×Dic₂₁₈	C₂³	1	3	yes	—
102	Q₈×D₁₀₉	—	2	1	no	—
103	Q₈×D₁₀₉	—	2	3	no	—
104	Q₈×D₁₀₉	—	2	3	no	—
105	Q₈×D₁₀₉	—	2	3	no	—
106	Q₈×D₁₀₉	—	2	3	no	—
107	Q₈×D₁₀₉	D₄	1	1	yes	characteristic
108	Q₈×D₁₀₉	C₂³	1	6	yes	—
109	Q₈×D₁₀₉	C₂³	1	3	yes	—
110	Q₈×D₁₀₉	C₂³	1	3	yes	—
111	C₂×D₄₃₆	—	2	3	no	—
112	C₂×D₄₃₆	—	2	3	no	—
113	C₂×D₄₃₆	C₂³	1	3	yes	—
114	D₄×D₁₀₉	—	2	3	no	—
115	D₄×D₁₀₉	—	2	3	no	—
116	D₄×D₁₀₉	—	2	3	no	—
117	D₄×D₁₀₉	—	2	6	no	—
118	D₄×D₁₀₉	D₄	1	3	yes	—
119	D₄×D₁₀₉	C₂³	1	3	yes	—
120	D₄×D₁₀₉	C₂³	1	1	yes	characteristic
121	C₂×C₄×D₁₀₉	—	2	3	no	—
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	3	yes	—
127	#13182019	C₂³	1	3	yes	—
128	#13182019	C₂³	1	6	yes	—
129	#13182019	C₂³	1	3	yes	—
130	#13182018	C₂³	1	6	yes	—
131	#13182018	C₂³	1	3	yes	—
132	#13182018	C₂³	1	1	yes	characteristic
133	#13182017	C₂³	1	3	yes	—
134	#13182017	C₂³	1	1	yes	characteristic
135	#13182016	C₂³	1	6	yes	—
136	#13182016	C₂³	1	3	yes	—
137	#13182016	C₂³	1	3	yes	—
138	D₈₇₂	C₂³	1	3	yes	—
139	#13182014	C₂³	1	1	yes	characteristic
140	#13182014	C₂³	1	3	yes	—
141	#13182013	C₂³	1	3	yes	—
142	#13182012	C₂³	1	3	yes	—
143	#13182012	C₂³	1	1	yes	characteristic
144	#13182012	C₂³	1	3	yes	—
145	#13182012	C₂³	1	3	yes	—
146	C₂×#11724784	C₂³	1	3	yes	—
147	C₈×D₁₀₉	C₂³	1	6	yes	—
148	#41×C₁₀₉	—	2	3	no	—
149	#41×C₁₀₉	—	2	3	no	—
150	#41×C₁₀₉	C₂³	1	3	yes	—
151	#41×C₁₀₉	C₂³	1	3	yes	—
152	#41×C₁₀₉	C₂³	1	1	yes	characteristic
153	C₂×Q₈×C₁₀₉	—	2	1	no	—
154	C₂×Q₈×C₁₀₉	—	2	1	no	—
155	C₂×Q₈×C₁₀₉	C₂³	1	3	yes	—
156	C₂×Q₈×C₁₀₉	C₂³	1	3	yes	—
157	Q₁₆×C₁₀₉	C₂³	1	3	yes	—
158	Q₁₆×C₁₀₉	C₂³	1	6	yes	—
159	SD₁₆×C₁₀₉	C₂³	1	3	yes	—
160	SD₁₆×C₁₀₉	C₂³	1	3	yes	—
161	D₈×C₁₀₉	C₂³	1	1	yes	characteristic
162	M₁₆×C₁₀₉	C₂³	1	3	yes	—
163	C₂×C₈×C₁₀₉	C₂³	1	3	yes	—
164	C₂²×D₁₀₉	—	2	3	no	—
165	C₂²×D₁₀₉	—	2	1	no	—
166	C₂²×D₁₀₉	—	2	3	no	—
167	C₂²×D₁₀₉	C₂×D₄	1	3	yes	—
168	Q₈×C₁₀₉	—	2	3	no	—
169	Q₈×C₁₀₉	—	2	3	no	—
170	Q₈×C₁₀₉	C₂×D₄	1	1	yes	characteristic
171	Q₈×C₁₀₉	C₂⁴	1	3	yes	—
172	Q₈×C₁₀₉	C₂⁴	1	3	yes	—
173	D₄×C₁₀₉	—	2	3	no	—
174	D₄×C₁₀₉	—	2	3	no	—
175	D₄×C₁₀₉	C₂×D₄	1	3	yes	—
176	D₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
177	D₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
178	C₂×C₄×C₁₀₉	—	2	3	no	—
179	C₂×C₄×C₁₀₉	—	2	3	no	—
180	C₂×C₄×C₁₀₉	—	2	3	no	—
181	C₂×C₄×C₁₀₉	—	2	3	no	—
182	C₂×C₄×C₁₀₉	C₂⁴	1	3	yes	—
183	C₂²⋊D₁₀₉	—	2	3	no	—
184	C₂²⋊D₁₀₉	—	2	3	no	—
185	C₂²⋊D₁₀₉	—	2	1	no	—
186	C₂²⋊D₁₀₉	—	2	3	no	—
187	C₂²⋊D₁₀₉	—	2	3	no	—
188	C₂²⋊D₁₀₉	—	2	1	no	—
189	C₂²⋊D₁₀₉	C₂×D₄	1	6	yes	—
190	C₂×Dic₁₀₉	—	2	3	no	—
191	C₂×Dic₁₀₉	—	2	1	no	—
192	C₂×Dic₁₀₉	—	2	3	no	—
193	C₂×Dic₁₀₉	C₂×D₄	1	3	yes	—
194	D₄₃₆	—	2	3	no	—
195	D₄₃₆	—	2	6	no	—
196	D₄₃₆	—	2	3	no	—
197	D₄₃₆	—	2	3	no	—
198	D₄₃₆	C₂×D₄	1	3	yes	—
199	D₄₃₆	C₂⁴	1	1	yes	characteristic
200	D₄₃₆	C₂⁴	1	3	yes	—
201	C₄×D₁₀₉	—	2	3	no	—
202	C₄×D₁₀₉	—	2	3	no	—
203	C₄×D₁₀₉	—	2	6	no	—
204	C₄×D₁₀₉	—	2	3	no	—
205	C₄×D₁₀₉	—	2	3	no	—
206	C₄×D₁₀₉	—	2	3	no	—
207	C₄×D₁₀₉	—	2	6	no	—
208	C₄×D₁₀₉	—	2	3	no	—
209	C₄×D₁₀₉	C₂×D₄	1	3	yes	—
210	C₄×D₁₀₉	C₂×D₄	1	3	yes	—
211	C₄×D₁₀₉	C₂⁴	1	3	yes	—
212	C₄×D₁₀₉	C₂⁴	1	1	yes	characteristic
213	Dic₂₁₈	—	2	3	no	—
214	Dic₂₁₈	—	2	6	no	—
215	Dic₂₁₈	—	2	3	no	—
216	Dic₂₁₈	—	2	3	no	—
217	Dic₂₁₈	C₂×D₄	1	3	yes	—
218	Dic₂₁₈	C₂⁴	1	3	yes	—
219	Dic₂₁₈	C₂⁴	1	1	yes	characteristic
220	C₈×C₁₀₉	C₂⁴	1	1	yes	characteristic
221	C₈×C₁₀₉	C₂⁴	1	3	yes	—
222	#11724784	C₂⁴	1	3	yes	—
223	#11724784	C₂⁴	1	1	yes	characteristic
224	C₂²×C₁₀₉	—	2	1	no	—
225	C₂²×C₁₀₉	—	2	1	no	—
226	C₂²×C₁₀₉	C₂²×D₄	1	3	yes	—
227	C₂×D₁₀₉	—	2	1	no	—
228	C₂×D₁₀₉	—	2	3	no	—
229	C₂×D₁₀₉	—	4	3	no	—
230	C₂×D₁₀₉	—	4	2	no	—
231	C₂×D₁₀₉	—	8	3	no	—
232	C₂×D₁₀₉	—	8	3	no	—
233	C₂×D₁₀₉	C₂²×D₄	1	1	yes	characteristic
234	C₂×D₁₀₉	C₂²×D₄	1	3	yes	—
235	C₄×C₁₀₉	—	2	3	no	—
236	C₄×C₁₀₉	—	2	3	no	—
237	C₄×C₁₀₉	C₂²×D₄	1	3	yes	—
238	C₄×C₁₀₉	C₂⁵	1	1	yes	characteristic
239	Dic₁₀₉	—	2	3	no	—
240	Dic₁₀₉	—	2	1	no	—
241	Dic₁₀₉	C₂²×D₄	1	3	yes	—
242	Dic₁₀₉	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₁₀₉	—	2	3	no	—
244	C₂×C₁₀₉	—	4	1	no	—
245	C₂×C₁₀₉	—	4	1	no	—
246	C₂×C₁₀₉	C₂³×D₄	1	1	yes	characteristic
247	D₁₀₉	—	2	1	no	—
248	D₁₀₉	—	2	3	no	—
249	D₁₀₉	—	4	1	no	—
250	D₁₀₉	—	4	3	no	—
251	#3586	—	109	1	no	maximal, Sylow
252	C₁₀₉	#3586	1	1	yes	characteristic, complemented, Sylow
253	#585	—	109	1	no	—
254	C₂×2₋¹⁺⁴	—	109	1	no	—
255	#578	—	109	1	no	—
256	#578	—	109	3	no	—
257	#578	—	109	3	no	—
258	#578	D₁₀₉	1	1	yes	characteristic, complemented
259	#577	—	109	1	no	—
260	#577	—	109	3	no	—
261	#577	—	109	3	no	—
262	#577	—	109	1	no	—
263	#575	—	109	3	no	—
264	#575	—	109	3	no	—
265	C₂×#137	—	109	3	no	—
266	C₂×#137	—	109	3	no	—
267	#568	—	109	1	no	—
268	2₋¹⁺⁴	—	109	3	no	—
269	2₋¹⁺⁴	—	109	1	no	—
270	2₋¹⁺⁴	—	109	3	no	—
271	2₋¹⁺⁴	—	109	3	no	—
272	2₋¹⁺⁴	—	218	1	no	—
273	2₋¹⁺⁴	—	218	1	no	—
274	2₋¹⁺⁴	—	218	3	no	—
275	2₋¹⁺⁴	C₂×D₁₀₉	1	1	yes	characteristic, complemented
276	2₋¹⁺⁴	C₂×D₁₀₉	1	1	yes	characteristic, complemented
277	H(5,𝔽₂)	—	109	3	no	—
278	H(5,𝔽₂)	—	109	1	no	—
279	H(5,𝔽₂)	—	218	3	no	—
280	C₂×#41	—	109	1	no	—
281	C₂×#41	—	109	3	no	—
282	C₂×#41	—	109	3	no	—
283	C₂×#41	—	109	3	no	—
284	C₂×#41	—	218	3	no	—
285	C₂×#41	—	218	1	no	—
286	C₂×#41	—	218	3	no	—
287	C₂²×Q₈	—	109	3	no	—
288	C₂²×Q₈	—	218	1	no	—
289	#137	—	109	3	no	—
290	#137	—	109	3	no	—
291	#137	—	109	3	no	—
292	#137	—	109	6	no	—
293	#137	—	109	3	no	—
294	#137	—	109	6	no	—
295	#137	—	109	6	no	—
296	#137	—	109	3	no	—
297	#137	—	109	3	no	—
298	#137	—	109	3	no	—
299	#137	—	109	3	no	—
300	#137	C₂×D₁₀₉	1	3	yes	complemented
301	#137	C₂×D₁₀₉	1	3	yes	complemented
302	AGL(1,ℤ/8)	—	109	3	no	—
303	AGL(1,ℤ/8)	—	109	3	no	—
304	AGL(1,ℤ/8)	—	109	3	no	—
305	AGL(1,ℤ/8)	—	109	1	no	—
306	AGL(1,ℤ/8)	—	109	3	no	—
307	AGL(1,ℤ/8)	—	109	3	no	—
308	#135	—	109	3	no	—
309	#135	—	109	3	no	—
310	#135	—	109	6	no	—
311	#135	—	109	6	no	—
312	#135	—	109	3	no	—
313	#135	C₂×D₁₀₉	1	3	yes	complemented
314	C₂×Q₁₆	—	109	3	no	—
315	C₂×Q₁₆	—	109	6	no	—
316	C₂×Q₁₆	C₂×D₁₀₉	1	3	yes	complemented
317	C₂×SD₁₆	—	109	3	no	—
318	C₂×SD₁₆	—	109	6	no	—
319	C₂×SD₁₆	—	109	3	no	—
320	#131	—	109	1	no	—
321	#131	—	109	3	no	—
322	#131	—	109	3	no	—
323	#131	C₂×D₁₀₉	1	1	yes	characteristic, complemented
324	C₂×M₁₆	—	109	3	no	—
325	C₂×M₁₆	—	109	3	no	—
326	#41	—	2	3	no	—
327	#41	—	2	3	no	—
328	#41	—	109	1	no	—
329	#41	—	109	3	no	—
330	#41	—	109	3	no	—
331	#41	—	109	3	no	—
332	#41	—	109	6	no	—
333	#41	—	109	3	no	—
334	#41	—	109	3	no	—
335	#41	—	109	1	no	—
336	#41	—	109	3	no	—
337	#41	—	109	3	no	—
338	#41	—	218	3	no	—
339	#41	—	218	3	no	—
340	#41	—	218	6	no	—
341	#41	—	218	6	no	—
342	#41	—	218	3	no	—
343	#41	—	218	3	no	—
344	#41	—	218	3	no	—
345	#41	—	218	3	no	—
346	#41	—	218	3	no	—
347	#41	—	218	3	no	—
348	#41	—	218	6	no	—
349	#41	—	218	3	no	—
350	#41	—	218	3	no	—
351	#41	—	218	1	no	—
352	#41	—	218	3	no	—
353	#41	C₂²×D₁₀₉	1	3	yes	—
354	#41	C₂²×D₁₀₉	1	3	yes	—
355	#41	C₂²×D₁₀₉	1	1	yes	characteristic
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	109	1	no	—
359	C₂×Q₈	—	109	6	no	—
360	C₂×Q₈	—	109	3	no	—
361	C₂×Q₈	—	109	3	no	—
362	C₂×Q₈	—	109	3	no	—
363	C₂×Q₈	—	218	3	no	—
364	C₂×Q₈	—	218	3	no	—
365	C₂×Q₈	—	218	3	no	—
366	C₂×Q₈	—	218	3	no	—
367	C₂×Q₈	—	218	3	no	—
368	C₂×Q₈	—	218	3	no	—
369	C₂×Q₈	—	218	1	no	—
370	C₂×Q₈	C₂²×D₁₀₉	1	3	yes	—
371	C₂×Q₈	C₂²×D₁₀₉	1	3	yes	—
372	C₂×D₄	—	109	3	no	—
373	C₂×D₄	—	109	3	no	—
374	C₂×D₄	—	109	1	no	—
375	C₂×D₄	—	109	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	3	no	—
381	C₂×D₄	—	218	3	no	—
382	C₂²×C₄	—	109	3	no	—
383	C₂²×C₄	—	218	3	no	—
384	C₂²×C₄	—	218	3	no	—
385	C₂²×C₄	—	218	3	no	—
386	C₂²×C₄	—	218	3	no	—
387	Q₁₆	—	109	6	no	—
388	Q₁₆	—	109	3	no	—
389	Q₁₆	—	109	3	no	—
390	Q₁₆	—	109	3	no	—
391	Q₁₆	C₂²×D₁₀₉	1	6	yes	—
392	Q₁₆	C₂²×D₁₀₉	1	3	yes	—
393	SD₁₆	—	109	6	no	—
394	SD₁₆	—	109	3	no	—
395	SD₁₆	—	109	3	no	—
396	SD₁₆	—	109	3	no	—
397	SD₁₆	—	109	1	no	—
398	SD₁₆	—	109	6	no	—
399	SD₁₆	—	109	3	no	—
400	SD₁₆	—	109	1	no	—
401	SD₁₆	C₂²×D₁₀₉	1	3	yes	—
402	SD₁₆	C₂²×D₁₀₉	1	3	yes	—
403	D₈	—	109	1	no	—
404	D₈	—	109	3	no	—
405	D₈	—	109	3	no	—
406	D₈	C₂²×D₁₀₉	1	1	yes	characteristic
407	M₁₆	—	109	3	no	—
408	M₁₆	—	109	3	no	—
409	M₁₆	—	109	1	no	—
410	M₁₆	—	109	3	no	—
411	M₁₆	—	109	3	no	—
412	M₁₆	C₂²×D₁₀₉	1	3	yes	—
413	C₂×C₈	—	109	3	no	—
414	C₂×C₈	—	109	6	no	—
415	C₂×C₈	C₂²×D₁₀₉	1	3	yes	—
416	C₂³	—	109	3	no	—
417	C₂³	—	218	3	no	—
418	C₂³	—	218	1	no	—
419	C₂³	—	218	3	no	—
420	Q₈	—	2	3	no	—
421	Q₈	—	2	3	no	—
422	Q₈	—	109	3	no	—
423	Q₈	—	109	3	no	—
424	Q₈	—	109	1	no	—
425	Q₈	—	218	3	no	—
426	Q₈	—	218	6	no	—
427	Q₈	—	218	3	no	—
428	Q₈	—	218	3	no	—
429	Q₈	D₄×D₁₀₉	1	1	yes	characteristic
430	Q₈	C₂³×D₁₀₉	1	3	yes	—
431	Q₈	C₂³×D₁₀₉	1	3	yes	—
432	D₄	—	2	3	no	—
433	D₄	—	2	3	no	—
434	D₄	—	109	6	no	—
435	D₄	—	109	3	no	—
436	D₄	—	109	1	no	—
437	D₄	—	109	3	no	—
438	D₄	—	218	3	no	—
439	D₄	—	218	6	no	—
440	D₄	—	218	3	no	—
441	D₄	—	218	3	no	—
442	D₄	—	218	1	no	—
443	D₄	—	218	1	no	—
444	D₄	—	218	3	no	—
445	D₄	—	218	3	no	—
446	D₄	—	218	3	no	—
447	D₄	—	218	3	no	—
448	D₄	D₄×D₁₀₉	1	3	yes	—
449	D₄	C₂³×D₁₀₉	1	1	yes	characteristic
450	D₄	C₂³×D₁₀₉	1	1	yes	characteristic
451	C₂×C₄	—	2	3	no	—
452	C₂×C₄	—	2	3	no	—
453	C₂×C₄	—	2	3	no	—
454	C₂×C₄	—	2	3	no	—
455	C₂×C₄	—	109	3	no	—
456	C₂×C₄	—	109	3	no	—
457	C₂×C₄	—	109	3	no	—
458	C₂×C₄	—	109	3	no	—
459	C₂×C₄	—	109	1	no	—
460	C₂×C₄	—	218	3	no	—
461	C₂×C₄	—	218	6	no	—
462	C₂×C₄	—	218	3	no	—
463	C₂×C₄	—	218	3	no	—
464	C₂×C₄	—	218	3	no	—
465	C₂×C₄	—	218	6	no	—
466	C₂×C₄	—	218	1	no	—
467	C₂×C₄	—	218	3	no	—
468	C₂×C₄	—	218	3	no	—
469	C₂×C₄	—	218	3	no	—
470	C₂×C₄	—	218	3	no	—
471	C₂×C₄	C₂³×D₁₀₉	1	3	yes	—
472	C₈	—	109	1	no	—
473	C₈	—	109	3	no	—
474	C₈	C₂³×D₁₀₉	1	3	yes	—
475	C₈	C₂³×D₁₀₉	1	1	yes	characteristic
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	872	3	no	—
479	C₂²	—	872	3	no	—
480	C₂²	—	109	1	no	—
481	C₂²	—	109	3	no	—
482	C₂²	—	436	3	no	—
483	C₂²	—	436	2	no	—
484	C₂²	—	218	1	no	—
485	C₂²	—	218	3	no	—
486	C₂²	C₂×D₄×D₁₀₉	1	3	yes	—
487	C₄	—	2	3	no	—
488	C₄	—	2	3	no	—
489	C₄	—	109	1	no	—
490	C₄	—	109	3	no	—
491	C₄	—	218	1	no	—
492	C₄	—	218	3	no	—
493	C₄	C₂×D₄×D₁₀₉	1	3	yes	—
494	C₄	C₂⁴×D₁₀₉	1	1	yes	characteristic
495	C₂	—	2	3	no	—
496	C₂	—	4	1	no	—
497	C₂	—	4	1	no	—
498	C₂	—	436	3	no	—
499	C₂	—	436	1	no	—
500	C₂	—	218	3	no	—
501	C₂	—	218	1	no	—
502	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	#578×C₁₀₉	C₂
socle	C₂×C₁₀₉	C₂³×D₄
hypercenter	#578	D₁₀₉
hypocenter	C₁₀₉	#3586
LCS	G ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂ ◁ #41 ◁ #578

Complements

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

N	H ≅ G/N	type
1. #20295863	C₂	semidirect
2. 2₋¹⁺⁴×D₁₀₉	C₂	semidirect
3. #20295842	C₂	semidirect
4. #20295841	C₂	semidirect
5. #20295839	C₂	semidirect
6. #20295838	C₂	semidirect
7. #20295835	C₂	semidirect
8. #20295834	C₂	semidirect
9. #20295833	C₂	semidirect
10. #20295825	C₂	semidirect
11. #20295823	C₂	semidirect
12. C₂×#16812731	C₂	semidirect
13. #137×D₁₀₉	C₂	semidirect
14. #20295791	C₂	semidirect
15. #578×C₁₀₉	C₂	semidirect
18. #16812747	C₂²	semidirect
19. #16812747	C₂²	semidirect
21. #16812746	C₂²	semidirect
22. #16812746	C₂²	semidirect
24. #16812745	C₂²	semidirect
25. #16812745	C₂²	semidirect
32. #41×D₁₀₉	C₂²	semidirect
34. C₂×Q₈×D₁₀₉	C₂²	semidirect
35. #16812732	C₂²	semidirect
36. #16812731	C₂²	semidirect
37. #16812731	C₂²	semidirect
38. #16812731	C₂²	semidirect
39. #16812731	C₂²	semidirect
40. #16812731	C₂²	semidirect
41. #16812730	C₂²	semidirect
42. #16812730	C₂²	semidirect
43. #16812729	C₂²	semidirect
44. #16812728	C₂²	semidirect
45. #16812728	C₂²	semidirect
46. #16812727	C₂²	semidirect
47. #16812726	C₂²	semidirect
48. #16812726	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×#13182019	C₂²	semidirect
58. Q₁₆×D₁₀₉	C₂²	semidirect
59. C₂×#13182018	C₂²	semidirect
60. C₂×#13182016	C₂²	semidirect
61. SD₁₆×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. 2₋¹⁺⁴×C₁₀₉	C₂²	semidirect
69. #137×C₁₀₉	C₂²	semidirect
70. #137×C₁₀₉	C₂²	semidirect
71. #135×C₁₀₉	C₂²	semidirect
72. C₂×Q₁₆×C₁₀₉	C₂²	semidirect
73. #131×C₁₀₉	C₂²	semidirect
252. C₁₀₉	#3586	semidirect
258. #578	D₁₀₉	semidirect
275. 2₋¹⁺⁴	C₂×D₁₀₉	semidirect
276. 2₋¹⁺⁴	C₂×D₁₀₉	semidirect
300. #137	C₂×D₁₀₉	semidirect
301. #137	C₂×D₁₀₉	semidirect
313. #135	C₂×D₁₀₉	semidirect
316. C₂×Q₁₆	C₂×D₁₀₉	semidirect
323. #131	C₂×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
2₋¹⁺⁴×D₁₀₉	2
#20295842	2
#20295841	2
#20295839	2
#20295838	2
#20295835	2
#20295834	2
#20295833	2
#20295825	2
#20295823	2
C₂×#16812731	2
#137×D₁₀₉	2
#20295791	2
#578×C₁₀₉	2
#3586	109