Subgroups — #28379555

Order 13952.

652 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×#89137	C₂	1	1	yes	maximal, characteristic
2	C₂×#16812778	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295977	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	#20295975	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295975	C₂	1	1	yes	maximal, characteristic, complemented
8	#20295974	C₂	1	1	yes	maximal, characteristic
9	#20295973	C₂	1	1	yes	maximal, characteristic, complemented
10	#20295973	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄⋊C₄×#89137	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²⋊C₄×#89137	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²⋊C₄×#89137	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×(C₂×#89137)⋊C₄	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	C₂³×#89137	C₂²	1	1	yes	characteristic
18	C₂³×#89137	C₂²	1	1	yes	characteristic
19	D₄×#89137	—	2	4	no	—
20	#16812778	—	2	4	no	—
21	C₂×C₄⋊#89137	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊#89137	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊#89137	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊#89137	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊#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×C₂²⋊#89137	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊#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×C₄×#89137	C₂²	1	1	yes	characteristic
35	C₂×C₄×#89137	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×#89137)⋊C₄	C₂²	1	1	yes	characteristic
45	(C₂×#89137)⋊C₄	C₂²	1	1	yes	characteristic
46	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
47	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
48	#16812684	C₄	1	1	yes	characteristic, complemented
49	#16812684	C₄	1	1	yes	characteristic, complemented
50	#16812683	C₄	1	1	yes	characteristic, complemented
51	#16812682	C₄	1	1	yes	characteristic, complemented
52	#16812681	C₄	1	1	yes	characteristic, complemented
53	#16812681	C₄	1	1	yes	characteristic, complemented
54	#16812680	C₄	1	1	yes	characteristic, complemented
55	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
56	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
57	C₂²⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
58	C₂²⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
59	C₂²⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
60	#123×C₁₀₉	C₄	1	1	yes	characteristic, complemented
61	C₂²×#89137	—	2	2	no	—
62	C₂²×#89137	—	2	2	no	—
63	C₂²×#89137	—	2	2	no	—
64	C₂²×#89137	—	2	2	no	—
65	C₂²×#89137	—	2	2	no	—
66	C₂²×#89137	—	2	2	no	—
67	C₂²×#89137	—	4	1	no	—
68	C₂²×#89137	—	4	1	no	—
69	C₂²×#89137	—	4	1	no	—
70	C₂²×#89137	C₂³	1	1	yes	characteristic
71	C₂²×#89137	C₂³	1	1	yes	characteristic
72	C₂²×#89137	C₂³	1	1	yes	characteristic
73	C₂²×#89137	C₂³	1	1	yes	characteristic
74	C₂²×#89137	C₂³	1	1	yes	characteristic
75	C₂²×#89137	C₂³	1	1	yes	characteristic
76	C₂²×#89137	C₂³	1	1	yes	characteristic
77	C₂²×#89137	C₂³	1	1	yes	characteristic
78	C₄⋊#89137	—	2	2	no	—
79	C₄⋊#89137	—	2	2	no	—
80	C₄⋊#89137	—	2	2	no	—
81	C₄⋊#89137	—	2	2	no	—
82	C₄⋊#89137	—	4	1	no	—
83	C₂²⋊#89137	—	2	2	no	—
84	C₂²⋊#89137	—	2	2	no	—
85	C₂²⋊#89137	—	2	2	no	—
86	C₂²⋊#89137	—	4	1	no	—
87	C₂²⋊#89137	D₄	1	4	yes	—
88	C₄×#89137	—	2	2	no	—
89	C₄×#89137	—	2	2	no	—
90	C₄×#89137	—	2	2	no	—
91	C₄×#89137	—	2	2	no	—
92	C₄×#89137	—	4	1	no	—
93	C₂³×D₁₀₉	C₂³	1	1	yes	characteristic
94	C₂³×D₁₀₉	C₂³	1	1	yes	characteristic
95	C₂×D₄₃₆	C₂×C₄	1	1	yes	characteristic
96	C₂×C₂²⋊D₁₀₉	C₂×C₄	1	1	yes	characteristic
97	C₂×C₂²⋊D₁₀₉	C₂×C₄	1	1	yes	characteristic
98	D₄×D₁₀₉	—	2	2	no	—
99	D₄×D₁₀₉	—	2	2	no	—
100	C₂²×Dic₁₀₉	C₂×C₄	1	1	yes	characteristic, complemented
101	C₂×C₄×D₁₀₉	—	2	2	no	—
102	C₂×C₄×D₁₀₉	—	2	2	no	—
103	C₂×C₄×D₁₀₉	C₂×C₄	1	1	yes	characteristic, complemented
104	C₂×C₄×D₁₀₉	C₂×C₄	1	1	yes	characteristic, complemented
105	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
107	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
108	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
109	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
110	C₄⋊Dic₁₀₉	C₂×C₄	1	1	yes	characteristic, complemented
111	C₄⋊Dic₁₀₉	C₂×C₄	1	1	yes	characteristic, complemented
112	#13182008	C₂×C₄	1	1	yes	characteristic, complemented
113	#13182008	C₂×C₄	1	1	yes	characteristic, complemented
114	#13182008	C₂×C₄	1	1	yes	characteristic, complemented
115	#13182008	C₂×C₄	1	1	yes	characteristic, complemented
116	C₂²⋊Dic₁₀₉	C₂×C₄	1	1	yes	characteristic, complemented
117	C₂²⋊Dic₁₀₉	C₂×C₄	1	1	yes	characteristic, complemented
118	C₂²⋊Dic₁₀₉	C₂×C₄	1	1	yes	characteristic, complemented
119	#13182006	C₂×C₄	1	1	yes	characteristic, complemented
120	#13182006	C₂×C₄	1	1	yes	characteristic, complemented
121	#13182006	C₂×C₄	1	1	yes	characteristic, complemented
122	#13182006	C₂×C₄	1	1	yes	characteristic, complemented
123	#13182006	C₂×C₄	1	1	yes	characteristic, complemented
124	#13182006	C₂×C₄	1	1	yes	characteristic, complemented
125	C₂×D₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic, complemented
127	C₄⋊C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic, complemented
128	C₄⋊C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic, complemented
129	C₂²⋊C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic, complemented
130	C₂²⋊C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic, complemented
131	C₂²⋊C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic, complemented
132	C₂³×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
133	C₂³×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
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	—	2	1	no	—
141	C₂²×D₁₀₉	—	2	1	no	—
142	C₂²×D₁₀₉	—	2	1	no	—
143	C₂²×D₁₀₉	—	2	1	no	—
144	C₂²×D₁₀₉	C₂²×C₄	1	1	yes	characteristic
145	C₂²×D₁₀₉	C₂²×C₄	1	1	yes	characteristic
146	C₂²×D₁₀₉	C₂×D₄	1	2	yes	—
147	C₂²×D₁₀₉	#41	1	2	yes	—
148	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
166	C₂×#89137	—	2	1	no	—
167	C₂×#89137	—	2	1	no	—
168	C₂×#89137	—	2	1	no	—
169	C₂×#89137	—	4	4	no	—
170	C₂×#89137	—	4	4	no	—
171	C₂×#89137	—	4	4	no	—
172	C₂×#89137	C₂×D₄	1	2	yes	—
173	C₂×#89137	C₂×D₄	1	2	yes	—
174	C₂×#89137	#41	1	2	yes	—
175	C₂×#89137	#41	1	2	yes	—
176	D₄×C₁₀₉	—	2	2	no	—
177	C₂×C₄×C₁₀₉	—	2	2	no	—
178	C₂×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
183	C₂²⋊D₁₀₉	—	2	2	no	—
184	C₂²⋊D₁₀₉	—	2	2	no	—
185	C₂×Dic₁₀₉	—	2	2	no	—
186	C₂×Dic₁₀₉	C₂²×C₄	1	1	yes	characteristic
187	C₂×Dic₁₀₉	C₂²×C₄	1	1	yes	characteristic
188	C₂×Dic₁₀₉	C₂²×C₄	1	1	yes	characteristic
189	C₂×Dic₁₀₉	C₂²×C₄	1	1	yes	characteristic
190	C₂×Dic₁₀₉	C₂²×C₄	1	1	yes	characteristic
191	D₄₃₆	—	2	2	no	—
192	C₄×D₁₀₉	—	2	2	no	—
193	C₄×D₁₀₉	—	2	2	no	—
194	C₄×D₁₀₉	—	2	1	no	—
195	C₄×D₁₀₉	—	2	1	no	—
196	C₄×D₁₀₉	—	2	1	no	—
197	C₄×D₁₀₉	—	2	1	no	—
198	C₄×D₁₀₉	—	2	1	no	—
199	C₄×D₁₀₉	—	2	1	no	—
200	C₄×D₁₀₉	—	2	1	no	—
201	C₄×D₁₀₉	—	2	1	no	—
202	C₄×D₁₀₉	—	2	1	no	—
203	C₄×D₁₀₉	—	2	1	no	—
204	C₂²×C₁₀₉	—	2	1	no	—
205	C₂²×C₁₀₉	—	2	1	no	—
206	C₂²×C₁₀₉	—	2	1	no	—
207	C₂²×C₁₀₉	—	2	1	no	—
208	C₂²×C₁₀₉	—	2	1	no	—
209	C₂²×C₁₀₉	C₄×D₄	1	2	yes	—
210	C₂²×C₁₀₉	C₂³×C₄	1	1	yes	characteristic
211	C₂×D₁₀₉	—	2	1	no	—
212	C₂×D₁₀₉	—	2	1	no	—
213	C₂×D₁₀₉	—	2	2	no	—
214	C₂×D₁₀₉	—	2	2	no	—
215	C₂×D₁₀₉	—	2	2	no	—
216	C₂×D₁₀₉	—	2	2	no	—
217	C₂×D₁₀₉	—	2	1	no	—
218	C₂×D₁₀₉	—	2	1	no	—
219	C₂×D₁₀₉	—	2	1	no	—
220	C₂×D₁₀₉	—	4	1	no	—
221	C₂×D₁₀₉	—	4	1	no	—
222	C₂×D₁₀₉	—	4	1	no	—
223	C₂×D₁₀₉	—	4	1	no	—
224	C₂×D₁₀₉	C₄×D₄	1	2	yes	—
225	C₂×D₁₀₉	C₂²×D₄	1	1	yes	characteristic
226	C₂×D₁₀₉	C₂×#41	1	1	yes	characteristic
227	C₂×D₁₀₉	C₂×#41	1	1	yes	characteristic
228	C₂×D₁₀₉	C₂×#41	1	1	yes	characteristic
229	C₂×D₁₀₉	H(5,𝔽₂)	1	1	yes	characteristic
230	C₂×D₁₀₉	2₋¹⁺⁴	1	1	yes	characteristic
231	#89137	—	2	2	no	—
232	#89137	—	2	2	no	—
233	#89137	—	2	2	no	—
234	#89137	—	2	2	no	—
235	#89137	—	4	1	no	—
236	#89137	—	4	1	no	—
237	#89137	—	4	1	no	—
238	#89137	—	4	1	no	—
239	C₄×C₁₀₉	—	2	1	no	—
240	C₄×C₁₀₉	—	2	1	no	—
241	C₄×C₁₀₉	—	2	1	no	—
242	C₄×C₁₀₉	—	2	1	no	—
243	C₄×C₁₀₉	—	2	1	no	—
244	Dic₁₀₉	—	2	1	no	—
245	Dic₁₀₉	—	2	1	no	—
246	Dic₁₀₉	—	2	1	no	—
247	Dic₁₀₉	—	2	1	no	—
248	Dic₁₀₉	—	2	1	no	—
249	C₂×C₁₀₉	—	2	2	no	—
250	C₂×C₁₀₉	—	4	1	no	—
251	C₂×C₁₀₉	C₂×C₄×D₄	1	1	yes	characteristic
252	C₂×C₁₀₉	C₄×#41	1	1	yes	characteristic
253	C₂×C₁₀₉	#520	1	1	yes	characteristic
254	D₁₀₉	—	2	2	no	—
255	D₁₀₉	—	4	1	no	—
256	D₁₀₉	#546	1	1	yes	characteristic
257	D₁₀₉	#547	1	1	yes	characteristic
258	D₁₀₉	#551	1	1	yes	characteristic
259	D₁₀₉	#552	1	1	yes	characteristic
260	#2359	—	109	1	no	maximal, Sylow
261	C₁₀₉	#2359	1	1	yes	characteristic, complemented, Sylow
262	C₂×#123	—	109	1	no	—
263	C₂×C₄×D₄	—	109	1	no	—
264	C₂×#117	—	109	1	no	—
265	#389	—	109	1	no	—
266	#388	—	109	1	no	—
267	#388	—	109	1	no	—
268	#387	—	109	1	no	—
269	#387	—	109	1	no	—
270	#386	—	109	1	no	—
271	#385	—	109	1	no	—
272	#385	—	109	1	no	—
273	C₄×C₄⋊C₄	—	109	1	no	—
274	C₄×C₂²⋊C₄	—	109	1	no	—
275	C₄×C₂²⋊C₄	—	109	1	no	—
276	C₂×#95	—	109	1	no	—
277	C₂²×D₄	—	109	1	no	—
278	C₂³×C₄	—	109	1	no	—
279	C₂³×C₄	—	109	1	no	—
280	C₂³×C₄	—	109	1	no	—
281	C₂³×C₄	—	109	1	no	—
282	#123	—	109	1	no	—
283	#123	—	109	1	no	—
284	#123	—	109	1	no	—
285	#123	—	109	1	no	—
286	#123	—	109	1	no	—
287	#123	—	109	1	no	—
288	#123	—	109	1	no	—
289	#123	#89137	1	1	yes	characteristic, complemented
290	C₄×D₄	—	218	4	no	—
291	#117	—	218	4	no	—
292	C₂×C₄⋊C₄	—	109	1	no	—
293	C₂×C₄⋊C₄	—	109	1	no	—
294	C₂×C₄⋊C₄	—	109	1	no	—
295	C₂×C₄⋊C₄	—	109	1	no	—
296	C₂×C₄⋊C₄	—	109	1	no	—
297	C₂×C₄⋊C₄	—	109	1	no	—
298	C₂×C₄⋊C₄	—	109	1	no	—
299	C₂×C₂²⋊C₄	—	109	1	no	—
300	C₂×C₂²⋊C₄	—	109	1	no	—
301	C₂×C₂²⋊C₄	—	109	1	no	—
302	C₂×C₂²⋊C₄	—	109	1	no	—
303	C₂×C₂²⋊C₄	—	109	1	no	—
304	C₂×C₂²⋊C₄	—	109	1	no	—
305	C₂×C₂²⋊C₄	—	109	1	no	—
306	C₂×C₂²⋊C₄	—	109	1	no	—
307	C₂×C₄²	—	109	1	no	—
308	C₂×C₄²	—	109	1	no	—
309	C₂×C₄²	—	109	1	no	—
310	C₂×C₄²	—	109	1	no	—
311	C₂×C₄²	—	109	1	no	—
312	#95	—	109	1	no	—
313	#95	—	109	1	no	—
314	#95	—	109	1	no	—
315	#95	—	109	1	no	—
316	#95	—	109	1	no	—
317	#95	—	109	1	no	—
318	#95	—	109	1	no	—
319	#95	—	109	1	no	—
320	#95	—	109	1	no	—
321	#95	—	109	1	no	—
322	C₂⁴	—	109	1	no	—
323	C₂⁴	—	109	1	no	—
324	C₂×D₄	—	109	1	no	—
325	C₂×D₄	—	109	1	no	—
326	C₂×D₄	—	109	1	no	—
327	C₂×D₄	—	218	2	no	—
328	C₂×D₄	—	218	2	no	—
329	C₂×D₄	C₂×#89137	1	1	yes	characteristic
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	—	109	1	no	—
337	C₂²×C₄	—	109	1	no	—
338	C₂²×C₄	—	109	1	no	—
339	C₂²×C₄	—	109	1	no	—
340	C₂²×C₄	—	109	1	no	—
341	C₂²×C₄	—	109	1	no	—
342	C₂²×C₄	—	109	1	no	—
343	C₂²×C₄	—	109	1	no	—
344	C₂²×C₄	—	109	1	no	—
345	C₂²×C₄	—	109	1	no	—
346	C₂²×C₄	—	436	1	no	—
347	C₂²×C₄	—	436	1	no	—
348	C₂²×C₄	—	436	1	no	—
349	C₂²×C₄	—	218	2	no	—
350	C₂²×C₄	—	218	2	no	—
351	C₂²×C₄	—	218	2	no	—
352	C₂²×C₄	—	218	2	no	—
353	C₂²×C₄	—	218	2	no	—
354	C₂²×C₄	—	218	2	no	—
355	C₂²×C₄	—	218	2	no	—
356	C₂²×C₄	—	218	2	no	—
357	C₂²×C₄	C₂×#89137	1	1	yes	characteristic, complemented
358	C₄⋊C₄	—	109	1	no	—
359	C₄⋊C₄	—	109	1	no	—
360	C₄⋊C₄	—	109	1	no	—
361	C₄⋊C₄	—	109	1	no	—
362	C₄⋊C₄	—	109	1	no	—
363	C₄⋊C₄	—	109	1	no	—
364	C₄⋊C₄	—	436	1	no	—
365	C₄⋊C₄	—	218	2	no	—
366	C₄⋊C₄	—	218	2	no	—
367	C₄⋊C₄	—	218	2	no	—
368	C₄⋊C₄	—	218	2	no	—
369	C₄⋊C₄	C₂×#89137	1	1	yes	characteristic, complemented
370	C₄⋊C₄	C₂×#89137	1	1	yes	characteristic, complemented
371	C₂²⋊C₄	—	109	4	no	—
372	C₂²⋊C₄	—	109	1	no	—
373	C₂²⋊C₄	—	109	1	no	—
374	C₂²⋊C₄	—	109	1	no	—
375	C₂²⋊C₄	—	109	1	no	—
376	C₂²⋊C₄	—	109	1	no	—
377	C₂²⋊C₄	—	109	1	no	—
378	C₂²⋊C₄	—	109	1	no	—
379	C₂²⋊C₄	—	109	1	no	—
380	C₂²⋊C₄	—	109	1	no	—
381	C₂²⋊C₄	—	436	1	no	—
382	C₂²⋊C₄	—	218	2	no	—
383	C₂²⋊C₄	—	218	2	no	—
384	C₂²⋊C₄	—	218	2	no	—
385	C₂²⋊C₄	C₂×#89137	1	1	yes	characteristic, complemented
386	C₂²⋊C₄	C₂×#89137	1	1	yes	characteristic, complemented
387	C₂²⋊C₄	C₂×#89137	1	1	yes	characteristic, complemented
388	C₄²	—	436	1	no	—
389	C₄²	—	218	2	no	—
390	C₄²	—	218	2	no	—
391	C₄²	—	218	2	no	—
392	C₄²	—	218	2	no	—
393	C₂³	—	109	1	no	—
394	C₂³	—	109	2	no	—
395	C₂³	—	109	2	no	—
396	C₂³	—	109	1	no	—
397	C₂³	—	109	1	no	—
398	C₂³	—	218	1	no	—
399	C₂³	—	218	1	no	—
400	C₂³	—	218	1	no	—
401	C₂³	—	218	1	no	—
402	C₂³	—	218	1	no	—
403	C₂³	—	218	1	no	—
404	C₂³	—	218	1	no	—
405	C₂³	—	218	1	no	—
406	C₂³	—	218	1	no	—
407	C₂³	—	218	1	no	—
408	C₂³	C₂²×#89137	1	1	yes	characteristic
409	C₂³	C₂²×#89137	1	1	yes	characteristic
410	D₄	—	2	2	no	—
411	D₄	—	218	2	no	—
412	D₄	—	218	2	no	—
413	D₄	—	218	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	109	2	no	—
416	C₂×C₄	—	109	2	no	—
417	C₂×C₄	—	109	2	no	—
418	C₂×C₄	—	109	2	no	—
419	C₂×C₄	—	109	1	no	—
420	C₂×C₄	—	109	1	no	—
421	C₂×C₄	—	109	1	no	—
422	C₂×C₄	—	109	1	no	—
423	C₂×C₄	—	109	1	no	—
424	C₂×C₄	—	436	4	no	—
425	C₂×C₄	—	436	4	no	—
426	C₂×C₄	—	436	4	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	2	no	—
436	C₂×C₄	—	218	2	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	—	218	1	no	—
445	C₂×C₄	—	218	1	no	—
446	C₂×C₄	—	218	1	no	—
447	C₂×C₄	—	218	1	no	—
448	C₂×C₄	—	218	1	no	—
449	C₂×C₄	—	218	1	no	—
450	C₂×C₄	—	218	1	no	—
451	C₂×C₄	—	218	1	no	—
452	C₂×C₄	—	218	1	no	—
453	C₂×C₄	—	218	1	no	—
454	C₂×C₄	—	218	1	no	—
455	C₂×C₄	—	218	1	no	—
456	C₂×C₄	—	218	1	no	—
457	C₂×C₄	—	218	1	no	—
458	C₂×C₄	—	218	1	no	—
459	C₂×C₄	—	218	2	no	—
460	C₂×C₄	C₂²×#89137	1	1	yes	characteristic
461	C₂×C₄	C₂²×#89137	1	1	yes	characteristic
462	C₂×C₄	C₂²×#89137	1	1	yes	characteristic
463	C₂×C₄	C₂²×#89137	1	1	yes	characteristic
464	C₂×C₄	C₂²×#89137	1	1	yes	characteristic
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	109	1	no	—
471	C₂²	—	109	1	no	—
472	C₂²	—	109	1	no	—
473	C₂²	—	109	1	no	—
474	C₂²	—	109	1	no	—
475	C₂²	—	109	1	no	—
476	C₂²	—	109	2	no	—
477	C₂²	—	436	1	no	—
478	C₂²	—	436	1	no	—
479	C₂²	—	436	1	no	—
480	C₂²	—	436	1	no	—
481	C₂²	—	218	2	no	—
482	C₂²	—	218	2	no	—
483	C₂²	—	218	2	no	—
484	C₂²	—	218	2	no	—
485	C₂²	—	218	1	no	—
486	C₂²	—	218	1	no	—
487	C₂²	—	218	1	no	—
488	C₂²	—	218	1	no	—
489	C₂²	—	218	1	no	—
490	C₂²	D₄×#89137	1	2	yes	—
491	C₂²	C₂³×#89137	1	1	yes	characteristic
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	2	1	no	—
496	C₄	—	2	1	no	—
497	C₄	—	436	1	no	—
498	C₄	—	436	1	no	—
499	C₄	—	436	1	no	—
500	C₄	—	436	1	no	—
501	C₄	—	218	2	no	—
502	C₄	—	218	2	no	—
503	C₄	—	218	2	no	—
504	C₄	—	218	2	no	—
505	C₄	—	218	1	no	—
506	C₄	—	218	1	no	—
507	C₄	—	218	1	no	—
508	C₄	—	218	1	no	—
509	C₄	—	218	1	no	—
510	C₂	—	2	2	no	—
511	C₂	—	4	1	no	—
512	C₂	—	109	1	no	—
513	C₂	—	109	1	no	—
514	C₂	—	109	1	no	—
515	C₂	—	109	1	no	—
516	C₂	—	436	1	no	—
517	C₂	—	218	2	no	—
518	C₂	C₂×D₄×#89137	1	1	yes	characteristic
519	C₂	#41×#89137	1	1	yes	characteristic
520	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	#2359
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. C₂×#16812778	C₂	semidirect
3. #20295977	C₂	semidirect
4. #20295976	C₂	semidirect
5. #20295976	C₂	semidirect
6. #20295975	C₂	semidirect
7. #20295975	C₂	semidirect
9. #20295973	C₂	semidirect
10. #20295973	C₂	semidirect
11. C₄⋊C₄×#89137	C₂	semidirect
12. C₂²⋊C₄×#89137	C₂	semidirect
13. C₂²⋊C₄×#89137	C₂	semidirect
14. C₂×(C₂×#89137)⋊C₄	C₂	semidirect
48. #16812684	C₄	semidirect
49. #16812684	C₄	semidirect
50. #16812683	C₄	semidirect
51. #16812682	C₄	semidirect
52. #16812681	C₄	semidirect
53. #16812681	C₄	semidirect
54. #16812680	C₄	semidirect
60. #123×C₁₀₉	C₄	semidirect
100. C₂²×Dic₁₀₉	C₂×C₄	semidirect
103. C₂×C₄×D₁₀₉	C₂×C₄	semidirect
104. C₂×C₄×D₁₀₉	C₂×C₄	semidirect
110. C₄⋊Dic₁₀₉	C₂×C₄	semidirect
111. C₄⋊Dic₁₀₉	C₂×C₄	semidirect
112. #13182008	C₂×C₄	semidirect
113. #13182008	C₂×C₄	semidirect
114. #13182008	C₂×C₄	semidirect
115. #13182008	C₂×C₄	semidirect
116. C₂²⋊Dic₁₀₉	C₂×C₄	semidirect
117. C₂²⋊Dic₁₀₉	C₂×C₄	semidirect
118. C₂²⋊Dic₁₀₉	C₂×C₄	semidirect
119. #13182006	C₂×C₄	semidirect
120. #13182006	C₂×C₄	semidirect
121. #13182006	C₂×C₄	semidirect
122. #13182006	C₂×C₄	semidirect
123. #13182006	C₂×C₄	semidirect
124. #13182006	C₂×C₄	semidirect
126. C₂²×C₄×C₁₀₉	C₂×C₄	semidirect
127. C₄⋊C₄×C₁₀₉	C₂×C₄	semidirect
128. C₄⋊C₄×C₁₀₉	C₂×C₄	semidirect
129. C₂²⋊C₄×C₁₀₉	C₂×C₄	semidirect
130. C₂²⋊C₄×C₁₀₉	C₂×C₄	semidirect
131. C₂²⋊C₄×C₁₀₉	C₂×C₄	semidirect
261. C₁₀₉	#2359	semidirect
289. #123	#89137	semidirect
357. C₂²×C₄	C₂×#89137	semidirect
369. C₄⋊C₄	C₂×#89137	semidirect
370. C₄⋊C₄	C₂×#89137	semidirect
385. C₂²⋊C₄	C₂×#89137	semidirect
386. C₂²⋊C₄	C₂×#89137	semidirect
387. 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
C₂×D₄×#89137	2
C₂×#16812778	2
#20295977	2
#20295976	2
#20295975	2
#20295974	2
#20295973	2
C₄⋊C₄×#89137	2
C₂²⋊C₄×#89137	2
C₂×(C₂×#89137)⋊C₄	2
#123×D₁₀₉	2
#2359	109