Subgroups — C₁₇×#61204 #16918948

Order 4352.

2032 conjugacy classes of subgroups.

The subgroup lattice has 1226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×#3497	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3327	C₂	1	2	yes	maximal, complemented
4	C₁₇×#3326	C₂	1	2	yes	maximal, complemented
5	C₁₇×#3320	C₂	1	2	yes	maximal, complemented
6	C₁₇×#3317	C₂	1	2	yes	maximal, complemented
7	C₁₇×#3312	C₂	1	2	yes	maximal, complemented
8	C₁₇×#3309	C₂	1	2	yes	maximal, complemented
9	C₁₇×#3301	C₂	1	2	yes	maximal, complemented
10	C₁₇×#3300	C₂	1	2	yes	maximal, complemented
11	C₁₇×#3142	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#3099	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#3098	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₇×#479	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#3061	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₇×#3060	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₇×#3035	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₇×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₇×#3013	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₁₇×#137	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₇×#2935	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₇×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₇×#2898	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₇×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂×C₁₇×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
26	C₂×C₁₇×#137	C₂²	1	1	yes	characteristic
27	C₂×C₁₇×#135	C₂²	1	1	yes	characteristic
28	C₂×C₁₇×#135	C₂²	1	1	yes	characteristic
29	C₂×C₁₇×#131	C₂²	1	1	yes	characteristic
30	C₂×C₁₇×#131	C₂²	1	1	yes	characteristic
31	C₁₇×#553	—	2	2	no	—
32	C₁₇×#553	—	2	2	no	—
33	C₁₇×#553	C₂²	1	2	yes	—
34	C₁₇×#553	C₂²	1	2	yes	—
35	C₁₇×#552	C₂²	1	2	yes	—
36	C₁₇×#552	C₂²	1	2	yes	—
37	C₁₇×#550	—	2	1	no	—
38	C₁₇×#550	C₂²	1	2	yes	—
39	D₄×Q₈×C₁₇	—	2	1	no	—
40	D₄×Q₈×C₁₇	C₂²	1	2	yes	—
41	C₁₇×#548	—	2	1	no	—
42	C₁₇×#548	—	2	1	no	—
43	C₁₇×#548	C₂²	1	2	yes	—
44	C₁₇×#548	C₂²	1	2	yes	—
45	C₁₇×#541	—	2	1	no	—
46	C₁₇×#540	—	2	1	no	—
47	C₁₇×#537	—	2	2	no	—
48	C₁₇×#537	C₂²	1	1	yes	characteristic
49	C₁₇×#537	C₂²	1	1	yes	characteristic
50	C₁₇×#537	C₂²	1	1	yes	characteristic
51	C₁₇×#537	C₂²	1	1	yes	characteristic
52	C₁₇×#532	—	2	2	no	—
53	C₁₇×#532	C₂²	1	1	yes	characteristic
54	C₁₇×#532	C₂²	1	1	yes	characteristic
55	C₁₇×#529	—	2	1	no	—
56	C₁₇×#529	—	2	1	no	—
57	C₂×C₁₇×#125	C₂²	1	1	yes	characteristic
58	C₁₇×#520	C₂²	1	1	yes	characteristic
59	C₁₇×#520	C₂²	1	1	yes	characteristic
60	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
61	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
62	C₁₇×#491	C₂²	1	2	yes	—
63	C₁₇×#490	C₂²	1	2	yes	—
64	C₁₇×#488	C₂²	1	2	yes	—
65	C₁₇×#488	C₂²	1	2	yes	—
66	C₁₇×#485	C₂²	1	2	yes	—
67	C₁₇×#485	C₂²	1	2	yes	—
68	C₁₇×#484	C₂²	1	2	yes	—
69	C₁₇×#483	C₂²	1	2	yes	—
70	C₁₇×#482	C₂²	1	2	yes	—
71	C₁₇×#482	C₂²	1	2	yes	—
72	C₁₇×#481	C₂²	1	2	yes	—
73	C₁₇×#480	C₂²	1	2	yes	—
74	C₁₇×#479	C₂²	1	2	yes	—
75	C₁₇×#479	C₂²	1	2	yes	—
76	C₁₇×#479	C₂²	1	2	yes	—
77	C₁₇×#479	C₂²	1	2	yes	—
78	C₁₇×#470	C₂²	1	2	yes	—
79	C₁₇×#469	C₂²	1	2	yes	—
80	C₁₇×#468	C₂²	1	2	yes	—
81	C₁₇×#468	C₂²	1	2	yes	—
82	C₁₇×#467	C₂²	1	2	yes	—
83	C₁₇×#466	C₂²	1	2	yes	—
84	C₁₇×#465	C₂²	1	2	yes	—
85	C₁₇×#465	C₂²	1	2	yes	—
86	C₁₇×#464	C₂²	1	1	yes	characteristic
87	C₁₇×#464	C₂²	1	1	yes	characteristic
88	C₁₇×#463	C₂²	1	1	yes	characteristic
89	C₁₇×#463	C₂²	1	1	yes	characteristic
90	C₁₇×#462	C₂²	1	1	yes	characteristic
91	C₁₇×#461	C₂²	1	1	yes	characteristic
92	C₁₇×#460	C₂²	1	1	yes	characteristic
93	C₁₇×#459	C₂²	1	1	yes	characteristic
94	C₁₇×#452	C₂²	1	2	yes	—
95	C₁₇×#452	C₂²	1	2	yes	—
96	C₁₇×#451	C₂²	1	2	yes	—
97	C₁₇×#451	C₂²	1	2	yes	—
98	C₁₇×#449	C₂²	1	2	yes	—
99	C₁₇×#449	C₂²	1	2	yes	—
100	C₁₇×#448	C₂²	1	2	yes	—
101	C₁₇×#448	C₂²	1	2	yes	—
102	C₁₇×#441	C₂²	1	2	yes	—
103	C₁₇×#440	C₂²	1	2	yes	—
104	C₄×Q₁₆×C₁₇	C₂²	1	2	yes	—
105	C₄×SD₁₆×C₁₇	C₂²	1	2	yes	—
106	C₁₇×#436	C₂²	1	2	yes	—
107	C₁₇×#435	C₂²	1	2	yes	—
108	C₁₇×#435	C₂²	1	2	yes	—
109	C₈×D₄×C₁₇	C₂²	1	2	yes	—
110	C₁₇×#428	C₂²	1	1	yes	characteristic
111	C₂×C₁₇×#107	C₂²	1	1	yes	characteristic
112	C₂×C₁₇×#106	C₂²	1	1	yes	characteristic
113	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
114	C₁₇×#419	C₂²	1	2	yes	—
115	C₁₇×#419	C₂²	1	2	yes	—
116	C₁₇×#419	C₂²	1	1	yes	characteristic
117	C₁₇×#417	C₂²	1	1	yes	characteristic
118	C₁₇×#417	C₂²	1	1	yes	characteristic
119	C₁₇×#417	C₂²	1	2	yes	—
120	C₁₇×#417	C₂²	1	1	yes	characteristic
121	C₁₇×#417	C₂²	1	1	yes	characteristic
122	C₁₇×#417	C₂²	1	1	yes	characteristic
123	C₁₇×#417	C₂²	1	2	yes	—
124	C₁₇×#416	C₂²	1	1	yes	characteristic
125	C₁₇×#416	C₂²	1	1	yes	characteristic
126	C₁₇×#416	C₂²	1	2	yes	—
127	C₁₇×#416	C₂²	1	2	yes	—
128	C₂×C₁₇×#103	C₂²	1	1	yes	characteristic
129	C₂×C₁₇×#103	C₂²	1	1	yes	characteristic
130	C₂×C₁₇×#103	C₂²	1	2	yes	—
131	C₂×C₁₇×#103	C₂²	1	2	yes	—
132	C₁₇×#408	C₂²	1	1	yes	characteristic
133	C₁₇×#408	C₂²	1	1	yes	characteristic
134	C₄×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
135	C₁₇×2₋¹⁺⁴	—	2	4	no	—
136	C₁₇×2₋¹⁺⁴	—	2	4	no	—
137	C₁₇×2₋¹⁺⁴	—	4	2	no	—
138	C₁₇×2₋¹⁺⁴	—	4	2	no	—
139	C₂×#41×C₁₇	—	2	2	no	—
140	C₂×#41×C₁₇	—	2	2	no	—
141	C₂×#41×C₁₇	—	2	1	no	—
142	C₂×#41×C₁₇	—	2	1	no	—
143	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
144	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
145	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
146	C₂×#41×C₁₇	C₂³	1	2	yes	—
147	C₂×#41×C₁₇	C₂³	1	2	yes	—
148	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
149	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
150	C₂²×Q₈×C₁₇	—	2	1	no	—
151	C₂²×Q₈×C₁₇	—	2	1	no	—
152	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
153	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
154	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
155	C₁₇×#137	—	2	4	no	—
156	C₁₇×#135	—	4	2	no	—
157	C₁₇×#135	—	4	2	no	—
158	C₂×Q₁₆×C₁₇	C₂³	1	2	yes	—
159	C₂×Q₁₆×C₁₇	C₂³	1	1	yes	characteristic
160	C₂×Q₁₆×C₁₇	C₂³	1	1	yes	characteristic
161	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
162	C₂×SD₁₆×C₁₇	C₂³	1	1	yes	characteristic
163	C₂×SD₁₆×C₁₇	C₂³	1	1	yes	characteristic
164	C₂×SD₁₆×C₁₇	C₂³	1	1	yes	characteristic
165	C₂×SD₁₆×C₁₇	C₂³	1	1	yes	characteristic
166	C₂×D₈×C₁₇	C₂³	1	1	yes	characteristic
167	C₂×D₈×C₁₇	C₂³	1	1	yes	characteristic
168	C₁₇×#131	—	4	2	no	—
169	C₁₇×#131	—	4	2	no	—
170	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
171	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
172	C₂×M₁₆×C₁₇	C₂³	1	2	yes	—
173	C₂×M₁₆×C₁₇	C₂³	1	2	yes	—
174	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
175	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
176	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
177	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
178	C₁₇×C₄⋊Q₈	—	2	2	no	—
179	C₁₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
180	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
181	C₁₇×#127	—	2	2	no	—
182	C₁₇×#127	D₄	1	1	yes	characteristic
183	C₁₇×#127	C₂³	1	1	yes	characteristic
184	C₁₇×#126	—	2	2	no	—
185	C₁₇×#126	—	2	2	no	—
186	C₁₇×#126	—	2	2	no	—
187	C₁₇×#126	—	2	2	no	—
188	C₁₇×#125	—	2	2	no	—
189	C₁₇×#125	—	2	2	no	—
190	C₁₇×#125	—	2	1	no	—
191	C₁₇×#125	—	2	1	no	—
192	C₁₇×#125	C₂³	1	2	yes	—
193	C₁₇×#125	C₂³	1	2	yes	—
194	C₁₇×#124	—	2	2	no	—
195	C₁₇×#124	—	2	2	no	—
196	C₁₇×#124	D₄	1	1	yes	characteristic
197	C₁₇×#124	D₄	1	1	yes	characteristic
198	C₁₇×#124	C₂³	1	1	yes	characteristic
199	C₁₇×#124	C₂³	1	1	yes	characteristic
200	C₁₇×#123	—	2	2	no	—
201	C₁₇×#123	—	2	2	no	—
202	C₁₇×#123	—	2	2	no	—
203	C₁₇×#123	—	2	2	no	—
204	C₁₇×C₂²⋊Q₈	—	2	1	no	—
205	C₁₇×C₂²⋊Q₈	—	2	1	no	—
206	C₁₇×C₂²⋊Q₈	—	2	1	no	—
207	C₁₇×C₂²⋊Q₈	—	2	1	no	—
208	C₁₇×C₂²⋊Q₈	—	2	2	no	—
209	C₁₇×C₂²⋊Q₈	—	2	2	no	—
210	C₁₇×C₂²⋊Q₈	—	2	2	no	—
211	C₁₇×C₂²⋊Q₈	—	2	2	no	—
212	C₁₇×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₁₇×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₁₇×C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₁₇×C₂²⋊Q₈	C₂³	1	2	yes	—
216	C₁₇×#121	—	2	1	no	—
217	C₁₇×#121	—	2	1	no	—
218	C₁₇×#121	—	2	2	no	—
219	C₁₇×#121	—	2	2	no	—
220	C₁₇×#121	—	2	2	no	—
221	C₁₇×#121	—	2	2	no	—
222	C₁₇×#121	—	2	1	no	—
223	C₁₇×#121	—	2	1	no	—
224	C₁₇×#121	—	2	2	no	—
225	C₁₇×#121	—	2	2	no	—
226	C₁₇×#121	—	2	2	no	—
227	C₁₇×#121	—	2	2	no	—
228	C₁₇×#121	—	2	1	no	—
229	C₁₇×#121	—	2	1	no	—
230	C₁₇×#121	—	2	2	no	—
231	C₁₇×#121	—	2	2	no	—
232	C₁₇×#121	D₄	1	2	yes	—
233	C₁₇×#121	D₄	1	2	yes	—
234	C₁₇×#121	C₂³	1	2	yes	—
235	C₁₇×#121	C₂³	1	2	yes	—
236	C₁₇×#121	C₂³	1	2	yes	—
237	C₁₇×#121	C₂³	1	2	yes	—
238	C₄×Q₈×C₁₇	—	2	1	no	—
239	C₄×Q₈×C₁₇	—	2	1	no	—
240	C₄×Q₈×C₁₇	—	2	1	no	—
241	C₄×Q₈×C₁₇	—	2	1	no	—
242	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
243	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
244	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
245	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₁₇	—	2	1	no	—
247	C₄×D₄×C₁₇	—	2	1	no	—
248	C₄×D₄×C₁₇	—	2	2	no	—
249	C₄×D₄×C₁₇	—	2	2	no	—
250	C₄×D₄×C₁₇	—	2	2	no	—
251	C₄×D₄×C₁₇	—	2	1	no	—
252	C₄×D₄×C₁₇	—	2	1	no	—
253	C₄×D₄×C₁₇	—	2	2	no	—
254	C₄×D₄×C₁₇	—	2	2	no	—
255	C₄×D₄×C₁₇	—	2	2	no	—
256	C₄×D₄×C₁₇	—	2	2	no	—
257	C₄×D₄×C₁₇	—	2	2	no	—
258	C₄×D₄×C₁₇	—	2	1	no	—
259	C₄×D₄×C₁₇	—	2	1	no	—
260	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
261	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
262	C₄×D₄×C₁₇	C₂³	1	2	yes	—
263	C₄×D₄×C₁₇	C₂³	1	2	yes	—
264	C₁₇×#117	—	2	2	no	—
265	C₁₇×#117	—	2	2	no	—
266	C₁₇×#117	—	2	1	no	—
267	C₁₇×#117	C₂³	1	1	yes	characteristic
268	C₁₇×#117	C₂³	1	2	yes	—
269	C₁₇×#117	C₂³	1	2	yes	—
270	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
271	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
272	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
273	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
275	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
276	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
277	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
278	C₂×C₄²×C₁₇	—	2	1	no	—
279	C₂×C₄²×C₁₇	—	2	1	no	—
280	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
281	C₁₇×#107	C₂³	1	2	yes	—
282	C₁₇×#107	C₂³	1	2	yes	—
283	C₁₇×#107	C₂³	1	2	yes	—
284	C₁₇×#106	C₂³	1	2	yes	—
285	C₁₇×#106	C₂³	1	2	yes	—
286	C₁₇×#106	C₂³	1	2	yes	—
287	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
288	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
289	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
290	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
291	C₁₇×#103	C₂³	1	2	yes	—
292	C₁₇×#103	C₂³	1	2	yes	—
293	C₁₇×#103	C₂³	1	2	yes	—
294	C₁₇×#103	C₂³	1	2	yes	—
295	C₁₇×#103	C₂³	1	2	yes	—
296	C₁₇×#103	C₂³	1	2	yes	—
297	C₁₇×#103	C₂³	1	1	yes	characteristic
298	C₁₇×#103	C₂³	1	1	yes	characteristic
299	C₁₇×#103	C₂³	1	2	yes	—
300	C₁₇×#103	C₂³	1	2	yes	—
301	C₁₇×#103	C₂³	1	2	yes	—
302	C₁₇×#103	C₂³	1	2	yes	—
303	C₁₇×#103	C₂³	1	1	yes	characteristic
304	C₁₇×#103	C₂³	1	1	yes	characteristic
305	C₁₇×#103	C₂³	1	2	yes	—
306	C₁₇×#102	C₂³	1	1	yes	characteristic
307	C₁₇×#102	C₂³	1	1	yes	characteristic
308	C₁₇×#102	C₂³	1	1	yes	characteristic
309	C₁₇×#102	C₂³	1	1	yes	characteristic
310	C₁₇×#102	C₂³	1	2	yes	—
311	C₁₇×#102	C₂³	1	2	yes	—
312	C₁₇×#102	C₂³	1	2	yes	—
313	C₁₇×#102	C₂³	1	2	yes	—
314	C₁₇×#102	C₂³	1	2	yes	—
315	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
316	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
317	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
318	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
319	C₁₇×#97	C₂³	1	2	yes	—
320	C₄×C₈×C₁₇	C₂³	1	2	yes	—
321	#41×C₁₇	—	2	2	no	—
322	#41×C₁₇	—	2	2	no	—
323	#41×C₁₇	—	2	2	no	—
324	#41×C₁₇	—	2	2	no	—
325	#41×C₁₇	—	2	4	no	—
326	#41×C₁₇	—	2	4	no	—
327	#41×C₁₇	—	2	2	no	—
328	#41×C₁₇	—	2	2	no	—
329	#41×C₁₇	—	2	2	no	—
330	#41×C₁₇	—	2	2	no	—
331	#41×C₁₇	—	2	2	no	—
332	#41×C₁₇	—	2	2	no	—
333	#41×C₁₇	—	4	2	no	—
334	#41×C₁₇	—	4	2	no	—
335	#41×C₁₇	—	4	8	no	—
336	#41×C₁₇	—	4	8	no	—
337	#41×C₁₇	—	4	4	no	—
338	#41×C₁₇	—	4	4	no	—
339	C₂×Q₈×C₁₇	—	2	1	no	—
340	C₂×Q₈×C₁₇	—	2	2	no	—
341	C₂×Q₈×C₁₇	—	2	2	no	—
342	C₂×Q₈×C₁₇	—	2	2	no	—
343	C₂×Q₈×C₁₇	—	2	4	no	—
344	C₂×Q₈×C₁₇	—	2	4	no	—
345	C₂×Q₈×C₁₇	—	4	2	no	—
346	C₂×Q₈×C₁₇	—	4	2	no	—
347	C₂×Q₈×C₁₇	—	4	4	no	—
348	C₂×Q₈×C₁₇	—	4	4	no	—
349	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
350	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
351	C₂×Q₈×C₁₇	#41	1	4	yes	—
352	C₂×Q₈×C₁₇	C₂⁴	1	1	yes	characteristic
353	C₂×Q₈×C₁₇	C₂⁴	1	1	yes	characteristic
354	C₂×Q₈×C₁₇	C₂⁴	1	1	yes	characteristic
355	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
356	C₂×D₄×C₁₇	—	2	2	no	—
357	C₂×D₄×C₁₇	—	2	2	no	—
358	C₂×D₄×C₁₇	—	2	1	no	—
359	C₂×D₄×C₁₇	—	2	1	no	—
360	C₂×D₄×C₁₇	—	2	1	no	—
361	C₂×D₄×C₁₇	—	2	2	no	—
362	C₂×D₄×C₁₇	—	2	2	no	—
363	C₂×D₄×C₁₇	—	2	2	no	—
364	C₂×D₄×C₁₇	—	2	2	no	—
365	C₂×D₄×C₁₇	—	2	1	no	—
366	C₂×D₄×C₁₇	—	2	1	no	—
367	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
368	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
369	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
370	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
371	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
372	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
373	C₂×D₄×C₁₇	C₂⁴	1	1	yes	characteristic
374	C₂×D₄×C₁₇	C₂⁴	1	1	yes	characteristic
375	C₂×D₄×C₁₇	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₁₇	—	2	1	no	—
377	C₂²×C₄×C₁₇	—	2	2	no	—
378	C₂²×C₄×C₁₇	—	2	2	no	—
379	C₂²×C₄×C₁₇	—	2	2	no	—
380	C₂²×C₄×C₁₇	—	2	2	no	—
381	C₂²×C₄×C₁₇	—	2	1	no	—
382	C₂²×C₄×C₁₇	—	2	1	no	—
383	C₂²×C₄×C₁₇	—	2	1	no	—
384	C₂²×C₄×C₁₇	—	2	1	no	—
385	C₂²×C₄×C₁₇	—	2	2	no	—
386	C₂²×C₄×C₁₇	—	2	2	no	—
387	C₂²×C₄×C₁₇	—	2	1	no	—
388	C₂²×C₄×C₁₇	—	2	1	no	—
389	C₂²×C₄×C₁₇	—	2	1	no	—
390	C₂²×C₄×C₁₇	—	2	1	no	—
391	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
392	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
394	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
395	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
396	Q₁₆×C₁₇	—	2	4	no	—
397	Q₁₆×C₁₇	—	4	1	no	—
398	Q₁₆×C₁₇	—	4	1	no	—
399	SD₁₆×C₁₇	—	2	4	no	—
400	SD₁₆×C₁₇	—	4	1	no	—
401	SD₁₆×C₁₇	—	4	1	no	—
402	SD₁₆×C₁₇	—	4	1	no	—
403	SD₁₆×C₁₇	—	4	1	no	—
404	D₈×C₁₇	—	4	1	no	—
405	D₈×C₁₇	—	4	1	no	—
406	M₁₆×C₁₇	—	2	2	no	—
407	M₁₆×C₁₇	—	2	2	no	—
408	M₁₆×C₁₇	—	4	2	no	—
409	M₁₆×C₁₇	—	4	2	no	—
410	C₂×C₈×C₁₇	—	2	2	no	—
411	C₂×C₈×C₁₇	—	2	2	no	—
412	C₂×C₈×C₁₇	—	4	2	no	—
413	C₂×C₈×C₁₇	—	4	2	no	—
414	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
415	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
416	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
417	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
418	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
419	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
420	C₄⋊C₄×C₁₇	—	2	1	no	—
421	C₄⋊C₄×C₁₇	—	2	2	no	—
422	C₄⋊C₄×C₁₇	—	2	2	no	—
423	C₄⋊C₄×C₁₇	—	2	2	no	—
424	C₄⋊C₄×C₁₇	—	2	2	no	—
425	C₄⋊C₄×C₁₇	—	2	1	no	—
426	C₄⋊C₄×C₁₇	—	2	2	no	—
427	C₄⋊C₄×C₁₇	—	2	2	no	—
428	C₄⋊C₄×C₁₇	—	2	1	no	—
429	C₄⋊C₄×C₁₇	—	2	1	no	—
430	C₄⋊C₄×C₁₇	—	2	1	no	—
431	C₄⋊C₄×C₁₇	—	2	1	no	—
432	C₄⋊C₄×C₁₇	—	2	2	no	—
433	C₄⋊C₄×C₁₇	—	2	2	no	—
434	C₄⋊C₄×C₁₇	—	2	2	no	—
435	C₄⋊C₄×C₁₇	—	2	2	no	—
436	C₄⋊C₄×C₁₇	—	2	2	no	—
437	C₄⋊C₄×C₁₇	—	2	2	no	—
438	C₄⋊C₄×C₁₇	—	2	1	no	—
439	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
440	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
441	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
442	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
443	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
444	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
445	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
446	C₂²⋊C₄×C₁₇	—	2	2	no	—
447	C₂²⋊C₄×C₁₇	—	2	2	no	—
448	C₂²⋊C₄×C₁₇	—	2	2	no	—
449	C₂²⋊C₄×C₁₇	—	2	2	no	—
450	C₂²⋊C₄×C₁₇	—	2	2	no	—
451	C₂²⋊C₄×C₁₇	—	2	2	no	—
452	C₂²⋊C₄×C₁₇	—	2	1	no	—
453	C₂²⋊C₄×C₁₇	—	2	2	no	—
454	C₂²⋊C₄×C₁₇	—	2	2	no	—
455	C₂²⋊C₄×C₁₇	—	2	1	no	—
456	C₂²⋊C₄×C₁₇	—	2	1	no	—
457	C₂²⋊C₄×C₁₇	—	2	2	no	—
458	C₂²⋊C₄×C₁₇	—	2	2	no	—
459	C₂²⋊C₄×C₁₇	—	2	1	no	—
460	C₂²⋊C₄×C₁₇	—	2	1	no	—
461	C₂²⋊C₄×C₁₇	—	2	1	no	—
462	C₂²⋊C₄×C₁₇	—	2	1	no	—
463	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
464	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
465	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
466	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
467	C₄²×C₁₇	—	2	2	no	—
468	C₄²×C₁₇	—	2	2	no	—
469	C₄²×C₁₇	—	2	2	no	—
470	C₄²×C₁₇	—	2	1	no	—
471	C₄²×C₁₇	—	2	1	no	—
472	C₄²×C₁₇	—	2	2	no	—
473	C₄²×C₁₇	—	2	1	no	—
474	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
475	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
476	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
477	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
478	#61204	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
479	C₂³×C₁₇	—	2	1	no	—
480	C₂³×C₁₇	—	2	1	no	—
481	C₂³×C₁₇	—	2	1	no	—
482	C₂³×C₁₇	C₂²×D₄	1	2	yes	—
483	C₂³×C₁₇	C₂²×D₄	1	2	yes	—
484	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
485	Q₈×C₁₇	—	2	4	no	—
486	Q₈×C₁₇	—	2	2	no	—
487	Q₈×C₁₇	—	2	2	no	—
488	Q₈×C₁₇	—	2	2	no	—
489	Q₈×C₁₇	—	2	1	no	—
490	Q₈×C₁₇	—	2	1	no	—
491	Q₈×C₁₇	—	2	1	no	—
492	Q₈×C₁₇	—	2	1	no	—
493	Q₈×C₁₇	—	2	1	no	—
494	Q₈×C₁₇	—	2	1	no	—
495	Q₈×C₁₇	—	4	4	no	—
496	Q₈×C₁₇	—	4	4	no	—
497	Q₈×C₁₇	C₂×#41	1	4	yes	—
498	D₄×C₁₇	—	2	4	no	—
499	D₄×C₁₇	—	2	4	no	—
500	D₄×C₁₇	—	2	2	no	—
501	D₄×C₁₇	—	2	2	no	—
502	D₄×C₁₇	—	2	1	no	—
503	D₄×C₁₇	—	2	1	no	—
504	D₄×C₁₇	—	2	1	no	—
505	D₄×C₁₇	—	2	1	no	—
506	D₄×C₁₇	—	2	1	no	—
507	D₄×C₁₇	—	2	1	no	—
508	D₄×C₁₇	—	4	2	no	—
509	D₄×C₁₇	—	4	2	no	—
510	D₄×C₁₇	—	4	4	no	—
511	D₄×C₁₇	—	4	4	no	—
512	D₄×C₁₇	—	4	2	no	—
513	D₄×C₁₇	—	4	2	no	—
514	D₄×C₁₇	—	4	2	no	—
515	D₄×C₁₇	—	4	2	no	—
516	D₄×C₁₇	—	8	1	no	—
517	D₄×C₁₇	—	8	2	no	—
518	D₄×C₁₇	—	8	2	no	—
519	D₄×C₁₇	—	8	2	no	—
520	D₄×C₁₇	—	8	2	no	—
521	C₂×C₄×C₁₇	—	2	4	no	—
522	C₂×C₄×C₁₇	—	2	2	no	—
523	C₂×C₄×C₁₇	—	2	2	no	—
524	C₂×C₄×C₁₇	—	2	2	no	—
525	C₂×C₄×C₁₇	—	2	2	no	—
526	C₂×C₄×C₁₇	—	2	2	no	—
527	C₂×C₄×C₁₇	—	2	1	no	—
528	C₂×C₄×C₁₇	—	2	1	no	—
529	C₂×C₄×C₁₇	—	2	1	no	—
530	C₂×C₄×C₁₇	—	2	2	no	—
531	C₂×C₄×C₁₇	—	2	2	no	—
532	C₂×C₄×C₁₇	—	2	2	no	—
533	C₂×C₄×C₁₇	—	2	1	no	—
534	C₂×C₄×C₁₇	—	2	1	no	—
535	C₂×C₄×C₁₇	—	4	1	no	—
536	C₂×C₄×C₁₇	—	4	1	no	—
537	C₂×C₄×C₁₇	—	4	4	no	—
538	C₂×C₄×C₁₇	—	4	4	no	—
539	C₂×C₄×C₁₇	—	4	4	no	—
540	C₂×C₄×C₁₇	—	4	4	no	—
541	C₂×C₄×C₁₇	—	4	2	no	—
542	C₂×C₄×C₁₇	—	4	2	no	—
543	C₂×C₄×C₁₇	—	4	2	no	—
544	C₂×C₄×C₁₇	—	8	1	no	—
545	C₂×C₄×C₁₇	—	8	1	no	—
546	C₂×C₄×C₁₇	—	8	2	no	—
547	C₂×C₄×C₁₇	—	8	1	no	—
548	C₂×C₄×C₁₇	—	8	1	no	—
549	C₂×C₄×C₁₇	—	8	2	no	—
550	C₂×C₄×C₁₇	—	8	1	no	—
551	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
555	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
556	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
557	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
558	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
559	C₂×C₄×C₁₇	H(5,𝔽₂)	1	2	yes	—
560	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
561	C₈×C₁₇	—	2	2	no	—
562	C₈×C₁₇	—	2	1	no	—
563	C₈×C₁₇	—	2	1	no	—
564	C₈×C₁₇	—	2	1	no	—
565	C₈×C₁₇	—	2	1	no	—
566	C₈×C₁₇	—	2	2	no	—
567	#3512	C₂×C₁₇	1	1	yes	characteristic, complemented
568	#3497	C₂×C₁₇	1	1	yes	characteristic, complemented
569	#3327	C₂×C₁₇	1	2	yes	complemented
570	#3326	C₂×C₁₇	1	2	yes	complemented
571	#3320	C₂×C₁₇	1	2	yes	complemented
572	#3317	C₂×C₁₇	1	2	yes	complemented
573	#3312	C₂×C₁₇	1	2	yes	complemented
574	#3309	C₂×C₁₇	1	2	yes	complemented
575	#3301	C₂×C₁₇	1	2	yes	complemented
576	#3300	C₂×C₁₇	1	2	yes	complemented
577	#3142	C₂×C₁₇	1	1	yes	characteristic, complemented
578	#3099	C₂×C₁₇	1	1	yes	characteristic, complemented
579	#3098	C₂×C₁₇	1	1	yes	characteristic, complemented
580	C₂×#479	C₂×C₁₇	1	1	yes	characteristic, complemented
581	#3061	C₂×C₁₇	1	1	yes	characteristic, complemented
582	#3060	C₂×C₁₇	1	1	yes	characteristic, complemented
583	#3035	C₂×C₁₇	1	1	yes	characteristic, complemented
584	#3013	C₂×C₁₇	1	1	yes	characteristic, complemented
585	#3013	C₂×C₁₇	1	1	yes	characteristic, complemented
586	C₄×#137	C₂×C₁₇	1	1	yes	characteristic, complemented
587	#2935	C₂×C₁₇	1	1	yes	characteristic, complemented
588	#2898	C₂×C₁₇	1	1	yes	characteristic, complemented
589	#2898	C₂×C₁₇	1	1	yes	characteristic, complemented
590	C₂²×C₁₇	—	2	1	no	—
591	C₂²×C₁₇	—	2	1	no	—
592	C₂²×C₁₇	—	2	2	no	—
593	C₂²×C₁₇	—	2	2	no	—
594	C₂²×C₁₇	—	2	2	no	—
595	C₂²×C₁₇	—	2	2	no	—
596	C₂²×C₁₇	—	2	2	no	—
597	C₂²×C₁₇	—	2	2	no	—
598	C₂²×C₁₇	—	4	1	no	—
599	C₂²×C₁₇	—	4	1	no	—
600	C₂²×C₁₇	—	4	1	no	—
601	C₂²×C₁₇	—	4	1	no	—
602	C₂²×C₁₇	—	4	1	no	—
603	C₂²×C₁₇	—	4	1	no	—
604	C₂²×C₁₇	—	4	1	no	—
605	C₂²×C₁₇	—	4	1	no	—
606	C₂²×C₁₇	—	4	1	no	—
607	C₂²×C₁₇	#546	1	2	yes	—
608	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
609	C₄×C₁₇	—	2	1	no	—
610	C₄×C₁₇	—	2	1	no	—
611	C₄×C₁₇	—	2	1	no	—
612	C₄×C₁₇	—	2	1	no	—
613	C₄×C₁₇	—	2	4	no	—
614	C₄×C₁₇	—	2	2	no	—
615	C₄×C₁₇	—	2	2	no	—
616	C₄×C₁₇	—	4	1	no	—
617	C₄×C₁₇	—	4	2	no	—
618	C₄×C₁₇	—	4	2	no	—
619	C₄×C₁₇	—	4	1	no	—
620	C₄×C₁₇	—	4	2	no	—
621	C₄×C₁₇	—	4	1	no	—
622	C₄×C₁₇	—	4	1	no	—
623	C₄×C₁₇	—	4	1	no	—
624	C₄×C₁₇	#546	1	2	yes	—
625	C₄×C₁₇	C₂²×#41	1	1	yes	characteristic
626	C₄×C₁₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
627	C₂×2₋¹⁺⁴	C₂²×C₁₇	1	1	yes	characteristic
628	C₂×2₋¹⁺⁴	C₂²×C₁₇	1	1	yes	characteristic
629	C₂×#137	C₂²×C₁₇	1	1	yes	characteristic
630	C₂×#135	C₂²×C₁₇	1	1	yes	characteristic
631	C₂×#135	C₂²×C₁₇	1	1	yes	characteristic
632	C₂×#131	C₂²×C₁₇	1	1	yes	characteristic
633	C₂×#131	C₂²×C₁₇	1	1	yes	characteristic
634	#553	—	2	2	no	—
635	#553	—	2	2	no	—
636	#553	C₂²×C₁₇	1	2	yes	—
637	#553	C₂²×C₁₇	1	2	yes	—
638	#552	C₂²×C₁₇	1	2	yes	—
639	#552	C₂²×C₁₇	1	2	yes	—
640	#550	—	2	1	no	—
641	#550	C₂²×C₁₇	1	2	yes	—
642	D₄×Q₈	—	2	1	no	—
643	D₄×Q₈	C₂²×C₁₇	1	2	yes	—
644	#548	—	2	1	no	—
645	#548	—	2	1	no	—
646	#548	C₂²×C₁₇	1	2	yes	—
647	#548	C₂²×C₁₇	1	2	yes	—
648	#541	—	2	1	no	—
649	#540	—	2	1	no	—
650	#537	—	2	2	no	—
651	#537	C₂²×C₁₇	1	1	yes	characteristic
652	#537	C₂²×C₁₇	1	1	yes	characteristic
653	#537	C₂²×C₁₇	1	1	yes	characteristic
654	#537	C₂²×C₁₇	1	1	yes	characteristic
655	#532	—	2	2	no	—
656	#532	C₂²×C₁₇	1	1	yes	characteristic
657	#532	C₂²×C₁₇	1	1	yes	characteristic
658	#529	—	2	1	no	—
659	#529	—	2	1	no	—
660	C₂×#125	C₂²×C₁₇	1	1	yes	characteristic
661	#520	C₂²×C₁₇	1	1	yes	characteristic
662	#520	C₂²×C₁₇	1	1	yes	characteristic
663	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
664	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
665	#491	C₂²×C₁₇	1	2	yes	—
666	#490	C₂²×C₁₇	1	2	yes	—
667	#488	C₂²×C₁₇	1	2	yes	—
668	#488	C₂²×C₁₇	1	2	yes	—
669	#485	C₂²×C₁₇	1	2	yes	—
670	#485	C₂²×C₁₇	1	2	yes	—
671	#484	C₂²×C₁₇	1	2	yes	—
672	#483	C₂²×C₁₇	1	2	yes	—
673	#482	C₂²×C₁₇	1	2	yes	—
674	#482	C₂²×C₁₇	1	2	yes	—
675	#481	C₂²×C₁₇	1	2	yes	—
676	#480	C₂²×C₁₇	1	2	yes	—
677	#479	C₂²×C₁₇	1	2	yes	—
678	#479	C₂²×C₁₇	1	2	yes	—
679	#479	C₂²×C₁₇	1	2	yes	—
680	#479	C₂²×C₁₇	1	2	yes	—
681	#470	C₂²×C₁₇	1	2	yes	—
682	#469	C₂²×C₁₇	1	2	yes	—
683	#468	C₂²×C₁₇	1	2	yes	—
684	#468	C₂²×C₁₇	1	2	yes	—
685	#467	C₂²×C₁₇	1	2	yes	—
686	#466	C₂²×C₁₇	1	2	yes	—
687	#465	C₂²×C₁₇	1	2	yes	—
688	#465	C₂²×C₁₇	1	2	yes	—
689	#464	C₂²×C₁₇	1	1	yes	characteristic
690	#464	C₂²×C₁₇	1	1	yes	characteristic
691	#463	C₂²×C₁₇	1	1	yes	characteristic
692	#463	C₂²×C₁₇	1	1	yes	characteristic
693	#462	C₂²×C₁₇	1	1	yes	characteristic
694	#461	C₂²×C₁₇	1	1	yes	characteristic
695	#460	C₂²×C₁₇	1	1	yes	characteristic
696	#459	C₂²×C₁₇	1	1	yes	characteristic
697	#452	C₂²×C₁₇	1	2	yes	—
698	#452	C₂²×C₁₇	1	2	yes	—
699	#451	C₂²×C₁₇	1	2	yes	—
700	#451	C₂²×C₁₇	1	2	yes	—
701	#449	C₂²×C₁₇	1	2	yes	—
702	#449	C₂²×C₁₇	1	2	yes	—
703	#448	C₂²×C₁₇	1	2	yes	—
704	#448	C₂²×C₁₇	1	2	yes	—
705	#441	C₂²×C₁₇	1	2	yes	—
706	#440	C₂²×C₁₇	1	2	yes	—
707	C₄×Q₁₆	C₂²×C₁₇	1	2	yes	—
708	C₄×SD₁₆	C₂²×C₁₇	1	2	yes	—
709	#436	C₂²×C₁₇	1	2	yes	—
710	#435	C₂²×C₁₇	1	2	yes	—
711	#435	C₂²×C₁₇	1	2	yes	—
712	C₈×D₄	C₂²×C₁₇	1	2	yes	—
713	#428	C₂²×C₁₇	1	1	yes	characteristic
714	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic
715	C₂×#106	C₂²×C₁₇	1	1	yes	characteristic
716	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
717	#419	C₂²×C₁₇	1	1	yes	characteristic
718	#419	C₂²×C₁₇	1	2	yes	—
719	#419	C₂²×C₁₇	1	2	yes	—
720	#417	C₂²×C₁₇	1	1	yes	characteristic
721	#417	C₂²×C₁₇	1	1	yes	characteristic
722	#417	C₂²×C₁₇	1	1	yes	characteristic
723	#417	C₂²×C₁₇	1	1	yes	characteristic
724	#417	C₂²×C₁₇	1	2	yes	—
725	#417	C₂²×C₁₇	1	2	yes	—
726	#417	C₂²×C₁₇	1	1	yes	characteristic
727	#416	C₂²×C₁₇	1	1	yes	characteristic
728	#416	C₂²×C₁₇	1	1	yes	characteristic
729	#416	C₂²×C₁₇	1	2	yes	—
730	#416	C₂²×C₁₇	1	2	yes	—
731	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
732	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
733	C₂×#103	C₂²×C₁₇	1	2	yes	—
734	C₂×#103	C₂²×C₁₇	1	2	yes	—
735	#408	C₂²×C₁₇	1	1	yes	characteristic
736	#408	C₂²×C₁₇	1	1	yes	characteristic
737	C₄×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
738	C₂×C₁₇	—	2	2	no	—
739	C₂×C₁₇	—	4	2	no	—
740	C₂×C₁₇	—	4	2	no	—
741	C₂×C₁₇	—	8	1	no	—
742	C₂×C₁₇	—	8	1	no	—
743	C₂×C₁₇	—	8	1	no	—
744	C₂×C₁₇	C₂×#546	1	1	yes	characteristic
745	C₂×C₁₇	#3584	1	1	yes	characteristic
746	C₂×C₁₇	#3586	1	1	yes	characteristic
747	2₋¹⁺⁴	—	2	4	no	—
748	2₋¹⁺⁴	—	2	4	no	—
749	2₋¹⁺⁴	—	4	2	no	—
750	2₋¹⁺⁴	—	4	2	no	—
751	C₂×#41	—	2	2	no	—
752	C₂×#41	—	2	2	no	—
753	C₂×#41	—	2	1	no	—
754	C₂×#41	—	2	1	no	—
755	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
756	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
757	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
758	C₂×#41	C₂³×C₁₇	1	2	yes	—
759	C₂×#41	C₂³×C₁₇	1	2	yes	—
760	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
761	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
762	C₂²×Q₈	—	2	1	no	—
763	C₂²×Q₈	—	2	1	no	—
764	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
765	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
766	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
767	#137	—	2	4	no	—
768	#135	—	4	2	no	—
769	#135	—	4	2	no	—
770	C₂×Q₁₆	C₂³×C₁₇	1	2	yes	—
771	C₂×Q₁₆	C₂³×C₁₇	1	1	yes	characteristic
772	C₂×Q₁₆	C₂³×C₁₇	1	1	yes	characteristic
773	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
774	C₂×SD₁₆	C₂³×C₁₇	1	1	yes	characteristic
775	C₂×SD₁₆	C₂³×C₁₇	1	1	yes	characteristic
776	C₂×SD₁₆	C₂³×C₁₇	1	1	yes	characteristic
777	C₂×SD₁₆	C₂³×C₁₇	1	1	yes	characteristic
778	C₂×D₈	C₂³×C₁₇	1	1	yes	characteristic
779	C₂×D₈	C₂³×C₁₇	1	1	yes	characteristic
780	#131	—	4	2	no	—
781	#131	—	4	2	no	—
782	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
783	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
784	C₂×M₁₆	C₂³×C₁₇	1	2	yes	—
785	C₂×M₁₆	C₂³×C₁₇	1	2	yes	—
786	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
787	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
788	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
789	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
790	C₄⋊Q₈	—	2	2	no	—
791	C₄⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
792	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
793	#127	—	2	2	no	—
794	#127	D₄×C₁₇	1	1	yes	characteristic
795	#127	C₂³×C₁₇	1	1	yes	characteristic
796	#126	—	2	2	no	—
797	#126	—	2	2	no	—
798	#126	—	2	2	no	—
799	#126	—	2	2	no	—
800	#125	—	2	2	no	—
801	#125	—	2	2	no	—
802	#125	—	2	1	no	—
803	#125	—	2	1	no	—
804	#125	C₂³×C₁₇	1	2	yes	—
805	#125	C₂³×C₁₇	1	2	yes	—
806	#124	—	2	2	no	—
807	#124	—	2	2	no	—
808	#124	D₄×C₁₇	1	1	yes	characteristic
809	#124	D₄×C₁₇	1	1	yes	characteristic
810	#124	C₂³×C₁₇	1	1	yes	characteristic
811	#124	C₂³×C₁₇	1	1	yes	characteristic
812	#123	—	2	2	no	—
813	#123	—	2	2	no	—
814	#123	—	2	2	no	—
815	#123	—	2	2	no	—
816	C₂²⋊Q₈	—	2	1	no	—
817	C₂²⋊Q₈	—	2	1	no	—
818	C₂²⋊Q₈	—	2	1	no	—
819	C₂²⋊Q₈	—	2	1	no	—
820	C₂²⋊Q₈	—	2	2	no	—
821	C₂²⋊Q₈	—	2	2	no	—
822	C₂²⋊Q₈	—	2	2	no	—
823	C₂²⋊Q₈	—	2	2	no	—
824	C₂²⋊Q₈	C₂³×C₁₇	1	2	yes	—
825	C₂²⋊Q₈	C₂³×C₁₇	1	2	yes	—
826	C₂²⋊Q₈	C₂³×C₁₇	1	2	yes	—
827	C₂²⋊Q₈	C₂³×C₁₇	1	2	yes	—
828	#121	—	2	1	no	—
829	#121	—	2	1	no	—
830	#121	—	2	2	no	—
831	#121	—	2	2	no	—
832	#121	—	2	2	no	—
833	#121	—	2	2	no	—
834	#121	—	2	1	no	—
835	#121	—	2	1	no	—
836	#121	—	2	2	no	—
837	#121	—	2	2	no	—
838	#121	—	2	2	no	—
839	#121	—	2	2	no	—
840	#121	—	2	1	no	—
841	#121	—	2	1	no	—
842	#121	—	2	2	no	—
843	#121	—	2	2	no	—
844	#121	D₄×C₁₇	1	2	yes	—
845	#121	D₄×C₁₇	1	2	yes	—
846	#121	C₂³×C₁₇	1	2	yes	—
847	#121	C₂³×C₁₇	1	2	yes	—
848	#121	C₂³×C₁₇	1	2	yes	—
849	#121	C₂³×C₁₇	1	2	yes	—
850	C₄×Q₈	—	2	1	no	—
851	C₄×Q₈	—	2	1	no	—
852	C₄×Q₈	—	2	1	no	—
853	C₄×Q₈	—	2	1	no	—
854	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
855	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
856	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
857	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
858	C₄×D₄	—	2	1	no	—
859	C₄×D₄	—	2	1	no	—
860	C₄×D₄	—	2	2	no	—
861	C₄×D₄	—	2	2	no	—
862	C₄×D₄	—	2	2	no	—
863	C₄×D₄	—	2	1	no	—
864	C₄×D₄	—	2	1	no	—
865	C₄×D₄	—	2	2	no	—
866	C₄×D₄	—	2	2	no	—
867	C₄×D₄	—	2	2	no	—
868	C₄×D₄	—	2	2	no	—
869	C₄×D₄	—	2	2	no	—
870	C₄×D₄	—	2	1	no	—
871	C₄×D₄	—	2	1	no	—
872	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
873	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
874	C₄×D₄	C₂³×C₁₇	1	2	yes	—
875	C₄×D₄	C₂³×C₁₇	1	2	yes	—
876	#117	—	2	2	no	—
877	#117	—	2	2	no	—
878	#117	—	2	1	no	—
879	#117	C₂³×C₁₇	1	1	yes	characteristic
880	#117	C₂³×C₁₇	1	2	yes	—
881	#117	C₂³×C₁₇	1	2	yes	—
882	C₂×C₄⋊C₄	—	2	1	no	—
883	C₂×C₄⋊C₄	—	2	1	no	—
884	C₂×C₄⋊C₄	—	2	1	no	—
885	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
886	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
887	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
888	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
889	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
890	C₂×C₄²	—	2	1	no	—
891	C₂×C₄²	—	2	1	no	—
892	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
893	#107	C₂³×C₁₇	1	2	yes	—
894	#107	C₂³×C₁₇	1	2	yes	—
895	#107	C₂³×C₁₇	1	2	yes	—
896	#106	C₂³×C₁₇	1	2	yes	—
897	#106	C₂³×C₁₇	1	2	yes	—
898	#106	C₂³×C₁₇	1	2	yes	—
899	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
900	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
901	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
902	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
903	#103	C₂³×C₁₇	1	2	yes	—
904	#103	C₂³×C₁₇	1	2	yes	—
905	#103	C₂³×C₁₇	1	1	yes	characteristic
906	#103	C₂³×C₁₇	1	1	yes	characteristic
907	#103	C₂³×C₁₇	1	2	yes	—
908	#103	C₂³×C₁₇	1	2	yes	—
909	#103	C₂³×C₁₇	1	2	yes	—
910	#103	C₂³×C₁₇	1	2	yes	—
911	#103	C₂³×C₁₇	1	2	yes	—
912	#103	C₂³×C₁₇	1	2	yes	—
913	#103	C₂³×C₁₇	1	1	yes	characteristic
914	#103	C₂³×C₁₇	1	1	yes	characteristic
915	#103	C₂³×C₁₇	1	2	yes	—
916	#103	C₂³×C₁₇	1	2	yes	—
917	#103	C₂³×C₁₇	1	2	yes	—
918	#102	C₂³×C₁₇	1	1	yes	characteristic
919	#102	C₂³×C₁₇	1	1	yes	characteristic
920	#102	C₂³×C₁₇	1	1	yes	characteristic
921	#102	C₂³×C₁₇	1	1	yes	characteristic
922	#102	C₂³×C₁₇	1	2	yes	—
923	#102	C₂³×C₁₇	1	2	yes	—
924	#102	C₂³×C₁₇	1	2	yes	—
925	#102	C₂³×C₁₇	1	2	yes	—
926	#102	C₂³×C₁₇	1	2	yes	—
927	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
928	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
929	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
930	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
931	#97	C₂³×C₁₇	1	2	yes	—
932	C₄×C₈	C₂³×C₁₇	1	2	yes	—
933	C₁₇	#61204	1	1	yes	characteristic, direct product factor, Sylow
934	#41	—	2	2	no	—
935	#41	—	2	2	no	—
936	#41	—	2	2	no	—
937	#41	—	2	2	no	—
938	#41	—	2	4	no	—
939	#41	—	2	4	no	—
940	#41	—	2	2	no	—
941	#41	—	2	2	no	—
942	#41	—	2	2	no	—
943	#41	—	2	2	no	—
944	#41	—	2	2	no	—
945	#41	—	2	2	no	—
946	#41	—	4	2	no	—
947	#41	—	4	2	no	—
948	#41	—	4	8	no	—
949	#41	—	4	8	no	—
950	#41	—	4	4	no	—
951	#41	—	4	4	no	—
952	C₂×Q₈	—	2	1	no	—
953	C₂×Q₈	—	2	2	no	—
954	C₂×Q₈	—	2	2	no	—
955	C₂×Q₈	—	2	2	no	—
956	C₂×Q₈	—	2	4	no	—
957	C₂×Q₈	—	2	4	no	—
958	C₂×Q₈	—	4	2	no	—
959	C₂×Q₈	—	4	2	no	—
960	C₂×Q₈	—	4	4	no	—
961	C₂×Q₈	—	4	4	no	—
962	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
963	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
964	C₂×Q₈	#41×C₁₇	1	4	yes	—
965	C₂×Q₈	C₂⁴×C₁₇	1	1	yes	characteristic
966	C₂×Q₈	C₂⁴×C₁₇	1	1	yes	characteristic
967	C₂×Q₈	C₂⁴×C₁₇	1	1	yes	characteristic
968	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
969	C₂×D₄	—	2	1	no	—
970	C₂×D₄	—	2	1	no	—
971	C₂×D₄	—	2	1	no	—
972	C₂×D₄	—	2	2	no	—
973	C₂×D₄	—	2	2	no	—
974	C₂×D₄	—	2	2	no	—
975	C₂×D₄	—	2	2	no	—
976	C₂×D₄	—	2	2	no	—
977	C₂×D₄	—	2	2	no	—
978	C₂×D₄	—	2	1	no	—
979	C₂×D₄	—	2	1	no	—
980	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
981	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
982	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
983	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
984	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
985	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
986	C₂×D₄	C₂⁴×C₁₇	1	1	yes	characteristic
987	C₂×D₄	C₂⁴×C₁₇	1	1	yes	characteristic
988	C₂×D₄	C₂⁴×C₁₇	1	1	yes	characteristic
989	C₂²×C₄	—	2	1	no	—
990	C₂²×C₄	—	2	2	no	—
991	C₂²×C₄	—	2	2	no	—
992	C₂²×C₄	—	2	1	no	—
993	C₂²×C₄	—	2	1	no	—
994	C₂²×C₄	—	2	1	no	—
995	C₂²×C₄	—	2	2	no	—
996	C₂²×C₄	—	2	2	no	—
997	C₂²×C₄	—	2	1	no	—
998	C₂²×C₄	—	2	2	no	—
999	C₂²×C₄	—	2	2	no	—
1000	C₂²×C₄	—	2	1	no	—
1001	C₂²×C₄	—	2	1	no	—
1002	C₂²×C₄	—	2	1	no	—
1003	C₂²×C₄	—	2	1	no	—
1004	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
1005	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
1006	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
1007	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
1008	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
1009	Q₁₆	—	2	4	no	—
1010	Q₁₆	—	4	1	no	—
1011	Q₁₆	—	4	1	no	—
1012	SD₁₆	—	2	4	no	—
1013	SD₁₆	—	4	1	no	—
1014	SD₁₆	—	4	1	no	—
1015	SD₁₆	—	4	1	no	—
1016	SD₁₆	—	4	1	no	—
1017	D₈	—	4	1	no	—
1018	D₈	—	4	1	no	—
1019	M₁₆	—	2	2	no	—
1020	M₁₆	—	2	2	no	—
1021	M₁₆	—	4	2	no	—
1022	M₁₆	—	4	2	no	—
1023	C₂×C₈	—	2	2	no	—
1024	C₂×C₈	—	2	2	no	—
1025	C₂×C₈	—	4	2	no	—
1026	C₂×C₈	—	4	2	no	—
1027	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
1028	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
1029	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
1030	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
1031	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
1032	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
1033	C₄⋊C₄	—	2	2	no	—
1034	C₄⋊C₄	—	2	2	no	—
1035	C₄⋊C₄	—	2	2	no	—
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	2	2	no	—
1038	C₄⋊C₄	—	2	2	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	2	2	no	—
1042	C₄⋊C₄	—	2	2	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	—	2	2	no	—
1047	C₄⋊C₄	—	2	2	no	—
1048	C₄⋊C₄	—	2	1	no	—
1049	C₄⋊C₄	—	2	1	no	—
1050	C₄⋊C₄	—	2	2	no	—
1051	C₄⋊C₄	—	2	2	no	—
1052	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
1053	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
1054	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
1055	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
1056	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
1057	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
1058	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	1	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	—	2	2	no	—
1065	C₂²⋊C₄	—	2	2	no	—
1066	C₂²⋊C₄	—	2	1	no	—
1067	C₂²⋊C₄	—	2	1	no	—
1068	C₂²⋊C₄	—	2	1	no	—
1069	C₂²⋊C₄	—	2	1	no	—
1070	C₂²⋊C₄	—	2	1	no	—
1071	C₂²⋊C₄	—	2	1	no	—
1072	C₂²⋊C₄	—	2	2	no	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	—	2	2	no	—
1075	C₂²⋊C₄	—	2	2	no	—
1076	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
1077	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
1078	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
1079	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
1080	C₄²	—	2	1	no	—
1081	C₄²	—	2	1	no	—
1082	C₄²	—	2	1	no	—
1083	C₄²	—	2	2	no	—
1084	C₄²	—	2	2	no	—
1085	C₄²	—	2	2	no	—
1086	C₄²	—	2	2	no	—
1087	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
1088	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
1089	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
1090	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
1091	C₂³	—	2	1	no	—
1092	C₂³	—	2	1	no	—
1093	C₂³	—	2	1	no	—
1094	C₂³	C₂²×D₄×C₁₇	1	2	yes	—
1095	C₂³	C₂²×D₄×C₁₇	1	2	yes	—
1096	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
1097	Q₈	—	2	4	no	—
1098	Q₈	—	2	2	no	—
1099	Q₈	—	2	2	no	—
1100	Q₈	—	2	2	no	—
1101	Q₈	—	2	1	no	—
1102	Q₈	—	2	1	no	—
1103	Q₈	—	2	1	no	—
1104	Q₈	—	2	1	no	—
1105	Q₈	—	2	1	no	—
1106	Q₈	—	2	1	no	—
1107	Q₈	—	4	4	no	—
1108	Q₈	—	4	4	no	—
1109	Q₈	C₂×#41×C₁₇	1	4	yes	—
1110	D₄	—	2	4	no	—
1111	D₄	—	2	4	no	—
1112	D₄	—	2	2	no	—
1113	D₄	—	2	2	no	—
1114	D₄	—	2	1	no	—
1115	D₄	—	2	1	no	—
1116	D₄	—	2	1	no	—
1117	D₄	—	2	1	no	—
1118	D₄	—	2	1	no	—
1119	D₄	—	2	1	no	—
1120	D₄	—	4	2	no	—
1121	D₄	—	4	2	no	—
1122	D₄	—	4	4	no	—
1123	D₄	—	4	4	no	—
1124	D₄	—	4	2	no	—
1125	D₄	—	4	2	no	—
1126	D₄	—	4	2	no	—
1127	D₄	—	4	2	no	—
1128	D₄	—	8	1	no	—
1129	D₄	—	8	2	no	—
1130	D₄	—	8	2	no	—
1131	D₄	—	8	2	no	—
1132	D₄	—	8	2	no	—
1133	C₂×C₄	—	2	4	no	—
1134	C₂×C₄	—	2	2	no	—
1135	C₂×C₄	—	2	2	no	—
1136	C₂×C₄	—	2	2	no	—
1137	C₂×C₄	—	2	2	no	—
1138	C₂×C₄	—	2	2	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	2	no	—
1143	C₂×C₄	—	2	2	no	—
1144	C₂×C₄	—	2	2	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	4	1	no	—
1148	C₂×C₄	—	4	1	no	—
1149	C₂×C₄	—	4	4	no	—
1150	C₂×C₄	—	4	4	no	—
1151	C₂×C₄	—	4	4	no	—
1152	C₂×C₄	—	4	4	no	—
1153	C₂×C₄	—	4	2	no	—
1154	C₂×C₄	—	4	2	no	—
1155	C₂×C₄	—	4	2	no	—
1156	C₂×C₄	—	8	1	no	—
1157	C₂×C₄	—	8	1	no	—
1158	C₂×C₄	—	8	2	no	—
1159	C₂×C₄	—	8	1	no	—
1160	C₂×C₄	—	8	1	no	—
1161	C₂×C₄	—	8	2	no	—
1162	C₂×C₄	—	8	1	no	—
1163	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
1164	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
1165	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
1166	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
1167	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
1168	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
1169	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
1170	C₂×C₄	C₂×#41×C₁₇	1	2	yes	—
1171	C₂×C₄	C₁₇×H(5,𝔽₂)	1	2	yes	—
1172	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
1173	C₈	—	2	2	no	—
1174	C₈	—	2	1	no	—
1175	C₈	—	2	1	no	—
1176	C₈	—	2	1	no	—
1177	C₈	—	2	1	no	—
1178	C₈	—	2	2	no	—
1179	C₂²	—	2	1	no	—
1180	C₂²	—	2	1	no	—
1181	C₂²	—	2	2	no	—
1182	C₂²	—	2	2	no	—
1183	C₂²	—	2	2	no	—
1184	C₂²	—	2	2	no	—
1185	C₂²	—	2	2	no	—
1186	C₂²	—	2	2	no	—
1187	C₂²	—	4	1	no	—
1188	C₂²	—	4	1	no	—
1189	C₂²	—	4	1	no	—
1190	C₂²	—	4	1	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	4	1	no	—
1193	C₂²	—	4	1	no	—
1194	C₂²	—	4	1	no	—
1195	C₂²	—	4	1	no	—
1196	C₂²	C₁₇×#546	1	2	yes	—
1197	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
1198	C₄	—	2	4	no	—
1199	C₄	—	2	2	no	—
1200	C₄	—	2	2	no	—
1201	C₄	—	2	1	no	—
1202	C₄	—	2	1	no	—
1203	C₄	—	2	1	no	—
1204	C₄	—	2	1	no	—
1205	C₄	—	4	1	no	—
1206	C₄	—	4	1	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	4	1	no	—
1209	C₄	—	4	2	no	—
1210	C₄	—	4	2	no	—
1211	C₄	—	4	1	no	—
1212	C₄	—	4	2	no	—
1213	C₄	C₁₇×#546	1	2	yes	—
1214	C₄	C₂²×#41×C₁₇	1	1	yes	characteristic
1215	C₄	C₂×C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
1216	C₂	—	2	2	no	—
1217	C₂	—	4	2	no	—
1218	C₂	—	4	2	no	—
1219	C₂	—	8	1	no	—
1220	C₂	—	8	1	no	—
1221	C₂	—	8	1	no	—
1222	C₂	C₂×C₁₇×#546	1	1	yes	characteristic
1223	C₂	C₁₇×#3584	1	1	yes	characteristic
1224	C₂	C₁₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₁₇×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×#3512	C₂	semidirect
2. C₁₇×#3497	C₂	semidirect
3. C₁₇×#3327	C₂	semidirect
4. C₁₇×#3326	C₂	semidirect
5. C₁₇×#3320	C₂	semidirect
6. C₁₇×#3317	C₂	semidirect
7. C₁₇×#3312	C₂	semidirect
8. C₁₇×#3309	C₂	semidirect
9. C₁₇×#3301	C₂	semidirect
10. C₁₇×#3300	C₂	semidirect
11. C₁₇×#3142	C₂	semidirect
12. C₁₇×#3099	C₂	semidirect
13. C₁₇×#3098	C₂	semidirect
14. C₂×C₁₇×#479	C₂	semidirect
15. C₁₇×#3061	C₂	semidirect
16. C₁₇×#3060	C₂	semidirect
17. C₁₇×#3035	C₂	semidirect
18. C₁₇×#3013	C₂	semidirect
19. C₁₇×#3013	C₂	semidirect
20. C₄×C₁₇×#137	C₂	semidirect
21. C₁₇×#2935	C₂	semidirect
22. C₁₇×#2898	C₂	semidirect
23. C₁₇×#2898	C₂	semidirect
478. #61204	C₁₇	direct (N × H)
567. #3512	C₂×C₁₇	semidirect
568. #3497	C₂×C₁₇	semidirect
569. #3327	C₂×C₁₇	semidirect
570. #3326	C₂×C₁₇	semidirect
571. #3320	C₂×C₁₇	semidirect
572. #3317	C₂×C₁₇	semidirect
573. #3312	C₂×C₁₇	semidirect
574. #3309	C₂×C₁₇	semidirect
575. #3301	C₂×C₁₇	semidirect
576. #3300	C₂×C₁₇	semidirect
577. #3142	C₂×C₁₇	semidirect
578. #3099	C₂×C₁₇	semidirect
579. #3098	C₂×C₁₇	semidirect
580. C₂×#479	C₂×C₁₇	semidirect
581. #3061	C₂×C₁₇	semidirect
582. #3060	C₂×C₁₇	semidirect
583. #3035	C₂×C₁₇	semidirect
584. #3013	C₂×C₁₇	semidirect
585. #3013	C₂×C₁₇	semidirect
586. C₄×#137	C₂×C₁₇	semidirect
587. #2935	C₂×C₁₇	semidirect
588. #2898	C₂×C₁₇	semidirect
589. #2898	C₂×C₁₇	semidirect
933. C₁₇	#61204	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×#3512	2
C₁₇×#3497	2
C₁₇×#3327	2
C₁₇×#3326	2
C₁₇×#3320	2
C₁₇×#3317	2
C₁₇×#3312	2
C₁₇×#3309	2
C₁₇×#3301	2
C₁₇×#3300	2
C₁₇×#3142	2
C₁₇×#3099	2
C₁₇×#3098	2
C₂×C₁₇×#479	2
C₁₇×#3061	2
C₁₇×#3060	2
C₁₇×#3035	2
C₁₇×#3013	2
C₄×C₁₇×#137	2
C₁₇×#2935	2
C₁₇×#2898	2
#61204	17

Subgroups — C17×#61204 #16918948

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#61204 #16918948