Subgroups — #28379531

Order 13952.

532 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20295978	C₂	1	1	yes	maximal, characteristic
2	#20295977	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295976	C₂	1	1	yes	maximal, characteristic, complemented
4	#20295976	C₂	1	1	yes	maximal, characteristic, complemented
5	#20295976	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295976	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295975	C₂	1	1	yes	maximal, characteristic, complemented
8	#20295975	C₂	1	1	yes	maximal, characteristic, complemented
9	#20295974	C₂	1	1	yes	maximal, characteristic
10	#20295973	C₂	1	1	yes	maximal, characteristic, complemented
11	#20295968	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄⋊C₄×#89137	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²⋊C₄×#89137	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₂²⋊#89137	C₂	1	1	yes	maximal, characteristic, complemented
15	#123×D₁₀₉	C₂	1	1	yes	maximal, characteristic
16	C₂³×#89137	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊#89137	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊#89137	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊#89137	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊#89137	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊#89137	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊#89137	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊#89137	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊#89137	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊#89137	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊#89137	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊#89137	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊#89137	C₂²	1	1	yes	characteristic
29	C₂×C₄×#89137	C₂²	1	1	yes	characteristic
30	C₂×C₄×#89137	C₂²	1	1	yes	characteristic
31	C₂×C₄×#89137	C₂²	1	1	yes	characteristic
32	C₂×C₄×#89137	C₂²	1	1	yes	characteristic
33	C₂×C₄×#89137	C₂²	1	1	yes	characteristic
34	(C₂×#89137)⋊C₄	C₂²	1	1	yes	characteristic
35	(C₂×#89137)⋊C₄	C₂²	1	1	yes	characteristic
36	(C₂×#89137)⋊C₄	C₂²	1	1	yes	characteristic
37	(C₂×#89137)⋊C₄	C₂²	1	1	yes	characteristic
38	(C₂×#89137)⋊C₄	C₂²	1	1	yes	characteristic
39	(C₂×#89137)⋊C₄	C₂²	1	1	yes	characteristic
40	(C₂×#89137)⋊C₄	C₂²	1	1	yes	characteristic
41	(C₂×#89137)⋊C₄	C₂²	1	1	yes	characteristic
42	(C₂×#89137)⋊C₄	C₂²	1	1	yes	characteristic
43	(C₂×#89137)⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
45	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
46	#16812684	C₄	1	1	yes	characteristic, complemented
47	#16812684	C₄	1	1	yes	characteristic, complemented
48	#16812683	C₄	1	1	yes	characteristic, complemented
49	#16812682	C₄	1	1	yes	characteristic, complemented
50	#16812681	C₄	1	1	yes	characteristic, complemented
51	#16812681	C₄	1	1	yes	characteristic, complemented
52	#16812680	C₄	1	1	yes	characteristic, complemented
53	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
54	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
55	C₂²⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
56	C₂²⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
57	C₂²⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
58	#123×C₁₀₉	C₄	1	1	yes	characteristic, complemented
59	C₂²×#89137	—	2	2	no	—
60	C₂²×#89137	—	4	1	no	—
61	C₂²×#89137	—	4	1	no	—
62	C₂²×#89137	C₂³	1	1	yes	characteristic
63	C₂²×#89137	C₂³	1	1	yes	characteristic
64	C₂²×#89137	C₂³	1	1	yes	characteristic
65	C₂²×#89137	C₂³	1	1	yes	characteristic
66	C₂²×#89137	C₂³	1	1	yes	characteristic
67	C₂²×#89137	C₂³	1	1	yes	characteristic
68	C₂²×#89137	C₂³	1	1	yes	characteristic
69	C₂²×#89137	C₂³	1	1	yes	characteristic
70	C₄⋊#89137	—	2	2	no	—
71	C₄⋊#89137	—	4	1	no	—
72	C₄⋊#89137	—	4	1	no	—
73	C₄⋊#89137	—	4	1	no	—
74	C₄⋊#89137	—	4	1	no	—
75	C₂²⋊#89137	—	2	2	no	—
76	C₂²⋊#89137	—	2	2	no	—
77	C₂²⋊#89137	—	2	2	no	—
78	C₂²⋊#89137	—	4	1	no	—
79	C₂²⋊#89137	—	4	1	no	—
80	C₂²⋊#89137	—	4	1	no	—
81	C₂²⋊#89137	—	4	1	no	—
82	C₄×#89137	—	2	2	no	—
83	C₄×#89137	—	4	1	no	—
84	C₄×#89137	—	4	1	no	—
85	C₄×#89137	—	4	1	no	—
86	C₄×#89137	—	4	1	no	—
87	C₂³×D₁₀₉	C₂³	1	1	yes	characteristic
88	C₂³×D₁₀₉	C₂³	1	1	yes	characteristic
89	C₂×D₄₃₆	C₂×C₄	1	1	yes	characteristic
90	C₂×C₂²⋊D₁₀₉	C₂×C₄	1	1	yes	characteristic
91	C₂×C₂²⋊D₁₀₉	C₂×C₄	1	1	yes	characteristic
92	D₄×D₁₀₉	—	4	1	no	—
93	D₄×D₁₀₉	—	4	1	no	—
94	C₂²×Dic₁₀₉	C₂×C₄	1	1	yes	characteristic, complemented
95	C₂×C₄×D₁₀₉	—	4	1	no	—
96	C₂×C₄×D₁₀₉	—	4	1	no	—
97	C₂×C₄×D₁₀₉	C₂×C₄	1	1	yes	characteristic, complemented
98	C₂×C₄×D₁₀₉	C₂×C₄	1	1	yes	characteristic, complemented
99	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
100	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
101	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
102	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
103	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
104	C₄⋊Dic₁₀₉	C₂×C₄	1	1	yes	characteristic, complemented
105	C₄⋊Dic₁₀₉	C₂×C₄	1	1	yes	characteristic, complemented
106	#13182008	C₂×C₄	1	1	yes	characteristic, complemented
107	#13182008	C₂×C₄	1	1	yes	characteristic, complemented
108	#13182008	C₂×C₄	1	1	yes	characteristic, complemented
109	#13182008	C₂×C₄	1	1	yes	characteristic, complemented
110	C₂²⋊Dic₁₀₉	C₂×C₄	1	1	yes	characteristic
111	C₂²⋊Dic₁₀₉	C₂×C₄	1	1	yes	characteristic
112	C₂²⋊Dic₁₀₉	C₂×C₄	1	1	yes	characteristic, complemented
113	#13182006	C₂×C₄	1	1	yes	characteristic
114	#13182006	C₂×C₄	1	1	yes	characteristic
115	#13182006	C₂×C₄	1	1	yes	characteristic
116	#13182006	C₂×C₄	1	1	yes	characteristic
117	#13182006	C₂×C₄	1	1	yes	characteristic, complemented
118	#13182006	C₂×C₄	1	1	yes	characteristic, complemented
119	C₂×D₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic, complemented
121	C₄⋊C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic, complemented
122	C₄⋊C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic, complemented
123	C₂²⋊C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
124	C₂²⋊C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
125	C₂²⋊C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic, complemented
126	C₂³×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
127	C₂³×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
128	C₂²×D₁₀₉	—	2	1	no	—
129	C₂²×D₁₀₉	—	2	1	no	—
130	C₂²×D₁₀₉	—	2	1	no	—
131	C₂²×D₁₀₉	—	2	1	no	—
132	C₂²×D₁₀₉	—	2	1	no	—
133	C₂²×D₁₀₉	—	2	1	no	—
134	C₂²×D₁₀₉	—	2	1	no	—
135	C₂²×D₁₀₉	—	2	1	no	—
136	C₂²×D₁₀₉	—	2	1	no	—
137	C₂²×D₁₀₉	—	2	1	no	—
138	C₂²×D₁₀₉	—	2	1	no	—
139	C₂²×D₁₀₉	—	2	1	no	—
140	C₂²×D₁₀₉	C₂²×C₄	1	1	yes	characteristic
141	C₂²×D₁₀₉	C₂²×C₄	1	1	yes	characteristic
142	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
143	C₂×#89137	—	2	1	no	—
144	C₂×#89137	—	2	1	no	—
145	C₂×#89137	—	2	1	no	—
146	C₂×#89137	—	2	1	no	—
147	C₂×#89137	—	2	1	no	—
148	C₂×#89137	—	2	1	no	—
149	C₂×#89137	—	2	1	no	—
150	C₂×#89137	—	2	1	no	—
151	C₂×#89137	—	2	1	no	—
152	C₂×#89137	—	2	1	no	—
153	C₂×#89137	—	2	1	no	—
154	C₂×#89137	—	2	1	no	—
155	C₂×#89137	—	2	1	no	—
156	C₂×#89137	—	2	1	no	—
157	C₂×#89137	—	2	1	no	—
158	C₂×#89137	—	2	1	no	—
159	C₂×#89137	—	2	1	no	—
160	C₂×#89137	—	2	1	no	—
161	C₂×#89137	—	2	1	no	—
162	C₂×#89137	—	2	1	no	—
163	C₂×#89137	—	2	1	no	—
164	C₂×#89137	—	2	1	no	—
165	C₂×#89137	—	4	4	no	—
166	C₂×#89137	#41	1	2	yes	—
167	C₂×#89137	#41	1	2	yes	—
168	D₄×C₁₀₉	—	4	1	no	—
169	C₂×C₄×C₁₀₉	—	4	1	no	—
170	C₂×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
175	C₂²⋊D₁₀₉	—	4	1	no	—
176	C₂²⋊D₁₀₉	—	4	1	no	—
177	C₂×Dic₁₀₉	—	4	1	no	—
178	C₂×Dic₁₀₉	C₂²×C₄	1	1	yes	characteristic
179	C₂×Dic₁₀₉	C₂²×C₄	1	1	yes	characteristic
180	C₂×Dic₁₀₉	C₂²×C₄	1	1	yes	characteristic
181	C₂×Dic₁₀₉	C₂²×C₄	1	1	yes	characteristic
182	C₂×Dic₁₀₉	C₂²×C₄	1	1	yes	characteristic
183	D₄₃₆	—	4	1	no	—
184	C₄×D₁₀₉	—	2	1	no	—
185	C₄×D₁₀₉	—	2	1	no	—
186	C₄×D₁₀₉	—	2	1	no	—
187	C₄×D₁₀₉	—	2	1	no	—
188	C₄×D₁₀₉	—	2	1	no	—
189	C₄×D₁₀₉	—	2	1	no	—
190	C₄×D₁₀₉	—	2	1	no	—
191	C₄×D₁₀₉	—	2	1	no	—
192	C₄×D₁₀₉	—	2	1	no	—
193	C₄×D₁₀₉	—	2	1	no	—
194	C₄×D₁₀₉	—	4	1	no	—
195	C₄×D₁₀₉	—	4	1	no	—
196	C₂²×C₁₀₉	—	2	1	no	—
197	C₂²×C₁₀₉	—	2	1	no	—
198	C₂²×C₁₀₉	—	2	1	no	—
199	C₂²×C₁₀₉	—	2	1	no	—
200	C₂²×C₁₀₉	—	2	1	no	—
201	C₂²×C₁₀₉	—	2	1	no	—
202	C₂²×C₁₀₉	C₂³×C₄	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	1	no	—
208	C₂×D₁₀₉	—	2	1	no	—
209	C₂×D₁₀₉	—	4	1	no	—
210	C₂×D₁₀₉	—	4	1	no	—
211	C₂×D₁₀₉	—	4	1	no	—
212	C₂×D₁₀₉	—	4	1	no	—
213	C₂×D₁₀₉	—	4	1	no	—
214	C₂×D₁₀₉	—	4	1	no	—
215	C₂×D₁₀₉	—	4	1	no	—
216	C₂×D₁₀₉	—	4	1	no	—
217	C₂×D₁₀₉	C₂×#41	1	1	yes	characteristic
218	C₂×D₁₀₉	C₂×#41	1	1	yes	characteristic
219	C₂×D₁₀₉	H(5,𝔽₂)	1	1	yes	characteristic
220	C₂×D₁₀₉	H(5,𝔽₂)	1	1	yes	characteristic
221	C₂×D₁₀₉	H(5,𝔽₂)	1	1	yes	characteristic
222	C₂×D₁₀₉	2₋¹⁺⁴	1	1	yes	characteristic
223	#89137	—	2	2	no	—
224	#89137	—	2	2	no	—
225	#89137	—	4	1	no	—
226	#89137	—	4	1	no	—
227	#89137	—	4	1	no	—
228	#89137	—	4	1	no	—
229	#89137	—	4	1	no	—
230	#89137	—	4	1	no	—
231	C₄×C₁₀₉	—	2	1	no	—
232	C₄×C₁₀₉	—	2	1	no	—
233	C₄×C₁₀₉	—	2	1	no	—
234	C₄×C₁₀₉	—	2	1	no	—
235	C₄×C₁₀₉	—	2	1	no	—
236	Dic₁₀₉	—	2	1	no	—
237	Dic₁₀₉	—	2	1	no	—
238	Dic₁₀₉	—	2	1	no	—
239	Dic₁₀₉	—	2	1	no	—
240	Dic₁₀₉	—	2	1	no	—
241	C₂×C₁₀₉	—	4	1	no	—
242	C₂×C₁₀₉	—	4	1	no	—
243	C₂×C₁₀₉	C₄×#41	1	1	yes	characteristic
244	C₂×C₁₀₉	#518	1	1	yes	characteristic
245	C₂×C₁₀₉	#520	1	1	yes	characteristic
246	D₁₀₉	—	4	1	no	—
247	D₁₀₉	—	4	1	no	—
248	D₁₀₉	#538	1	1	yes	characteristic
249	D₁₀₉	#539	1	1	yes	characteristic
250	D₁₀₉	#540	1	1	yes	characteristic
251	D₁₀₉	#542	1	1	yes	characteristic
252	#2335	—	109	1	no	maximal, Sylow
253	C₁₀₉	#2335	1	1	yes	characteristic, complemented, Sylow
254	C₂×#123	—	109	1	no	—
255	#390	—	109	1	no	—
256	#389	—	109	1	no	—
257	#388	—	109	1	no	—
258	#388	—	109	1	no	—
259	#388	—	109	1	no	—
260	#388	—	109	1	no	—
261	#387	—	109	1	no	—
262	#387	—	109	1	no	—
263	#386	—	109	1	no	—
264	#385	—	109	1	no	—
265	#380	—	109	1	no	—
266	C₄×C₄⋊C₄	—	109	1	no	—
267	C₄×C₂²⋊C₄	—	109	1	no	—
268	C₄×C₂²⋊C₄	—	109	1	no	—
269	C₂²×D₄	—	109	1	no	—
270	C₂³×C₄	—	109	1	no	—
271	C₂³×C₄	—	109	1	no	—
272	#123	—	109	1	no	—
273	#123	—	109	1	no	—
274	#123	—	109	1	no	—
275	#123	—	109	1	no	—
276	#123	—	109	1	no	—
277	#123	—	109	1	no	—
278	#123	—	109	1	no	—
279	#123	#89137	1	1	yes	characteristic, complemented
280	C₂×C₄⋊C₄	—	109	1	no	—
281	C₂×C₄⋊C₄	—	109	1	no	—
282	C₂×C₄⋊C₄	—	109	1	no	—
283	C₂×C₄⋊C₄	—	109	1	no	—
284	C₂×C₄⋊C₄	—	109	1	no	—
285	C₂×C₄⋊C₄	—	109	1	no	—
286	C₂×C₄⋊C₄	—	109	1	no	—
287	C₂×C₂²⋊C₄	—	109	1	no	—
288	C₂×C₂²⋊C₄	—	109	1	no	—
289	C₂×C₂²⋊C₄	—	109	1	no	—
290	C₂×C₂²⋊C₄	—	109	1	no	—
291	C₂×C₂²⋊C₄	—	109	1	no	—
292	C₂×C₂²⋊C₄	—	109	1	no	—
293	C₂×C₂²⋊C₄	—	109	1	no	—
294	C₂×C₂²⋊C₄	—	109	1	no	—
295	C₂×C₂²⋊C₄	—	109	1	no	—
296	C₂×C₂²⋊C₄	—	109	1	no	—
297	C₂×C₄²	—	109	1	no	—
298	C₂×C₄²	—	109	1	no	—
299	C₂×C₄²	—	109	1	no	—
300	C₂×C₄²	—	109	1	no	—
301	C₂×C₄²	—	109	1	no	—
302	#95	—	109	1	no	—
303	#95	—	109	1	no	—
304	#95	—	109	1	no	—
305	#95	—	109	1	no	—
306	#95	—	109	1	no	—
307	#95	—	109	1	no	—
308	#95	—	109	1	no	—
309	#95	—	109	1	no	—
310	#95	—	109	1	no	—
311	#95	—	109	1	no	—
312	C₂⁴	—	109	1	no	—
313	C₂⁴	—	109	1	no	—
314	C₂×D₄	—	109	1	no	—
315	C₂×D₄	—	109	1	no	—
316	C₂×D₄	—	109	1	no	—
317	C₂×D₄	—	436	1	no	—
318	C₂×D₄	—	436	1	no	—
319	C₂×D₄	C₂×#89137	1	1	yes	characteristic
320	C₂²×C₄	—	109	1	no	—
321	C₂²×C₄	—	109	1	no	—
322	C₂²×C₄	—	109	1	no	—
323	C₂²×C₄	—	109	1	no	—
324	C₂²×C₄	—	109	1	no	—
325	C₂²×C₄	—	109	1	no	—
326	C₂²×C₄	—	109	1	no	—
327	C₂²×C₄	—	109	1	no	—
328	C₂²×C₄	—	109	1	no	—
329	C₂²×C₄	—	109	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	—	109	1	no	—
336	C₂²×C₄	—	436	1	no	—
337	C₂²×C₄	—	436	1	no	—
338	C₂²×C₄	—	436	1	no	—
339	C₂²×C₄	—	436	1	no	—
340	C₂²×C₄	—	218	2	no	—
341	C₂²×C₄	C₂×#89137	1	1	yes	characteristic, complemented
342	C₄⋊C₄	—	109	1	no	—
343	C₄⋊C₄	—	109	1	no	—
344	C₄⋊C₄	—	109	1	no	—
345	C₄⋊C₄	—	109	1	no	—
346	C₄⋊C₄	—	109	1	no	—
347	C₄⋊C₄	—	109	1	no	—
348	C₄⋊C₄	—	436	1	no	—
349	C₄⋊C₄	—	436	1	no	—
350	C₄⋊C₄	—	436	1	no	—
351	C₄⋊C₄	—	436	1	no	—
352	C₄⋊C₄	—	218	2	no	—
353	C₄⋊C₄	C₂×#89137	1	1	yes	characteristic, complemented
354	C₄⋊C₄	C₂×#89137	1	1	yes	characteristic, complemented
355	C₂²⋊C₄	—	109	1	no	—
356	C₂²⋊C₄	—	109	1	no	—
357	C₂²⋊C₄	—	109	1	no	—
358	C₂²⋊C₄	—	109	1	no	—
359	C₂²⋊C₄	—	109	1	no	—
360	C₂²⋊C₄	—	109	1	no	—
361	C₂²⋊C₄	—	109	1	no	—
362	C₂²⋊C₄	—	109	1	no	—
363	C₂²⋊C₄	—	109	1	no	—
364	C₂²⋊C₄	—	436	1	no	—
365	C₂²⋊C₄	—	436	1	no	—
366	C₂²⋊C₄	—	436	1	no	—
367	C₂²⋊C₄	—	436	1	no	—
368	C₂²⋊C₄	—	218	2	no	—
369	C₂²⋊C₄	—	218	2	no	—
370	C₂²⋊C₄	—	218	2	no	—
371	C₂²⋊C₄	C₂×#89137	1	1	yes	characteristic
372	C₂²⋊C₄	C₂×#89137	1	1	yes	characteristic
373	C₂²⋊C₄	C₂×#89137	1	1	yes	characteristic, complemented
374	C₄²	—	436	1	no	—
375	C₄²	—	436	1	no	—
376	C₄²	—	436	1	no	—
377	C₄²	—	436	1	no	—
378	C₄²	—	218	2	no	—
379	C₂³	—	109	1	no	—
380	C₂³	—	109	1	no	—
381	C₂³	—	109	1	no	—
382	C₂³	—	218	1	no	—
383	C₂³	—	218	1	no	—
384	C₂³	—	218	1	no	—
385	C₂³	—	218	1	no	—
386	C₂³	—	218	1	no	—
387	C₂³	—	218	1	no	—
388	C₂³	—	218	1	no	—
389	C₂³	—	218	1	no	—
390	C₂³	—	218	1	no	—
391	C₂³	—	218	1	no	—
392	C₂³	—	218	1	no	—
393	C₂³	—	218	1	no	—
394	C₂³	C₂²×#89137	1	1	yes	characteristic
395	C₂³	C₂²×#89137	1	1	yes	characteristic
396	D₄	—	4	1	no	—
397	D₄	—	436	1	no	—
398	D₄	—	436	1	no	—
399	D₄	—	436	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	109	2	no	—
402	C₂×C₄	—	109	2	no	—
403	C₂×C₄	—	109	1	no	—
404	C₂×C₄	—	109	1	no	—
405	C₂×C₄	—	109	1	no	—
406	C₂×C₄	—	109	1	no	—
407	C₂×C₄	—	109	1	no	—
408	C₂×C₄	—	436	1	no	—
409	C₂×C₄	—	436	1	no	—
410	C₂×C₄	—	436	4	no	—
411	C₂×C₄	—	436	1	no	—
412	C₂×C₄	—	218	1	no	—
413	C₂×C₄	—	218	1	no	—
414	C₂×C₄	—	218	1	no	—
415	C₂×C₄	—	218	1	no	—
416	C₂×C₄	—	218	1	no	—
417	C₂×C₄	—	218	1	no	—
418	C₂×C₄	—	218	1	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	—	218	1	no	—
425	C₂×C₄	—	218	1	no	—
426	C₂×C₄	—	218	1	no	—
427	C₂×C₄	—	218	1	no	—
428	C₂×C₄	—	218	1	no	—
429	C₂×C₄	—	218	1	no	—
430	C₂×C₄	—	218	1	no	—
431	C₂×C₄	—	218	1	no	—
432	C₂×C₄	—	218	1	no	—
433	C₂×C₄	—	218	1	no	—
434	C₂×C₄	—	218	1	no	—
435	C₂×C₄	—	218	1	no	—
436	C₂×C₄	—	218	1	no	—
437	C₂×C₄	—	218	1	no	—
438	C₂×C₄	—	218	1	no	—
439	C₂×C₄	—	218	1	no	—
440	C₂×C₄	—	218	1	no	—
441	C₂×C₄	—	218	1	no	—
442	C₂×C₄	—	218	1	no	—
443	C₂×C₄	—	218	1	no	—
444	C₂×C₄	C₂²×#89137	1	1	yes	characteristic
445	C₂×C₄	C₂²×#89137	1	1	yes	characteristic
446	C₂×C₄	C₂²×#89137	1	1	yes	characteristic
447	C₂×C₄	C₂²×#89137	1	1	yes	characteristic
448	C₂×C₄	C₂²×#89137	1	1	yes	characteristic
449	C₂²	—	2	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	109	1	no	—
456	C₂²	—	109	1	no	—
457	C₂²	—	109	1	no	—
458	C₂²	—	109	1	no	—
459	C₂²	—	109	1	no	—
460	C₂²	—	109	1	no	—
461	C₂²	—	436	1	no	—
462	C₂²	—	436	1	no	—
463	C₂²	—	436	1	no	—
464	C₂²	—	436	1	no	—
465	C₂²	—	436	1	no	—
466	C₂²	—	436	1	no	—
467	C₂²	—	436	1	no	—
468	C₂²	—	436	1	no	—
469	C₂²	—	218	1	no	—
470	C₂²	—	218	1	no	—
471	C₂²	—	218	1	no	—
472	C₂²	—	218	1	no	—
473	C₂²	—	218	1	no	—
474	C₂²	—	218	1	no	—
475	C₂²	C₂³×#89137	1	1	yes	characteristic
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	436	1	no	—
482	C₄	—	436	1	no	—
483	C₄	—	436	1	no	—
484	C₄	—	436	1	no	—
485	C₄	—	436	1	no	—
486	C₄	—	436	1	no	—
487	C₄	—	218	2	no	—
488	C₄	—	218	2	no	—
489	C₄	—	218	1	no	—
490	C₄	—	218	1	no	—
491	C₄	—	218	1	no	—
492	C₄	—	218	1	no	—
493	C₄	—	218	1	no	—
494	C₂	—	4	1	no	—
495	C₂	—	4	1	no	—
496	C₂	—	109	1	no	—
497	C₂	—	109	1	no	—
498	C₂	—	109	1	no	—
499	C₂	—	109	1	no	—
500	C₂	—	436	1	no	—
501	C₂	—	436	1	no	—
502	C₂	#41×#89137	1	1	yes	characteristic
503	C₂	#20296093	1	1	yes	characteristic
504	C₂	#20296095	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×#89137
commutator, socle	C₂²×C₁₀₉	C₂³×C₄
Fitting	#123×C₁₀₉	C₄
prime radical	C₂×D₄×D₁₀₉	C₂²
cosocle	C₂²×D₁₀₉	C₂⁴
hypercenter	#123	#89137
hypocenter	C₁₀₉	#2335
LCS	G ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ #123

Complements

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

N	H ≅ G/N	type
2. #20295977	C₂	semidirect
3. #20295976	C₂	semidirect
4. #20295976	C₂	semidirect
5. #20295976	C₂	semidirect
6. #20295976	C₂	semidirect
7. #20295975	C₂	semidirect
8. #20295975	C₂	semidirect
10. #20295973	C₂	semidirect
11. #20295968	C₂	semidirect
12. C₄⋊C₄×#89137	C₂	semidirect
13. C₂²⋊C₄×#89137	C₂	semidirect
14. C₄×C₂²⋊#89137	C₂	semidirect
46. #16812684	C₄	semidirect
47. #16812684	C₄	semidirect
48. #16812683	C₄	semidirect
49. #16812682	C₄	semidirect
50. #16812681	C₄	semidirect
51. #16812681	C₄	semidirect
52. #16812680	C₄	semidirect
58. #123×C₁₀₉	C₄	semidirect
94. C₂²×Dic₁₀₉	C₂×C₄	semidirect
97. C₂×C₄×D₁₀₉	C₂×C₄	semidirect
98. C₂×C₄×D₁₀₉	C₂×C₄	semidirect
104. C₄⋊Dic₁₀₉	C₂×C₄	semidirect
105. C₄⋊Dic₁₀₉	C₂×C₄	semidirect
106. #13182008	C₂×C₄	semidirect
107. #13182008	C₂×C₄	semidirect
108. #13182008	C₂×C₄	semidirect
109. #13182008	C₂×C₄	semidirect
112. C₂²⋊Dic₁₀₉	C₂×C₄	semidirect
117. #13182006	C₂×C₄	semidirect
118. #13182006	C₂×C₄	semidirect
120. C₂²×C₄×C₁₀₉	C₂×C₄	semidirect
121. C₄⋊C₄×C₁₀₉	C₂×C₄	semidirect
122. C₄⋊C₄×C₁₀₉	C₂×C₄	semidirect
125. C₂²⋊C₄×C₁₀₉	C₂×C₄	semidirect
253. C₁₀₉	#2335	semidirect
279. #123	#89137	semidirect
341. C₂²×C₄	C₂×#89137	semidirect
353. C₄⋊C₄	C₂×#89137	semidirect
354. C₄⋊C₄	C₂×#89137	semidirect
373. C₂²⋊C₄	C₂×#89137	semidirect

Maximal subgroups

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

subgroup	index
#20295978	2
#20295977	2
#20295976	2
#20295975	2
#20295974	2
#20295973	2
#20295968	2
C₄⋊C₄×#89137	2
C₂²⋊C₄×#89137	2
C₄×C₂²⋊#89137	2
#123×D₁₀₉	2
#2335	109