Subgroups — #22623533

Order 9344.

1242 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989321	C₂	1	1	yes	maximal, characteristic, complemented
2	#17989291	C₂	1	2	yes	maximal, complemented
3	#17989282	C₂	1	2	yes	maximal, complemented
4	#17989280	C₂	1	2	yes	maximal, complemented
5	#17989268	C₂	1	1	yes	maximal, characteristic, complemented
6	#17989265	C₂	1	1	yes	maximal, characteristic, complemented
7	#17989264	C₂	1	2	yes	maximal, complemented
8	#17989226	C₂	1	2	yes	maximal, complemented
9	#17989224	C₂	1	2	yes	maximal, complemented
10	#17989219	C₂	1	1	yes	maximal, characteristic, complemented
11	#17989133	C₂	1	1	yes	maximal, characteristic, complemented
12	#17989117	C₂	1	2	yes	maximal, complemented
13	#17989115	C₂	1	2	yes	maximal, complemented
14	#17989096	C₂	1	2	yes	maximal, complemented
15	#17989094	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#11924027	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₂²⋊D₇₃	C₂	1	2	yes	maximal, complemented
18	C₄×D₄×D₇₃	C₂	1	2	yes	maximal, complemented
19	#525×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#11924028	C₂²	1	1	yes	characteristic, complemented
21	C₂×#11924027	C₂²	1	2	yes	—
22	C₂²×C₂²⋊D₇₃	C₂²	1	2	yes	—
23	C₂×D₄×D₇₃	C₂²	1	2	yes	—
24	C₂²×C₄×D₇₃	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₄×D₇₃	C₂²	1	2	yes	complemented
26	#14556589	C₂²	1	1	yes	characteristic, complemented
27	#14556587	C₂²	1	1	yes	characteristic
28	#14556586	C₂²	1	2	yes	complemented
29	#14556586	C₂²	1	2	yes	complemented
30	#14556584	C₂²	1	2	yes	complemented
31	#14556584	C₂²	1	2	yes	complemented
32	#14556581	C₂²	1	2	yes	complemented
33	#14556581	C₂²	1	2	yes	complemented
34	#14556580	C₂²	1	1	yes	characteristic, complemented
35	#14556578	C₂²	1	1	yes	characteristic, complemented
36	#14556577	C₂²	1	2	yes	complemented
37	#14556577	C₂²	1	2	yes	complemented
38	#14556576	C₂²	1	2	yes	complemented
39	#14556576	C₂²	1	2	yes	complemented
40	#14556575	C₂²	1	2	yes	complemented
41	#14556573	C₂²	1	2	yes	complemented
42	#14556573	C₂²	1	2	yes	complemented
43	#14556572	C₂²	1	2	yes	complemented
44	#14556572	C₂²	1	1	yes	characteristic, complemented
45	#14556572	C₂²	1	1	yes	characteristic, complemented
46	#14556569	C₂²	1	2	yes	complemented
47	#14556569	C₂²	1	2	yes	complemented
48	#14556568	C₂²	1	2	yes	complemented
49	#14556568	C₂²	1	2	yes	complemented
50	#14556567	C₂²	1	2	yes	complemented
51	#14556564	C₂²	1	2	yes	—
52	#14556564	C₂²	1	2	yes	complemented
53	#14556563	C₂²	1	2	yes	—
54	#14556563	C₂²	1	2	yes	complemented
55	#14556563	C₂²	1	2	yes	complemented
56	#14556563	C₂²	1	2	yes	complemented
57	#14556562	C₂²	1	2	yes	complemented
58	#14556561	C₂²	1	2	yes	—
59	#14556559	C₂²	1	1	yes	characteristic
60	#14556559	C₂²	1	2	yes	complemented
61	#14556559	C₂²	1	1	yes	characteristic, complemented
62	C₄×Dic₁₄₆	C₂²	1	2	yes	complemented
63	#14556556	C₂²	1	2	yes	complemented
64	C₄×D₂₉₂	C₂²	1	2	yes	complemented
65	D₄×Dic₇₃	C₂²	1	2	yes	complemented
66	D₄×Dic₇₃	C₂²	1	2	yes	complemented
67	#14556553	C₂²	1	2	yes	complemented
68	C₄×C₂²⋊D₇₃	C₂²	1	2	yes	—
69	C₄×C₂²⋊D₇₃	C₂²	1	2	yes	—
70	C₄×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
71	C₄×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
72	C₄×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
73	C₄×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
74	C₄×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
75	C₄×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
76	C₄×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
77	C₄×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
78	#14556551	C₂²	1	2	yes	—
79	#14556551	C₂²	1	2	yes	—
80	#14556551	C₂²	1	2	yes	complemented
81	#14556551	C₂²	1	2	yes	complemented
82	#14556550	C₂²	1	1	yes	characteristic, complemented
83	#14556549	C₂²	1	2	yes	complemented
84	#14556548	C₂²	1	2	yes	complemented
85	#14556547	C₂²	1	2	yes	complemented
86	#14556547	C₂²	1	2	yes	complemented
87	C₂×#11924007	C₂²	1	2	yes	complemented
88	C₄⋊C₄×D₇₃	C₂²	1	2	yes	complemented
89	C₂×C₂²⋊Dic₇₃	C₂²	1	2	yes	complemented
90	C₂×#11924005	C₂²	1	2	yes	complemented
91	C₂²⋊C₄×D₇₃	C₂²	1	2	yes	complemented
92	C₂²⋊C₄×D₇₃	C₂²	1	2	yes	complemented
93	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
94	C₂×C₄×Dic₇₃	C₂²	1	2	yes	complemented
95	C₄²×D₇₃	C₂²	1	2	yes	complemented
96	C₂×#41×C₇₃	C₂²	1	1	yes	characteristic, complemented
97	C₂³×C₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
98	#123×C₇₃	C₂²	1	1	yes	characteristic, complemented
99	#123×C₇₃	C₂²	1	1	yes	characteristic, complemented
100	C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	complemented
101	#121×C₇₃	C₂²	1	2	yes	complemented
102	#120×C₇₃	C₂²	1	1	yes	characteristic
103	#120×C₇₃	C₂²	1	1	yes	characteristic, complemented
104	C₄×D₄×C₇₃	C₂²	1	2	yes	complemented
105	C₄×D₄×C₇₃	C₂²	1	2	yes	complemented
106	#117×C₇₃	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₇₃	C₂³	1	1	yes	characteristic
108	C₂³×D₇₃	C₂³	1	2	yes	—
109	#11924028	—	4	2	no	—
110	#11924027	—	2	8	no	—
111	C₂×Dic₁₄₆	C₂³	1	2	yes	—
112	C₂×Dic₁₄₆	C₂³	1	1	yes	characteristic
113	C₂×D₂₉₂	C₂³	1	2	yes	—
114	C₂×D₂₉₂	C₂³	1	1	yes	characteristic
115	C₂×C₂²⋊D₇₃	—	2	8	no	—
116	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
117	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
118	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
119	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
120	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
121	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
122	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
123	D₄×D₇₃	—	2	8	no	—
124	C₂²×Dic₇₃	C₂³	1	2	yes	—
125	C₂²×Dic₇₃	C₂³	1	2	yes	—
126	C₂²×Dic₇₃	C₂³	1	2	yes	—
127	C₂²×Dic₇₃	C₂³	1	2	yes	—
128	C₂²×Dic₇₃	C₂³	1	1	yes	characteristic
129	C₂×C₄×D₇₃	—	4	2	no	—
130	C₂×C₄×D₇₃	—	4	4	no	—
131	C₂×C₄×D₇₃	C₂³	1	2	yes	—
132	C₂×C₄×D₇₃	C₂³	1	2	yes	—
133	C₂×C₄×D₇₃	C₂³	1	2	yes	—
134	C₂×C₄×D₇₃	C₂³	1	2	yes	—
135	C₂×C₄×D₇₃	C₂³	1	2	yes	—
136	C₂×C₄×D₇₃	C₂³	1	2	yes	—
137	C₂×C₄×D₇₃	C₂³	1	2	yes	—
138	C₄⋊Dic₇₃	C₂³	1	2	yes	—
139	C₄⋊Dic₇₃	C₂³	1	2	yes	—
140	C₄⋊Dic₇₃	C₂³	1	2	yes	—
141	#11924007	C₂³	1	2	yes	—
142	#11924007	C₂³	1	2	yes	—
143	#11924007	C₂³	1	2	yes	—
144	#11924007	C₂³	1	2	yes	—
145	#11924007	C₂³	1	2	yes	—
146	#11924007	C₂³	1	2	yes	—
147	#11924007	C₂³	1	2	yes	—
148	#11924007	C₂³	1	2	yes	—
149	#11924007	C₂³	1	2	yes	—
150	#11924007	C₂³	1	2	yes	—
151	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
152	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
153	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
154	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
155	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
156	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
157	C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
158	C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
159	#11924005	C₂³	1	2	yes	—
160	#11924005	C₂³	1	2	yes	—
161	#11924005	C₂³	1	2	yes	—
162	#11924005	C₂³	1	2	yes	—
163	#11924005	C₂³	1	2	yes	—
164	#11924005	C₂³	1	2	yes	—
165	#11924005	C₂³	1	2	yes	—
166	#11924005	C₂³	1	2	yes	—
167	#11924005	C₂³	1	2	yes	—
168	#11924005	C₂³	1	2	yes	—
169	C₄×Dic₇₃	C₂³	1	2	yes	—
170	C₄×Dic₇₃	C₂³	1	2	yes	—
171	C₄×Dic₇₃	C₂³	1	2	yes	—
172	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
173	C₄×Dic₇₃	C₂³	1	2	yes	—
174	C₄×Dic₇₃	C₂³	1	2	yes	—
175	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
176	C₄×Dic₇₃	C₂³	1	2	yes	—
177	C₂⁴×C₇₃	C₂³	1	1	yes	characteristic
178	#41×C₇₃	—	4	2	no	—
179	C₂×Q₈×C₇₃	C₂³	1	1	yes	characteristic
180	C₂×D₄×C₇₃	C₂³	1	2	yes	—
181	C₂×D₄×C₇₃	C₂³	1	2	yes	—
182	C₂×D₄×C₇₃	C₂³	1	1	yes	characteristic
183	C₂×D₄×C₇₃	C₂³	1	1	yes	characteristic
184	C₂×D₄×C₇₃	C₂³	1	1	yes	characteristic
185	C₂²×C₄×C₇₃	—	4	2	no	—
186	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
187	C₂²×C₄×C₇₃	C₂³	1	2	yes	—
188	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
189	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
190	C₂²×C₄×C₇₃	C₂³	1	2	yes	—
191	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
192	C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
193	C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
194	C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
195	C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
196	C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
197	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
198	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
199	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
200	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
201	C₄²×C₇₃	C₂³	1	2	yes	—
202	C₂³×C₇₃	—	2	4	no	—
203	C₂³×C₇₃	—	4	1	no	—
204	C₂³×C₇₃	C₂⁴	1	1	yes	characteristic
205	C₂³×C₇₃	C₂⁴	1	1	yes	characteristic
206	C₂³×C₇₃	C₂⁴	1	1	yes	characteristic
207	C₂³×C₇₃	C₂⁴	1	2	yes	—
208	C₂²×D₇₃	—	2	4	no	—
209	C₂²×D₇₃	—	2	4	no	—
210	C₂²×D₇₃	—	2	4	no	—
211	C₂²×D₇₃	—	4	1	no	—
212	C₂²×D₇₃	—	4	2	no	—
213	C₂²×D₇₃	C₂⁴	1	2	yes	—
214	C₂²×D₇₃	C₂⁴	1	2	yes	—
215	Q₈×C₇₃	—	4	1	no	—
216	D₄×C₇₃	—	2	4	no	—
217	D₄×C₇₃	—	2	4	no	—
218	D₄×C₇₃	—	4	1	no	—
219	D₄×C₇₃	—	4	1	no	—
220	D₄×C₇₃	—	4	1	no	—
221	C₂×C₄×C₇₃	—	2	2	no	—
222	C₂×C₄×C₇₃	—	2	4	no	—
223	C₂×C₄×C₇₃	—	2	2	no	—
224	C₂×C₄×C₇₃	—	2	2	no	—
225	C₂×C₄×C₇₃	—	4	1	no	—
226	C₂×C₄×C₇₃	—	4	2	no	—
227	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
228	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
229	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
230	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
231	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
232	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
233	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
234	C₂²⋊D₇₃	—	2	4	no	—
235	C₂²⋊D₇₃	—	2	4	no	—
236	C₂²⋊D₇₃	—	2	4	no	—
237	C₂²⋊D₇₃	—	2	4	no	—
238	C₂²⋊D₇₃	—	2	4	no	—
239	C₂²⋊D₇₃	—	4	2	no	—
240	C₂²⋊D₇₃	#41	1	8	yes	complemented
241	C₂×Dic₇₃	—	2	4	no	—
242	C₂×Dic₇₃	—	2	4	no	—
243	C₂×Dic₇₃	—	2	4	no	—
244	C₂×Dic₇₃	—	4	2	no	—
245	C₂×Dic₇₃	—	4	1	no	—
246	C₂×Dic₇₃	C₂⁴	1	2	yes	—
247	C₂×Dic₇₃	C₂⁴	1	2	yes	—
248	C₂×Dic₇₃	C₂⁴	1	2	yes	—
249	C₂×Dic₇₃	C₂⁴	1	2	yes	—
250	C₂×Dic₇₃	C₂⁴	1	2	yes	—
251	C₂×Dic₇₃	C₂⁴	1	2	yes	—
252	D₂₉₂	—	2	4	no	—
253	D₂₉₂	—	4	1	no	—
254	C₄×D₇₃	—	2	4	no	—
255	C₄×D₇₃	—	2	4	no	—
256	C₄×D₇₃	—	2	4	no	—
257	C₄×D₇₃	—	2	4	no	—
258	C₄×D₇₃	—	4	2	no	—
259	C₄×D₇₃	—	4	2	no	—
260	C₄×D₇₃	—	4	2	no	—
261	Dic₁₄₆	—	2	4	no	—
262	Dic₁₄₆	—	4	1	no	—
263	C₂²×C₇₃	—	2	2	no	—
264	C₂²×C₇₃	—	2	2	no	—
265	C₂²×C₇₃	—	2	2	no	—
266	C₂²×C₇₃	—	2	2	no	—
267	C₂²×C₇₃	—	2	2	no	—
268	C₂²×C₇₃	—	2	1	no	—
269	C₂²×C₇₃	—	2	1	no	—
270	C₂²×C₇₃	—	2	1	no	—
271	C₂²×C₇₃	—	4	4	no	—
272	C₂²×C₇₃	C₂×#41	1	4	yes	—
273	C₂²×C₇₃	C₂⁵	1	1	yes	characteristic
274	C₂×D₇₃	—	2	2	no	—
275	C₂×D₇₃	—	2	2	no	—
276	C₂×D₇₃	—	2	2	no	—
277	C₂×D₇₃	—	2	2	no	—
278	C₂×D₇₃	—	2	2	no	—
279	C₂×D₇₃	—	4	4	no	—
280	C₂×D₇₃	—	4	8	no	—
281	C₂×D₇₃	C₂×#41	1	4	yes	—
282	C₄×C₇₃	—	2	2	no	—
283	C₄×C₇₃	—	2	2	no	—
284	C₄×C₇₃	—	2	1	no	—
285	C₄×C₇₃	—	2	2	no	—
286	C₄×C₇₃	—	2	1	no	—
287	C₄×C₇₃	—	2	1	no	—
288	C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
289	Dic₇₃	—	2	2	no	—
290	Dic₇₃	—	2	2	no	—
291	Dic₇₃	—	2	2	no	—
292	Dic₇₃	—	2	2	no	—
293	Dic₇₃	—	2	2	no	—
294	Dic₇₃	C₂×#41	1	4	yes	—
295	C₂×C₇₃	—	2	4	no	—
296	C₂×C₇₃	—	4	1	no	—
297	C₂×C₇₃	—	4	1	no	—
298	C₂×C₇₃	—	4	1	no	—
299	C₂×C₇₃	C₂²×#41	1	2	yes	—
300	C₂×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
301	D₇₃	—	2	4	no	—
302	D₇₃	—	4	2	no	—
303	#3481	—	73	1	no	maximal, Sylow
304	C₇₃	#3481	1	1	yes	characteristic, complemented, Sylow
305	#559	—	73	1	no	—
306	#554	—	73	2	no	—
307	#553	—	73	2	no	—
308	#553	—	73	2	no	—
309	#551	—	73	1	no	—
310	#551	—	73	2	no	—
311	#551	—	73	1	no	—
312	#546	—	73	2	no	—
313	#546	—	73	2	no	—
314	D₄²	—	73	1	no	—
315	#532	—	73	1	no	—
316	#529	—	73	2	no	—
317	#529	—	73	2	no	—
318	#525	—	73	1	no	—
319	#525	—	73	2	no	—
320	#525	D₇₃	1	1	yes	characteristic, complemented
321	C₄×#41	—	73	2	no	—
322	C₂×C₄×D₄	—	73	2	no	—
323	C₂×C₄×D₄	—	73	2	no	—
324	C₂×#41	—	73	2	no	—
325	C₂×#41	—	73	1	no	—
326	C₂×#41	C₂×D₇₃	1	1	yes	characteristic, complemented
327	C₂²×D₄	—	73	2	no	—
328	C₂²×D₄	—	73	2	no	—
329	C₂³×C₄	—	73	2	no	—
330	C₂³×C₄	—	73	1	no	—
331	C₂³×C₄	C₂×D₇₃	1	1	yes	characteristic, complemented
332	C₄⋊Q₈	—	73	1	no	—
333	#127	—	73	1	no	—
334	#126	—	73	2	no	—
335	#126	—	73	2	no	—
336	#126	—	73	2	no	—
337	#126	—	73	2	no	—
338	#125	—	73	2	no	—
339	#125	—	73	2	no	—
340	#124	—	73	1	no	—
341	#124	—	73	1	no	—
342	#124	—	73	2	no	—
343	#124	—	73	2	no	—
344	#123	—	73	1	no	—
345	#123	—	73	1	no	—
346	#123	—	73	2	no	—
347	#123	—	73	2	no	—
348	#123	—	73	2	no	—
349	#123	—	73	2	no	—
350	#123	—	73	2	no	—
351	#123	—	73	2	no	—
352	#123	C₂×D₇₃	1	1	yes	characteristic, complemented
353	#123	C₂×D₇₃	1	1	yes	characteristic, complemented
354	C₂²⋊Q₈	—	73	2	no	—
355	C₂²⋊Q₈	—	73	2	no	—
356	C₂²⋊Q₈	—	73	2	no	—
357	C₂²⋊Q₈	—	73	2	no	—
358	C₂²⋊Q₈	—	73	2	no	—
359	C₂²⋊Q₈	C₂×D₇₃	1	2	yes	complemented
360	#121	—	73	2	no	—
361	#121	—	73	2	no	—
362	#121	—	73	2	no	—
363	#121	—	73	2	no	—
364	#121	—	73	2	no	—
365	#121	—	73	2	no	—
366	#121	—	73	2	no	—
367	#121	C₂×D₇₃	1	2	yes	complemented
368	#120	—	73	1	no	—
369	#120	—	73	2	no	—
370	#120	—	73	1	no	—
371	#120	—	73	2	no	—
372	#120	C₂×D₇₃	1	1	yes	characteristic
373	#120	C₂×D₇₃	1	1	yes	characteristic, complemented
374	C₄×Q₈	—	73	2	no	—
375	C₄×Q₈	—	73	2	no	—
376	C₄×D₄	—	73	2	no	—
377	C₄×D₄	—	73	2	no	—
378	C₄×D₄	—	73	2	no	—
379	C₄×D₄	—	73	2	no	—
380	C₄×D₄	—	73	2	no	—
381	C₄×D₄	—	73	2	no	—
382	C₄×D₄	—	73	2	no	—
383	C₄×D₄	—	73	2	no	—
384	C₄×D₄	—	73	2	no	—
385	C₄×D₄	—	73	2	no	—
386	C₄×D₄	—	73	2	no	—
387	C₄×D₄	—	73	2	no	—
388	C₄×D₄	—	73	2	no	—
389	C₄×D₄	—	73	2	no	—
390	C₄×D₄	—	73	2	no	—
391	C₄×D₄	—	73	2	no	—
392	C₄×D₄	—	73	2	no	—
393	C₄×D₄	—	73	2	no	—
394	C₄×D₄	C₂×D₇₃	1	2	yes	complemented
395	C₄×D₄	C₂×D₇₃	1	2	yes	complemented
396	#117	—	73	1	no	—
397	#117	—	73	2	no	—
398	#117	—	73	2	no	—
399	#117	—	73	2	no	—
400	#117	—	73	2	no	—
401	#117	C₂×D₇₃	1	1	yes	characteristic, complemented
402	C₂×C₄⋊C₄	—	73	2	no	—
403	C₂×C₄⋊C₄	—	73	2	no	—
404	C₂×C₂²⋊C₄	—	73	2	no	—
405	C₂×C₂²⋊C₄	—	73	2	no	—
406	C₂×C₂²⋊C₄	—	73	2	no	—
407	C₂×C₂²⋊C₄	—	73	2	no	—
408	C₂×C₄²	—	73	2	no	—
409	C₂×C₄²	—	73	1	no	—
410	C₂×C₄²	—	73	2	no	—
411	C₂⁴	—	73	1	no	—
412	C₂⁴	—	73	2	no	—
413	C₂⁴	C₂²×D₇₃	1	1	yes	characteristic
414	#41	—	4	2	no	—
415	#41	—	292	2	no	—
416	#41	—	146	8	no	—
417	C₂×Q₈	—	73	1	no	—
418	C₂×Q₈	—	73	2	no	—
419	C₂×Q₈	C₂²×D₇₃	1	1	yes	characteristic
420	C₂×D₄	—	73	2	no	—
421	C₂×D₄	—	73	2	no	—
422	C₂×D₄	—	73	2	no	—
423	C₂×D₄	—	73	2	no	—
424	C₂×D₄	—	73	2	no	—
425	C₂×D₄	—	73	2	no	—
426	C₂×D₄	—	73	2	no	—
427	C₂×D₄	—	73	1	no	—
428	C₂×D₄	—	73	2	no	—
429	C₂×D₄	—	146	8	no	—
430	C₂×D₄	—	146	8	no	—
431	C₂×D₄	C₂²×D₇₃	1	2	yes	—
432	C₂×D₄	C₂²×D₇₃	1	2	yes	—
433	C₂×D₄	C₂²×D₇₃	1	1	yes	characteristic
434	C₂×D₄	C₂²×D₇₃	1	1	yes	characteristic
435	C₂×D₄	C₂²×D₇₃	1	1	yes	characteristic
436	C₂²×C₄	—	4	2	no	—
437	C₂²×C₄	—	292	4	no	—
438	C₂²×C₄	—	292	2	no	—
439	C₂²×C₄	—	73	2	no	—
440	C₂²×C₄	—	73	1	no	—
441	C₂²×C₄	—	73	2	no	—
442	C₂²×C₄	—	73	2	no	—
443	C₂²×C₄	—	73	2	no	—
444	C₂²×C₄	—	73	2	no	—
445	C₂²×C₄	—	73	2	no	—
446	C₂²×C₄	—	73	2	no	—
447	C₂²×C₄	—	73	2	no	—
448	C₂²×C₄	—	73	2	no	—
449	C₂²×C₄	—	73	2	no	—
450	C₂²×C₄	—	73	2	no	—
451	C₂²×C₄	C₂²×D₇₃	1	2	yes	—
452	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
453	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
454	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
455	C₂²×C₄	C₂²×D₇₃	1	2	yes	—
456	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
457	C₄⋊C₄	—	73	2	no	—
458	C₄⋊C₄	—	73	2	no	—
459	C₄⋊C₄	—	73	2	no	—
460	C₄⋊C₄	—	73	2	no	—
461	C₄⋊C₄	—	73	2	no	—
462	C₄⋊C₄	—	73	2	no	—
463	C₄⋊C₄	—	73	2	no	—
464	C₄⋊C₄	—	73	2	no	—
465	C₄⋊C₄	—	73	2	no	—
466	C₄⋊C₄	—	73	2	no	—
467	C₄⋊C₄	—	73	2	no	—
468	C₄⋊C₄	—	73	2	no	—
469	C₄⋊C₄	—	73	2	no	—
470	C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
471	C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
472	C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
473	C₂²⋊C₄	—	73	2	no	—
474	C₂²⋊C₄	—	73	2	no	—
475	C₂²⋊C₄	—	73	2	no	—
476	C₂²⋊C₄	—	73	2	no	—
477	C₂²⋊C₄	—	73	2	no	—
478	C₂²⋊C₄	—	73	2	no	—
479	C₂²⋊C₄	—	73	1	no	—
480	C₂²⋊C₄	—	73	1	no	—
481	C₂²⋊C₄	—	73	2	no	—
482	C₂²⋊C₄	—	73	2	no	—
483	C₂²⋊C₄	—	73	2	no	—
484	C₂²⋊C₄	—	73	2	no	—
485	C₂²⋊C₄	—	73	2	no	—
486	C₂²⋊C₄	—	73	2	no	—
487	C₂²⋊C₄	—	73	2	no	—
488	C₂²⋊C₄	—	73	2	no	—
489	C₂²⋊C₄	—	73	2	no	—
490	C₂²⋊C₄	—	73	2	no	—
491	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
492	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
493	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
494	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
495	C₂²⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
496	C₂²⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
497	C₄²	—	73	1	no	—
498	C₄²	—	73	2	no	—
499	C₄²	—	73	2	no	—
500	C₄²	—	73	2	no	—
501	C₄²	—	73	2	no	—
502	C₄²	—	73	1	no	—
503	C₄²	—	73	2	no	—
504	C₄²	—	73	2	no	—
505	C₄²	C₂²×D₇₃	1	2	yes	—
506	C₂³	—	2	4	no	—
507	C₂³	—	4	1	no	—
508	C₂³	—	292	2	no	—
509	C₂³	—	292	1	no	—
510	C₂³	—	73	2	no	—
511	C₂³	—	73	2	no	—
512	C₂³	—	146	4	no	—
513	C₂³	—	146	4	no	—
514	C₂³	—	146	4	no	—
515	C₂³	C₂³×D₇₃	1	1	yes	characteristic
516	C₂³	C₂³×D₇₃	1	1	yes	characteristic
517	C₂³	C₂³×D₇₃	1	1	yes	characteristic
518	C₂³	C₂³×D₇₃	1	2	yes	—
519	Q₈	—	4	1	no	—
520	Q₈	—	292	1	no	—
521	Q₈	—	146	4	no	—
522	D₄	—	2	4	no	—
523	D₄	—	2	4	no	—
524	D₄	—	4	1	no	—
525	D₄	—	4	1	no	—
526	D₄	—	4	1	no	—
527	D₄	—	292	1	no	—
528	D₄	—	292	2	no	—
529	D₄	—	73	8	no	—
530	D₄	—	146	4	no	—
531	D₄	—	146	4	no	—
532	D₄	—	146	4	no	—
533	D₄	—	146	4	no	—
534	D₄	—	146	4	no	—
535	D₄	—	146	4	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	292	2	no	—
543	C₂×C₄	—	292	2	no	—
544	C₂×C₄	—	292	2	no	—
545	C₂×C₄	—	292	1	no	—
546	C₂×C₄	—	292	2	no	—
547	C₂×C₄	—	73	2	no	—
548	C₂×C₄	—	73	2	no	—
549	C₂×C₄	—	73	2	no	—
550	C₂×C₄	—	73	2	no	—
551	C₂×C₄	—	73	2	no	—
552	C₂×C₄	—	73	2	no	—
553	C₂×C₄	—	146	4	no	—
554	C₂×C₄	—	146	4	no	—
555	C₂×C₄	—	146	4	no	—
556	C₂×C₄	—	146	4	no	—
557	C₂×C₄	—	146	4	no	—
558	C₂×C₄	—	146	4	no	—
559	C₂×C₄	—	146	4	no	—
560	C₂×C₄	C₂³×D₇₃	1	2	yes	—
561	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
562	C₂×C₄	C₂³×D₇₃	1	2	yes	—
563	C₂×C₄	C₂³×D₇₃	1	2	yes	—
564	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
565	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
566	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	4	4	no	—
576	C₂²	—	292	8	no	—
577	C₂²	—	292	4	no	—
578	C₂²	—	73	4	no	—
579	C₂²	—	146	2	no	—
580	C₂²	—	146	2	no	—
581	C₂²	—	146	2	no	—
582	C₂²	—	146	2	no	—
583	C₂²	—	146	2	no	—
584	C₂²	#41×D₇₃	1	4	yes	—
585	C₂²	C₂⁴×D₇₃	1	1	yes	characteristic
586	C₄	—	2	2	no	—
587	C₄	—	2	2	no	—
588	C₄	—	2	2	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	73	4	no	—
593	C₄	—	146	2	no	—
594	C₄	—	146	2	no	—
595	C₄	—	146	2	no	—
596	C₄	—	146	2	no	—
597	C₄	—	146	2	no	—
598	C₄	#14556636	1	2	yes	—
599	C₂	—	2	4	no	—
600	C₂	—	4	1	no	—
601	C₂	—	4	1	no	—
602	C₂	—	4	1	no	—
603	C₂	—	292	2	no	—
604	C₂	—	146	4	no	—
605	C₂	C₂×#41×D₇₃	1	2	yes	—
606	C₂	C₂×#14556636	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₇₃
commutator, socle	C₂²×C₇₃	C₂⁵
Frattini	C₂²	C₂⁴×D₇₃
Fitting	#525×C₇₃	C₂
hypercenter	#525	D₇₃
hypocenter	C₇₃	#3481
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ #525

Complements

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

N	H ≅ G/N	type
1. #17989321	C₂	semidirect
2. #17989291	C₂	semidirect
3. #17989282	C₂	semidirect
4. #17989280	C₂	semidirect
5. #17989268	C₂	semidirect
6. #17989265	C₂	semidirect
7. #17989264	C₂	semidirect
8. #17989226	C₂	semidirect
9. #17989224	C₂	semidirect
10. #17989219	C₂	semidirect
11. #17989133	C₂	semidirect
12. #17989117	C₂	semidirect
13. #17989115	C₂	semidirect
14. #17989096	C₂	semidirect
15. #17989094	C₂	semidirect
16. C₄×#11924027	C₂	semidirect
17. C₂×C₄×C₂²⋊D₇₃	C₂	semidirect
18. C₄×D₄×D₇₃	C₂	semidirect
19. #525×C₇₃	C₂	semidirect
20. C₂×#11924028	C₂²	semidirect
24. C₂²×C₄×D₇₃	C₂²	semidirect
25. C₂²×C₄×D₇₃	C₂²	semidirect
26. #14556589	C₂²	semidirect
28. #14556586	C₂²	semidirect
29. #14556586	C₂²	semidirect
30. #14556584	C₂²	semidirect
31. #14556584	C₂²	semidirect
32. #14556581	C₂²	semidirect
33. #14556581	C₂²	semidirect
34. #14556580	C₂²	semidirect
35. #14556578	C₂²	semidirect
36. #14556577	C₂²	semidirect
37. #14556577	C₂²	semidirect
38. #14556576	C₂²	semidirect
39. #14556576	C₂²	semidirect
40. #14556575	C₂²	semidirect
41. #14556573	C₂²	semidirect
42. #14556573	C₂²	semidirect
43. #14556572	C₂²	semidirect
44. #14556572	C₂²	semidirect
45. #14556572	C₂²	semidirect
46. #14556569	C₂²	semidirect
47. #14556569	C₂²	semidirect
48. #14556568	C₂²	semidirect
49. #14556568	C₂²	semidirect
50. #14556567	C₂²	semidirect
52. #14556564	C₂²	semidirect
54. #14556563	C₂²	semidirect
55. #14556563	C₂²	semidirect
56. #14556563	C₂²	semidirect
57. #14556562	C₂²	semidirect
60. #14556559	C₂²	semidirect
61. #14556559	C₂²	semidirect
62. C₄×Dic₁₄₆	C₂²	semidirect
63. #14556556	C₂²	semidirect
64. C₄×D₂₉₂	C₂²	semidirect
65. D₄×Dic₇₃	C₂²	semidirect
66. D₄×Dic₇₃	C₂²	semidirect
67. #14556553	C₂²	semidirect
70. C₄×C₂²⋊D₇₃	C₂²	semidirect
71. C₄×C₂²⋊D₇₃	C₂²	semidirect
72. C₄×C₂²⋊D₇₃	C₂²	semidirect
73. C₄×C₂²⋊D₇₃	C₂²	semidirect
74. C₄×C₂²⋊D₇₃	C₂²	semidirect
75. C₄×C₂²⋊D₇₃	C₂²	semidirect
76. C₄×C₂²⋊D₇₃	C₂²	semidirect
77. C₄×C₂²⋊D₇₃	C₂²	semidirect
80. #14556551	C₂²	semidirect
81. #14556551	C₂²	semidirect
82. #14556550	C₂²	semidirect
83. #14556549	C₂²	semidirect
84. #14556548	C₂²	semidirect
85. #14556547	C₂²	semidirect
86. #14556547	C₂²	semidirect
87. C₂×#11924007	C₂²	semidirect
88. C₄⋊C₄×D₇₃	C₂²	semidirect
89. C₂×C₂²⋊Dic₇₃	C₂²	semidirect
90. C₂×#11924005	C₂²	semidirect
91. C₂²⋊C₄×D₇₃	C₂²	semidirect
92. C₂²⋊C₄×D₇₃	C₂²	semidirect
93. C₂×C₄×Dic₇₃	C₂²	semidirect
94. C₂×C₄×Dic₇₃	C₂²	semidirect
95. C₄²×D₇₃	C₂²	semidirect
96. C₂×#41×C₇₃	C₂²	semidirect
97. C₂³×C₄×C₇₃	C₂²	semidirect
98. #123×C₇₃	C₂²	semidirect
99. #123×C₇₃	C₂²	semidirect
100. C₂²⋊Q₈×C₇₃	C₂²	semidirect
101. #121×C₇₃	C₂²	semidirect
103. #120×C₇₃	C₂²	semidirect
104. C₄×D₄×C₇₃	C₂²	semidirect
105. C₄×D₄×C₇₃	C₂²	semidirect
106. #117×C₇₃	C₂²	semidirect
240. C₂²⋊D₇₃	#41	semidirect
304. C₇₃	#3481	semidirect
320. #525	D₇₃	semidirect
326. C₂×#41	C₂×D₇₃	semidirect
331. C₂³×C₄	C₂×D₇₃	semidirect
352. #123	C₂×D₇₃	semidirect
353. #123	C₂×D₇₃	semidirect
359. C₂²⋊Q₈	C₂×D₇₃	semidirect
367. #121	C₂×D₇₃	semidirect
373. #120	C₂×D₇₃	semidirect
394. C₄×D₄	C₂×D₇₃	semidirect
395. C₄×D₄	C₂×D₇₃	semidirect
401. #117	C₂×D₇₃	semidirect