Subgroups — #27185214

Order 12928.

1104 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20265909	C₂	1	2	yes	maximal, complemented
2	Q₈×Dic₂₀₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#20265887	C₂	1	1	yes	maximal, characteristic, complemented
4	#20265886	C₂	1	2	yes	maximal, complemented
5	#20265847	C₂	1	1	yes	maximal, characteristic, complemented
6	#20265835	C₂	1	2	yes	maximal, complemented
7	#20265832	C₂	1	2	yes	maximal, complemented
8	#20265825	C₂	1	4	yes	maximal, complemented
9	#20265796	C₂	1	2	yes	maximal, complemented
10	#20265795	C₂	1	4	yes	maximal, complemented
11	#20265725	C₂	1	1	yes	maximal, characteristic, complemented
12	#20265724	C₂	1	2	yes	maximal, complemented
13	#20265714	C₂	1	1	yes	maximal, characteristic, complemented
14	#20265706	C₂	1	2	yes	maximal, complemented
15	#20265656	C₂	1	2	yes	maximal, complemented
16	C₄×Q₈×D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
17	#559×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13108074	C₂²	1	4	yes	—
19	C₂×#13108073	C₂²	1	2	yes	—
20	C₂×#13108073	C₂²	1	2	yes	—
21	C₂×Q₈×D₁₀₁	C₂²	1	1	yes	characteristic
22	#15692255	C₂²	1	2	yes	—
23	#15692255	C₂²	1	1	yes	characteristic
24	#15692254	C₂²	1	4	yes	—
25	#15692254	C₂²	1	2	yes	—
26	#15692251	C₂²	1	2	yes	—
27	#15692250	C₂²	1	2	yes	—
28	#15692248	C₂²	1	4	yes	—
29	#15692247	C₂²	1	2	yes	—
30	#15692246	C₂²	1	1	yes	characteristic
31	#15692244	C₂²	1	1	yes	characteristic
32	#15692242	C₂²	1	2	yes	—
33	#15692241	C₂²	1	4	yes	—
34	#15692241	C₂²	1	4	yes	—
35	#15692240	C₂²	1	2	yes	—
36	#15692239	C₂²	1	4	yes	—
37	#15692237	C₂²	1	4	yes	—
38	#15692237	C₂²	1	4	yes	—
39	#15692234	C₂²	1	4	yes	—
40	#15692233	C₂²	1	4	yes	—
41	#15692232	C₂²	1	4	yes	—
42	#15692232	C₂²	1	4	yes	—
43	#15692231	C₂²	1	2	yes	—
44	#15692231	C₂²	1	1	yes	characteristic
45	#15692230	C₂²	1	1	yes	characteristic
46	#15692228	C₂²	1	4	yes	—
47	#15692227	C₂²	1	4	yes	—
48	#15692226	C₂²	1	2	yes	—
49	#15692226	C₂²	1	2	yes	—
50	#15692226	C₂²	1	2	yes	—
51	Q₈×Dic₁₀₁	C₂²	1	1	yes	characteristic
52	Q₈×Dic₁₀₁	C₂²	1	2	yes	—
53	C₄×Dic₂₀₂	C₂²	1	2	yes	—
54	C₄×Dic₂₀₂	C₂²	1	1	yes	characteristic
55	C₄×Dic₂₀₂	C₂²	1	2	yes	—
56	#15692220	C₂²	1	2	yes	—
57	#15692220	C₂²	1	1	yes	characteristic
58	C₄×D₄₀₄	C₂²	1	2	yes	—
59	C₄×D₄₀₄	C₂²	1	1	yes	characteristic
60	C₄×D₄₀₄	C₂²	1	2	yes	—
61	D₄×Dic₁₀₁	C₂²	1	2	yes	—
62	D₄×Dic₁₀₁	C₂²	1	2	yes	—
63	D₄×Dic₁₀₁	C₂²	1	2	yes	—
64	C₄×C₂²⋊D₁₀₁	C₂²	1	4	yes	—
65	#15692215	C₂²	1	4	yes	—
66	#15692215	C₂²	1	4	yes	—
67	#15692212	C₂²	1	2	yes	—
68	#15692211	C₂²	1	4	yes	—
69	C₂×#13108053	C₂²	1	4	yes	—
70	C₄⋊C₄×D₁₀₁	C₂²	1	2	yes	—
71	C₄⋊C₄×D₁₀₁	C₂²	1	1	yes	characteristic
72	C₄⋊C₄×D₁₀₁	C₂²	1	2	yes	—
73	C₄²×D₁₀₁	C₂²	1	2	yes	—
74	C₄²×D₁₀₁	C₂²	1	1	yes	characteristic
75	#127×C₁₀₁	C₂²	1	1	yes	characteristic
76	#124×C₁₀₁	C₂²	1	2	yes	—
77	#124×C₁₀₁	C₂²	1	2	yes	—
78	#123×C₁₀₁	C₂²	1	4	yes	—
79	C₄×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
80	C₄×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
81	C₄×D₄×C₁₀₁	C₂²	1	2	yes	—
82	C₄×D₄×C₁₀₁	C₂²	1	2	yes	—
83	#13108074	—	4	8	no	—
84	#13108073	—	2	8	no	—
85	#13108073	—	4	4	no	—
86	C₂×Dic₂₀₂	C₂³	1	2	yes	—
87	C₂×Dic₂₀₂	C₂³	1	2	yes	—
88	C₂×Dic₂₀₂	C₂³	1	4	yes	—
89	C₂×Dic₂₀₂	C₂³	1	1	yes	characteristic
90	Q₈×D₁₀₁	—	2	4	no	—
91	C₂×D₄₀₄	C₂³	1	2	yes	—
92	C₂×D₄₀₄	C₂³	1	1	yes	characteristic
93	C₂×C₂²⋊D₁₀₁	C₂³	1	4	yes	—
94	C₂×C₂²⋊D₁₀₁	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₁₀₁	C₂³	1	4	yes	—
96	C₂²×Dic₁₀₁	C₂³	1	4	yes	—
97	C₂²×Dic₁₀₁	C₂³	1	4	yes	—
98	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
99	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
100	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
101	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
102	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
103	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
104	C₂×C₄×D₁₀₁	C₂³	1	4	yes	—
105	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
106	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
107	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
108	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
109	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
110	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
111	C₄⋊Dic₁₀₁	C₂³	1	4	yes	—
112	#13108053	C₂³	1	2	yes	—
113	#13108053	C₂³	1	4	yes	—
114	#13108053	C₂³	1	2	yes	—
115	#13108053	C₂³	1	2	yes	—
116	#13108053	C₂³	1	2	yes	—
117	#13108053	C₂³	1	4	yes	—
118	#13108053	C₂³	1	2	yes	—
119	#13108053	C₂³	1	4	yes	—
120	C₂²⋊Dic₁₀₁	C₂³	1	4	yes	—
121	C₂²⋊Dic₁₀₁	C₂³	1	4	yes	—
122	C₂²⋊Dic₁₀₁	C₂³	1	4	yes	—
123	#13108051	C₂³	1	2	yes	—
124	#13108051	C₂³	1	2	yes	—
125	#13108051	C₂³	1	2	yes	—
126	#13108051	C₂³	1	2	yes	—
127	#13108051	C₂³	1	4	yes	—
128	#13108051	C₂³	1	2	yes	—
129	C₄×Dic₁₀₁	C₂³	1	2	yes	—
130	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
131	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
132	C₄×Dic₁₀₁	C₂³	1	2	yes	—
133	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
134	C₄×Dic₁₀₁	C₂³	1	2	yes	—
135	C₄×Dic₁₀₁	C₂³	1	4	yes	—
136	C₂×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
137	C₂×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
138	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
139	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
140	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
141	C₂²×C₄×C₁₀₁	C₂³	1	4	yes	—
142	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
143	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
144	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
145	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
146	C₂²⋊C₄×C₁₀₁	C₂³	1	4	yes	—
147	C₂²⋊C₄×C₁₀₁	C₂³	1	4	yes	—
148	C₂²⋊C₄×C₁₀₁	C₂³	1	4	yes	—
149	C₄²×C₁₀₁	C₂³	1	2	yes	—
150	C₄²×C₁₀₁	C₂³	1	2	yes	—
151	C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
152	C₂³×C₁₀₁	C₂⁴	1	4	yes	—
153	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
154	C₂²×D₁₀₁	C₂⁴	1	1	yes	characteristic
155	Q₈×C₁₀₁	—	2	2	no	—
156	Q₈×C₁₀₁	—	2	2	no	—
157	D₄×C₁₀₁	—	2	4	no	—
158	D₄×C₁₀₁	—	2	4	no	—
159	D₄×C₁₀₁	—	4	2	no	—
160	C₂×C₄×C₁₀₁	—	4	4	no	—
161	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
162	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
163	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
164	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
165	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
166	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
167	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
168	C₂²⋊D₁₀₁	—	2	8	no	—
169	C₂²⋊D₁₀₁	—	2	8	no	—
170	C₂²⋊D₁₀₁	—	4	4	no	—
171	C₂×Dic₁₀₁	—	2	8	no	—
172	C₂×Dic₁₀₁	—	4	4	no	—
173	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
174	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
175	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
176	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
177	C₂×Dic₁₀₁	C₂⁴	1	4	yes	—
178	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
179	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
180	D₄₀₄	—	2	4	no	—
181	D₄₀₄	—	2	2	no	—
182	C₄×D₁₀₁	—	2	2	no	—
183	C₄×D₁₀₁	—	2	4	no	—
184	C₄×D₁₀₁	—	2	2	no	—
185	C₄×D₁₀₁	—	2	4	no	—
186	C₄×D₁₀₁	—	2	2	no	—
187	C₄×D₁₀₁	—	2	4	no	—
188	C₄×D₁₀₁	—	4	4	no	—
189	Dic₂₀₂	—	2	4	no	—
190	Dic₂₀₂	—	4	2	no	—
191	Dic₂₀₂	—	4	4	no	—
192	Dic₂₀₂	#41	1	4	yes	complemented
193	C₂²×C₁₀₁	—	2	4	no	—
194	C₂²×C₁₀₁	—	2	4	no	—
195	C₂²×C₁₀₁	—	2	4	no	—
196	C₂²×C₁₀₁	C₂⁵	1	1	yes	characteristic
197	C₂×D₁₀₁	—	2	1	no	—
198	C₂×D₁₀₁	—	2	1	no	—
199	C₂×D₁₀₁	—	2	2	no	—
200	C₂×D₁₀₁	—	2	2	no	—
201	C₂×D₁₀₁	—	2	2	no	—
202	C₂×D₁₀₁	H(5,𝔽₂)	1	2	yes	—
203	C₄×C₁₀₁	—	2	2	no	—
204	C₄×C₁₀₁	—	2	1	no	—
205	C₄×C₁₀₁	—	2	2	no	—
206	C₄×C₁₀₁	—	2	2	no	—
207	C₄×C₁₀₁	—	2	2	no	—
208	C₄×C₁₀₁	C₂×#41	1	2	yes	—
209	C₄×C₁₀₁	2₋¹⁺⁴	1	2	yes	—
210	Dic₁₀₁	—	2	1	no	—
211	Dic₁₀₁	—	2	2	no	—
212	Dic₁₀₁	—	2	2	no	—
213	Dic₁₀₁	—	2	4	no	—
214	Dic₁₀₁	—	2	1	no	—
215	Dic₁₀₁	—	2	1	no	—
216	Dic₁₀₁	C₂×#41	1	4	yes	—
217	C₂×C₁₀₁	—	4	4	no	—
218	C₂×C₁₀₁	C₂²×#41	1	1	yes	characteristic
219	C₂×C₁₀₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
220	C₂×C₁₀₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
221	D₁₀₁	—	2	2	no	—
222	D₁₀₁	—	4	2	no	—
223	#3522	—	101	1	no	maximal, Sylow
224	C₁₀₁	#3522	1	1	yes	characteristic, complemented, Sylow
225	#559	—	101	2	no	—
226	#559	D₁₀₁	1	1	yes	characteristic, complemented
227	Q₈²	—	101	1	no	—
228	#554	—	101	1	no	—
229	#554	—	101	2	no	—
230	#550	—	101	1	no	—
231	#548	—	101	2	no	—
232	#547	—	101	4	no	—
233	#547	—	101	2	no	—
234	#542	—	101	2	no	—
235	#542	—	101	4	no	—
236	#532	—	101	1	no	—
237	#532	—	101	2	no	—
238	#529	—	101	2	no	—
239	#529	—	101	1	no	—
240	#520	—	101	2	no	—
241	C₂×C₄×Q₈	—	101	1	no	—
242	C₂×#41	—	101	2	no	—
243	C₂×#41	—	101	2	no	—
244	C₂×#41	—	101	4	no	—
245	C₂²×Q₈	—	101	1	no	—
246	C₄⋊Q₈	—	101	2	no	—
247	C₄⋊Q₈	—	101	4	no	—
248	C₄⋊Q₈	—	101	1	no	—
249	C₄⋊Q₈	—	101	2	no	—
250	#127	—	101	2	no	—
251	#127	C₂×D₁₀₁	1	1	yes	characteristic
252	#126	—	101	2	no	—
253	#126	—	101	4	no	—
254	#125	—	101	1	no	—
255	#125	—	101	2	no	—
256	#124	—	101	1	no	—
257	#124	—	101	2	no	—
258	#124	—	101	4	no	—
259	#124	—	101	4	no	—
260	#124	C₂×D₁₀₁	1	2	yes	—
261	#124	C₂×D₁₀₁	1	2	yes	—
262	#123	—	101	2	no	—
263	#123	—	101	4	no	—
264	#123	—	101	4	no	—
265	#123	—	101	4	no	—
266	#123	C₂×D₁₀₁	1	4	yes	—
267	C₂²⋊Q₈	—	101	1	no	—
268	C₂²⋊Q₈	—	101	2	no	—
269	C₂²⋊Q₈	—	101	4	no	—
270	C₂²⋊Q₈	—	101	4	no	—
271	C₂²⋊Q₈	—	101	4	no	—
272	C₂²⋊Q₈	—	101	4	no	—
273	#121	—	101	2	no	—
274	#121	—	101	2	no	—
275	#121	—	101	2	no	—
276	#121	—	101	4	no	—
277	#121	—	101	1	no	—
278	#121	—	101	4	no	—
279	C₄×Q₈	—	101	1	no	—
280	C₄×Q₈	—	101	2	no	—
281	C₄×Q₈	—	101	1	no	—
282	C₄×Q₈	—	101	2	no	—
283	C₄×Q₈	—	101	1	no	—
284	C₄×Q₈	—	101	2	no	—
285	C₄×Q₈	—	101	2	no	—
286	C₄×Q₈	C₂×D₁₀₁	1	1	yes	characteristic
287	C₄×Q₈	C₂×D₁₀₁	1	1	yes	characteristic
288	C₄×D₄	—	101	2	no	—
289	C₄×D₄	—	101	2	no	—
290	C₄×D₄	—	101	2	no	—
291	C₄×D₄	—	101	4	no	—
292	C₄×D₄	—	101	4	no	—
293	C₄×D₄	—	101	4	no	—
294	C₄×D₄	—	101	2	no	—
295	C₄×D₄	—	101	1	no	—
296	C₄×D₄	—	101	2	no	—
297	C₄×D₄	C₂×D₁₀₁	1	2	yes	—
298	C₄×D₄	C₂×D₁₀₁	1	2	yes	—
299	#117	—	101	4	no	—
300	#117	—	101	2	no	—
301	C₂×C₄⋊C₄	—	101	4	no	—
302	C₂×C₄⋊C₄	—	101	2	no	—
303	C₂×C₄⋊C₄	—	101	1	no	—
304	C₂×C₄⋊C₄	—	101	2	no	—
305	C₂×C₄²	—	101	1	no	—
306	C₂×C₄²	—	101	2	no	—
307	#41	—	404	8	no	—
308	#41	—	404	4	no	—
309	#41	—	202	8	no	—
310	C₂×Q₈	—	101	1	no	—
311	C₂×Q₈	—	101	4	no	—
312	C₂×Q₈	—	101	2	no	—
313	C₂×Q₈	—	101	2	no	—
314	C₂×Q₈	—	202	4	no	—
315	C₂×Q₈	C₂²×D₁₀₁	1	1	yes	characteristic
316	C₂×Q₈	C₂²×D₁₀₁	1	1	yes	characteristic
317	C₂×D₄	—	101	4	no	—
318	C₂×D₄	—	101	4	no	—
319	C₂×D₄	—	101	4	no	—
320	C₂×D₄	—	101	1	no	—
321	C₂×D₄	—	101	2	no	—
322	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
323	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
324	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
325	C₂²×C₄	—	101	4	no	—
326	C₂²×C₄	—	101	4	no	—
327	C₂²×C₄	—	101	4	no	—
328	C₂²×C₄	—	101	1	no	—
329	C₂²×C₄	—	101	1	no	—
330	C₂²×C₄	—	101	2	no	—
331	C₂²×C₄	—	101	2	no	—
332	C₂²×C₄	—	101	1	no	—
333	C₂²×C₄	—	101	2	no	—
334	C₂²×C₄	C₂²×D₁₀₁	1	4	yes	—
335	C₄⋊C₄	—	101	2	no	—
336	C₄⋊C₄	—	101	2	no	—
337	C₄⋊C₄	—	101	4	no	—
338	C₄⋊C₄	—	101	4	no	—
339	C₄⋊C₄	—	101	2	no	—
340	C₄⋊C₄	—	101	2	no	—
341	C₄⋊C₄	—	101	2	no	—
342	C₄⋊C₄	—	101	4	no	—
343	C₄⋊C₄	—	101	2	no	—
344	C₄⋊C₄	—	101	1	no	—
345	C₄⋊C₄	—	101	2	no	—
346	C₄⋊C₄	—	101	1	no	—
347	C₄⋊C₄	—	101	2	no	—
348	C₄⋊C₄	—	101	2	no	—
349	C₄⋊C₄	—	101	4	no	—
350	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
351	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
352	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
353	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
354	C₂²⋊C₄	—	101	4	no	—
355	C₂²⋊C₄	—	101	4	no	—
356	C₂²⋊C₄	—	101	4	no	—
357	C₂²⋊C₄	—	101	2	no	—
358	C₂²⋊C₄	—	101	2	no	—
359	C₂²⋊C₄	—	101	2	no	—
360	C₂²⋊C₄	—	101	2	no	—
361	C₂²⋊C₄	—	101	4	no	—
362	C₂²⋊C₄	—	101	2	no	—
363	C₂²⋊C₄	C₂²×D₁₀₁	1	4	yes	—
364	C₂²⋊C₄	C₂²×D₁₀₁	1	4	yes	—
365	C₂²⋊C₄	C₂²×D₁₀₁	1	4	yes	—
366	C₄²	—	101	2	no	—
367	C₄²	—	101	1	no	—
368	C₄²	—	101	1	no	—
369	C₄²	—	101	2	no	—
370	C₄²	—	101	1	no	—
371	C₄²	—	101	2	no	—
372	C₄²	—	101	4	no	—
373	C₄²	C₂²×D₁₀₁	1	2	yes	—
374	C₄²	C₂²×D₁₀₁	1	1	yes	characteristic
375	C₄²	C₂²×D₁₀₁	1	2	yes	—
376	C₂³	—	101	1	no	—
377	C₂³	—	101	2	no	—
378	C₂³	C₂³×D₁₀₁	1	4	yes	—
379	Q₈	—	2	2	no	—
380	Q₈	—	2	2	no	—
381	Q₈	—	101	4	no	—
382	Q₈	—	404	4	no	—
383	Q₈	—	404	2	no	—
384	Q₈	—	202	4	no	—
385	D₄	—	2	4	no	—
386	D₄	—	2	4	no	—
387	D₄	—	4	2	no	—
388	D₄	—	404	4	no	—
389	D₄	—	202	4	no	—
390	D₄	—	202	8	no	—
391	D₄	—	202	8	no	—
392	D₄	—	202	2	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	—	101	2	no	—
395	C₂×C₄	—	101	1	no	—
396	C₂×C₄	—	101	1	no	—
397	C₂×C₄	—	101	1	no	—
398	C₂×C₄	—	101	2	no	—
399	C₂×C₄	—	101	4	no	—
400	C₂×C₄	—	101	2	no	—
401	C₂×C₄	—	404	4	no	—
402	C₂×C₄	—	404	4	no	—
403	C₂×C₄	—	202	4	no	—
404	C₂×C₄	—	202	4	no	—
405	C₂×C₄	—	202	2	no	—
406	C₂×C₄	—	202	8	no	—
407	C₂×C₄	—	202	2	no	—
408	C₂×C₄	—	202	4	no	—
409	C₂×C₄	—	202	2	no	—
410	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
411	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
412	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
413	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
414	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
415	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
416	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
417	C₂²	—	2	4	no	—
418	C₂²	—	2	4	no	—
419	C₂²	—	2	4	no	—
420	C₂²	—	101	2	no	—
421	C₂²	—	202	2	no	—
422	C₂²	—	202	2	no	—
423	C₂²	—	202	2	no	—
424	C₂²	—	202	1	no	—
425	C₂²	—	202	1	no	—
426	C₂²	C₂⁴×D₁₀₁	1	1	yes	characteristic
427	C₄	—	2	2	no	—
428	C₄	—	2	2	no	—
429	C₄	—	2	2	no	—
430	C₄	—	2	1	no	—
431	C₄	—	2	2	no	—
432	C₄	—	101	4	no	—
433	C₄	—	202	2	no	—
434	C₄	—	202	1	no	—
435	C₄	—	202	1	no	—
436	C₄	—	202	4	no	—
437	C₄	—	202	2	no	—
438	C₄	—	202	1	no	—
439	C₄	#41×D₁₀₁	1	2	yes	—
440	C₄	#15692302	1	2	yes	—
441	C₂	—	4	4	no	—
442	C₂	—	404	2	no	—
443	C₂	—	202	2	no	—
444	C₂	C₂×#41×D₁₀₁	1	1	yes	characteristic
445	C₂	H(5,𝔽₂)×D₁₀₁	1	1	yes	characteristic
446	C₂	C₂×#15692302	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₀₁
commutator, socle, cosocle	C₂²×C₁₀₁	C₂⁵
Fitting	#559×C₁₀₁	C₂
hypercenter	#559	D₁₀₁
hypocenter	C₁₀₁	#3522
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ #559

Complements

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

N	H ≅ G/N	type
1. #20265909	C₂	semidirect
2. Q₈×Dic₂₀₂	C₂	semidirect
3. #20265887	C₂	semidirect
4. #20265886	C₂	semidirect
5. #20265847	C₂	semidirect
6. #20265835	C₂	semidirect
7. #20265832	C₂	semidirect
8. #20265825	C₂	semidirect
9. #20265796	C₂	semidirect
10. #20265795	C₂	semidirect
11. #20265725	C₂	semidirect
12. #20265724	C₂	semidirect
13. #20265714	C₂	semidirect
14. #20265706	C₂	semidirect
15. #20265656	C₂	semidirect
16. C₄×Q₈×D₁₀₁	C₂	semidirect
17. #559×C₁₀₁	C₂	semidirect
192. Dic₂₀₂	#41	semidirect
224. C₁₀₁	#3522	semidirect
226. #559	D₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
#20265909	2
Q₈×Dic₂₀₂	2
#20265887	2
#20265886	2
#20265847	2
#20265835	2
#20265832	2
#20265825	2
#20265796	2
#20265795	2
#20265725	2
#20265724	2
#20265714	2
#20265706	2
#20265656	2
C₄×Q₈×D₁₀₁	2
#559×C₁₀₁	2
#3522	101