Subgroups — #27209922

Order 13184.

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	#20268628	C₂	1	1	yes	maximal, characteristic, complemented
2	H(5,𝔽₂)×D₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#20268600	C₂	1	3	yes	maximal, complemented
4	#20268599	C₂	1	1	yes	maximal, characteristic, complemented
5	#20268597	C₂	1	3	yes	maximal, complemented
6	#20268596	C₂	1	1	yes	maximal, characteristic, complemented
7	#20268595	C₂	1	3	yes	maximal, complemented
8	#20268594	C₂	1	1	yes	maximal, characteristic, complemented
9	#20268593	C₂	1	3	yes	maximal, complemented
10	#20268590	C₂	1	3	yes	maximal, complemented
11	#20268588	C₂	1	3	yes	maximal, complemented
12	C₂×#15693048	C₂	1	3	yes	maximal, complemented
13	AGL(1,ℤ/8)×D₁₀₃	C₂	1	3	yes	maximal, complemented
14	#20268556	C₂	1	1	yes	maximal, characteristic, complemented
15	#577×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
16	#15693069	—	2	1	no	—
17	#15693069	C₂²	1	3	yes	complemented
18	#15693067	—	2	1	no	—
19	#15693067	—	2	3	no	—
20	#15693067	C₂²	1	1	yes	characteristic, complemented
21	#15693067	C₂²	1	1	yes	characteristic, complemented
22	#15693067	C₂²	1	3	yes	complemented
23	#15693067	C₂²	1	3	yes	complemented
24	#15693066	—	2	3	no	—
25	#15693066	C₂²	1	3	yes	complemented
26	C₂×#13110106	—	2	1	no	—
27	C₂×#13110106	C₂²	1	3	yes	complemented
28	#41×D₁₀₃	—	2	3	no	—
29	#41×D₁₀₃	—	2	1	no	—
30	#41×D₁₀₃	C₂²	1	1	yes	characteristic
31	#41×D₁₀₃	C₂²	1	3	yes	complemented
32	#41×D₁₀₃	C₂²	1	3	yes	complemented
33	C₂×D₄×D₁₀₃	—	2	3	no	—
34	C₂×D₄×D₁₀₃	C₂²	1	3	yes	complemented
35	#15693053	C₂²	1	3	yes	complemented
36	#15693053	C₂²	1	3	yes	complemented
37	#15693052	C₂²	1	3	yes	complemented
38	#15693050	C₂²	1	1	yes	characteristic, complemented
39	#15693050	C₂²	1	3	yes	complemented
40	#15693049	C₂²	1	3	yes	complemented
41	#15693049	C₂²	1	3	yes	complemented
42	#15693048	C₂²	1	6	yes	complemented
43	#15693048	C₂²	1	3	yes	complemented
44	#15693048	C₂²	1	6	yes	complemented
45	#15693048	C₂²	1	6	yes	complemented
46	#15693048	C₂²	1	3	yes	complemented
47	#15693047	C₂²	1	3	yes	complemented
48	#15693046	C₂²	1	3	yes	complemented
49	#15693046	C₂²	1	3	yes	complemented
50	#15693045	C₂²	1	3	yes	complemented
51	#15693045	C₂²	1	3	yes	complemented
52	#15693044	C₂²	1	6	yes	complemented
53	#15693043	C₂²	1	3	yes	complemented
54	#15693042	C₂²	1	6	yes	complemented
55	#15693041	C₂²	1	3	yes	complemented
56	#15693041	C₂²	1	3	yes	complemented
57	C₂×#13110092	C₂²	1	3	yes	complemented
58	SD₁₆×D₁₀₃	C₂²	1	6	yes	complemented
59	C₂×D₈₂₄	C₂²	1	3	yes	complemented
60	C₂×#13110090	C₂²	1	3	yes	complemented
61	D₈×D₁₀₃	C₂²	1	6	yes	complemented
62	#15693029	C₂²	1	3	yes	complemented
63	#15693028	C₂²	1	1	yes	characteristic, complemented
64	#15693027	C₂²	1	3	yes	complemented
65	C₂×#13110088	C₂²	1	3	yes	complemented
66	M₁₆×D₁₀₃	C₂²	1	3	yes	complemented
67	2₋¹⁺⁴×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
68	H(5,𝔽₂)×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
69	#137×C₁₀₃	C₂²	1	3	yes	complemented
70	AGL(1,ℤ/8)×C₁₀₃	C₂²	1	3	yes	complemented
71	#135×C₁₀₃	C₂²	1	3	yes	complemented
72	C₂×SD₁₆×C₁₀₃	C₂²	1	3	yes	complemented
73	#131×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
74	C₂³×D₁₀₃	—	2	3	no	—
75	#13110106	—	2	1	no	—
76	#13110106	—	2	1	no	—
77	#13110106	—	2	3	no	—
78	#13110106	—	2	3	no	—
79	#13110106	—	2	3	no	—
80	#13110106	D₄	1	1	yes	characteristic
81	#13110106	C₂³	1	3	yes	—
82	#13110106	C₂³	1	3	yes	—
83	#13110106	C₂³	1	6	yes	complemented
84	#13110105	—	2	6	no	—
85	#13110105	—	2	3	no	—
86	#13110105	—	2	3	no	—
87	#13110105	—	2	3	no	—
88	#13110105	—	2	3	no	—
89	#13110105	C₂³	1	3	yes	—
90	#13110105	C₂³	1	3	yes	—
91	#13110105	C₂³	1	3	yes	complemented
92	#13110104	—	2	3	no	—
93	#13110104	—	2	3	no	—
94	#13110104	—	2	3	no	—
95	#13110104	D₄	1	3	yes	—
96	#13110104	C₂³	1	1	yes	characteristic
97	#13110104	C₂³	1	3	yes	—
98	Q₈×D₁₀₃	—	2	3	no	—
99	Q₈×D₁₀₃	D₄	1	1	yes	characteristic
100	Q₈×D₁₀₃	C₂³	1	1	yes	characteristic
101	Q₈×D₁₀₃	C₂³	1	3	yes	complemented
102	C₂×D₄₁₂	—	2	3	no	—
103	C₂×D₄₁₂	—	2	3	no	—
104	C₂×D₄₁₂	—	2	3	no	—
105	C₂×D₄₁₂	C₂³	1	3	yes	—
106	C₂×D₄₁₂	C₂³	1	3	yes	complemented
107	C₂×C₂²⋊D₁₀₃	—	2	6	no	—
108	C₂×C₂²⋊D₁₀₃	—	2	3	no	—
109	D₄×D₁₀₃	—	2	3	no	—
110	D₄×D₁₀₃	—	2	3	no	—
111	D₄×D₁₀₃	—	2	3	no	—
112	D₄×D₁₀₃	—	2	3	no	—
113	D₄×D₁₀₃	—	2	6	no	—
114	D₄×D₁₀₃	—	2	6	no	—
115	D₄×D₁₀₃	—	2	3	no	—
116	D₄×D₁₀₃	—	2	3	no	—
117	D₄×D₁₀₃	—	2	3	no	—
118	D₄×D₁₀₃	D₄	1	3	yes	—
119	D₄×D₁₀₃	C₂³	1	3	yes	—
120	D₄×D₁₀₃	C₂³	1	6	yes	—
121	D₄×D₁₀₃	C₂³	1	3	yes	complemented
122	C₂×C₄×D₁₀₃	—	2	3	no	—
123	C₂×C₄×D₁₀₃	—	2	3	no	—
124	C₂×C₄×D₁₀₃	—	2	3	no	—
125	C₂×C₄×D₁₀₃	C₂³	1	3	yes	—
126	Dic₄₁₂	C₂³	1	1	yes	characteristic, complemented
127	#13110095	C₂³	1	1	yes	characteristic, complemented
128	#13110095	C₂³	1	3	yes	complemented
129	#13110094	C₂³	1	3	yes	complemented
130	#13110094	C₂³	1	3	yes	complemented
131	#13110093	C₂³	1	3	yes	complemented
132	#13110093	C₂³	1	1	yes	characteristic, complemented
133	#13110092	C₂³	1	6	yes	complemented
134	#13110092	C₂³	1	3	yes	complemented
135	#13110092	C₂³	1	3	yes	complemented
136	D₈₂₄	C₂³	1	6	yes	complemented
137	D₈₂₄	C₂³	1	3	yes	complemented
138	#13110090	C₂³	1	3	yes	complemented
139	#13110090	C₂³	1	6	yes	complemented
140	#13110090	C₂³	1	3	yes	complemented
141	#13110089	C₂³	1	3	yes	complemented
142	#13110088	C₂³	1	3	yes	—
143	#13110088	C₂³	1	1	yes	characteristic
144	#13110088	C₂³	1	3	yes	complemented
145	#13110088	C₂³	1	3	yes	complemented
146	C₂×C₁₀₃⋊C₈	C₂³	1	3	yes	complemented
147	C₈×D₁₀₃	C₂³	1	6	yes	complemented
148	#41×C₁₀₃	—	2	1	no	—
149	#41×C₁₀₃	—	2	3	no	—
150	#41×C₁₀₃	C₂³	1	3	yes	—
151	#41×C₁₀₃	C₂³	1	1	yes	characteristic
152	#41×C₁₀₃	C₂³	1	3	yes	complemented
153	C₂×Q₈×C₁₀₃	—	2	1	no	—
154	C₂×Q₈×C₁₀₃	C₂³	1	3	yes	complemented
155	C₂×D₄×C₁₀₃	—	2	3	no	—
156	C₂×D₄×C₁₀₃	C₂³	1	3	yes	—
157	Q₁₆×C₁₀₃	C₂³	1	3	yes	complemented
158	SD₁₆×C₁₀₃	C₂³	1	3	yes	complemented
159	SD₁₆×C₁₀₃	C₂³	1	6	yes	complemented
160	SD₁₆×C₁₀₃	C₂³	1	1	yes	characteristic, complemented
161	D₈×C₁₀₃	C₂³	1	3	yes	complemented
162	M₁₆×C₁₀₃	C₂³	1	3	yes	complemented
163	C₂×C₈×C₁₀₃	C₂³	1	3	yes	complemented
164	C₂³×C₁₀₃	—	2	3	no	—
165	C₂²×D₁₀₃	—	2	3	no	—
166	C₂²×D₁₀₃	—	2	3	no	—
167	C₂²×D₁₀₃	—	2	3	no	—
168	C₂²×D₁₀₃	—	2	3	no	—
169	C₂²×D₁₀₃	—	2	6	no	—
170	C₂²×D₁₀₃	—	8	6	no	—
171	C₂²×D₁₀₃	C₂×D₄	1	3	yes	—
172	Q₈×C₁₀₃	—	2	3	no	—
173	Q₈×C₁₀₃	C₂×D₄	1	1	yes	characteristic
174	Q₈×C₁₀₃	C₂⁴	1	3	yes	—
175	Q₈×C₁₀₃	C₂⁴	1	1	yes	characteristic
176	D₄×C₁₀₃	—	2	3	no	—
177	D₄×C₁₀₃	—	2	3	no	—
178	D₄×C₁₀₃	—	2	3	no	—
179	D₄×C₁₀₃	C₂×D₄	1	3	yes	—
180	D₄×C₁₀₃	C₂⁴	1	1	yes	characteristic
181	D₄×C₁₀₃	C₂⁴	1	3	yes	—
182	C₂×C₄×C₁₀₃	—	2	3	no	—
183	C₂×C₄×C₁₀₃	—	2	3	no	—
184	C₂×C₄×C₁₀₃	—	2	3	no	—
185	C₂×C₄×C₁₀₃	C₂⁴	1	3	yes	—
186	C₂²⋊D₁₀₃	—	2	3	no	—
187	C₂²⋊D₁₀₃	—	2	3	no	—
188	C₂²⋊D₁₀₃	—	2	3	no	—
189	C₂²⋊D₁₀₃	—	2	1	no	—
190	C₂²⋊D₁₀₃	—	2	6	no	—
191	C₂²⋊D₁₀₃	—	2	3	no	—
192	C₂²⋊D₁₀₃	—	2	3	no	—
193	C₂²⋊D₁₀₃	C₂×D₄	1	6	yes	—
194	C₂×Dic₁₀₃	—	2	1	no	—
195	C₂×Dic₁₀₃	—	2	3	no	—
196	C₂×Dic₁₀₃	C₂×D₄	1	3	yes	—
197	D₄₁₂	—	2	3	no	—
198	D₄₁₂	—	2	3	no	—
199	D₄₁₂	—	2	6	no	—
200	D₄₁₂	—	2	3	no	—
201	D₄₁₂	—	2	3	no	—
202	D₄₁₂	C₂×D₄	1	3	yes	—
203	D₄₁₂	C₂⁴	1	3	yes	—
204	D₄₁₂	C₂⁴	1	3	yes	—
205	C₄×D₁₀₃	—	2	1	no	—
206	C₄×D₁₀₃	—	2	3	no	—
207	C₄×D₁₀₃	—	2	3	no	—
208	C₄×D₁₀₃	—	2	3	no	—
209	C₄×D₁₀₃	—	2	3	no	—
210	C₄×D₁₀₃	—	2	3	no	—
211	C₄×D₁₀₃	—	2	6	no	—
212	C₄×D₁₀₃	C₂×D₄	1	3	yes	—
213	C₄×D₁₀₃	C₂×D₄	1	3	yes	—
214	C₄×D₁₀₃	C₂⁴	1	3	yes	—
215	C₄×D₁₀₃	C₂⁴	1	1	yes	characteristic
216	Dic₂₀₆	—	2	3	no	—
217	Dic₂₀₆	—	2	1	no	—
218	Dic₂₀₆	C₂×D₄	1	3	yes	—
219	Dic₂₀₆	C₂⁴	1	1	yes	characteristic
220	Dic₂₀₆	C₂⁴	1	1	yes	characteristic
221	C₈×C₁₀₃	C₂⁴	1	1	yes	characteristic
222	C₈×C₁₀₃	C₂⁴	1	3	yes	—
223	C₁₀₃⋊C₈	C₂⁴	1	3	yes	—
224	C₁₀₃⋊C₈	C₂⁴	1	1	yes	characteristic
225	C₂²×C₁₀₃	—	2	1	no	—
226	C₂²×C₁₀₃	—	2	3	no	—
227	C₂²×C₁₀₃	—	8	3	no	—
228	C₂²×C₁₀₃	C₂²×D₄	1	3	yes	—
229	C₂×D₁₀₃	—	2	3	no	—
230	C₂×D₁₀₃	—	2	3	no	—
231	C₂×D₁₀₃	—	4	3	no	—
232	C₂×D₁₀₃	—	4	6	no	—
233	C₂×D₁₀₃	—	8	3	no	—
234	C₂×D₁₀₃	—	8	6	no	—
235	C₂×D₁₀₃	—	8	3	no	—
236	C₂×D₁₀₃	—	8	3	no	—
237	C₂×D₁₀₃	C₂²×D₄	1	1	yes	characteristic
238	C₂×D₁₀₃	C₂²×D₄	1	3	yes	—
239	C₄×C₁₀₃	—	2	1	no	—
240	C₄×C₁₀₃	—	2	3	no	—
241	C₄×C₁₀₃	C₂²×D₄	1	3	yes	—
242	C₄×C₁₀₃	C₂⁵	1	1	yes	characteristic
243	Dic₁₀₃	—	2	1	no	—
244	Dic₁₀₃	—	2	1	no	—
245	Dic₁₀₃	C₂²×D₄	1	3	yes	—
246	Dic₁₀₃	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₁₀₃	—	2	3	no	—
248	C₂×C₁₀₃	—	4	3	no	—
249	C₂×C₁₀₃	—	4	1	no	—
250	C₂×C₁₀₃	C₂³×D₄	1	1	yes	characteristic
251	D₁₀₃	—	2	1	no	—
252	D₁₀₃	—	2	3	no	—
253	D₁₀₃	—	4	3	no	—
254	D₁₀₃	—	4	3	no	—
255	#3585	—	103	1	no	maximal, Sylow
256	C₁₀₃	#3585	1	1	yes	characteristic, complemented, Sylow
257	#585	—	103	1	no	—
258	C₂×H(5,𝔽₂)	—	103	1	no	—
259	#577	—	103	1	no	—
260	#577	—	103	3	no	—
261	#577	—	103	3	no	—
262	#577	D₁₀₃	1	1	yes	characteristic, complemented
263	#576	—	103	1	no	—
264	#576	—	103	3	no	—
265	#576	—	103	3	no	—
266	#576	—	103	1	no	—
267	#575	—	103	3	no	—
268	#575	—	103	3	no	—
269	C₂×AGL(1,ℤ/8)	—	103	3	no	—
270	C₂×AGL(1,ℤ/8)	—	103	3	no	—
271	#568	—	103	1	no	—
272	2₋¹⁺⁴	—	103	3	no	—
273	2₋¹⁺⁴	—	206	1	no	—
274	2₋¹⁺⁴	C₂×D₁₀₃	1	1	yes	characteristic, complemented
275	H(5,𝔽₂)	—	103	3	no	—
276	H(5,𝔽₂)	—	103	1	no	—
277	H(5,𝔽₂)	—	103	1	no	—
278	H(5,𝔽₂)	—	103	3	no	—
279	H(5,𝔽₂)	—	103	3	no	—
280	H(5,𝔽₂)	—	206	3	no	—
281	H(5,𝔽₂)	—	206	3	no	—
282	H(5,𝔽₂)	—	206	1	no	—
283	H(5,𝔽₂)	C₂×D₁₀₃	1	1	yes	characteristic, complemented
284	C₂×#41	—	103	1	no	—
285	C₂×#41	—	103	3	no	—
286	C₂×#41	—	103	3	no	—
287	C₂×#41	—	103	3	no	—
288	C₂×#41	—	206	1	no	—
289	C₂×#41	—	206	1	no	—
290	C₂×#41	—	206	3	no	—
291	C₂²×D₄	—	103	3	no	—
292	C₂²×D₄	—	206	3	no	—
293	#137	—	103	3	no	—
294	#137	—	103	3	no	—
295	#137	—	103	3	no	—
296	#137	—	103	1	no	—
297	#137	—	103	3	no	—
298	#137	C₂×D₁₀₃	1	3	yes	complemented
299	AGL(1,ℤ/8)	—	103	3	no	—
300	AGL(1,ℤ/8)	—	103	3	no	—
301	AGL(1,ℤ/8)	—	103	3	no	—
302	AGL(1,ℤ/8)	—	103	6	no	—
303	AGL(1,ℤ/8)	—	103	3	no	—
304	AGL(1,ℤ/8)	—	103	6	no	—
305	AGL(1,ℤ/8)	—	103	6	no	—
306	AGL(1,ℤ/8)	—	103	3	no	—
307	AGL(1,ℤ/8)	—	103	3	no	—
308	AGL(1,ℤ/8)	—	103	3	no	—
309	AGL(1,ℤ/8)	—	103	3	no	—
310	AGL(1,ℤ/8)	—	103	3	no	—
311	AGL(1,ℤ/8)	C₂×D₁₀₃	1	3	yes	complemented
312	#135	—	103	3	no	—
313	#135	—	103	3	no	—
314	#135	—	103	6	no	—
315	#135	—	103	6	no	—
316	#135	—	103	3	no	—
317	#135	C₂×D₁₀₃	1	3	yes	complemented
318	C₂×SD₁₆	—	103	3	no	—
319	C₂×SD₁₆	—	103	6	no	—
320	C₂×SD₁₆	C₂×D₁₀₃	1	3	yes	complemented
321	C₂×D₈	—	103	3	no	—
322	C₂×D₈	—	103	6	no	—
323	C₂×D₈	—	103	3	no	—
324	#131	—	103	1	no	—
325	#131	—	103	3	no	—
326	#131	—	103	3	no	—
327	#131	C₂×D₁₀₃	1	1	yes	characteristic, complemented
328	C₂×M₁₆	—	103	3	no	—
329	C₂×M₁₆	—	103	3	no	—
330	C₂⁴	—	206	3	no	—
331	#41	—	2	1	no	—
332	#41	—	2	3	no	—
333	#41	—	103	1	no	—
334	#41	—	103	3	no	—
335	#41	—	103	3	no	—
336	#41	—	103	3	no	—
337	#41	—	103	3	no	—
338	#41	—	103	6	no	—
339	#41	—	103	3	no	—
340	#41	—	103	1	no	—
341	#41	—	103	3	no	—
342	#41	—	103	3	no	—
343	#41	—	206	3	no	—
344	#41	—	206	3	no	—
345	#41	—	206	6	no	—
346	#41	—	206	3	no	—
347	#41	—	206	3	no	—
348	#41	—	206	3	no	—
349	#41	—	206	3	no	—
350	#41	—	206	3	no	—
351	#41	—	206	3	no	—
352	#41	—	206	3	no	—
353	#41	—	206	3	no	—
354	#41	—	206	1	no	—
355	#41	—	206	1	no	—
356	#41	C₂²×D₁₀₃	1	3	yes	—
357	#41	C₂²×D₁₀₃	1	1	yes	characteristic
358	#41	C₂²×D₁₀₃	1	3	yes	complemented
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	103	1	no	—
361	C₂×Q₈	—	103	1	no	—
362	C₂×Q₈	—	103	3	no	—
363	C₂×Q₈	—	206	3	no	—
364	C₂×Q₈	C₂²×D₁₀₃	1	3	yes	complemented
365	C₂×D₄	—	2	3	no	—
366	C₂×D₄	—	103	3	no	—
367	C₂×D₄	—	103	6	no	—
368	C₂×D₄	—	103	3	no	—
369	C₂×D₄	—	103	3	no	—
370	C₂×D₄	—	103	3	no	—
371	C₂×D₄	—	103	3	no	—
372	C₂×D₄	—	206	3	no	—
373	C₂×D₄	—	206	3	no	—
374	C₂×D₄	—	206	3	no	—
375	C₂×D₄	—	206	3	no	—
376	C₂×D₄	—	206	3	no	—
377	C₂×D₄	—	206	3	no	—
378	C₂×D₄	—	206	6	no	—
379	C₂×D₄	—	206	3	no	—
380	C₂×D₄	—	206	6	no	—
381	C₂×D₄	—	206	3	no	—
382	C₂×D₄	—	206	3	no	—
383	C₂×D₄	—	206	6	no	—
384	C₂×D₄	—	206	3	no	—
385	C₂×D₄	—	206	3	no	—
386	C₂×D₄	C₂²×D₁₀₃	1	3	yes	—
387	C₂²×C₄	—	103	3	no	—
388	C₂²×C₄	—	206	3	no	—
389	C₂²×C₄	—	206	3	no	—
390	C₂²×C₄	—	206	3	no	—
391	Q₁₆	—	103	1	no	—
392	Q₁₆	—	103	3	no	—
393	Q₁₆	—	103	1	no	—
394	Q₁₆	C₂²×D₁₀₃	1	3	yes	complemented
395	SD₁₆	—	103	6	no	—
396	SD₁₆	—	103	3	no	—
397	SD₁₆	—	103	3	no	—
398	SD₁₆	—	103	3	no	—
399	SD₁₆	—	103	1	no	—
400	SD₁₆	—	103	3	no	—
401	SD₁₆	—	103	3	no	—
402	SD₁₆	C₂²×D₁₀₃	1	6	yes	complemented
403	SD₁₆	C₂²×D₁₀₃	1	3	yes	complemented
404	SD₁₆	C₂²×D₁₀₃	1	1	yes	characteristic, complemented
405	D₈	—	103	6	no	—
406	D₈	—	103	3	no	—
407	D₈	—	103	3	no	—
408	D₈	—	103	6	no	—
409	D₈	—	103	3	no	—
410	D₈	C₂²×D₁₀₃	1	3	yes	complemented
411	M₁₆	—	103	3	no	—
412	M₁₆	—	103	3	no	—
413	M₁₆	—	103	1	no	—
414	M₁₆	—	103	3	no	—
415	M₁₆	—	103	3	no	—
416	M₁₆	C₂²×D₁₀₃	1	3	yes	complemented
417	C₂×C₈	—	103	3	no	—
418	C₂×C₈	—	103	6	no	—
419	C₂×C₈	C₂²×D₁₀₃	1	3	yes	complemented
420	C₂³	—	2	3	no	—
421	C₂³	—	824	6	no	—
422	C₂³	—	103	3	no	—
423	C₂³	—	206	3	no	—
424	C₂³	—	206	6	no	—
425	C₂³	—	206	3	no	—
426	C₂³	—	206	3	no	—
427	C₂³	—	206	3	no	—
428	Q₈	—	2	3	no	—
429	Q₈	—	103	3	no	—
430	Q₈	—	103	1	no	—
431	Q₈	—	103	1	no	—
432	Q₈	—	206	3	no	—
433	Q₈	—	206	1	no	—
434	Q₈	D₄×D₁₀₃	1	1	yes	characteristic
435	Q₈	C₂³×D₁₀₃	1	3	yes	—
436	Q₈	C₂³×D₁₀₃	1	1	yes	characteristic
437	D₄	—	2	3	no	—
438	D₄	—	2	3	no	—
439	D₄	—	2	3	no	—
440	D₄	—	103	6	no	—
441	D₄	—	103	3	no	—
442	D₄	—	103	3	no	—
443	D₄	—	103	3	no	—
444	D₄	—	206	3	no	—
445	D₄	—	206	3	no	—
446	D₄	—	206	6	no	—
447	D₄	—	206	3	no	—
448	D₄	—	206	6	no	—
449	D₄	—	206	3	no	—
450	D₄	—	206	3	no	—
451	D₄	—	206	1	no	—
452	D₄	—	206	3	no	—
453	D₄	—	206	3	no	—
454	D₄	—	206	3	no	—
455	D₄	—	206	3	no	—
456	D₄	D₄×D₁₀₃	1	3	yes	—
457	D₄	C₂³×D₁₀₃	1	1	yes	characteristic
458	D₄	C₂³×D₁₀₃	1	3	yes	—
459	C₂×C₄	—	2	3	no	—
460	C₂×C₄	—	2	3	no	—
461	C₂×C₄	—	2	3	no	—
462	C₂×C₄	—	103	3	no	—
463	C₂×C₄	—	103	3	no	—
464	C₂×C₄	—	103	3	no	—
465	C₂×C₄	—	103	3	no	—
466	C₂×C₄	—	103	1	no	—
467	C₂×C₄	—	206	3	no	—
468	C₂×C₄	—	206	3	no	—
469	C₂×C₄	—	206	6	no	—
470	C₂×C₄	—	206	1	no	—
471	C₂×C₄	—	206	3	no	—
472	C₂×C₄	—	206	1	no	—
473	C₂×C₄	—	206	3	no	—
474	C₂×C₄	—	206	3	no	—
475	C₂×C₄	—	206	3	no	—
476	C₂×C₄	C₂³×D₁₀₃	1	3	yes	—
477	C₈	—	103	1	no	—
478	C₈	—	103	3	no	—
479	C₈	C₂³×D₁₀₃	1	3	yes	—
480	C₈	C₂³×D₁₀₃	1	1	yes	characteristic
481	C₂²	—	2	1	no	—
482	C₂²	—	2	3	no	—
483	C₂²	—	8	3	no	—
484	C₂²	—	824	3	no	—
485	C₂²	—	824	3	no	—
486	C₂²	—	824	6	no	—
487	C₂²	—	824	3	no	—
488	C₂²	—	103	1	no	—
489	C₂²	—	103	3	no	—
490	C₂²	—	412	3	no	—
491	C₂²	—	412	6	no	—
492	C₂²	—	206	3	no	—
493	C₂²	—	206	3	no	—
494	C₂²	C₂×D₄×D₁₀₃	1	3	yes	—
495	C₄	—	2	1	no	—
496	C₄	—	2	3	no	—
497	C₄	—	103	1	no	—
498	C₄	—	103	3	no	—
499	C₄	—	206	1	no	—
500	C₄	—	206	1	no	—
501	C₄	C₂×D₄×D₁₀₃	1	3	yes	—
502	C₄	C₂⁴×D₁₀₃	1	1	yes	characteristic
503	C₂	—	2	3	no	—
504	C₂	—	4	3	no	—
505	C₂	—	4	1	no	—
506	C₂	—	412	3	no	—
507	C₂	—	412	3	no	—
508	C₂	—	206	3	no	—
509	C₂	—	206	1	no	—
510	C₂	C₂²×D₄×D₁₀₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₄×D₁₀₃
commutator, cosocle	C₄×C₁₀₃	C₂⁵
Frattini	C₄	C₂⁴×D₁₀₃
Fitting	#577×C₁₀₃	C₂
socle	C₂×C₁₀₃	C₂³×D₄
hypercenter	#577	D₁₀₃
hypocenter	C₁₀₃	#3585
LCS	G ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂ ◁ #41 ◁ #577

Complements

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

N	H ≅ G/N	type
1. #20268628	C₂	semidirect
2. H(5,𝔽₂)×D₁₀₃	C₂	semidirect
3. #20268600	C₂	semidirect
4. #20268599	C₂	semidirect
5. #20268597	C₂	semidirect
6. #20268596	C₂	semidirect
7. #20268595	C₂	semidirect
8. #20268594	C₂	semidirect
9. #20268593	C₂	semidirect
10. #20268590	C₂	semidirect
11. #20268588	C₂	semidirect
12. C₂×#15693048	C₂	semidirect
13. AGL(1,ℤ/8)×D₁₀₃	C₂	semidirect
14. #20268556	C₂	semidirect
15. #577×C₁₀₃	C₂	semidirect
17. #15693069	C₂²	semidirect
20. #15693067	C₂²	semidirect
21. #15693067	C₂²	semidirect
22. #15693067	C₂²	semidirect
23. #15693067	C₂²	semidirect
25. #15693066	C₂²	semidirect
27. C₂×#13110106	C₂²	semidirect
31. #41×D₁₀₃	C₂²	semidirect
32. #41×D₁₀₃	C₂²	semidirect
34. C₂×D₄×D₁₀₃	C₂²	semidirect
35. #15693053	C₂²	semidirect
36. #15693053	C₂²	semidirect
37. #15693052	C₂²	semidirect
38. #15693050	C₂²	semidirect
39. #15693050	C₂²	semidirect
40. #15693049	C₂²	semidirect
41. #15693049	C₂²	semidirect
42. #15693048	C₂²	semidirect
43. #15693048	C₂²	semidirect
44. #15693048	C₂²	semidirect
45. #15693048	C₂²	semidirect
46. #15693048	C₂²	semidirect
47. #15693047	C₂²	semidirect
48. #15693046	C₂²	semidirect
49. #15693046	C₂²	semidirect
50. #15693045	C₂²	semidirect
51. #15693045	C₂²	semidirect
52. #15693044	C₂²	semidirect
53. #15693043	C₂²	semidirect
54. #15693042	C₂²	semidirect
55. #15693041	C₂²	semidirect
56. #15693041	C₂²	semidirect
57. C₂×#13110092	C₂²	semidirect
58. SD₁₆×D₁₀₃	C₂²	semidirect
59. C₂×D₈₂₄	C₂²	semidirect
60. C₂×#13110090	C₂²	semidirect
61. D₈×D₁₀₃	C₂²	semidirect
62. #15693029	C₂²	semidirect
63. #15693028	C₂²	semidirect
64. #15693027	C₂²	semidirect
65. C₂×#13110088	C₂²	semidirect
66. M₁₆×D₁₀₃	C₂²	semidirect
67. 2₋¹⁺⁴×C₁₀₃	C₂²	semidirect
68. H(5,𝔽₂)×C₁₀₃	C₂²	semidirect
69. #137×C₁₀₃	C₂²	semidirect
70. AGL(1,ℤ/8)×C₁₀₃	C₂²	semidirect
71. #135×C₁₀₃	C₂²	semidirect
72. C₂×SD₁₆×C₁₀₃	C₂²	semidirect
73. #131×C₁₀₃	C₂²	semidirect
83. #13110106	C₂³	semidirect
91. #13110105	C₂³	semidirect
101. Q₈×D₁₀₃	C₂³	semidirect
106. C₂×D₄₁₂	C₂³	semidirect
121. D₄×D₁₀₃	C₂³	semidirect
126. Dic₄₁₂	C₂³	semidirect
127. #13110095	C₂³	semidirect
128. #13110095	C₂³	semidirect
129. #13110094	C₂³	semidirect
130. #13110094	C₂³	semidirect
131. #13110093	C₂³	semidirect
132. #13110093	C₂³	semidirect
133. #13110092	C₂³	semidirect
134. #13110092	C₂³	semidirect
135. #13110092	C₂³	semidirect
136. D₈₂₄	C₂³	semidirect
137. D₈₂₄	C₂³	semidirect
138. #13110090	C₂³	semidirect
139. #13110090	C₂³	semidirect
140. #13110090	C₂³	semidirect
141. #13110089	C₂³	semidirect
144. #13110088	C₂³	semidirect
145. #13110088	C₂³	semidirect
146. C₂×C₁₀₃⋊C₈	C₂³	semidirect
147. C₈×D₁₀₃	C₂³	semidirect
152. #41×C₁₀₃	C₂³	semidirect
154. C₂×Q₈×C₁₀₃	C₂³	semidirect
157. Q₁₆×C₁₀₃	C₂³	semidirect
158. SD₁₆×C₁₀₃	C₂³	semidirect
159. SD₁₆×C₁₀₃	C₂³	semidirect
160. SD₁₆×C₁₀₃	C₂³	semidirect
161. D₈×C₁₀₃	C₂³	semidirect
162. M₁₆×C₁₀₃	C₂³	semidirect
163. C₂×C₈×C₁₀₃	C₂³	semidirect
256. C₁₀₃	#3585	semidirect
262. #577	D₁₀₃	semidirect
274. 2₋¹⁺⁴	C₂×D₁₀₃	semidirect
283. H(5,𝔽₂)	C₂×D₁₀₃	semidirect
298. #137	C₂×D₁₀₃	semidirect
311. AGL(1,ℤ/8)	C₂×D₁₀₃	semidirect
317. #135	C₂×D₁₀₃	semidirect
320. C₂×SD₁₆	C₂×D₁₀₃	semidirect
327. #131	C₂×D₁₀₃	semidirect
358. #41	C₂²×D₁₀₃	semidirect
364. C₂×Q₈	C₂²×D₁₀₃	semidirect
394. Q₁₆	C₂²×D₁₀₃	semidirect
402. SD₁₆	C₂²×D₁₀₃	semidirect
403. SD₁₆	C₂²×D₁₀₃	semidirect
404. SD₁₆	C₂²×D₁₀₃	semidirect
410. D₈	C₂²×D₁₀₃	semidirect
416. M₁₆	C₂²×D₁₀₃	semidirect
419. C₂×C₈	C₂²×D₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
#20268628	2
H(5,𝔽₂)×D₁₀₃	2
#20268600	2
#20268599	2
#20268597	2
#20268596	2
#20268595	2
#20268594	2
#20268593	2
#20268590	2
#20268588	2
C₂×#15693048	2
AGL(1,ℤ/8)×D₁₀₃	2
#20268556	2
#577×C₁₀₃	2
#3585	103