Subgroups — C₁₇×#61568 #16919312

Order 4352.

2142 conjugacy classes of subgroups.

The subgroup lattice has 1224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3304	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#3302	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#3300	C₂	1	2	yes	maximal, complemented
6	C₁₇×#3298	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#3296	C₂	1	2	yes	maximal, complemented
8	C₁₇×#3294	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×Q₁₆×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#3285	C₂	1	2	yes	maximal, complemented
11	C₁₇×#3284	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#3283	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#3282	C₂	1	2	yes	maximal, complemented
14	D₄×SD₁₆×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#3212	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₇×#3210	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₇×#3191	C₂	1	2	yes	maximal, complemented
18	C₁₇×#3190	C₂	1	2	yes	maximal, complemented
19	C₁₇×#3107	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₇×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₇×#3002	C₂	1	2	yes	maximal, complemented
22	C₂×C₁₇×#452	C₂	1	2	yes	maximal, complemented
23	C₁₇×#2972	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₁₇	C₂²	1	2	yes	—
25	C₂×C₁₇×#135	C₂²	1	2	yes	complemented
26	C₂×C₁₇×#135	C₂²	1	2	yes	complemented
27	C₂²×Q₁₆×C₁₇	C₂²	1	2	yes	complemented
28	C₂²×SD₁₆×C₁₇	C₂²	1	2	yes	complemented
29	C₁₇×#556	C₂²	1	1	yes	characteristic, complemented
30	C₁₇×#554	—	2	1	no	—
31	C₁₇×#552	C₂²	1	2	yes	complemented
32	C₁₇×#551	—	2	2	no	—
33	C₁₇×#550	C₂²	1	1	yes	characteristic
34	D₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
35	D₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
36	C₁₇×#548	C₂²	1	2	yes	—
37	C₁₇×#548	C₂²	1	2	yes	complemented
38	C₁₇×#547	—	2	1	no	—
39	C₁₇×#547	C₂²	1	1	yes	characteristic
40	C₁₇×#547	C₂²	1	1	yes	characteristic
41	C₁₇×#547	C₂²	1	1	yes	characteristic, complemented
42	C₁₇×#546	—	2	2	no	—
43	C₁₇×#546	—	2	1	no	—
44	C₁₇×#546	C₂²	1	2	yes	—
45	D₄²×C₁₇	—	2	1	no	—
46	D₄²×C₁₇	C₂²	1	1	yes	characteristic
47	C₁₇×#542	—	2	1	no	—
48	C₁₇×#539	—	2	2	no	—
49	C₁₇×#533	C₂²	1	1	yes	characteristic, complemented
50	C₁₇×#532	—	2	1	no	—
51	C₁₇×#532	C₂²	1	1	yes	characteristic
52	C₁₇×#529	C₂²	1	1	yes	characteristic, complemented
53	C₁₇×#525	—	2	2	no	—
54	C₁₇×#525	C₂²	1	2	yes	—
55	C₁₇×#525	C₂²	1	2	yes	complemented
56	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
57	C₁₇×#520	—	2	1	no	—
58	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
59	C₂×C₄×D₄×C₁₇	—	2	1	no	—
60	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
61	C₁₇×#495	C₂²	1	2	yes	complemented
62	C₁₇×#494	C₂²	1	1	yes	characteristic, complemented
63	C₁₇×#492	C₂²	1	1	yes	characteristic, complemented
64	C₁₇×#488	C₂²	1	2	yes	complemented
65	C₁₇×#487	C₂²	1	1	yes	characteristic, complemented
66	C₁₇×#486	C₂²	1	1	yes	characteristic, complemented
67	C₁₇×#485	C₂²	1	2	yes	complemented
68	C₁₇×#485	C₂²	1	1	yes	characteristic, complemented
69	C₁₇×#485	C₂²	1	2	yes	complemented
70	C₁₇×#483	C₂²	1	2	yes	complemented
71	C₁₇×#482	C₂²	1	2	yes	complemented
72	C₁₇×#482	C₂²	1	1	yes	characteristic, complemented
73	C₁₇×#480	C₂²	1	2	yes	complemented
74	C₁₇×#479	C₂²	1	1	yes	characteristic, complemented
75	C₁₇×#478	C₂²	1	1	yes	characteristic, complemented
76	C₁₇×#475	C₂²	1	1	yes	characteristic, complemented
77	C₁₇×#474	C₂²	1	1	yes	characteristic, complemented
78	C₁₇×#467	C₂²	1	2	yes	complemented
79	C₁₇×#467	C₂²	1	2	yes	complemented
80	C₁₇×#467	C₂²	1	2	yes	complemented
81	C₁₇×#466	C₂²	1	2	yes	complemented
82	C₁₇×#465	C₂²	1	2	yes	complemented
83	C₁₇×#465	C₂²	1	2	yes	complemented
84	C₁₇×#465	C₂²	1	2	yes	complemented
85	C₁₇×#465	C₂²	1	2	yes	complemented
86	C₁₇×#464	C₂²	1	2	yes	complemented
87	C₁₇×#464	C₂²	1	2	yes	complemented
88	C₁₇×#464	C₂²	1	1	yes	characteristic, complemented
89	C₁₇×#463	C₂²	1	1	yes	characteristic, complemented
90	C₁₇×#462	C₂²	1	1	yes	characteristic, complemented
91	C₁₇×#462	C₂²	1	1	yes	characteristic, complemented
92	C₁₇×#461	C₂²	1	1	yes	characteristic, complemented
93	C₁₇×#461	C₂²	1	1	yes	characteristic, complemented
94	C₁₇×#460	C₂²	1	1	yes	characteristic, complemented
95	C₁₇×#459	C₂²	1	1	yes	characteristic, complemented
96	C₁₇×#452	C₂²	1	1	yes	characteristic
97	C₁₇×#452	C₂²	1	2	yes	—
98	C₁₇×#452	C₂²	1	2	yes	complemented
99	C₁₇×#452	C₂²	1	2	yes	complemented
100	C₁₇×#452	C₂²	1	2	yes	complemented
101	C₁₇×#452	C₂²	1	2	yes	complemented
102	C₁₇×#452	C₂²	1	2	yes	complemented
103	C₁₇×#452	C₂²	1	2	yes	complemented
104	C₁₇×#452	C₂²	1	2	yes	complemented
105	C₁₇×#452	C₂²	1	2	yes	complemented
106	C₁₇×#451	C₂²	1	2	yes	complemented
107	C₁₇×#451	C₂²	1	2	yes	complemented
108	C₁₇×#450	C₂²	1	2	yes	complemented
109	C₁₇×#449	C₂²	1	1	yes	characteristic
110	C₁₇×#449	C₂²	1	2	yes	complemented
111	C₁₇×#449	C₂²	1	2	yes	complemented
112	C₁₇×#448	C₂²	1	2	yes	complemented
113	C₁₇×#448	C₂²	1	2	yes	complemented
114	C₁₇×#447	C₂²	1	2	yes	complemented
115	C₄×Q₁₆×C₁₇	C₂²	1	2	yes	complemented
116	C₄×Q₁₆×C₁₇	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆×C₁₇	C₂²	1	2	yes	complemented
119	C₄×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
121	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic
122	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic
123	C₈×D₄×C₁₇	C₂²	1	2	yes	complemented
124	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
125	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
126	C₈×D₄×C₁₇	C₂²	1	2	yes	complemented
127	C₁₇×#431	C₂²	1	1	yes	characteristic, complemented
128	C₁₇×#431	C₂²	1	1	yes	characteristic, complemented
129	C₁₇×#416	C₂²	1	2	yes	complemented
130	C₁₇×#416	C₂²	1	2	yes	complemented
131	C₂×C₁₇×#103	C₂²	1	2	yes	complemented
132	C₂×C₁₇×#102	C₂²	1	2	yes	complemented
133	C₂×C₁₇×C₂²⋊C₈	C₂²	1	2	yes	complemented
134	C₂×C₁₇×C₂²⋊C₈	C₂²	1	2	yes	complemented
135	C₂×#41×C₁₇	—	2	1	no	—
136	C₂×#41×C₁₇	—	2	2	no	—
137	C₂×#41×C₁₇	—	2	2	no	—
138	C₂×#41×C₁₇	—	4	4	no	—
139	C₂×#41×C₁₇	—	4	4	no	—
140	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
141	C₂×#41×C₁₇	C₂³	1	2	yes	—
142	C₂×#41×C₁₇	C₂³	1	2	yes	—
143	C₂×#41×C₁₇	C₂³	1	2	yes	—
144	C₂×#41×C₁₇	C₂³	1	2	yes	—
145	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
146	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
147	C₂²×D₄×C₁₇	—	2	2	no	—
148	C₂²×D₄×C₁₇	—	2	1	no	—
149	C₂²×D₄×C₁₇	D₄	1	1	yes	characteristic
150	C₂²×D₄×C₁₇	C₂³	1	2	yes	—
151	C₂³×C₄×C₁₇	—	2	2	no	—
152	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
153	C₁₇×#135	—	4	4	no	—
154	C₁₇×#135	—	4	4	no	—
155	C₂×Q₁₆×C₁₇	—	4	4	no	—
156	C₂×Q₁₆×C₁₇	C₂³	1	1	yes	characteristic
157	C₂×Q₁₆×C₁₇	C₂³	1	2	yes	—
158	C₂×Q₁₆×C₁₇	C₂³	1	2	yes	—
159	C₂×Q₁₆×C₁₇	C₂³	1	2	yes	—
160	C₂×Q₁₆×C₁₇	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₁₇	—	4	4	no	—
162	C₂×SD₁₆×C₁₇	C₂³	1	1	yes	characteristic
163	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
164	C₂×SD₁₆×C₁₇	C₂³	1	1	yes	characteristic
165	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
166	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
167	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
168	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
169	C₂×D₈×C₁₇	C₂³	1	1	yes	characteristic
170	C₂×D₈×C₁₇	C₂³	1	2	yes	—
171	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
172	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
173	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
174	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
175	C₁₇×C₄⋊Q₈	—	2	1	no	—
176	C₁₇×C₄⋊Q₈	—	2	1	no	—
177	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
178	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
179	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
180	C₁₇×#127	—	2	1	no	—
181	C₁₇×#127	C₂³	1	1	yes	characteristic
182	C₁₇×#126	—	2	2	no	—
183	C₁₇×#126	—	2	2	no	—
184	C₁₇×#126	—	2	1	no	—
185	C₁₇×#125	—	2	2	no	—
186	C₁₇×#125	—	2	1	no	—
187	C₁₇×#125	C₂³	1	1	yes	characteristic
188	C₁₇×#124	—	2	1	no	—
189	C₁₇×#124	—	2	2	no	—
190	C₁₇×#124	—	2	2	no	—
191	C₁₇×#124	C₂³	1	1	yes	characteristic
192	C₁₇×#124	C₂³	1	2	yes	—
193	C₁₇×#123	—	2	2	no	—
194	C₁₇×#123	—	2	2	no	—
195	C₁₇×#123	—	2	2	no	—
196	C₁₇×#123	—	2	1	no	—
197	C₁₇×#123	—	2	2	no	—
198	C₁₇×#123	—	2	2	no	—
199	C₁₇×#123	—	2	2	no	—
200	C₁₇×#123	—	2	2	no	—
201	C₁₇×C₂²⋊Q₈	—	2	2	no	—
202	C₁₇×C₂²⋊Q₈	—	2	2	no	—
203	C₁₇×C₂²⋊Q₈	—	2	1	no	—
204	C₁₇×C₂²⋊Q₈	—	2	2	no	—
205	C₁₇×C₂²⋊Q₈	—	2	2	no	—
206	C₁₇×C₂²⋊Q₈	—	2	1	no	—
207	C₁₇×C₂²⋊Q₈	—	2	2	no	—
208	C₁₇×C₂²⋊Q₈	—	2	2	no	—
209	C₁₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
210	C₁₇×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₁₇×C₂²⋊Q₈	C₂³	1	2	yes	—
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	2	no	—
217	C₁₇×#121	—	2	1	no	—
218	C₁₇×#121	—	2	2	no	—
219	C₁₇×#121	—	2	1	no	—
220	C₁₇×#121	—	2	1	no	—
221	C₁₇×#121	—	2	1	no	—
222	C₁₇×#121	—	2	1	no	—
223	C₁₇×#121	—	2	2	no	—
224	C₁₇×#121	—	2	2	no	—
225	C₁₇×#121	C₂³	1	2	yes	—
226	C₁₇×#121	C₂³	1	2	yes	—
227	C₁₇×#121	C₂³	1	1	yes	characteristic
228	C₁₇×#121	C₂³	1	2	yes	—
229	C₁₇×#120	—	2	2	no	—
230	C₁₇×#120	—	2	2	no	—
231	C₁₇×#120	—	2	2	no	—
232	C₁₇×#120	—	2	2	no	—
233	C₄×Q₈×C₁₇	—	2	1	no	—
234	C₄×Q₈×C₁₇	—	2	1	no	—
235	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
238	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
239	C₄×D₄×C₁₇	—	2	1	no	—
240	C₄×D₄×C₁₇	—	2	1	no	—
241	C₄×D₄×C₁₇	—	2	2	no	—
242	C₄×D₄×C₁₇	—	2	1	no	—
243	C₄×D₄×C₁₇	—	2	1	no	—
244	C₄×D₄×C₁₇	—	2	2	no	—
245	C₄×D₄×C₁₇	—	2	2	no	—
246	C₄×D₄×C₁₇	—	2	2	no	—
247	C₄×D₄×C₁₇	—	2	1	no	—
248	C₄×D₄×C₁₇	—	2	1	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	D₄	1	1	yes	characteristic
254	C₄×D₄×C₁₇	D₄	1	2	yes	—
255	C₄×D₄×C₁₇	D₄	1	1	yes	characteristic
256	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₁₇	C₂³	1	2	yes	—
261	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
262	C₁₇×#117	—	2	1	no	—
263	C₁₇×#117	—	2	2	no	—
264	C₁₇×#117	—	2	1	no	—
265	C₁₇×#117	—	2	1	no	—
266	C₁₇×#117	C₂³	1	1	yes	characteristic
267	C₁₇×#117	C₂³	1	2	yes	—
268	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
269	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
270	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
271	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
272	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
273	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
274	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
275	C₂×C₂²⋊C₄×C₁₇	D₄	1	2	yes	—
276	C₂×C₄²×C₁₇	—	2	1	no	—
277	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
278	C₁₇×#107	C₂³	1	1	yes	characteristic
279	C₁₇×#107	C₂³	1	2	yes	—
280	C₁₇×#107	C₂³	1	1	yes	characteristic
281	C₁₇×#106	C₂³	1	2	yes	—
282	C₁₇×#106	C₂³	1	1	yes	characteristic
283	C₁₇×#106	C₂³	1	1	yes	characteristic
284	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
288	C₁₇×#103	C₂³	1	1	yes	characteristic
289	C₁₇×#103	C₂³	1	2	yes	—
290	C₁₇×#103	C₂³	1	2	yes	—
291	C₁₇×#103	C₂³	1	2	yes	—
292	C₁₇×#103	C₂³	1	1	yes	characteristic
293	C₁₇×#103	C₂³	1	2	yes	—
294	C₁₇×#103	C₂³	1	2	yes	—
295	C₁₇×#103	C₂³	1	1	yes	characteristic
296	C₁₇×#103	C₂³	1	2	yes	—
297	C₁₇×#103	C₂³	1	2	yes	—
298	C₁₇×#103	C₂³	1	1	yes	characteristic
299	C₁₇×#102	C₂³	1	1	yes	characteristic
300	C₁₇×#102	C₂³	1	2	yes	—
301	C₁₇×#102	C₂³	1	2	yes	—
302	C₁₇×#102	C₂³	1	2	yes	—
303	C₁₇×#102	C₂³	1	1	yes	characteristic
304	C₁₇×#102	C₂³	1	2	yes	—
305	C₁₇×#102	C₂³	1	2	yes	—
306	C₁₇×#102	C₂³	1	1	yes	characteristic
307	C₁₇×#102	C₂³	1	1	yes	characteristic
308	C₁₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₁₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
311	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
313	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
314	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
315	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
316	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
317	C₄×C₈×C₁₇	C₂³	1	2	yes	—
318	C₂⁴×C₁₇	—	2	2	no	—
319	C₂⁴×C₁₇	C₂×D₄	1	2	yes	—
320	#41×C₁₇	—	2	2	no	—
321	#41×C₁₇	—	2	2	no	—
322	#41×C₁₇	—	2	4	no	—
323	#41×C₁₇	—	2	4	no	—
324	#41×C₁₇	—	4	2	no	—
325	#41×C₁₇	—	4	2	no	—
326	#41×C₁₇	—	4	2	no	—
327	#41×C₁₇	—	4	2	no	—
328	#41×C₁₇	—	4	8	no	—
329	#41×C₁₇	—	4	2	no	—
330	#41×C₁₇	—	4	2	no	—
331	#41×C₁₇	—	4	8	no	—
332	#41×C₁₇	—	4	4	no	—
333	C₂×Q₈×C₁₇	—	2	2	no	—
334	C₂×Q₈×C₁₇	—	2	1	no	—
335	C₂×Q₈×C₁₇	—	2	2	no	—
336	C₂×Q₈×C₁₇	—	2	4	no	—
337	C₂×Q₈×C₁₇	—	4	2	no	—
338	C₂×Q₈×C₁₇	—	4	2	no	—
339	C₂×Q₈×C₁₇	—	4	2	no	—
340	C₂×Q₈×C₁₇	C₂⁴	1	1	yes	characteristic
341	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
342	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
343	C₂×Q₈×C₁₇	C₂⁴	1	1	yes	characteristic
344	C₂×D₄×C₁₇	—	2	1	no	—
345	C₂×D₄×C₁₇	—	2	4	no	—
346	C₂×D₄×C₁₇	—	2	4	no	—
347	C₂×D₄×C₁₇	—	2	2	no	—
348	C₂×D₄×C₁₇	—	2	2	no	—
349	C₂×D₄×C₁₇	—	2	2	no	—
350	C₂×D₄×C₁₇	—	2	1	no	—
351	C₂×D₄×C₁₇	—	2	2	no	—
352	C₂×D₄×C₁₇	—	2	2	no	—
353	C₂×D₄×C₁₇	—	2	2	no	—
354	C₂×D₄×C₁₇	—	2	2	no	—
355	C₂×D₄×C₁₇	—	2	2	no	—
356	C₂×D₄×C₁₇	—	2	1	no	—
357	C₂×D₄×C₁₇	—	2	1	no	—
358	C₂×D₄×C₁₇	—	4	2	no	—
359	C₂×D₄×C₁₇	—	4	8	no	—
360	C₂×D₄×C₁₇	—	4	4	no	—
361	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
362	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
363	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
364	C₂×D₄×C₁₇	C₂⁴	1	2	yes	—
365	C₂×D₄×C₁₇	C₂⁴	1	1	yes	characteristic
366	C₂×D₄×C₁₇	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₁₇	—	2	1	no	—
368	C₂²×C₄×C₁₇	—	2	2	no	—
369	C₂²×C₄×C₁₇	—	2	2	no	—
370	C₂²×C₄×C₁₇	—	2	2	no	—
371	C₂²×C₄×C₁₇	—	2	2	no	—
372	C₂²×C₄×C₁₇	—	2	1	no	—
373	C₂²×C₄×C₁₇	—	2	2	no	—
374	C₂²×C₄×C₁₇	—	2	2	no	—
375	C₂²×C₄×C₁₇	—	2	1	no	—
376	C₂²×C₄×C₁₇	—	2	2	no	—
377	C₂²×C₄×C₁₇	—	2	1	no	—
378	C₂²×C₄×C₁₇	—	4	2	no	—
379	C₂²×C₄×C₁₇	—	4	2	no	—
380	C₂²×C₄×C₁₇	—	4	8	no	—
381	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
382	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
383	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
384	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
385	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
386	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
387	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
389	Q₁₆×C₁₇	—	2	2	no	—
390	Q₁₆×C₁₇	—	2	4	no	—
391	Q₁₆×C₁₇	—	4	2	no	—
392	Q₁₆×C₁₇	—	4	2	no	—
393	Q₁₆×C₁₇	—	4	2	no	—
394	SD₁₆×C₁₇	—	2	2	no	—
395	SD₁₆×C₁₇	—	2	2	no	—
396	SD₁₆×C₁₇	—	2	4	no	—
397	SD₁₆×C₁₇	—	4	2	no	—
398	SD₁₆×C₁₇	—	4	2	no	—
399	SD₁₆×C₁₇	—	4	2	no	—
400	SD₁₆×C₁₇	—	4	2	no	—
401	D₈×C₁₇	—	2	2	no	—
402	D₈×C₁₇	—	4	2	no	—
403	C₂×C₈×C₁₇	—	4	2	no	—
404	C₂×C₈×C₁₇	—	4	2	no	—
405	C₂×C₈×C₁₇	—	4	2	no	—
406	C₂×C₈×C₁₇	—	4	2	no	—
407	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
408	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
409	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
410	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
411	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
412	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₁₇	—	2	2	no	—
414	C₄⋊C₄×C₁₇	—	2	1	no	—
415	C₄⋊C₄×C₁₇	—	2	2	no	—
416	C₄⋊C₄×C₁₇	—	2	1	no	—
417	C₄⋊C₄×C₁₇	—	2	1	no	—
418	C₄⋊C₄×C₁₇	—	2	2	no	—
419	C₄⋊C₄×C₁₇	—	2	1	no	—
420	C₄⋊C₄×C₁₇	—	2	1	no	—
421	C₄⋊C₄×C₁₇	—	2	1	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	2	no	—
426	C₄⋊C₄×C₁₇	—	2	2	no	—
427	C₄⋊C₄×C₁₇	—	2	1	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	C₂×D₄	1	2	yes	—
433	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
434	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
435	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
436	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
437	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
438	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
440	C₂²⋊C₄×C₁₇	—	2	1	no	—
441	C₂²⋊C₄×C₁₇	—	2	2	no	—
442	C₂²⋊C₄×C₁₇	—	2	2	no	—
443	C₂²⋊C₄×C₁₇	—	2	2	no	—
444	C₂²⋊C₄×C₁₇	—	2	2	no	—
445	C₂²⋊C₄×C₁₇	—	2	2	no	—
446	C₂²⋊C₄×C₁₇	—	2	2	no	—
447	C₂²⋊C₄×C₁₇	—	2	2	no	—
448	C₂²⋊C₄×C₁₇	—	2	1	no	—
449	C₂²⋊C₄×C₁₇	—	2	2	no	—
450	C₂²⋊C₄×C₁₇	—	2	1	no	—
451	C₂²⋊C₄×C₁₇	—	2	2	no	—
452	C₂²⋊C₄×C₁₇	—	2	2	no	—
453	C₂²⋊C₄×C₁₇	—	2	1	no	—
454	C₂²⋊C₄×C₁₇	—	2	1	no	—
455	C₂²⋊C₄×C₁₇	—	2	2	no	—
456	C₂²⋊C₄×C₁₇	—	2	1	no	—
457	C₂²⋊C₄×C₁₇	—	2	1	no	—
458	C₂²⋊C₄×C₁₇	—	2	1	no	—
459	C₂²⋊C₄×C₁₇	—	2	2	no	—
460	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
461	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
462	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
463	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
464	C₄²×C₁₇	—	2	1	no	—
465	C₄²×C₁₇	—	2	2	no	—
466	C₄²×C₁₇	—	2	1	no	—
467	C₄²×C₁₇	—	2	2	no	—
468	C₄²×C₁₇	—	2	1	no	—
469	C₄²×C₁₇	—	2	1	no	—
470	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
471	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
472	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
473	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
474	#61568	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
475	C₂³×C₁₇	—	2	1	no	—
476	C₂³×C₁₇	—	2	4	no	—
477	C₂³×C₁₇	—	2	1	no	—
478	C₂³×C₁₇	—	2	2	no	—
479	C₂³×C₁₇	—	4	2	no	—
480	C₂³×C₁₇	—	4	2	no	—
481	C₂³×C₁₇	—	4	4	no	—
482	C₂³×C₁₇	—	4	4	no	—
483	C₂³×C₁₇	—	8	2	no	—
484	C₂³×C₁₇	C₂²×D₄	1	2	yes	—
485	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
486	C₂³×C₁₇	C₂²×D₄	1	2	yes	—
487	Q₈×C₁₇	—	2	1	no	—
488	Q₈×C₁₇	—	2	1	no	—
489	Q₈×C₁₇	—	2	2	no	—
490	Q₈×C₁₇	—	2	2	no	—
491	Q₈×C₁₇	—	2	2	no	—
492	Q₈×C₁₇	—	2	1	no	—
493	Q₈×C₁₇	—	2	2	no	—
494	Q₈×C₁₇	—	4	4	no	—
495	Q₈×C₁₇	—	4	2	no	—
496	Q₈×C₁₇	—	8	2	no	—
497	Q₈×C₁₇	H(5,𝔽₂)	1	2	yes	—
498	D₄×C₁₇	—	2	4	no	—
499	D₄×C₁₇	—	2	4	no	—
500	D₄×C₁₇	—	2	2	no	—
501	D₄×C₁₇	—	2	1	no	—
502	D₄×C₁₇	—	2	1	no	—
503	D₄×C₁₇	—	2	1	no	—
504	D₄×C₁₇	—	2	2	no	—
505	D₄×C₁₇	—	2	2	no	—
506	D₄×C₁₇	—	4	4	no	—
507	D₄×C₁₇	—	4	4	no	—
508	D₄×C₁₇	—	4	4	no	—
509	D₄×C₁₇	—	4	2	no	—
510	D₄×C₁₇	—	4	4	no	—
511	D₄×C₁₇	—	4	4	no	—
512	D₄×C₁₇	—	4	4	no	—
513	D₄×C₁₇	—	4	2	no	—
514	D₄×C₁₇	—	8	1	no	—
515	D₄×C₁₇	—	8	2	no	—
516	D₄×C₁₇	—	8	2	no	—
517	D₄×C₁₇	#135	1	4	yes	complemented
518	D₄×C₁₇	H(5,𝔽₂)	1	2	yes	—
519	C₂×C₄×C₁₇	—	2	4	no	—
520	C₂×C₄×C₁₇	—	2	1	no	—
521	C₂×C₄×C₁₇	—	2	2	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	1	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	1	no	—
531	C₂×C₄×C₁₇	—	2	2	no	—
532	C₂×C₄×C₁₇	—	2	1	no	—
533	C₂×C₄×C₁₇	—	2	2	no	—
534	C₂×C₄×C₁₇	—	2	1	no	—
535	C₂×C₄×C₁₇	—	2	2	no	—
536	C₂×C₄×C₁₇	—	4	2	no	—
537	C₂×C₄×C₁₇	—	4	2	no	—
538	C₂×C₄×C₁₇	—	4	2	no	—
539	C₂×C₄×C₁₇	—	4	1	no	—
540	C₂×C₄×C₁₇	—	4	4	no	—
541	C₂×C₄×C₁₇	—	4	4	no	—
542	C₂×C₄×C₁₇	—	4	4	no	—
543	C₂×C₄×C₁₇	—	4	4	no	—
544	C₂×C₄×C₁₇	—	4	4	no	—
545	C₂×C₄×C₁₇	—	4	2	no	—
546	C₂×C₄×C₁₇	—	4	2	no	—
547	C₂×C₄×C₁₇	—	8	1	no	—
548	C₂×C₄×C₁₇	—	8	2	no	—
549	C₂×C₄×C₁₇	—	8	2	no	—
550	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
553	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
555	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
556	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
557	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
558	C₈×C₁₇	—	2	1	no	—
559	C₈×C₁₇	—	2	2	no	—
560	C₈×C₁₇	—	2	1	no	—
561	C₈×C₁₇	—	2	1	no	—
562	C₈×C₁₇	—	2	2	no	—
563	C₈×C₁₇	—	2	1	no	—
564	#3520	C₂×C₁₇	1	1	yes	characteristic, complemented
565	D₄×#41	C₂×C₁₇	1	1	yes	characteristic, complemented
566	#3304	C₂×C₁₇	1	1	yes	characteristic, complemented
567	#3302	C₂×C₁₇	1	1	yes	characteristic, complemented
568	#3300	C₂×C₁₇	1	2	yes	complemented
569	#3298	C₂×C₁₇	1	1	yes	characteristic, complemented
570	#3296	C₂×C₁₇	1	2	yes	complemented
571	#3294	C₂×C₁₇	1	1	yes	characteristic, complemented
572	D₄×Q₁₆	C₂×C₁₇	1	1	yes	characteristic, complemented
573	#3285	C₂×C₁₇	1	2	yes	complemented
574	#3284	C₂×C₁₇	1	1	yes	characteristic, complemented
575	#3283	C₂×C₁₇	1	1	yes	characteristic, complemented
576	#3282	C₂×C₁₇	1	2	yes	complemented
577	D₄×SD₁₆	C₂×C₁₇	1	1	yes	characteristic, complemented
578	#3212	C₂×C₁₇	1	1	yes	characteristic, complemented
579	#3210	C₂×C₁₇	1	1	yes	characteristic, complemented
580	#3191	C₂×C₁₇	1	2	yes	complemented
581	#3190	C₂×C₁₇	1	2	yes	complemented
582	#3107	C₂×C₁₇	1	1	yes	characteristic, complemented
583	#3102	C₂×C₁₇	1	1	yes	characteristic, complemented
584	#3002	C₂×C₁₇	1	2	yes	complemented
585	C₂×#452	C₂×C₁₇	1	2	yes	complemented
586	#2972	C₂×C₁₇	1	1	yes	characteristic, complemented
587	C₂²×C₁₇	—	2	2	no	—
588	C₂²×C₁₇	—	2	2	no	—
589	C₂²×C₁₇	—	2	1	no	—
590	C₂²×C₁₇	—	2	2	no	—
591	C₂²×C₁₇	—	2	1	no	—
592	C₂²×C₁₇	—	2	2	no	—
593	C₂²×C₁₇	—	2	2	no	—
594	C₂²×C₁₇	—	2	1	no	—
595	C₂²×C₁₇	—	2	2	no	—
596	C₂²×C₁₇	—	4	1	no	—
597	C₂²×C₁₇	—	4	1	no	—
598	C₂²×C₁₇	—	4	1	no	—
599	C₂²×C₁₇	—	4	2	no	—
600	C₂²×C₁₇	—	4	2	no	—
601	C₂²×C₁₇	—	4	1	no	—
602	C₂²×C₁₇	—	4	1	no	—
603	C₂²×C₁₇	—	4	2	no	—
604	C₂²×C₁₇	—	8	4	no	—
605	C₂²×C₁₇	—	8	8	no	—
606	C₂²×C₁₇	C₂×#135	1	4	yes	—
607	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
608	C₄×C₁₇	—	2	1	no	—
609	C₄×C₁₇	—	2	1	no	—
610	C₄×C₁₇	—	2	1	no	—
611	C₄×C₁₇	—	2	2	no	—
612	C₄×C₁₇	—	2	2	no	—
613	C₄×C₁₇	—	2	2	no	—
614	C₄×C₁₇	—	2	1	no	—
615	C₄×C₁₇	—	4	1	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	1	no	—
621	C₄×C₁₇	—	4	1	no	—
622	C₄×C₁₇	—	4	2	no	—
623	C₄×C₁₇	C₂×#135	1	2	yes	—
624	C₄×C₁₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
625	C₄×C₁₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
626	C₂²×#41	C₂²×C₁₇	1	2	yes	—
627	C₂×#135	C₂²×C₁₇	1	2	yes	complemented
628	C₂×#135	C₂²×C₁₇	1	2	yes	complemented
629	C₂²×Q₁₆	C₂²×C₁₇	1	2	yes	complemented
630	C₂²×SD₁₆	C₂²×C₁₇	1	2	yes	complemented
631	#556	C₂²×C₁₇	1	1	yes	characteristic, complemented
632	#554	—	2	1	no	—
633	#552	C₂²×C₁₇	1	2	yes	complemented
634	#551	—	2	2	no	—
635	#550	C₂²×C₁₇	1	1	yes	characteristic
636	D₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
637	D₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
638	#548	C₂²×C₁₇	1	2	yes	—
639	#548	C₂²×C₁₇	1	2	yes	complemented
640	#547	—	2	1	no	—
641	#547	C₂²×C₁₇	1	1	yes	characteristic
642	#547	C₂²×C₁₇	1	1	yes	characteristic
643	#547	C₂²×C₁₇	1	1	yes	characteristic, complemented
644	#546	—	2	1	no	—
645	#546	—	2	2	no	—
646	#546	C₂²×C₁₇	1	2	yes	—
647	D₄²	—	2	1	no	—
648	D₄²	C₂²×C₁₇	1	1	yes	characteristic
649	#542	—	2	1	no	—
650	#539	—	2	2	no	—
651	#533	C₂²×C₁₇	1	1	yes	characteristic, complemented
652	#532	—	2	1	no	—
653	#532	C₂²×C₁₇	1	1	yes	characteristic
654	#529	C₂²×C₁₇	1	1	yes	characteristic, complemented
655	#525	—	2	2	no	—
656	#525	C₂²×C₁₇	1	2	yes	—
657	#525	C₂²×C₁₇	1	2	yes	complemented
658	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	2	yes	complemented
659	#520	—	2	1	no	—
660	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
661	C₂×C₄×D₄	—	2	1	no	—
662	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
663	#495	C₂²×C₁₇	1	2	yes	complemented
664	#494	C₂²×C₁₇	1	1	yes	characteristic, complemented
665	#492	C₂²×C₁₇	1	1	yes	characteristic, complemented
666	#488	C₂²×C₁₇	1	2	yes	complemented
667	#487	C₂²×C₁₇	1	1	yes	characteristic, complemented
668	#486	C₂²×C₁₇	1	1	yes	characteristic, complemented
669	#485	C₂²×C₁₇	1	1	yes	characteristic, complemented
670	#485	C₂²×C₁₇	1	2	yes	complemented
671	#485	C₂²×C₁₇	1	2	yes	complemented
672	#483	C₂²×C₁₇	1	2	yes	complemented
673	#482	C₂²×C₁₇	1	1	yes	characteristic, complemented
674	#482	C₂²×C₁₇	1	2	yes	complemented
675	#480	C₂²×C₁₇	1	2	yes	complemented
676	#479	C₂²×C₁₇	1	1	yes	characteristic, complemented
677	#478	C₂²×C₁₇	1	1	yes	characteristic, complemented
678	#475	C₂²×C₁₇	1	1	yes	characteristic, complemented
679	#474	C₂²×C₁₇	1	1	yes	characteristic, complemented
680	#467	C₂²×C₁₇	1	2	yes	complemented
681	#467	C₂²×C₁₇	1	2	yes	complemented
682	#467	C₂²×C₁₇	1	2	yes	complemented
683	#466	C₂²×C₁₇	1	2	yes	complemented
684	#465	C₂²×C₁₇	1	2	yes	complemented
685	#465	C₂²×C₁₇	1	2	yes	complemented
686	#465	C₂²×C₁₇	1	2	yes	complemented
687	#465	C₂²×C₁₇	1	2	yes	complemented
688	#464	C₂²×C₁₇	1	1	yes	characteristic, complemented
689	#464	C₂²×C₁₇	1	2	yes	complemented
690	#464	C₂²×C₁₇	1	2	yes	complemented
691	#463	C₂²×C₁₇	1	1	yes	characteristic, complemented
692	#462	C₂²×C₁₇	1	1	yes	characteristic, complemented
693	#462	C₂²×C₁₇	1	1	yes	characteristic, complemented
694	#461	C₂²×C₁₇	1	1	yes	characteristic, complemented
695	#461	C₂²×C₁₇	1	1	yes	characteristic, complemented
696	#460	C₂²×C₁₇	1	1	yes	characteristic, complemented
697	#459	C₂²×C₁₇	1	1	yes	characteristic, complemented
698	#452	C₂²×C₁₇	1	1	yes	characteristic
699	#452	C₂²×C₁₇	1	2	yes	—
700	#452	C₂²×C₁₇	1	2	yes	complemented
701	#452	C₂²×C₁₇	1	2	yes	complemented
702	#452	C₂²×C₁₇	1	2	yes	complemented
703	#452	C₂²×C₁₇	1	2	yes	complemented
704	#452	C₂²×C₁₇	1	2	yes	complemented
705	#452	C₂²×C₁₇	1	2	yes	complemented
706	#452	C₂²×C₁₇	1	2	yes	complemented
707	#452	C₂²×C₁₇	1	2	yes	complemented
708	#451	C₂²×C₁₇	1	2	yes	complemented
709	#451	C₂²×C₁₇	1	2	yes	complemented
710	#450	C₂²×C₁₇	1	2	yes	complemented
711	#449	C₂²×C₁₇	1	1	yes	characteristic
712	#449	C₂²×C₁₇	1	2	yes	complemented
713	#449	C₂²×C₁₇	1	2	yes	complemented
714	#448	C₂²×C₁₇	1	2	yes	complemented
715	#448	C₂²×C₁₇	1	2	yes	complemented
716	#447	C₂²×C₁₇	1	2	yes	complemented
717	C₄×Q₁₆	C₂²×C₁₇	1	1	yes	characteristic, complemented
718	C₄×Q₁₆	C₂²×C₁₇	1	2	yes	complemented
719	C₄×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic, complemented
720	C₄×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic, complemented
721	C₄×SD₁₆	C₂²×C₁₇	1	2	yes	complemented
722	C₄×D₈	C₂²×C₁₇	1	1	yes	characteristic, complemented
723	C₈×D₄	C₂²×C₁₇	1	1	yes	characteristic
724	C₈×D₄	C₂²×C₁₇	1	1	yes	characteristic
725	C₈×D₄	C₂²×C₁₇	1	2	yes	complemented
726	C₈×D₄	C₂²×C₁₇	1	1	yes	characteristic, complemented
727	C₈×D₄	C₂²×C₁₇	1	1	yes	characteristic, complemented
728	C₈×D₄	C₂²×C₁₇	1	2	yes	complemented
729	#431	C₂²×C₁₇	1	1	yes	characteristic, complemented
730	#431	C₂²×C₁₇	1	1	yes	characteristic, complemented
731	#416	C₂²×C₁₇	1	2	yes	complemented
732	#416	C₂²×C₁₇	1	2	yes	complemented
733	C₂×#103	C₂²×C₁₇	1	2	yes	complemented
734	C₂×#102	C₂²×C₁₇	1	2	yes	complemented
735	C₂×C₂²⋊C₈	C₂²×C₁₇	1	2	yes	complemented
736	C₂×C₂²⋊C₈	C₂²×C₁₇	1	2	yes	complemented
737	C₂×C₁₇	—	2	4	no	—
738	C₂×C₁₇	—	4	2	no	—
739	C₂×C₁₇	—	4	1	no	—
740	C₂×C₁₇	—	4	2	no	—
741	C₂×C₁₇	—	8	1	no	—
742	C₂×C₁₇	—	8	2	no	—
743	C₂×C₁₇	#3484	1	1	yes	characteristic
744	C₂×C₁₇	C₂²×#135	1	1	yes	characteristic
745	C₂×C₁₇	#3586	1	1	yes	characteristic
746	C₂×#41	—	2	1	no	—
747	C₂×#41	—	2	2	no	—
748	C₂×#41	—	2	2	no	—
749	C₂×#41	—	4	4	no	—
750	C₂×#41	—	4	4	no	—
751	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
752	C₂×#41	C₂³×C₁₇	1	2	yes	—
753	C₂×#41	C₂³×C₁₇	1	2	yes	—
754	C₂×#41	C₂³×C₁₇	1	2	yes	—
755	C₂×#41	C₂³×C₁₇	1	2	yes	—
756	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
757	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
758	C₂²×D₄	—	2	2	no	—
759	C₂²×D₄	—	2	1	no	—
760	C₂²×D₄	D₄×C₁₇	1	1	yes	characteristic
761	C₂²×D₄	C₂³×C₁₇	1	2	yes	—
762	C₂³×C₄	—	2	2	no	—
763	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
764	#135	—	4	4	no	—
765	#135	—	4	4	no	—
766	C₂×Q₁₆	—	4	4	no	—
767	C₂×Q₁₆	C₂³×C₁₇	1	1	yes	characteristic
768	C₂×Q₁₆	C₂³×C₁₇	1	2	yes	—
769	C₂×Q₁₆	C₂³×C₁₇	1	2	yes	—
770	C₂×Q₁₆	C₂³×C₁₇	1	2	yes	—
771	C₂×Q₁₆	C₂³×C₁₇	1	2	yes	—
772	C₂×SD₁₆	—	4	4	no	—
773	C₂×SD₁₆	C₂³×C₁₇	1	1	yes	characteristic
774	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
775	C₂×SD₁₆	C₂³×C₁₇	1	1	yes	characteristic
776	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
777	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
778	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
779	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
780	C₂×D₈	C₂³×C₁₇	1	1	yes	characteristic
781	C₂×D₈	C₂³×C₁₇	1	2	yes	—
782	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
783	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
784	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
785	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
786	C₄⋊Q₈	—	2	1	no	—
787	C₄⋊Q₈	—	2	1	no	—
788	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
789	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
790	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
791	#127	—	2	1	no	—
792	#127	C₂³×C₁₇	1	1	yes	characteristic
793	#126	—	2	2	no	—
794	#126	—	2	2	no	—
795	#126	—	2	1	no	—
796	#125	—	2	2	no	—
797	#125	—	2	1	no	—
798	#125	C₂³×C₁₇	1	1	yes	characteristic
799	#124	—	2	1	no	—
800	#124	—	2	2	no	—
801	#124	—	2	2	no	—
802	#124	C₂³×C₁₇	1	1	yes	characteristic
803	#124	C₂³×C₁₇	1	2	yes	—
804	#123	—	2	2	no	—
805	#123	—	2	2	no	—
806	#123	—	2	2	no	—
807	#123	—	2	1	no	—
808	#123	—	2	2	no	—
809	#123	—	2	2	no	—
810	#123	—	2	2	no	—
811	#123	—	2	2	no	—
812	C₂²⋊Q₈	—	2	2	no	—
813	C₂²⋊Q₈	—	2	2	no	—
814	C₂²⋊Q₈	—	2	1	no	—
815	C₂²⋊Q₈	—	2	2	no	—
816	C₂²⋊Q₈	—	2	2	no	—
817	C₂²⋊Q₈	—	2	1	no	—
818	C₂²⋊Q₈	—	2	2	no	—
819	C₂²⋊Q₈	—	2	2	no	—
820	C₂²⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
821	C₂²⋊Q₈	C₂³×C₁₇	1	2	yes	—
822	C₂²⋊Q₈	C₂³×C₁₇	1	2	yes	—
823	C₂²⋊Q₈	C₂³×C₁₇	1	2	yes	—
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	#121	—	2	2	no	—
828	#121	—	2	1	no	—
829	#121	—	2	2	no	—
830	#121	—	2	1	no	—
831	#121	—	2	1	no	—
832	#121	—	2	1	no	—
833	#121	—	2	1	no	—
834	#121	—	2	2	no	—
835	#121	—	2	2	no	—
836	#121	C₂³×C₁₇	1	2	yes	—
837	#121	C₂³×C₁₇	1	2	yes	—
838	#121	C₂³×C₁₇	1	1	yes	characteristic
839	#121	C₂³×C₁₇	1	2	yes	—
840	#120	—	2	2	no	—
841	#120	—	2	2	no	—
842	#120	—	2	2	no	—
843	#120	—	2	2	no	—
844	C₄×Q₈	—	2	1	no	—
845	C₄×Q₈	—	2	1	no	—
846	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
847	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
848	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
849	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
850	C₄×D₄	—	2	1	no	—
851	C₄×D₄	—	2	1	no	—
852	C₄×D₄	—	2	2	no	—
853	C₄×D₄	—	2	1	no	—
854	C₄×D₄	—	2	1	no	—
855	C₄×D₄	—	2	2	no	—
856	C₄×D₄	—	2	2	no	—
857	C₄×D₄	—	2	2	no	—
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	1	no	—
863	C₄×D₄	—	2	1	no	—
864	C₄×D₄	D₄×C₁₇	1	1	yes	characteristic
865	C₄×D₄	D₄×C₁₇	1	2	yes	—
866	C₄×D₄	D₄×C₁₇	1	1	yes	characteristic
867	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
868	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
869	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
870	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
871	C₄×D₄	C₂³×C₁₇	1	2	yes	—
872	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
873	#117	—	2	1	no	—
874	#117	—	2	2	no	—
875	#117	—	2	1	no	—
876	#117	—	2	1	no	—
877	#117	C₂³×C₁₇	1	1	yes	characteristic
878	#117	C₂³×C₁₇	1	2	yes	—
879	C₂×C₄⋊C₄	—	2	2	no	—
880	C₂×C₄⋊C₄	—	2	1	no	—
881	C₂×C₄⋊C₄	—	2	1	no	—
882	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
883	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
884	C₂×C₂²⋊C₄	—	2	2	no	—
885	C₂×C₂²⋊C₄	—	2	2	no	—
886	C₂×C₂²⋊C₄	D₄×C₁₇	1	2	yes	—
887	C₂×C₄²	—	2	1	no	—
888	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
889	#107	C₂³×C₁₇	1	1	yes	characteristic
890	#107	C₂³×C₁₇	1	2	yes	—
891	#107	C₂³×C₁₇	1	1	yes	characteristic
892	#106	C₂³×C₁₇	1	2	yes	—
893	#106	C₂³×C₁₇	1	1	yes	characteristic
894	#106	C₂³×C₁₇	1	1	yes	characteristic
895	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
896	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
897	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
898	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
899	#103	C₂³×C₁₇	1	1	yes	characteristic
900	#103	C₂³×C₁₇	1	2	yes	—
901	#103	C₂³×C₁₇	1	2	yes	—
902	#103	C₂³×C₁₇	1	2	yes	—
903	#103	C₂³×C₁₇	1	1	yes	characteristic
904	#103	C₂³×C₁₇	1	2	yes	—
905	#103	C₂³×C₁₇	1	2	yes	—
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	1	yes	characteristic
910	#102	C₂³×C₁₇	1	1	yes	characteristic
911	#102	C₂³×C₁₇	1	2	yes	—
912	#102	C₂³×C₁₇	1	2	yes	—
913	#102	C₂³×C₁₇	1	2	yes	—
914	#102	C₂³×C₁₇	1	1	yes	characteristic
915	#102	C₂³×C₁₇	1	2	yes	—
916	#102	C₂³×C₁₇	1	2	yes	—
917	#102	C₂³×C₁₇	1	1	yes	characteristic
918	#102	C₂³×C₁₇	1	1	yes	characteristic
919	C₂²⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
920	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
921	C₂²⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
922	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
923	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
924	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
925	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
926	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
927	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
928	C₄×C₈	C₂³×C₁₇	1	2	yes	—
929	C₁₇	#61568	1	1	yes	characteristic, direct product factor, Sylow
930	C₂⁴	—	2	2	no	—
931	C₂⁴	C₂×D₄×C₁₇	1	2	yes	—
932	#41	—	2	2	no	—
933	#41	—	2	2	no	—
934	#41	—	2	4	no	—
935	#41	—	2	4	no	—
936	#41	—	4	2	no	—
937	#41	—	4	2	no	—
938	#41	—	4	2	no	—
939	#41	—	4	2	no	—
940	#41	—	4	8	no	—
941	#41	—	4	2	no	—
942	#41	—	4	2	no	—
943	#41	—	4	8	no	—
944	#41	—	4	4	no	—
945	C₂×Q₈	—	2	1	no	—
946	C₂×Q₈	—	2	2	no	—
947	C₂×Q₈	—	2	2	no	—
948	C₂×Q₈	—	2	4	no	—
949	C₂×Q₈	—	4	2	no	—
950	C₂×Q₈	—	4	2	no	—
951	C₂×Q₈	—	4	2	no	—
952	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
953	C₂×Q₈	C₂⁴×C₁₇	1	1	yes	characteristic
954	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
955	C₂×Q₈	C₂⁴×C₁₇	1	1	yes	characteristic
956	C₂×D₄	—	2	1	no	—
957	C₂×D₄	—	2	4	no	—
958	C₂×D₄	—	2	4	no	—
959	C₂×D₄	—	2	1	no	—
960	C₂×D₄	—	2	2	no	—
961	C₂×D₄	—	2	2	no	—
962	C₂×D₄	—	2	2	no	—
963	C₂×D₄	—	2	2	no	—
964	C₂×D₄	—	2	2	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	2	2	no	—
967	C₂×D₄	—	2	1	no	—
968	C₂×D₄	—	2	2	no	—
969	C₂×D₄	—	2	1	no	—
970	C₂×D₄	—	4	2	no	—
971	C₂×D₄	—	4	8	no	—
972	C₂×D₄	—	4	4	no	—
973	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
974	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
975	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
976	C₂×D₄	C₂⁴×C₁₇	1	2	yes	—
977	C₂×D₄	C₂⁴×C₁₇	1	1	yes	characteristic
978	C₂×D₄	C₂⁴×C₁₇	1	1	yes	characteristic
979	C₂²×C₄	—	2	1	no	—
980	C₂²×C₄	—	2	2	no	—
981	C₂²×C₄	—	2	2	no	—
982	C₂²×C₄	—	2	2	no	—
983	C₂²×C₄	—	2	1	no	—
984	C₂²×C₄	—	2	2	no	—
985	C₂²×C₄	—	2	1	no	—
986	C₂²×C₄	—	2	2	no	—
987	C₂²×C₄	—	2	2	no	—
988	C₂²×C₄	—	2	1	no	—
989	C₂²×C₄	—	2	2	no	—
990	C₂²×C₄	—	4	2	no	—
991	C₂²×C₄	—	4	2	no	—
992	C₂²×C₄	—	4	8	no	—
993	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
994	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
995	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
996	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
997	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
998	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
999	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
1000	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
1001	Q₁₆	—	2	2	no	—
1002	Q₁₆	—	2	4	no	—
1003	Q₁₆	—	4	2	no	—
1004	Q₁₆	—	4	2	no	—
1005	Q₁₆	—	4	2	no	—
1006	SD₁₆	—	2	2	no	—
1007	SD₁₆	—	2	2	no	—
1008	SD₁₆	—	2	4	no	—
1009	SD₁₆	—	4	2	no	—
1010	SD₁₆	—	4	2	no	—
1011	SD₁₆	—	4	2	no	—
1012	SD₁₆	—	4	2	no	—
1013	D₈	—	2	2	no	—
1014	D₈	—	4	2	no	—
1015	C₂×C₈	—	4	2	no	—
1016	C₂×C₈	—	4	2	no	—
1017	C₂×C₈	—	4	2	no	—
1018	C₂×C₈	—	4	2	no	—
1019	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
1020	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
1021	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
1022	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
1023	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
1024	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
1025	C₄⋊C₄	—	2	1	no	—
1026	C₄⋊C₄	—	2	2	no	—
1027	C₄⋊C₄	—	2	1	no	—
1028	C₄⋊C₄	—	2	2	no	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	—	2	2	no	—
1031	C₄⋊C₄	—	2	2	no	—
1032	C₄⋊C₄	—	2	2	no	—
1033	C₄⋊C₄	—	2	1	no	—
1034	C₄⋊C₄	—	2	1	no	—
1035	C₄⋊C₄	—	2	1	no	—
1036	C₄⋊C₄	—	2	1	no	—
1037	C₄⋊C₄	—	2	1	no	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	2	no	—
1040	C₄⋊C₄	—	2	2	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	2	2	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
1045	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
1046	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
1047	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
1048	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
1049	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
1050	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
1051	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
1052	C₂²⋊C₄	—	2	1	no	—
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	2	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	2	no	—
1057	C₂²⋊C₄	—	2	2	no	—
1058	C₂²⋊C₄	—	2	1	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	—	2	1	no	—
1064	C₂²⋊C₄	—	2	1	no	—
1065	C₂²⋊C₄	—	2	1	no	—
1066	C₂²⋊C₄	—	2	1	no	—
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	1	no	—
1070	C₂²⋊C₄	—	2	2	no	—
1071	C₂²⋊C₄	—	2	1	no	—
1072	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
1073	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
1074	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
1075	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
1076	C₄²	—	2	1	no	—
1077	C₄²	—	2	1	no	—
1078	C₄²	—	2	1	no	—
1079	C₄²	—	2	2	no	—
1080	C₄²	—	2	2	no	—
1081	C₄²	—	2	1	no	—
1082	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
1083	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
1084	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
1085	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
1086	C₂³	—	2	1	no	—
1087	C₂³	—	2	4	no	—
1088	C₂³	—	2	1	no	—
1089	C₂³	—	2	2	no	—
1090	C₂³	—	4	2	no	—
1091	C₂³	—	4	2	no	—
1092	C₂³	—	4	4	no	—
1093	C₂³	—	4	4	no	—
1094	C₂³	—	8	2	no	—
1095	C₂³	C₂²×D₄×C₁₇	1	2	yes	—
1096	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
1097	C₂³	C₂²×D₄×C₁₇	1	2	yes	—
1098	Q₈	—	2	1	no	—
1099	Q₈	—	2	1	no	—
1100	Q₈	—	2	2	no	—
1101	Q₈	—	2	2	no	—
1102	Q₈	—	2	2	no	—
1103	Q₈	—	2	1	no	—
1104	Q₈	—	2	2	no	—
1105	Q₈	—	4	4	no	—
1106	Q₈	—	4	2	no	—
1107	Q₈	—	8	2	no	—
1108	Q₈	C₁₇×H(5,𝔽₂)	1	2	yes	—
1109	D₄	—	2	4	no	—
1110	D₄	—	2	4	no	—
1111	D₄	—	2	2	no	—
1112	D₄	—	2	1	no	—
1113	D₄	—	2	1	no	—
1114	D₄	—	2	1	no	—
1115	D₄	—	2	2	no	—
1116	D₄	—	2	2	no	—
1117	D₄	—	4	4	no	—
1118	D₄	—	4	4	no	—
1119	D₄	—	4	4	no	—
1120	D₄	—	4	4	no	—
1121	D₄	—	4	2	no	—
1122	D₄	—	4	4	no	—
1123	D₄	—	4	4	no	—
1124	D₄	—	4	2	no	—
1125	D₄	—	8	1	no	—
1126	D₄	—	8	2	no	—
1127	D₄	—	8	2	no	—
1128	D₄	C₁₇×#135	1	4	yes	complemented
1129	D₄	C₁₇×H(5,𝔽₂)	1	2	yes	—
1130	C₂×C₄	—	2	4	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	2	no	—
1133	C₂×C₄	—	2	2	no	—
1134	C₂×C₄	—	2	2	no	—
1135	C₂×C₄	—	2	2	no	—
1136	C₂×C₄	—	2	2	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	1	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	1	no	—
1144	C₂×C₄	—	2	2	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	2	no	—
1147	C₂×C₄	—	4	2	no	—
1148	C₂×C₄	—	4	2	no	—
1149	C₂×C₄	—	4	2	no	—
1150	C₂×C₄	—	4	1	no	—
1151	C₂×C₄	—	4	4	no	—
1152	C₂×C₄	—	4	4	no	—
1153	C₂×C₄	—	4	4	no	—
1154	C₂×C₄	—	4	4	no	—
1155	C₂×C₄	—	4	4	no	—
1156	C₂×C₄	—	4	2	no	—
1157	C₂×C₄	—	4	2	no	—
1158	C₂×C₄	—	8	2	no	—
1159	C₂×C₄	—	8	1	no	—
1160	C₂×C₄	—	8	2	no	—
1161	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
1162	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
1163	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
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	1	yes	characteristic
1168	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
1169	C₈	—	2	1	no	—
1170	C₈	—	2	2	no	—
1171	C₈	—	2	1	no	—
1172	C₈	—	2	1	no	—
1173	C₈	—	2	2	no	—
1174	C₈	—	2	1	no	—
1175	C₂²	—	2	2	no	—
1176	C₂²	—	2	2	no	—
1177	C₂²	—	2	1	no	—
1178	C₂²	—	2	2	no	—
1179	C₂²	—	2	2	no	—
1180	C₂²	—	2	1	no	—
1181	C₂²	—	2	2	no	—
1182	C₂²	—	2	1	no	—
1183	C₂²	—	2	2	no	—
1184	C₂²	—	4	1	no	—
1185	C₂²	—	4	1	no	—
1186	C₂²	—	4	2	no	—
1187	C₂²	—	4	1	no	—
1188	C₂²	—	4	1	no	—
1189	C₂²	—	4	2	no	—
1190	C₂²	—	4	1	no	—
1191	C₂²	—	4	2	no	—
1192	C₂²	—	8	4	no	—
1193	C₂²	—	8	8	no	—
1194	C₂²	C₂×C₁₇×#135	1	4	yes	—
1195	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
1196	C₄	—	2	1	no	—
1197	C₄	—	2	2	no	—
1198	C₄	—	2	2	no	—
1199	C₄	—	2	2	no	—
1200	C₄	—	2	1	no	—
1201	C₄	—	2	1	no	—
1202	C₄	—	2	1	no	—
1203	C₄	—	4	2	no	—
1204	C₄	—	4	2	no	—
1205	C₄	—	4	1	no	—
1206	C₄	—	4	1	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	4	2	no	—
1209	C₄	—	4	1	no	—
1210	C₄	—	4	1	no	—
1211	C₄	C₂×C₁₇×#135	1	2	yes	—
1212	C₄	C₂×C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
1213	C₄	C₂×C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
1214	C₂	—	2	4	no	—
1215	C₂	—	4	1	no	—
1216	C₂	—	4	2	no	—
1217	C₂	—	4	2	no	—
1218	C₂	—	8	2	no	—
1219	C₂	—	8	1	no	—
1220	C₂	C₁₇×#3484	1	1	yes	characteristic
1221	C₂	C₂²×C₁₇×#135	1	1	yes	characteristic
1222	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 ◁ C₂×C₄×D₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×#3520	C₂	semidirect
2. D₄×#41×C₁₇	C₂	semidirect
3. C₁₇×#3304	C₂	semidirect
4. C₁₇×#3302	C₂	semidirect
5. C₁₇×#3300	C₂	semidirect
6. C₁₇×#3298	C₂	semidirect
7. C₁₇×#3296	C₂	semidirect
8. C₁₇×#3294	C₂	semidirect
9. D₄×Q₁₆×C₁₇	C₂	semidirect
10. C₁₇×#3285	C₂	semidirect
11. C₁₇×#3284	C₂	semidirect
12. C₁₇×#3283	C₂	semidirect
13. C₁₇×#3282	C₂	semidirect
14. D₄×SD₁₆×C₁₇	C₂	semidirect
15. C₁₇×#3212	C₂	semidirect
16. C₁₇×#3210	C₂	semidirect
17. C₁₇×#3191	C₂	semidirect
18. C₁₇×#3190	C₂	semidirect
19. C₁₇×#3107	C₂	semidirect
20. C₁₇×#3102	C₂	semidirect
21. C₁₇×#3002	C₂	semidirect
22. C₂×C₁₇×#452	C₂	semidirect
23. C₁₇×#2972	C₂	semidirect
25. C₂×C₁₇×#135	C₂²	semidirect
26. C₂×C₁₇×#135	C₂²	semidirect
27. C₂²×Q₁₆×C₁₇	C₂²	semidirect
28. C₂²×SD₁₆×C₁₇	C₂²	semidirect
29. C₁₇×#556	C₂²	semidirect
31. C₁₇×#552	C₂²	semidirect
37. C₁₇×#548	C₂²	semidirect
41. C₁₇×#547	C₂²	semidirect
49. C₁₇×#533	C₂²	semidirect
52. C₁₇×#529	C₂²	semidirect
55. C₁₇×#525	C₂²	semidirect
56. C₂×C₁₇×C₂²⋊Q₈	C₂²	semidirect
61. C₁₇×#495	C₂²	semidirect
62. C₁₇×#494	C₂²	semidirect
63. C₁₇×#492	C₂²	semidirect
64. C₁₇×#488	C₂²	semidirect
65. C₁₇×#487	C₂²	semidirect
66. C₁₇×#486	C₂²	semidirect
67. C₁₇×#485	C₂²	semidirect
68. C₁₇×#485	C₂²	semidirect
69. C₁₇×#485	C₂²	semidirect
70. C₁₇×#483	C₂²	semidirect
71. C₁₇×#482	C₂²	semidirect
72. C₁₇×#482	C₂²	semidirect
73. C₁₇×#480	C₂²	semidirect
74. C₁₇×#479	C₂²	semidirect
75. C₁₇×#478	C₂²	semidirect
76. C₁₇×#475	C₂²	semidirect
77. C₁₇×#474	C₂²	semidirect
78. C₁₇×#467	C₂²	semidirect
79. C₁₇×#467	C₂²	semidirect
80. C₁₇×#467	C₂²	semidirect
81. C₁₇×#466	C₂²	semidirect
82. C₁₇×#465	C₂²	semidirect
83. C₁₇×#465	C₂²	semidirect
84. C₁₇×#465	C₂²	semidirect
85. C₁₇×#465	C₂²	semidirect
86. C₁₇×#464	C₂²	semidirect
87. C₁₇×#464	C₂²	semidirect
88. C₁₇×#464	C₂²	semidirect
89. C₁₇×#463	C₂²	semidirect
90. C₁₇×#462	C₂²	semidirect
91. C₁₇×#462	C₂²	semidirect
92. C₁₇×#461	C₂²	semidirect
93. C₁₇×#461	C₂²	semidirect
94. C₁₇×#460	C₂²	semidirect
95. C₁₇×#459	C₂²	semidirect
98. C₁₇×#452	C₂²	semidirect
99. C₁₇×#452	C₂²	semidirect
100. C₁₇×#452	C₂²	semidirect
101. C₁₇×#452	C₂²	semidirect
102. C₁₇×#452	C₂²	semidirect
103. C₁₇×#452	C₂²	semidirect
104. C₁₇×#452	C₂²	semidirect
105. C₁₇×#452	C₂²	semidirect
106. C₁₇×#451	C₂²	semidirect
107. C₁₇×#451	C₂²	semidirect
108. C₁₇×#450	C₂²	semidirect
110. C₁₇×#449	C₂²	semidirect
111. C₁₇×#449	C₂²	semidirect
112. C₁₇×#448	C₂²	semidirect
113. C₁₇×#448	C₂²	semidirect
114. C₁₇×#447	C₂²	semidirect
115. C₄×Q₁₆×C₁₇	C₂²	semidirect
116. C₄×Q₁₆×C₁₇	C₂²	semidirect
117. C₄×SD₁₆×C₁₇	C₂²	semidirect
118. C₄×SD₁₆×C₁₇	C₂²	semidirect
119. C₄×SD₁₆×C₁₇	C₂²	semidirect
120. C₄×D₈×C₁₇	C₂²	semidirect
123. C₈×D₄×C₁₇	C₂²	semidirect
124. C₈×D₄×C₁₇	C₂²	semidirect
125. C₈×D₄×C₁₇	C₂²	semidirect
126. C₈×D₄×C₁₇	C₂²	semidirect
127. C₁₇×#431	C₂²	semidirect
128. C₁₇×#431	C₂²	semidirect
129. C₁₇×#416	C₂²	semidirect
130. C₁₇×#416	C₂²	semidirect
131. C₂×C₁₇×#103	C₂²	semidirect
132. C₂×C₁₇×#102	C₂²	semidirect
133. C₂×C₁₇×C₂²⋊C₈	C₂²	semidirect
134. C₂×C₁₇×C₂²⋊C₈	C₂²	semidirect
474. #61568	C₁₇	direct (N × H)
517. D₄×C₁₇	#135	semidirect
564. #3520	C₂×C₁₇	semidirect
565. D₄×#41	C₂×C₁₇	semidirect
566. #3304	C₂×C₁₇	semidirect
567. #3302	C₂×C₁₇	semidirect
568. #3300	C₂×C₁₇	semidirect
569. #3298	C₂×C₁₇	semidirect
570. #3296	C₂×C₁₇	semidirect
571. #3294	C₂×C₁₇	semidirect
572. D₄×Q₁₆	C₂×C₁₇	semidirect
573. #3285	C₂×C₁₇	semidirect
574. #3284	C₂×C₁₇	semidirect
575. #3283	C₂×C₁₇	semidirect
576. #3282	C₂×C₁₇	semidirect
577. D₄×SD₁₆	C₂×C₁₇	semidirect
578. #3212	C₂×C₁₇	semidirect
579. #3210	C₂×C₁₇	semidirect
580. #3191	C₂×C₁₇	semidirect
581. #3190	C₂×C₁₇	semidirect
582. #3107	C₂×C₁₇	semidirect
583. #3102	C₂×C₁₇	semidirect
584. #3002	C₂×C₁₇	semidirect
585. C₂×#452	C₂×C₁₇	semidirect
586. #2972	C₂×C₁₇	semidirect
627. C₂×#135	C₂²×C₁₇	semidirect
628. C₂×#135	C₂²×C₁₇	semidirect
629. C₂²×Q₁₆	C₂²×C₁₇	semidirect
630. C₂²×SD₁₆	C₂²×C₁₇	semidirect
631. #556	C₂²×C₁₇	semidirect
633. #552	C₂²×C₁₇	semidirect
639. #548	C₂²×C₁₇	semidirect
643. #547	C₂²×C₁₇	semidirect
651. #533	C₂²×C₁₇	semidirect
654. #529	C₂²×C₁₇	semidirect
657. #525	C₂²×C₁₇	semidirect
658. C₂×C₂²⋊Q₈	C₂²×C₁₇	semidirect
663. #495	C₂²×C₁₇	semidirect
664. #494	C₂²×C₁₇	semidirect
665. #492	C₂²×C₁₇	semidirect
666. #488	C₂²×C₁₇	semidirect
667. #487	C₂²×C₁₇	semidirect
668. #486	C₂²×C₁₇	semidirect
669. #485	C₂²×C₁₇	semidirect
670. #485	C₂²×C₁₇	semidirect
671. #485	C₂²×C₁₇	semidirect
672. #483	C₂²×C₁₇	semidirect
673. #482	C₂²×C₁₇	semidirect
674. #482	C₂²×C₁₇	semidirect
675. #480	C₂²×C₁₇	semidirect
676. #479	C₂²×C₁₇	semidirect
677. #478	C₂²×C₁₇	semidirect
678. #475	C₂²×C₁₇	semidirect
679. #474	C₂²×C₁₇	semidirect
680. #467	C₂²×C₁₇	semidirect
681. #467	C₂²×C₁₇	semidirect
682. #467	C₂²×C₁₇	semidirect
683. #466	C₂²×C₁₇	semidirect
684. #465	C₂²×C₁₇	semidirect
685. #465	C₂²×C₁₇	semidirect
686. #465	C₂²×C₁₇	semidirect
687. #465	C₂²×C₁₇	semidirect
688. #464	C₂²×C₁₇	semidirect
689. #464	C₂²×C₁₇	semidirect
690. #464	C₂²×C₁₇	semidirect
691. #463	C₂²×C₁₇	semidirect
692. #462	C₂²×C₁₇	semidirect
693. #462	C₂²×C₁₇	semidirect
694. #461	C₂²×C₁₇	semidirect
695. #461	C₂²×C₁₇	semidirect
696. #460	C₂²×C₁₇	semidirect
697. #459	C₂²×C₁₇	semidirect
700. #452	C₂²×C₁₇	semidirect
701. #452	C₂²×C₁₇	semidirect
702. #452	C₂²×C₁₇	semidirect
703. #452	C₂²×C₁₇	semidirect
704. #452	C₂²×C₁₇	semidirect
705. #452	C₂²×C₁₇	semidirect
706. #452	C₂²×C₁₇	semidirect
707. #452	C₂²×C₁₇	semidirect
708. #451	C₂²×C₁₇	semidirect
709. #451	C₂²×C₁₇	semidirect
710. #450	C₂²×C₁₇	semidirect
712. #449	C₂²×C₁₇	semidirect
713. #449	C₂²×C₁₇	semidirect
714. #448	C₂²×C₁₇	semidirect
715. #448	C₂²×C₁₇	semidirect
716. #447	C₂²×C₁₇	semidirect
717. C₄×Q₁₆	C₂²×C₁₇	semidirect
718. C₄×Q₁₆	C₂²×C₁₇	semidirect
719. C₄×SD₁₆	C₂²×C₁₇	semidirect
720. C₄×SD₁₆	C₂²×C₁₇	semidirect
721. C₄×SD₁₆	C₂²×C₁₇	semidirect
722. C₄×D₈	C₂²×C₁₇	semidirect
725. C₈×D₄	C₂²×C₁₇	semidirect
726. C₈×D₄	C₂²×C₁₇	semidirect
727. C₈×D₄	C₂²×C₁₇	semidirect
728. C₈×D₄	C₂²×C₁₇	semidirect
729. #431	C₂²×C₁₇	semidirect
730. #431	C₂²×C₁₇	semidirect
731. #416	C₂²×C₁₇	semidirect
732. #416	C₂²×C₁₇	semidirect
733. C₂×#103	C₂²×C₁₇	semidirect
734. C₂×#102	C₂²×C₁₇	semidirect
735. C₂×C₂²⋊C₈	C₂²×C₁₇	semidirect
736. C₂×C₂²⋊C₈	C₂²×C₁₇	semidirect
929. C₁₇	#61568	direct (N × H)
1128. D₄	C₁₇×#135	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×#3520	2
D₄×#41×C₁₇	2
C₁₇×#3304	2
C₁₇×#3302	2
C₁₇×#3300	2
C₁₇×#3298	2
C₁₇×#3296	2
C₁₇×#3294	2
D₄×Q₁₆×C₁₇	2
C₁₇×#3285	2
C₁₇×#3284	2
C₁₇×#3283	2
C₁₇×#3282	2
D₄×SD₁₆×C₁₇	2
C₁₇×#3212	2
C₁₇×#3210	2
C₁₇×#3191	2
C₁₇×#3190	2
C₁₇×#3107	2
C₁₇×#3102	2
C₁₇×#3002	2
C₂×C₁₇×#452	2
C₁₇×#2972	2
#61568	17

Subgroups — C17×#61568 #16919312

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#61568 #16919312